Fusion and the cosmos: a fabulous voyage through the universe

FUSION AND THE COSMOS A FABULOUS VOYAGE THROUGH THE UNIVERSE Hans Wilhelmsson

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Ганс Вільгельмсон Ядерний синтез та космос Гіпотетична подорож крізь Всесвіт В цій книзі розповідається про ядерний синтез. Цей процес забезпечує горіння зірок та галактик і є основним джерелом енергії у Всесвіті. Може статися, що лише ядерний синтез дозволить задовольнити енергетичні потреби сучасного суспільства. Hans Wilhelmsson Fusion and the Cosmos A Fabulous Voyage Through the Universe This book tells the fascinating story of fusion. As the process that fuels the stars and galaxies lighting up the night sky, fusion is the main source of energy in our Universe. Fusion may prove to be the only sustainable way to meet the long-term energy demands of modern society.

ISBN 966-7653-22-4 © Hans Wilhelmsson

Contents Foreword........................................................................................ 7 Intended audience and way of presentation................................ 10 The aim of the book....................................................................... 16 Introduction and Summary.......................................................... 17 1 Gravitation.................................................................................. 20 1.1 God’s force in the cosmos .................................................. 20 1.2 Newton’s law...................................................................... 21 1.3 Space – and time scales ...................................................... 23 2 Plasmas and nuclear fusion ....................................................... 25 2.1 The secrets of plasmas ........................................................ 26 2.2 Plasma physics: peculiarities and games ............................ 29 2.3 Nuclear fusion reactions ..................................................... 32 2.4 Nuclear fusion plasmas....................................................... 35 3 The cosmos.................................................................................. 40 3.1 What is new in the sky Mr Hubble? ................................... 40 3.1.1 Plasma and fusion in the cosmos .............................. 41 3.1.2 How it all began........................................................ 42 3.1.3 Galaxies and stars ..................................................... 45 3.1.4 The sun’s metabolism ............................................... 48 3.2 Albert Einstein and some of his work................................. 53 3.2.1 From Leonardo to Einstein ....................................... 54 3.2.2 Albert Einstein at work ............................................. 59 3.2.3 The fifth state of matter (BEC) and related topics......................................................................... 63 3.2.4 The bending of light and the principle of gravitational lensing.................................................. 73 4 The plasma universe................................................................... 81 4.1 Around the sun ................................................................... 81 4.1.1 Plasma motion and magnetic fields .......................... 81 3

CONTENTS

4.1.1.1 The magnetoplasma revolution ....................... 81 4.1.1.2 The challenge of space plasma exploration...................................................... 87 4.1.1.3 Cosmic plasma jets.......................................... 88 4.1.1.4 The all-pervasive Alfvén wave ....................... 93 4.1.2 Transient spectacles on the sun................................. 95 4.1.2.1 The dynamic face of the sun ........................... 95 4.1.2.2 Solar flares and prominences .......................... 97 4.1.3 Unusual visitors on the sky ....................................... 101 4.1.3.1 Comets ............................................................ 102 4.1.3.2 The extraordinary voyage of MIR (1986-2001) .................................................... 107 4.2 The sun – Earth interplay.................................................... 108 4.2.1 The solar wind .......................................................... 109 4.2.2 The Earth’s magnetosphere....................................... 113 4.2.3 The ionosphere.......................................................... 116 4.2.4 Auroras ..................................................................... 118 4.3 Far beyond the sun: superstrong emitters of radiation........ 120 4.3.1 Supernovas................................................................ 120 4.3.2 Pulsars: lighthouses of the cosmos............................ 121 4.3.3 Quasars ..................................................................... 124 4.4 The expanding universe...................................................... 126 4.4.1 From plasmas to gravitation; The complex medium and the fields............................................... 126 4.4.2 The nonlinear universe.............................................. 129 4.4.3 The small and the large; atoms and the cosmos ........ 131 4.4.4 Neutrino astrophysics ............................................... 134 4.4.5 X-ray astophysics...................................................... 136 4.4.6 Gravitational lensing as a tool for cosmological observations........................................ 141 5 Lightnings, jets and beams ........................................................ 147 6 Lasers and inertial confinement................................................ 150 6.1 The principle of inertial confinement ................................. 150 6.2 Instabilities ......................................................................... 151 4

CONTENTS

6.3 The concept of direct and indirect drive ............................. 152 6.4 Laser fusion ........................................................................ 152 6.5 Ion beam drivers ................................................................. 155 7 Dynamic fine structure of plasmas: From micro to macro behaviour .................................................................................... 160 7.1 Waves and instabilities ....................................................... 160 7.2 Nonlinear effects................................................................. 166 7.3 Three-wave interaction ....................................................... 168 7.4 Evolution of populations: explosive instabilities................ 171 7.5 Vortices .............................................................................. 174 7.6 Wavelets and turbulence..................................................... 176 7.7 From fine structure to global dynamics of fusion plasmas .............................................................................. 177 8 Magnetic confinement in space and laboratory plasmas ........ 185 8.1 Toroids, magnetospheres, beams, filamentations and blobs............................................................................ 185 8.2 The principle of magnetic confinement .............................. 187 8.3 Fusion energy generation and self-sustained fusion ........... 189 8.4 The architecture of magnetic confinement ........................ 190 8.5 History of alternative concepts .......................................... 190 8.6 Stellators and tokamaks ...................................................... 192 8.7 The struggle for life: electromagnetics in the laboratory and in the cosmos............................................................... 194 Play in seven scenes S I – S 7: «A glimpse into the theatre of science and technology» S.1 (Göteborg 1951-1955)........................................................ 194 S.2 (Lund and Copenhagen 1955-1958) ................................... 202 S.3 (Göteborg 1959-1960)........................................................ 219 S.4 Astro and fusion plasma physics ....................................... 222 (Princeton 1960 -1961) ...................................................... 222 (Göteborg 1959-1964) ....................................................... 226 S.5 Personalities....................................................................... 233 Chalmers and its Presidents ............................................... 233 From Pole to Pole: the two Roalds .................................... 241 S.6 Lasers, holography, rocket flames (Stockholm 1964-1967) ..................................................... 242 5

CONTENTS

Electrodynamics, plasmas, fusion; Technical physics education and the USA again (Uppsala 1967-1971) ......................................................... 249 S.7 (Göteborg and the World 1971-2003)................................ 255 9 The universe: exclusive phenomena and their interpretation: Big Bang, Black Holes; gravitation, strings and quanta ..................................................................... 282 10 The fusion reactor .................................................................... 296 10.1 Reactor requirements ........................................................ 296 10.2 Reactor design .................................................................. 297 10.3 Heating and confinement.................................................. 297 11 Outlook into the future ............................................................ 299 Conclusions – the great fusion plant............................................ 303 Afterword....................................................................................... 304 Epilogue.......................................................................................... 313 Appendix: Universal expansion and an extended Hubble’s law .................. 314 A.1 Basic NL PDE and solutions ............................................. 314 A.2 Extended formulation ........................................................ 317 A.3 Conclusions and discussion ............................................... 318 Acknowledgement ......................................................................... 321 Short gravitation-fusion-plasma dictionary................................ 324 Character index ............................................................................. 339

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Foreword Neutrinos, γ-rays and gravitational lensing techniques are new tools for astrophysical observations. They seem to be introducing a revolution in our view of the cosmos. The fields of neutrino – and γ-ray astronomy have been established. Precise neutrino detections have settled that nuclear fusion is, in fact, the source of solar radiation and confirm as an example, the role of the fusion-plasma state in the universe. Conceptual speculations on the nature of the gravitational field are simulated by the new observations describing matter under extreme conditions (super-strong fields and super-high densities). Thanks to extremely high-intensity lasers, ultra highenergy particles may now be accelerated in the laboratory to simulate extreme astrophysical conditions. In the present book I stress the influence of Albert Einstein on the evolution of modern physics and the extraordinary impact of his ideas on the development of new scientific measurements and interpretations. [1.1 – 1.4]. In a previous book FUSION [2.8] I paid special attention to the «plasma universe». I also introduced a modern view on fusion plasmas covering fusion in the laboratory and in the cosmos. In this new volume it seems appropriate to extend the view to universal aspects, considering also gravitation. Part of the preface of the forerunner to the present book is quoted as follows. The term «plasma universe» was coined by Hannes Alfvèn to emphasize the decisive role of plasmas, or electrically conductive ionized gases, in our universe. Nuclear fusion is the fuel for all the stars and galaxies in space. Fusion therefore plays a very significant role.One could even talk about a 7

FOREWORD

«fusion universe». In the long term, fusion plasma may become the natural source of energy on Earth. We take a voyage through the universe and discover some remarkable and unexpected things. We will also examine some of the attemps to master the confinement of nuclear fusion plasmas in the laboratory. Many of the events observed in the laboratory can be tied in to discoveries that we make on our exciting voyage. I adopt a novel approach to fusion plasmas, covering fusion both in the laboratory and in the cosmos. I discuss the evolution of the field from early plasma research more than half a century ago to the gigantic scientific efforts of today covering basic fusion plasma science and laboratory fusion experiments, as well as geocosmophysical and astrophysical projects. The description is interspersed with passages which suggest relationships between science and art or poetry. I also relate meetings that I have had with famous scientists like Niels Bohr, Hannes Alfvèn, Piotr Kapitza, Subrahmanyan Chandrasekhar, Lyman Spitzer, Dennis Gabor and others. There are several ways in which the similarities between fusion plasma phenomena in the laboratory and in outer space could be described. The natural connection comes from plasma physics, notably from the physics of waves and particles as well as of magnetic confinement of particles and energy in plasmas. Let us mention here magnetohydrodynamics (MHD), Alfvèn waves, plasma waves, shock waves and other nonlinear phenomena. To understand the general outline of the book it should be emphasized from the very beginning that we must visualise two systems of fusion plant, each of a very different scale. One is the usual concept of a laboratory-designed thermonuclear reactor feeding an electric power station from which energy is distribued to consumers. The other type of fusion plant is the whole universe, which generates thermonuclear energy in the interior of the stars which distribute their energy in the form of radiation (electomagnetic and particle radiation), to the rest of the cosmos and create the conditions for life on Earth. 8

FOREWORD

In both systems plasma phenomena play a significant role. In fact, all phenomena of an electromagnetic and plasma nature which scientists try to use for confining and heating a plasma to thermonuclear conditions have counterparts in the natural universe, which is why I give many examples from astrophysics and geocosmophysics. Interestingly enough, very important progress in our understanding of numerous natural plasma phenomena is currently being made by the use of rockets and satellites. Simultaneously our knowledge of plasma phenomena in large artificial fusion devices is reaching a mature state. In writing this book I wanted to present to the reader certain points and ideas which have not been widely emphasized. The style is mainly popular, but the content is based on scientific analyses and observations. It is supported by a wide variety of illustrations in the form of photographs and drawings. The book should be of interest to anyone with some curiosity about fusion and plasma physics and their current state of development, and should be accessible to readers with a fairly basic physics background from beginning undergraduate or even senior school level upwards. It emphasizes the very considerable achievements which have been made towards the use of fusion as the large-scale energy source for our society in the future. It furthermore forms the base for including, in the new extension, gravitation and questions on the expanding universe.

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Intended audience and way of presentation The book is written for the academic readership principally and will have a wide coverage, elucidated by a tour in the universe, which should be of considerable interest also for a non-specialized audience. It uses simple manners explaining essential things, avoiding formal complications and will not contain any formulas (except in an appendix). It provides extensive references to original scientific literature with full titles of the publications. The text is based on real facts, which are rapidly accumulating from astronomical observations and laboratory experiments, as well as from results modelling physical behaviour by computer or «brain» analysis. To make the style attractive and sometimes amusing a number of anecdotes are included. Numerous characters, many of them Nobel Prize winners are presented. As a result of widening the coverage of the text, concepts and experiences from various fields of science can be naturally interrelated one of the best examples being the use of self-formation and /or selforganization. These concepts denote the tendency of natural formation and internal organization of structures in astrophysical as well as chemical and biological systems. In almost all sciences the role of such structures, which in essence relies on multiple couplings (nonlinear phenomena) between different quantities (densities, temperatures, magnetic fields, etc, denoting dynamic variables), becomes all the more noticeable and often of decisive influence. Examples are found e.g in the formation of galactic clusters, even of the universe as whole, and in the creation of life in the cosmos. Furthermore in the formation of equilibria and stabilization of fusion reactor plasma, or the corresponding problem of star- formation or decay. Not to 10

INTENDED AUDIENCE AND WAY OF PRESENTATION

mention the black hole and neutron star (pulsar) problems. The population on Earth is another «nearby» problem also discussed in the text. The Earth’s population is growing at a rate corresponding to an increase of two or three times its present size by the end of the 21st century. For anyone interested in the future evolution of our society an essential question is how to satisfy the needs of a continously growing energy consumption. It seems, indeed, that in the future fusion could provide our large-scale energy supply on Earth as it does already for the natural universe. It would also offer great ecologial and safety advantages. Fusion is directly related to what is called plasma, the hot ionised electrically conducting gas in which the fusion processes occur by reactions between light nuclei, e.g. hydrogen isotopes. The universe consists of more than 99% plasma, and hence there are obvious reasons why fusion and plasma science should be of the utmost general interest. The dream of an energy source based on nuclear fusion on Earth has stimulated significant activities in fusion research since the middle of the 20th century.Many nations today support large-scale fusion experiments. They all have the same goal - to harness nuclear fusion energy for the production of electricity. Important progress in fusion plasma science and technology has been made through the years but there is still a long way to go before a final version of a practical fusion reactor plant can be established. Fusion reactions occur when nuclei of light atoms fuse together under the influence of nuclear forces. The hydrogen isotopes of deuterium (D) and tritium (T) are the most relevant ones to consider for fusion energy production. The state of matter in which the reactions occur is a hot plasma, where at high temperatures the atoms have split into free electrons and free nuclei which move as intermixed gases with opposite electric polarities. For the fusion processes to become efficient exceedingly 8 high temperatures (10 kelvin) and sufficiently high densities 11

INTENDED AUDIENCE AND WAY OF PRESENTATION

14

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(10 cm ) are required. Also, the plasma has to be maintained for sufficiently long that energy has time to be produced before the plasma disappear due to destructive mechanisms (instabilities) or losses (radiation). The dynamic behaviour of the plasma itself plays an essential rôle. The fusion reaction processes and the plasma dynamic processes (diffusion of particles and conduction of temperature) are mutually dependent. Together they determine how the plasma will evolve in space and time. The presence of plasma in all parts of the universe, in stars, galaxies, plasma jets and geocosmological environments causes a close relationship between plasma physics and astrophysics, where recently extraordinary discoveries and technoligical developments (light and X-ray observations by space telescopes) have been made. The many spectacular plasma phenomena, exhibited in large scale universal contexts, as well as a detailed understanding of these phenomena, are of great interest for the interpretation of the experimental results obtained in laboratory fusion plasmas. Examples of spectacular plasma phenomena, e.g. plasma streams, comets, waves and instabilities, whirls and turbulences are abundant in the universe. These phenomena may be caused directly or indirectly by fusion reactions. Similarities between those large-scale phenomena and events occurring at a much smaller scale in laboratory plasmas are of basic interest in plasma science. Also, comparisons with fluid phenomena in hydrodynamics, often studied by computer simulation experiments, give an insight into the behaviour of the more complex plasma systems. Until recently, practically all fusion research has dealt with plasmas in the absence of fusion processes. In the presence of strong fusion activity (which requires advanced technological developments and which makes the interior of the fusion plasma device radioactive) the plasma behaviour may be considerably modified. The resulting heat and particle diffusion of the burning plasma affects the possibility of realizing a future reactor for electric energy production. 12

INTENDED AUDIENCE AND WAY OF PRESENTATION

The new results and extensive experience obtained in laboratory experiments are important not only for the future planning of fusion reactors but also for the results of observations in astroplasmas and geocosmophysical plasmas. Ancient cultures used fire and flames to heat and prepare materials. Around 7000 years BC fire was used to make pottery and later on objects of copper, silver and gold. In the Middle Ages smiths made tools, swords and armours out of iron using fire and ovens to produce the heat. In early days flames were considered as signs of purification and were even used to burn witches. In Greek mythology Prometheus, a Titan who stole fire from Olympus, to give to mankind, was chained to a rock where an eagle tore at his liver until Hercules freed him. The myth of Prometheus inspired Aeschylus to write a tragedy: «The Chained Prometheus», and the British poet Shelley to write the lyric drama: «Prometheus Unbound» (1820) In a recent painting «Cosmos» 1997 by Pierre-Marie Brisson one may imagine Prometheus close to the fire (see Plate 1). In the space age we are used to see rockets take off carried by jet engines accompanied by plumes of luminous gas. Space telescopes are taking magnificent pictures of plasma jets extending through many thousands of light years and exhibiting structures like filaments and islands of plasma. The jets are thought to be created by energetic activity in the center of a galaxy, possibly of matter from a supermassive black hole: this matter which once came, before at the beginning of the universe, as dilute clouds of hydrogen to form the fuel of the slowly burning stars- the fusion plasma. These fascinating aspects have attracted the interest of numerous scientists all over the world and have also engaged great authors and artists over the centuries. As a research student I was fortunate to spend a rather long period in Copenhagen at the Niels Bohr Institute, which was at that time considered to be the Mecca of theoretical physics. Many of the most famous physicists in the world came to the Institute and numerous seminars on the frontiers of physics were given. 13

INTENDED AUDIENCE AND WAY OF PRESENTATION

Niels Bohr, the father of atomic physics, sometimes attended the seminars himself, puffing his impressive pipe. The seminars were quite outstanding, often rather informal. A particular type of seminar was called the circus. It was intended to be on new ideas, or even on rumours of what was going on in international physics research. The common language was «broken English», spoken without hesitation. It was astonishing and often amusing to see how a mixture of broken English and complicated formulae could support each other in the debate on models of the physical world.Even for the masters, however, the route to glory was hard. Niels Bohr told that he had rewritten the manuscript for his famous publication on atomic theory (N. Bohr 1913 On the Constitution of Atoms and Molecules,Part I-III Phil.Mag. 26, 1) at least 14 times and that he thought that every time it became worse. Many years later I was invited to Kiev in Ukraine to do research and give seminars in plasma physics. The first morning a young physicist came to my office and said: «I want to work with you». I responded: «fine» and tried to explain what kind of research I was doing. However, it became clear very soon that we had no spoken language in common. I did not speak Ukrainian and he did not speak English, not even «broken English», nor any other European language, for various reasons. But he was gifted and could handle formulae and understand physics. He continued to speak Ukrainian more or less to himself, but we found that we could communicate by another useful common language: mathematics in terms of formulae. His enthusiasm and my interest in the science and in Ukrainian culture led to a fruitful collaboration and resulted in several publications from my stay in Kiev. On one of my other visits to Kiev several years later, I arrived well prepared for a talk, with a considerable number of view-graphs and many slides, most of them filled with formulae and graphs. But it turned out that the overhead projector had broken down and the slide projector was not sufficiently strong to compensate for the Ukrainian light that came in through the windows, which had no curtains. So I used words, just simple 14

INTENDED AUDIENCE AND WAY OF PRESENTATION

words in English, to explain for three hours with an interpreter, what I had intended to communicate. It was on plasmas with nonlinearities, on wave interactions, on lasers and on physical models. And it became, under the circumstances, a great success, more so than it might have been with all the formulae on the slides! This experience and some others stimulated me to write this book simply in words. To illustrate our own experiences from the daily work and furthermore to give a certain coherence to the space and time ordering in the presentation of the research there is a section entitled:The struggle for life: A glimpse into the theatre of science and technology. An Appendix on the expanding universe contains a new and original contribution, where a nonlinear cosmodynamic formulation is given, which includes the Hubble law in an extended form. It discusses ideas based on a recent (2002) publication by the author [4.33]. The role of astrophysical observations in solar and large scale universal contexts, as well as the competition between gravitational and nuclear fusion processes in the cosmos, are particularly emphasized.

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The aim of the book (i)

to emphasize the extreme importance of the numerous new discoveries in astrophysics

(ii)

to expose new results and methods from fusion plasma physics, where an extensive data-base now exists from many years of systematic research (JET, ASDEX etc.)

(iii)

to attempt to find and make use of similarities between laboratory and space science activities in order to develop new concepts and new approaches

(iv)

to increase and synthesize the information to a general academic audience

(v)

to interrelate scientific methods from fusion description

(vi)

to stimulate the interest of young students and scientists to enter a promising field, including astrophysics, fusion plasmas, gravitation and elementary particles

(vii)

to introduce the readers to the internet Nobel Website for providing information about the Nobel Prizes and the work of the Prize Winners.

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Introduction and summary Astrophysics and cosmology is to-day full of question marks. What does it mean that convincing results obtained by Neta Bahcall [3.10] from Princeton University tells us «that the density of mass in the universe is only 20% of the density that would be needed to effect a slowing down of the expansion…» What mysterious source lies behind, what kind of dark matter may be active? Is the main content of the universe unknown to us? Is there a mysterious radiation, or are unmeasurable particles present? Could the vacuum provide a negative pressure? What is the secret of the God’s Equation? Should there after all be an extra term, such as Albert Einstein introduced, but finally discarded, or what else? Can new combinations of gravitation and quantum theory help us out of the labyrint [3.1]. Are we, perhaps, not even close to the beginning of the end? Or is there an end? The amazing images from the Hubble Space Telescope as well as the extraordinary new possibilities offered by the x-ray telescopes on the Einstein and Chandra Observatories and the neutrino detectors, inspired the revolution in astrophysics. They have opened the windows to the gigantic laboratory of the cosmos. Questions about the nature of black holes, neutron stars (pulsars), and about the presence of «dark matter» in the universe are indeed challenging. Or what about measuring the weight of the whole universe or of certain galaxies or galactic clusters. The search for extra solar planets and their atmospheric conditions are related to humanity’s place in the universe. The Hubble telescope pictures in 1995 of the Titan moon of the saturn planet was a great challenge for the studies of the atmospheres of extrasolar planets. Exciting information also arrived in the official news on November 2001, annoucing for the first time ever the existence 17

INTRODUCTION AND SUMMARY

of an atmosphere, a mixture of gases, around a distant planet, situated outside our solar system, 153 light years from us in the constellation of Pegasus. The planet is a giant planet (HD 209458), larger than Jupiter but less heavy (69%), a sphere of gas whith a temperature about 1200°C. A decisive new step in the exploration of the universe. Today we know that the source of energy of all the stars and galaxies that we see on the sky comes from nuclear fusion reactions. But we can not see the fusion processes directly. What we see is only secondary effects, like the optical radiation from our sun, or from beautiful patterns of nebulae or galaxies, from which we can approach the detailed structures by means of optical instruments. Sir Arthur Eddington, in 1920, suggested that nuclear fusion was the energy source of the sun, but it was not until in the late 1980’is, after the pioneering work by R Davis (NP 2002) and independently by M. Koshiba (NP 2002) on neutrino detection that it could be settled that fusion was in fact the source of the solar radiation. In the meanwhile R. Giacconi developed x-ray telescopes to perfection for more than 20 years (e.g the Einstein and the Chandrasekhar observatories in space) and paved the way to x-ray astronomy and particularly to studies of supernova remnants and double-stars, where one star circles around another object, which might be a neutron star or even a black hole. Recently the possibilities of even higher densities of matter in such objects have been envisaged in the form of quark stars, representing «strange» states where the quarks are thought not to belong to any specific nuclei (protons or neutrons) but are thought to be free to move around in a crashed state, where the density is as high as in the nuclei. We may say that it corresponds to a plasma, not only fully ionized, but so enormously dense and hot that the nuclei are completely crashed (may be even the quarks!). Less than a century ago our knowledge about the universe came from the observation of objects which emitted light from the sky, and classical mechanics was used as a tool to follow up what was happening. Radio astronomy and space science came along after the second world war. They opened up new possibilities of 18

INTRODUCTION AND SUMMARY

observation and widened the spectrum of observable radiation. The propagation and generation of waves became important topics and brought electomagnetics and fluid motion into new light. The plasma, an ionized gas, and therefore conductive, became important for exploration of space and for laboratory investigations. The field of Magnetohydrodynamics (MHD) was born. The hot plasma, in which thermonuclear fusion reactions might occur, attracted particular interest since the early 1950 ies with an aim of future large scale energy production on Earth. Masers and lasers were developed, based on the stimulated emission of radiation on microwave and light wavelenghts. Simultaneously astrophysics started to grew appreciably as a part of physical sciences and came to establish itself in recent years as one of the most interesting growth-points of modern science, with particle physics, fusion and plasma physics, chemistry (astrochemistry) as well as gravitation as building blocks. The influence of Albert Einstein on the evolution of physics in the last century has been unique and of outstanding depth and enormous width. The special theory of relativity (1905) and, in the same year, the photo-electric effect, and the general theory of relativity (1917) are all extraodinary contributions. The recent experimental verification of the BoseEinstein condensation (BEC) confirms beautifully the soundness of the early (1924) ideas of Einstein. The results are of astrophysical interest, e.g, for white dwarf stars. The bending of light by gravitation, envisioned by Einstein in 1912 also lies behind the new gravitational tools in astrophysics, introduced in the form of gravitational lensing. They may even lead to new possibilities for anlyzing the role of plasmas in the universe and to provide a better understanding of the fusion plasma under extreme conditions. What a magnificent cosmos to exploit! Let us go on a fabulous voyage through the universe starting at the very beginning of time, at the Big Bang, in a very small domain, where everything was hidden to be thrown out into the unknown. 19

The force of gravitation is everywhere in the cosmos. It participates the evolution at large as well as the localized events as the Big Bang and the black holes. It provides the confinement of stars and galaxies. It competes with the nuclear fusion reactions between light nuclei in producing stable equilibria. The Newton’s law for the universal gravitation tells us that all objects in the universe are attracted to all the other objects by a force which is larger the closer the objects are and the heavier they are. It is the force which makes bodies fall to the ground and which allows the moon to circle aroud the Earth and the Earth around the sun. A particularly important feature of the gravitation forces is that they are always attractive and of long-range character. Their total influence in large volumes is therefore considerable. Those and other questions related to the very different space-and time scales occuring in the cosmos are discussed in the chapter.

1.1 God’s force in the cosmos Gravitation is always present in the control of cosmic behaviour. It has a decisive influence on the distribution and motion of matter in the universe. It governs the evolution of the universe from the beginning in the Big Bang as well as to the 20

GOD’S FORCE IN THE COSMOS

formation and evolution of stars and galaxies, neutron stars (pulsars) and Black Holes. One could say that gravitation plays the role of the great brother to fusion and plasmas in the universe. Often are members of this family teated separately in literature, which could be natural for practical reasons, but unfortunate for a balanced account of modern astrophysics, geocosmophysics and fusion-plasma physics. Did you ever come to think of what would happen if nuclear fusion, the source of heating the sun, and providing energy for us on Earth, suddenly disappeared? The centre of the sun would become cool,leaving the outer part to expand in the form of a red giant star, at the same time as the centre would contract and become a white dwarf star. The red giant would ultimately encompass our Earth. In the absence of fusion, larger stars would finally contract to form black holes. Only certain nebulae would remain visible. Otherwise the darkness would be complete. If instead we imagine that gravity was taken away, the Earth would orbit away out into the cool space, since no force would remain to keep it circling around the sun continuously. At the same time the absence of gravity would make the stars explode, since nothing would be there to confine them. The whole beautiful universal architecture would be completely destroyed. It is obvious that we need both gravity and fusion to maintain the cosmos. The plasmas and the magnetic fields will be there to support the formation of e.g.. spiral galaxies, magneto-spheres, prominencies as well as our efforts to produce fusion plasmas in the laboratory.

1.2

Newton’s law

In 1687 Isaac Newton published his famous Theory of Gravitation in Philosophia Naturalis Mathematica. It has been considered to be the most important contribution to physics, ever [3.1] Newton’s theory tells us that the gravitation force between two bodies depends only on the masses of the bodies 21

CHAPTER 1

GRAVITATION

and this independently of the constitution of the bodies. It means that one does not have to consider the structure of the sun and the planets to calculate their orbits.The law is simply, as we know, an inverse square of the distance separating the bodies, multiplied by the respective masses. Contrary to the corresponding law of repulsion between two electric charges of equal signs, let us say two positive charges of e.g. protons, the gravitational force between masses is attractive. According to Newton all bodies in the universe are attached to one another by a force which is determined by the gravitation theory. But how is it possible then that the whole universe expands, i.e. that on a large scale all parts of the universe move away from one another? At the very first instants of time, on the occasion of the Big Bang, an enormous amount of free energy became liberated in a very small local volume of space. Where this happened was completely arbitrary. It is only to be imagined as a point, where the exceedingly small «universe» existed at the very beginning. From there it expanded to our present day, and will perhaps continue to expand for ever (see Appendix). As the great French thinker Blaise Pascal saw the problem: «The world is an infinit sphere where the centre is everywhere and the circonference nowhere».

Successively, nuclei and atoms, later on stars and galaxies, pulsars and black holes developed and were distributed everywhere. The expansion occurs everywhere against the gravitational force, as a result of a continuous coolong of the whole universe. It means that energy is delivered in the space of the universe itself (galaxies, stars, interstellar gas, and perhaps something we do not know anything about, some exotic matter) to carry out work necessary to support the large scale expansion. Like the fuel supporting a rocket penetrating the space, up through and against the gravitational field of the Earth. The description of how the entire universe develops and what secrets lie behind the forces supporting the development 22

GOD’S FORCE IN THE COSMOS

are outstanding questions in present day astrophysical and cosmological research. Often gravitation is not included, but simply neglected, when treating elementary particles or atoms. The reason is that it can be considered a weak force in this connection. In parenthesis it could be mentioned, however, that for particle motions in the giant accelerators at CERN the motion of the moon affects the particle orbits. Since gravitational forces are always additive and of long range character, the total effect of gravitation of many particles and on many particles accounts for its decisive role in the universe. For the Big Bang, neutron stars, white dwarf stars and black holes the exceptionnal conditions seem to require that quantum effects have to be considered in combination with the gravitational influence to expalin the behaviour in those objects. The gravitation force is weak, but in the cosmos it has a gigantic power.

1.3

Space-and time scales

It is, indeed, an interesting circumstance to notice how similar problems of competition between gravitation and other processes enter the scene of the cosmos, and this to widely different scales of space and time. The whole universe, as we experience it to-day has a dimension of around 14 billion light years, as compared to the tiny domain occupied by the same «universe» at the very beginning of the Big Bang when everything started from almost a point (or even a singularity), outside which there was nothing. Everywhere in the cosmos, «local» cosmic objects exhibit competitions between different types of forces.They prevail in stars, where the formation and evolution exhibit how nuclear fusion burn produces a pressure which balances the gravitational compression, also in galaxies, where rotation and angular momentum occur in the presence of large scale magnetic fields; in the development of white dwarfs and neutron stars (pulsars) all the way to black holes which could indeed be very small (even «singularities») but enormously dense, and for which gravitation wins the battle 23

CHAPTER 1

GRAVITATION

against any other competing force, affected possibly by quantum effects . It might seem as if gravitation sometimes has a tendency to produce destructive effects in the cosmos, introducing collaps here and there. On the other hand, gravitation has confining effects on the universe as a whole and on stars and galaxies in particular.Gravitation, as we have seen, also keeps the planets circling around the sun, providing suitable conditions for life on Earth, and possibly also life on planets belonging to other solar systems, ex-solar planets, which are being discovered and studied actively as a new branch of modern astrophysics and even bio-astrophysics . Magnetic fields provide confinement of geocosmophysical plasmas, for example the magnetosphere of our Earth, and «blobs» of plasma thrown out of the solar surface to reach Earth, entering along the Earth’s own magnetic field lines. These plasma phenomena all have time scales which are intermediaite between those which characterize the extremely short or exceedingly long ones of the universe, as discussed above. References [1.1]

Al-Khalili J 1999 Black holes wormholes & time machines (Bristol: IOP)

[1.2]

Eliezer S and Eliezer Y 2001 The fourth state of matter An introduction to plasma science (second edition) Bristol: IOP)

[1.3]

Aczel A 2000 God’s equation Einstein, relativity and the expanding universe (London: Piatkus Publ.)

[1.4]

de Closets F 2004 Ne dites pas à Dieu ce qu’il doit faire (Paris: Seuil)

24

A plasma is an ionized gas, where electric charges play an essential role for particle motions. The electrons and the positive ions are influenced by electric fields and when the particles move also by magnetic fields. The large difference in mass in between the electrons and ions have important consequencies. The light electrons react strongly to rapid variations in time, whereas the heavier ions hardly feel the variations if these are not sufficiently slow. Thus electron as well as ion waves may occur. In particular magnetic fields can have a significant influence and for slow variations lead to magneto-hydrodynamic waves, which combine features of hydrodynamic and electromagnetic variations. These MHD waves where first suggested by Hannes Alfvén, who discovered them in 1942 (Nobel Prize for Physics in 1970). They were thought to play a role in solar physics to explain the origin of sunspots and have later been found to have a profound interest for applications in numerous connections which characterize modern astrophysics. A plasma also exhibits collective oscillations and waves as a result of the long-range nature of the active forces. The thermonuclear reactions happening in a plasma for extremely high temperatures are a result of very short-range forces which lie behind the energy generation in our sun and all other stars and galaxies. This chapter introduces the reader to the secrets of plasmas and to nuclear fusion reactions. 25

CHAPTER 2 PLASMAS AND NUCLEAR FUSION

2.1 The secrets of plasmas What mysteries lie behind all the beautiful objects that shine in the sky – those stars and galaxies, pulsars and nebulae, or the auroras, which produce glorious and colourful arcs in the northern regions of the globe. The light comes from gases which occupy different regions of space and exist under very different conditions. Ordinary gases like air at room temperature do not shine.They are not electrically conductive, which means that one cannot see any effect of a small electric voltage, e.g. from a battery, in the gas. However, if energy is transferred to the gas in order to heat it, e.g. by radiation, the atoms of the gas may be ionized. The electrons which are bound by electric forces to the nuclei, will then be separated from their mother nuclei and they will fly away to other parts of the gas, to move around among all the nuclei. The gas then becomes a new state of matter which is electrically conductive and which is called a plasma [2.1–2.3]. If sufficient amounts of energy are transferred to the gas it becomes fully ionized, i.e. all the atoms of the gas will lose all their bound electrons. Before the atoms become ionized, the electrons could stay bound to their nuclei but in excited states. These have a higher energy than the original ground state. The electrons later decay from these excited states accompanied by the emission of radiation in the visible domain of the spectrum. This happens, for example, in auroras where the atoms high up in the atmosphere become excited by electrons, which enter from the solar wind and become trapped by the Earth’s magnetic field in the polar region. The decay of the excited atoms may subsequently generate beautiful luminous curtains of auroral radiation. In astrophysical plasmas as well as in plasmas studied in the laboratory the motion of electrically charged particles, electrons and ions, are influenced by the presence of magnetic fields. The charged particles perform spiralling motions around the magnetic field lines. Magnetic fields could be generated by 26

THE SECRETS OF PLASMAS

currents in the plasma itself, i.e. self- generated, or could be generated by external magnetic field coils carrying currents generated in the laboratory [2.2] In certain astrophysical objects like the Crab nebula a particular radiation, named syncrotron radiation is generated by highly energetic, relativistic electrons which spiral around magnetic field lines generated by electron currents in the nebula itself. The beautiful visible structure of the nebula originates from this basic mechanism. Another phenomenon where the magnetic field has a confining effect on a plasma, is that where plasma blobs are thrown out from the solar surface, carrying with them circulating currents which themselves create magnetic fields in the plasma by which the plasma stays confined. Plasma blobs could in this way be carried all the way to the Earth. The state of a plasma has sometimes been called the fourth state of matter to emphasize its specific nature [2.9]. Plasma occupies the following place among the various states of matter. In heating successively from low to high temperature one may identify various transitions between the different states of aggregation, namely (a) The solid state (b) When a solid is heated sufficiently it becomes a liquid. This occurs when the thermal motion of the atoms breaks the crystal lattice of the solid. (c) When the liquid is heated to such an extent that its atoms become vaporized from a surface faster than condensation occurs on the surface it becomes a gas. (d) At temperatures sufficiently high to ionize the gas, i.e. breaking the electron-nucleon bonds by collisions between the atoms in the gas so that the electrons become free, a plasma is created. For plasmas heated to extremly high temperatures (hundreds of millions of degrees) nuclear fusion reactions may occur. The thermal velocities of the nuclei then become so high that the nuclei sometimes have a chance to approach each other 27

CHAPTER 2 PLASMAS AND NUCLEAR FUSION

so closely, that the short-range attractive nuclear forces come into play and compensate for the electrically repelling forces. The nuclei then fuse together and enormous power becomes liberated. Various combinations of hydrogen isotopes may undergo such reactions in stars and in fusion reactor plasmas. Selfsustaining burn conditions could then be achieved and the fusion plasmas could be efficient energy producing units for a long time. Such burning plasmas are the origin of energy production in the stars, including our sun (14-16 million degrees central temperature), which provides conditions for life on Earth. They will also be the source of energy production in future fusion reactors (200 million degrees burning temperature). The classification of the elements given here is almost identical to that introduced by the Yin-Yang philosophy from ancien China, namely: earth, water, air and fire. As a curiosity in this connection it may be mentioned that the noble coat of arms of Niels Bohr in the Fredriksborg Castle in Denmark carries the Yin-Yang sign. In the coat of arms of Niels Bohr the Yin-Yang sign signifies the concept of complementarity in physics, i.e. the fact that an electron can behave like a particle under certain circumstances whereas in other connections it exhibits a wavelike nature. Complementarity is analysed on philosophical grounds in the literature of Søren Kierkegaard (1813-1855) the great Danish author, whose ideas inspired Niels Bohr. The physicist Louis de Broglie (1812-1987) also did fundamental work in pioneering the implications of the principle of waveparticle duality in atomic physics and was awarded the Nobel Prize in 1929. As students in Sweden we were tought about Louis de Broglie and his work and we learnt that he lived in a beautiful French castle. I recently had the opportunity of visiting the castle Chaumont-sur-Loire, belonging to the de Broglie family and happened to find that it was situated only some kilometers from another famous Loire Valley castle, Amboise, which 28

THE SECRETS OF PLASMAS

belonged to the French Royal family and where Leonardo da Vinci spent the four last years of his life. There is now also an impressive museum in the city of Amboise exhibiting the many inventions by da Vinci. One can not help thinking that new developments in the architecture of fusion plasma devices might benefit from the imagination of Leonardo (see Chapter 8).

2.2 Plasma physics: pecularities and games Plasma physics is a comparatively young science. Although some experiments relating to what is today called plasmas were done back in the 18 th century it was not until some decades into the 20 th century that plasma physics started to develop as a separate science. The American scientist Irving Langmuir pioneered the field. He discovered that oscillations, so called plasma oscillations, could occur in a plasma at a particular frequency the plasma frequency νp determinded by the density of free electrons in the plasma, ne with νp2 being proportional to ne. Langmuir also introduced the name «plasma» and was awarded the Nobel prize for chemistry in 1932. Plasma oscillations can be visualized as follows. The electrons in the plasma are repelled from each other due to their negative charges and adopt an equilibrium position. Suppose that we move a bunch of them by brute force in a certain direction and leave them suddenly. Restoring forces from the electric charges will then be set up and try to bring them back towards their original equilibrium positions. As a result they will swing back, but beyond their equilibrium positions, due to their moments of inertia. They will subsequently return from the opposite side like a swinging pendulum and the process will be repeated. Imagine another model from daily life: compare the electrons with cars which move on a road at a certain speed and with a certain distance between them. For some reason one of 29

CHAPTER 2 PLASMAS AND NUCLEAR FUSION

the cars brakes. To avoid collisions the following cars will also brake and so on, until the first car decides to recover it’s earlier speed followed by the others. The processes may be repeated. Along the line of traffic there will be a bunching of cars accompanied by a depletion of the density of cars. Motion of this character, longitudinal oscillations and waves, occur frequently in plasmas as in mechanical systems. The accompanying electric oscillating fields are obviously in the direction of the motion. Electromagnetic waves, like microwaves, which are transverse waves with their electric and magnetic fields oscillating at right angles to the direction of propagation, become modified when they penetrate a plasma and change their velocity of propagation due to the presence of the plasma. In the presence of static (non-oscillating) magnetic fields in the plasma a rich variety of waves of different character may occur. These may strongly affect the properties of the plasma. If the amplitudes of the waves increase to high values the waves may influence the transport of particles and temperature in fusion plasma. Turbulent and chaotic phenomena in this connection are topics of high interest in today's plasma physics research. There are certain low-frequency waves, for which the dynamics of the ions in the presence of a magnetic field in the plasma are important. They play a significant role in astrophysics as well as in laboratory plasmas. The pionering work of the Swedish scientist Hannes Alfvén should be emphasized here. He was the creator of the field named magneto-hydrodynamics and he greatly stimulated plasmaastrophysics in general. Alfvén was awarded a Nobel prize for physics in 1970. So called Alfvén waves are low-frequency waves in magnetized plasmas. They can simply be simulated by the motion of an oscillatory suspended string. The analogy can be used to calculate the velocity of an Alfvén wave [2.4, 2.10]. Hannes Alfvén’s pioneering one page publication «Existence of electromagnetic-hydrodynamics waves» was published in Nature in 1942 [4.1]. 30

PLASMA PHYSICS: PECULARITIES AND GAMES

It was followed by the first simple experimental demonstration of magneto-hydrodynamic waves also in one page by Stig Lundquist Nature in 1949 [4.6]. Both these articles are also reproduced as appendices in [2.8]. The physics of plasmas is nowadays studied by experimental, analytical and computer simulation methods. Experience has shown that plasmas are very complex media. The interplay between the different methods of investigation have, however, revealed important results even for the most complicated plasma structures. A presentation in terms of analytic formulae is, however, so lengthy and cumbersome that it is far beyond the aim of this discussion. Instead, it seems that comparisons with certain other activities and with games may be used to model, or at least crudely visionalize, some features of plasma behaviour in complex situations. The motions of the particles or groups of particles in plasmas may be compared with: (a) Ordered motions like ballet or square-dancing The motions of the particles in a plasma may be compared with the dancers of a modern ballet, where numerous dancers participate. The ballet «Notre Dame de Paris» by the great French choreographer Roland Petit (La Scala, Milan, April 1998) was a marvellous performance of individual and collective motions, order and disorder, oscillation and waves stimulated by the music. Flames and sparks seemed to come from the vibration of the fingers of the dancers in coherence with the music. (b) Collective drag, like a rugby team in action (c) Ice-hockey, for high speed behaviour (d) Individual and collective motions for a set of chess pieces (slow motion) (e) A tennis player in action, whose traces on the court would correspond to projections of the particle trajectories in the plasma. The ball could simulate an intermediary force. The lines on the court and the rules of the game might simulate 31

CHAPTER 2 PLASMAS AND NUCLEAR FUSION

the fusion device geometry and the influence of the confining magnetic field. There could be singles or doubles competitions depending on the configuration of the plasma, etc. The umpire of the competition would be the scientist, who controls that the laws of Nature apply and that they are skilfully used to win the game! In parenthesis it might be mentioned that games and sports seem to have been much in the minds of famous scientists: Niels Bohr, the father of atomic theory, and his brother Harald, who pioneered the field of almost periodic functions, were both prominent football players. Harald was in the Danish national team. Lyman Spitzer, pioneer of the American fusion program was also an active mountaineer. Rumour has it that he got some of his ideas about particles in fusion plasma configurations (figure-eight configurations) from traces he made in the snow, skiing on the Matterhorn, the mountain which gave its name to the early American fusion program, Project Matterhorn.

2.3 Nuclear fusion reactions Nuclear energy can be liberated by two different processes: fission and fusion. In fission a heavy nucleus (uranium, plutonium, etc...) is split in two or more fragments by bombardment of neutrons, simultaneously producing large amounts of energy. If uranium 235, consisting of 143 neutrons and 92 protons, is bombarded it produces 200 MeV for each nucleus that undergoes fission, two or three neutrons and also two radioactive nuclei. Fusion occurs when two light nuclei of hydrogen isotopes unite to undergo a fusion reaction from which neutrons of several MeV are emitted. For reaction of the hydrogen isotopes deuterium and tritium, the most studied process, a 14.1 MeV neutron is produced, and in addition an alpha particle, a He-4 nucleus, of 3.5 MeV. 32

NUCLEAR FUSION REACTIONS

In the process an intermediate compound nucleus of two protons and three neutrons is formed, which is unstable and immediately splits into a neutron and an alpha particle. When do nuclear fusion reactions occur in a plasma? They can only occur when the temperature is very high, many millions of degrees. The reason is that the repulsion which always exists between the positive electric charges of colliding nuclei has to be overcome by attractive nuclear forces. This can only happen when the nuclei with high mutual velocity come -13 within the grasp of the strong but short-ranged (10 cm) nuclear forces, which occurs only for enormously high temperatures about 200 millions of degrees. Nuclear fusion reactions can also be produced in a gas containing only deuterium, which would, however, require even higher temperatures, about 10 times higher than deuteriumtritium reactions, considering burning conditions for a reactor. Deuterium can be produced from ordinary sea water. The use of deuterium alone as fuel in a reactor would accordingly allow us to tap into an inexhaustable source of energy. Tritium, on the other hand, is a radioactive gas (half-life of 12 years) which can be generated from lithium by reactions with neutrons, directly in a reactor. Natural resources of lithium on Earth are estimated to be sufficient for tenths of thousands of years. A large scale mechanical analogy of nuclear fusion would be to consider a gigantic rolling stone that is given a sufficiently high up-hill velocity to mount a vulcano and fall into the crater to fuse with the magma! To achieve nuclear fusion it is clear that the natural choice of nuclei would be to try the simplest ones, namely hydrogen or isotopes of hydrogen, which have the lowest electric charge to compensate and therefore require the lowest temperature. For fusion plasmas the nuclei and light particles (electrons, etc...) participating in the fusion reactions are shown in table 2.1.

33

CHAPTER 2 PLASMAS AND NUCLEAR FUSION

Table 2.1 Particles participating in fusion reactions proton, p

⊕

positron, e+

neutron, n Ο deuterium, D

Ο⊕

Ο Ο⊕ helium 4, 4 He (alpha particle) ⊕Ο Ο⊕ helium 3, 3 He ⊕ Ο⊕

tritium, T

electron, e–

neutrino, ν gamma, γ

It might be interesting to see how Nature has solved the fusion problem in the stars, notably in the sun, which is responsible for life on Earth and which is the centre of our own solar system. It has been determied by H. Bethe (who won the Nobel prize physics in 1967), among others, that the nuclear fusion reactions which provide the energy in the sun, and essentially in all the stars, belong to a cycle of proton-proton reactions. The first step in the sequence is the one where the reaction between two protons produces one deuterium nucleus and in addition one positron, one neutrino and, gamma radiation. This type of reaction liberates 9 MeV of energy. The deuterium produced reacts with a proton to form a helium-3 nucleus and in addition gamma radiation. The liberated energy amounts to 5.5 MeV. Finally two produced helium-3 nuclei react to reproduce two protons like the ones that started the chain, plus a helium-4 and further gamma radiation, the process liberating 2.8 MeV. The reactions require a temperature of 6 million degrees, whereas according to available theory the center of the sun has a temperature of 14 million degrees. This chain of nuclear processes is summarized below using the following notation: p denotes a proton, D is deuterium, e+ a positron, ν is a neutrino, γ is gamma radiation and 3He and 4He are helium-3 and helium-4 nuclei respectively. 34

NUCLEAR FUSION REACTIONS

Step 1: Step 2: Step 3:

+

p + p → D+ e + ν + γ (9 MeV liberated) 3 D + p → He + γ (5.5 MeV liberated) 3 3 4 He + He → He+ p + p + γ (2.8 MeV liberated)

The energy carried by the gamma rays is finally transformed into visible light etc... after a long complex journey through the sun.

2.4 Nuclear fusion plasmas What else is there that is important and characteristic of the fusion plasmas? There is a basic phenomenon which has to do with the property of all plasmas to attempt to be electrically neutral on a scale larger than a certain value, called the Debye distance (named after Peter Debye who was awarded the Nobel prize for chemistry in 1936). The square of the Debye distance denoted λD is proportional to the ratio between the plasma temperature T and 2 the density of free electrons n, i.e. λD ~ T/n [2.2] If one considers free electrons, which are attracted to some nuclei, there is compensation for the influence of this attraction by the thermal motion of the electrons. As a result shielding of the positive charges by the electrons occurs, such that outside a very small distance from the positive charges the plasma is electrically neutral. This means that the positive charges are electrically hidden to an observer outside the Debye distance which is, of the order of or less than a few millimeters in a fusion plasma. The concept of a neutral plasma has a meaning only for plasmas larger than the Debye distance. For comparison, it could be mentioned that rocket flame plasmas could have cross sections of the order of the Debye distance and might therefore not be considered as neutral plasmas. A fusion plasma, being a fully ionized gas, has certain similarities with the properties of a metal. The abundance of free electrons is the reason why the plasma is a good electric and thermal conductor. 35

CHAPTER 2 PLASMAS AND NUCLEAR FUSION

The total energy W liberated by fusion per unit volume of the plasma of temperature T is proportional to the product of the density of the two reacting nuclei n1, and n2 and to the energy Q liberated in each reaction as well as to a factor P, the probability of reaction, which depends on T and accounts for how often a nucleus of one type has a fusion reaction with a nucleus of the other type. In the energy budget of the plasma one has to take into account losses by various mechanisms such as electromagnetic radiation and thermal conduction. As a result heat energy will diffuse away from regions of high temperature, where the fusion reactions occur most frequently. Fine structure effects like turbulence and instabilities may considerably change the diffusion from what would be expected from elementary classic theory [2.3]. The diffusion of particles and the conduction of heat may be considerably reduced by the influence of a confining magnetic field generated by currents external to the plasma or by currents in the plasma itself, as in the tokamak experiments, the most successful ones to date. It seems that in present fusion plasma research we may be able to master the confinement problem by using magnetic fields. The process of magnetic confinement originates from the phenomenon that electrically charged particles tend to perform spiral motions around the magnetic field lines which define the direction of the magnetic field in each point in space. Thus, the particles will not be free to penetrate space perpendicular to the direction of the magnetic fields. Dangerous effects, similar to the explosion of a nuclear bomb, which uses the same fusion reactions, can not occur in a fusion reactor plasma. The metallic walls of the vessel surrouding the plasma would cool the expanding plasma in a short while. Another interesting alternative for producing fusion plasmas, in addition to magnetic confinement, has attracted considerable attention for a long time, namely the process of inertial confinement. In essence the principle amounts to 36

NUCLEAR FUSION PLASMAS

performing the experiment so quickly that the plasma has virtually no time to expand because of inertial forces. The energy for heating the solid materials used in the experiment, in fact small ice pellets, to fusion temperatures is supplied by pulses of high power laser radiation or of ion beam pulses with appropriate repetition rates. It is still an open question as to which of the two principal confinement schemes, magnetic confinement or inertial confinement, is the more attractive or more realistic. The inertial confinement scheme is highly dependent on the evolution of high power lasers, such as those which are currently being developed in the megajoule energy domain. The successful operation of fusion reactors using to either of the two main confinement schemes relies strongly on the simultaneous optimization of the complex nuclear fusion plasma and surrounding active auxiliary devices (plasma geometry and size, heating systems, superconductive coils, etc...) But how is the work carried out? What do the plasma physicists do? There is a story that goes back to professor Victor Weisskopf, when he was Director General of the European Organization for Nuclear Research (CERN). He was asked one day about what physicist in general do. We may here transform his answer to explain what a plasma physicist does: There are different kinds of plasma physicists. Some work close to engineers, building big devices like accelerators or fusion machines. Let us compare them with shipbuilders constructing big boats. Then there are those who use the devices to make new experiments and discover important things. They lecture to their students and report about their work as they go around the world to meet other plasma physicist and discuss their results. Those are to be compared with sailors who set their sails to go across the oceans to meet many difficulties and perhaps discover new continents. But then there are also plasma theoreticians. They are to be compared with people who remained in Spain to make calculations and to prepare and 37

CHAPTER 2 PLASMAS AND NUCLEAR FUSION

guide Christopher Columbus for his voyage to India but who made him end up in America! References [2.1]

Spitzer L 1962 Physics of Fully Ionized Gases (New York: Interscience)

[2.2]

Sturrock PA 1994 Plasma Physics (Cambridge: Cambridge University Press)

[2.3]

Goldston RJ and Rutherford PH 1995 Introduction to Plasma Physics (Bristol: Institute of Physics Publishing)

[2.4]

Cross R 1998 An Introduction to Alfvén Waves (Bristol: Institute of Physics Publishing)

[2.5]

Lehnert B 1952 On the behaviour of an electrically conductive liquid in a magnetic field Arkiv Fysik 5 69

[2.6]

Lehnert B 1955 The decay of magneto-turbulence in the presence of a magnetic field and Coriolis force Quart.of Appl.Math. XII 321

[2.7]

Lehnert B 1964 Dynamics of Charged Particles (Amsterdam, New York, Oxford: North Holland)

[2.8]

Wilhelmsson H 2000 FUSION A Voyage through the Plasma Universe (Bristol:IOP)

[2.9]

Eliezer Y 2001 The Fourth State of Matter: An Introduction to Plasma Science (Bristol: IOP)

[2.10]

Wilhelmsson H 2005 Alfvén waves Encyclopedia of Nonlinear Science (ed. Alwyn Scott. New York and London: Routledge)

[2.11]

Les enigmes de l’Univers 2002 Enquêtes sur des mondes inconnus, Science et Vie (Hors série) n°221 Décembre (Paris)

[2.12]

Chen FF 1984 Introduction to Plasma Physics (Dortrecht: Kluver) 38

NUCLEAR FUSION PLASMAS

[2.13]

Miyamoto K 1976 Plasma Physics for Nuclear Fusion (Cambridge, MA: MIT PRESS

[2.14]

Herman R 1991 Fusion: The search for Endless Energy (Cambridge: Cambridge University Press)

[2.15]

Fowler TK 1997 The Fusion Quest (Baltimore, MD: John Hopkins University Press

[2.16]

Lehnert B 1961 Stability of an inhomogeneous plasma in a magnetic field Physics of Fluids 4 525

[2.17]

Lehnert B 1966 Short-circuit of flute disturbances at a plasma boundary Physics of Fluids 9 1367

[2.18]

Lehnert B 1987 Large Larmor radius effects on density perturbations in a magnetized plasma Plasma and Contr. Fusion 29 341

[2.19]

Elskens Y and Escande D 2003 Microscopic dynamics of plasmas and chaos (Bristol: IOP)

[2.20]

Yoshizawa A, Itoh S-I and Itoh K 2003 Plasma and Fluid Turbulence (Bristol:IOP)

39

3.1 What is new in the sky Mr Hubble? The stars and galaxies are not only extremely interesting objects themselves. Their distribution in space of the universe poses questions of fundamental importance. The stars can be grouped differently to form various types of galaxies. The galaxies, on the other hand, show tendencies of forming groups or clusters in specific patterns, which resemble structures found in other fields of science. It was the American astronomer Edwin Hubble who in 1923 showed that the spiral galaxy Andromeda was a separate galaxy far out of our Milky Way. He also reported in 1929 a remarkable discovery namely that all galaxies move away from each other. It turned out that the mutual velocity of separation was proportional to the distance between the galaxies. The constant describing the motion was given the name of the Hubble constant. His name was also remembered in babtising the extraordinary Hubble Space Telescope (HST) that led to a revolution in optical astronomy and cosmic sciences. The chapter discusses these and related questions as well as the fundamental properties of our sun, the sun’s metabolism, including the early work in 1930 at the age of 20, by S. Chandrasekhar, determining the critical size of a star. This limit corresponds to a mass equal to 1.4 times the mass of our sun (Nobel Prize for Physics 1983). For higher masses the stars collapse, since the electron gas becomes degenerate, and may finally become black holes. 40

WHAT IS NEW IN THE SKY MR HUBBLE?

3.1.1 Plasma and fusion in the cosmos Messages about new scientific discoveries or new technological achievements reach us frequently. Often these come from the field of astronomy or space science. New instruments of observation are developed using rockets, satellites or space shuttles. The exploration of our solar system has opened up a new era of scientific investigation. The development of data communication techniques has made it possible for us on Earth to stay in contact not only with astronauts making more and more distant trajectories in their spacecrafts, but also with observing instruments and recorders on unmanned spacecrafts sailing further and further out in the archipelago of remote planets, passing through belts of asteroids and the continuously blowing solar wind, measuring parameters of distant magnetospheres and studying magnetic fields and space plasmas. Observations of galactic systems and other extremely remote sources like quasars offer great challenges. Large optical telescopes and radioastronomy antennas are detecting radiation and signals from the outer limits of the universe. In this enormous stream of fascinating news and observations on cosmic events we all remain full of admiration the scientific progress. But seldom are questions raised about what is driving this gigantic machine of celestial objects – our universe. Where does the energy come from? The unique anwer is that the origin of the power driving the universe is fusion energy generated in a plasma. But how does this system evolve and how does the originally generated energy become distributed among the tremendous variety of stars and galaxies and other celestial objects that we find in our universe? Visual observations only give information about the light from the objects or gases which are kept together by gravitational forces. But what is the function behind the emission? What role do the magnetic fields and currents play in the process of evolution of the system? We are now in position to find out much more about those questions. One may wonder 41

CHAPTER 3 THE COSMOS

why we have not already paid more attention to energy problems on a universal scale. One reason is that we cannot see or directly observe the celestial fusion energy processes or the plasma-magnetic phenomena occurring in space plasmas and remote magnetic fields. The frequencies associated with the plasma-magnetic phenomena are simply not in the visual regime but in the regions of centimeters, meters or even longer wavelengths. However, the possibility of clarifying the role of fusion and of plasma-magnetic field systems in the universe has increased tremendously in recent years. The situation provides a great challenge for surveying fusion plasma problems in the universe and for encouraging continued studies of problems common to both cosmic fusion-plasma electromagnetics and device-oriented fusion plasma research aimed at production of electric power by fusion reactors on Earth.

3.1.2 How it all began ... The universe is considered to be about 15 billion years old. «News» can be brought to us on Earth by light or radiowaves over distances of billions of light years. What we can see today, looking out into the universe with the naked eye or sophisticated instruments is something exceedingly spectacular. It tells us that, since the beginning of the universe. Nature has played an extremely active game and created many of structures. Each of them is evidence of a certain moment in the history of the universe. Dramatic events exhibiting many features of what we today call modern physics have occurred in gigantic dimensions at enormous distances. The story of the evolution of the universe is, in fact, recorded in the scenario around us, telling us about galaxies, stars, nebulae, supernovas and pulsars. One might even say that in a certain sense the scenario is a visualization of evolution in four-dimensional space. What a fantastic source of information! What an extraordinary exhibition of organization and indeed self-organization of matter.! How did it all come about? 42

WHAT IS NEW IN THE SKY MR HUBBLE?

The field is as open to speculation as it is fascinating and complex. To what extent can we hope to describe the very beginning of the universe? We may even ask: was there really a beginning? Perhaps the universe has been always oscillating, creating and annihilating itself over a huge timescale? Perhaps it has a different evolution from what we can even imagine today? We now think, or at least many astrophysicists think, that there was a beginning and that it was manifested by an event resembling some kind of enormous lightning flash which occurred simultaneously everywhere and that it resulted in a state of extremely high density and temperature. As the poet may have expressed it This is the way the world began not with a whimper but with a BANG

(with apologies to TS Eliot, 1885-1965) We now think that during the very first moments of the universe there were no galaxies or stars, no atoms or nucleons, no structures whatsoever. Photons, electrons and quarks, as building blocks of Nature, were somehow hidden in a uniform background, where there were also gluons ready to help the quarks (one talks about quark-gluon plasma) to combine in triples to form protons or neutrons. Each of these would then include two quarks of one type (charge 2/3) and one quark of another type (charge-1/3), which would give a proton (charge 1), or include one quark of type one (charge 2/3) and two quarks of the other (charge-1/3) yielding a neutron (charge 0). Returning to the initial instants of the universe the opinion is that during the very first minutes essentially only hydrogen and, as a result of fusion reactions, helium as well as isotopes of these elements existed. All other elements were formed much later, in fact some hundreds of millions of years later, in the 43

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interior of heavy stars. What happened to the light, the tremendous flash that accompanied the initial bang? To answer this question it is necessary to emphasize another important point. That has to do with the overall motion in the universe, which is believed to be characterized by expansion in every point of the universe. It means that wherever we imagine that we are in the universe we see all other points disappearing away from us, the near ones as well as the distant ones. Since this expansion is uniform everywhere in the universe it follows that the distant points move away from us with higher velocities, which are, in fact, proportional to the distance. In the same way as an implosion raises the temperature in a gas the expansion has the tendency of cooling not only the expanding matter but also the light, making the light less energetic. Since red light is less energetic than blue light it follows that one would expect the cooling effect from the expansion to shift the blue light to become transferred more and more into the red domain of the spectrum and to the invisible part of even longer wavelengths occupied by radio waves. The light which existed in the very beginning exists today in the form of radio waves in the whole universe as a background radiation or as a 3K radiation, referring to the temperature in degrees of Kelvin of its black-body radiation. It can be observed by radio telescopes on Earth. The discovery in 1965 of the 3 K background radiation (−270° C) by the radioastronomers Arno Penzias and Robert Wilson was awarded the Nobel prize for physics in 1978. 3 K is remarkable in that it witnessed the very beginning of the universe. In his poetry Harry Martinson, the great Swedish author (1904-1978) describes the formation of the universe in the following way: The soul of ideas in space out of infinite haze gathered the seeds to the suns’ patient blaze

From far beyond time came the hydrogen out of its modest dress and built the atoms’ ingenious nests to God bless

(freely translated from the original Swedish!) 44

WHAT IS NEW IN THE SKY MR HUBBLE?

On your voyage through the universe you may, like Nils Holgersson (Lagerlöf Selma 1858-1940) on his marvellous voyage, travel on a goose-shaped space shuttle and land in areas, where you find new and unexpected friends, revealing to you secrets about new landscapes of the universe, you may come across many regions which you find fascinating and perhaps others which you find less attractive. Like Gulliver (in Jonathan Swift’s Gulliver’s Travels), you may encounter domains and perhaps inhabitants, which seem quite strange and of very different size, both giants and dwarfs. You will hear cosmic music and different signals whistling when you pass plasmas surrounding cosmic bodies. You will see gigantic plasma jets crossing through space and enormous eruptions of plasmas emerging from the stars. The source behind all this is fusion energy – the immense cosmic burn out of nuclear matter.

3.1.3 Galaxies and stars In the universe the galaxies are not distributed uniformly. They tend to form groups or clusters. Our galaxy is a member of such a group of about 30 galaxies. It is one of the largest in the group, to which belongs also the spiral galaxy Andromeda, the largest member of the group. Other types are elliptic, irregular and spiral-bar galaxies. Typical values of the diameters of the spiral galaxies are 100 thousand light years and the distances between them are about 10 million light-years. As a comparison light takes eight minutes to go from the sun to the Earth. An average galaxy contains many hundreds of billions of stars. The spiral arms of the galaxies are regions from where the stars originate. At a distance a spiral galaxy looks like a rotating firework. In reality the time of rotation of a galaxy amounts to some million years. But where did the structures in the universe, come from in the very beginning? One thinks today that out of the enormous temperatures and densities some kind of state emerged where certain regions contained sligthly more of matter than others and that gravitational forces which rule the universe led to 45

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concentrations of matter which subsequently developed to individual galaxies and stars. This process took a very long time. Even millions of years from the very first moment nothing but hydrogen and helium is thought to have existed in the universe in the form of gas clouds. The temperatures were still thousands of degrees. When structures started to develop the regions between the stars still contained matter, essentially hydrogen and helium, but also beginning forms of molecules and fine dust which came to form interstellar clouds and nebulae, visible in telescopes as gigantic formations, the environment of the origin of life. In the history of cosmology it should be noted that it was in 1923 that the American astronomer Edwin Hubble showed that Andromeda was a separate galaxy far out of our Milky Way, and in 1929 that the galaxies moved away from each other. His name was given to the characteristic constant that describes the mutual velocity dependence on the distance of separation, and subsequently, in this decade, to the extraordinary Hubble Space Telescope has led to a revolution in optical astronomy and cosmic sciences. In art and literature the wonders of the heavens have been great sources of challenge and inspiration. In some paintings by the great Dutch master Vincent Van Gogh (1863-1890) the artist stresses the effects of light by emphasizing the contrast between the blue-green and the yellow colours. As a result he obtains effects like enhanced vibrations in the light (see Plates 2 and 3). The cypresses in these paintings, given dark green and bronze colours, are also important contrasts to the galaxies and stars. Those cypresses take the form of fire-flames similar to those observed in eruptions from the solar surface. The contrasts as well as the strong and even mysterious impressions which the paintings give are furthermore accentuated by the typical stream-like patterns which Van Gogh produces in his paintings by the strokes of his paintbrush. Ilia Zdanevitch (1894-1975), (after 1920 Iliazd),a poet from Tbilisi (Tiflis), Georgia, published in 1964 an extraordinary book illustrated by Max Ernst (1891-1976): 46

WHAT IS NEW IN THE SKY MR HUBBLE?

«Maximiliana ou l’exercice illegal de l’astronomie». Iliazd’s typography introduces the words like patterns of galaxies, comets and meteors exhibiting and relating the macrocosmos and the micro-cosmos, even touching upon the creation of life. Max Ernst invented for the book a special strange alphabet of hieroglyphs which give the pages an expression of invisible forces like those interlinking celestial bodies. The book recognizes the work of Guillaume Tempel, an autodidact in astronomy who in 1861 discovered a small planet between Mars and Jupiter. He gave to it the name Maximiliana in honour of Maximilian II of Bavaria. He became, however, discredited by the official astronomers, who gave the name Cybèle to the planet and deprived Tempel of his discovery. Iliazd and Max Ernst, fascinated as they were by astronomy and cosmic events, decided to collaborate in the written language of the «alphabet of the stars» and they succeeded in combining the text with splendid etchings to produce the magnificent book «Maximiliana» and to shed proper light on the achievements of Guillaume Tempel, (see Plate 4). There are several other great authors, among them Victor Hugo (1802-1885): «La Comète», p. 219 and «Abîme», p. 411, «La légende des siècles II», (Paris Flammarion)1967) who in their works have been inspired by cosmic sources. Present day research provides evidence of a new and unexpected feature, namely that there is an inherent anisotropy of the entire universe, i.e. that there is a preferred direction in the universe. The evidence comes from changes in the polarization of radiation, which has propagated over very long distances, and where the observed data cannot be explained by existing models of an isotropic universe. The indications have, however, to be examined in great detail and checked by more observations and statistical analyses of the results before safe conclusions can be drawn. If correct, the results could have important consequences for cosmology. There is apparently still room for exceedingly complex and far-reaching studies of the Cosmos! 47

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One may wonder what rôle interstellar magnetic fields and plasmas play in this connection. The Earth and the sun, and presumably also all the other stars, have magnetic fields with preferred directions which change polarity periodically. The galaxies have individual spin-directions of their vortex motions. So why could not our whole universe be anisotropic? The first observations of anisotropies in the cosmic microwave radiation by the Cosmic Background Explorer Satellite (COBE) in 1992 had an important impact on the research in the field of cosmology. The discovery of the anisotropies, followed by a large number of detailed studies using different types of observational technique, may give a clue to the formation of seeds in the universe that subsequently developed into galaxies and larger structures. It should be noticed that the relative anisotropies are tiny, one part in 100 000 as obtained by the COBE satellite. However, those small deviations could have extremely important consequences for the evolution of the universe.

3.1.4 The sun’s metabolism The sun is the only star where details, for example dimensions of less than some hundred kilometers, of the motions of ionized gas in the presence of magnetic fields can be studied by optical instruments. All other stars appear as point sources even in the largest telescopes, which can therefore only observe and analyse the properties of the emitted radiation. The mass of the sun is 2.1033 g, or 330,000 times larger than the mass of the Earth. The solar diameter is 1,4 106 km which is more than 100 times larger than that of the Earth. The sun is about 150 million km from the Earth, a distance which it takes eight minutes for light to travel. The surface temperature of the sun is about 6,000° C. For many thousands of millions of years the sun has been emitting a total amount of radiation of 4.1023 kilowatts of energy per second in the form of light as electromagnetic 48

WHAT IS NEW IN THE SKY MR HUBBLE?

waves, which corresponds to hundreds of billions times the power consumption of the whole United States . This would correspond to a kilowatt of power on every square meter of the Earth’s surface exposed to the sun's isotropic radiation. One knows that this radiation has been emitted for billions of years, the age of the oldest organic fossils found. The source of emitted energy lies deep in the sun, where the temperature is about 15 million degrees. Optical observations can give us direct information about only a thin layer of the solar surface. To explain what happens inside the sun one must rely on theoretical modelling. The models should account for everything that one knows about the sun, in steady state as well as under perturbed conditions, i.e. in the presence of solar activity. As far as the steady-state situation is concerned one knows that there is a force of gravity at every point of the sun which tends to contract the sun, and also that there is a gas pressure which tends to expand the sun. The force of gravity and the gas pressure have to balance each other to maintain equilibrium. The stable situation has remained for billions of years, and the size of the sun and its brightness have been essentially unchanged. In 1960 an oscillation of the sun with a period of 5 minutes was discovered. Today it is known that the periods of the oscillations of the sun have values between 5 minutes and more than one hour. These oscillations can be used to analyse the internal structure of the sun. Only for central temperatures of tens of millions of degrees is the gas pressure sufficiently high to balance the enormous gravitional forces from the total volume of the sun. The equilibrium pressure corresponds to a density of matter in the center of the sun of 100 grams per cubic centimeter, which is maintained in a region of one quarter of the solar radius from the center. This region contains almost half of the total solar mass, whereas one-quarter of the solar radius from the surface would define a shell where the density would be less than a tenth of a gram per cubic centimeter. It is in the central sphere where the energy is liberated by nuclear reactions transforming 49

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hydrogen into helium. The nuclear processes provide about one million kilowatt hours per five grams of helium, which would not occupy more than a few cubic millimeters. By the way, did you happen to think a little more in detail about how the sun maintains its equilibrium? It is, as we mentioned, determined by the balance between the total effect of the gravitational forces acting from the outside on the central part of the sun, providing the confinement, and the action from the hot nuclear matter which sets up the pressure toward the gravitation as a result of the high temperature, 15 million degrees. This is the necessary amount, and the lucky circumstance is that these 15 million degrees is just precisely what is needed to run the equilibrium thermonuclear reactions, which provide the high temperature. The sun is thus a selfsustaining system, burning the nuclear matter. What a miracle! And how well Nature has arranged things. This brings us to another point of fundamental interest, namely the equivalence between mass and energy as expressed by the Einstein equation E= mc2, where E is the energy, m the mass and c the velocity of light (3×1010 cm/s). The equation tells us that one gram of mass is equivalent to 25×106 kilowatt hours. The liberation of energy by transmutation of protons and neutrons to helium is accompanied by a mass defect multiplied by c2. There is no other possible explanation for the enormous energy liberated by the sun or the other stars than nuclear fusion. The form of hydrogen burning to helium in the initial phase of evolution is the natural solution to the problem of solar energy production. In fact, the sun is essentially a gigantic fusion reactor. A fusion reactor on Earth is presumed to operate with tritium and deuterium, the isotopes of hydrogen to be efficient at available temperatures (2×108 ºC), whereas the sun uses only hydrogen (protons) to generate the helium. At such high temperatures the atoms are always completely stripped of their electrons. When during the passage through the sun the gamma rays, which are also produced by the nuclear reactions, carry the energy outwards from the inner central region and 50

WHAT IS NEW IN THE SKY MR HUBBLE?

reach the outer quarter radius of the sun, the energy will start to be carried further by convection. Like boiling water the solar matter starts to seethe and evaporate and then reaches the photosphere, a thin gaseous layer (10–16 grams per cubic centimeter) which has a granule structure of irregular convection cells. Above the photosphere lies the chromosphere, which is more turbulent than the photosphere, and has a density of only 10–11 grams per cubic centimeter, which further out falls to 10–16 g/cm3 and suddenly drops even further and becomes the corona, a rarified layer of gas, which stretches out for millions of kilometers. The corona can be seen only during total eclipses when the moon passes in front of the sun to fully hide its luminous surface. Returning to the problem of energy production in the centre of the sun, the most important cycle of fusion reactions is p + p→ D + e+ + ν + γ +9 MeV D + p → 3H e +γ + 5.5 MeV 3

H e + 3H e → 6Be→ 4He + p + p + ‫ ץ‬+ 2.8 MeV

where the proton-proton reaction produces deuterium (and simultaneously a positron and a neutrino and in the second step the deuterium reacts with a proton to produce a helium 3 isotope and a quantum of gamma-radiation. The generated positron may annihilate with an electron to produce further gamma radiation (e++e→2 γ). Finally, two helium isotopes react to produce helium and recover two protons. The net effect of the cycle is that one helium nucleus is produced by four hydrogen nuclei. Each step liberates several MeV. The gamma rays become transformed to visible light on its way through the sun. The cycle of processes here described is what gives the sun and the Earth their energies. For solar fusion to occur a temperature of 6 million degrees is required, whereas the centre of the sun has a temperature of about 14 million degrees. For stars which are heavier than 2 MΟ (MΟ denotes the solar mass), for which the 51

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temperature in the centre becomes higher than 20 million degrees, another cycle where carbon, nitrogen and oxygen are involved, will be responsible for the energy production [3.51, 3.52] The reaction producing deuterium out of protons is fortunately very slow. The average reaction time per particle is estimated to be 1.2 1011 years in the centre of the sun. This peaceful burning is the reason for the long life-time of the sun. The age of the sun is about 5 billion years and it is estimated that the sun has sufficient hydrogen fuel to burn for another 5 billion years. But what will happen then? The central part of the sun will contract to heat and produce more energy whereas the outer parts will expand and cool. The colour of the radiation will change from white, via yellow to red. The sun becomes a red giant and later on a planetary nebula. Meanwhile the central part of helium will continue to contract, and when the increasing temperature reaches about 80 million degrees the helium starts to burn. The helium nuclei will indergo nuclear fusion reactions to produce carbon and radiation with an intermediary production of beryllium, 8Be, 4

He + 4He→ 8Be,

4

He + 8Be → 12C + γ.

The carbon may further react with helium to produce oxygen and gamma radiation, 4

12

16

He + C → O + γ.

The central part, which will now have a mass of about half the original total solar mass will form a so-called white dwarf star, which can be observed, by using telescope, in the central region of planetary nebulae. The density of a white dwarf is about one ton per cubic centimeter. Stars which are heavier than our sun can continue to build up even heavier nuclei with masses which are multiples of the helium mass. The central part will, however, not have a mass 52

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higher than 1.4 MΟ, the Chandrasekhar limit, determined by the fact that for the high pressures prevailing in the central star the electron gas does not behave normally but becomes degenerate. The Chandrasekhar limit is an interesting one conceptually and has important astrophysical consequences. The result of detailed theoretical calculations shows that the Chandrasekhar mass is proportional to the factor (hc/2πG)3/2, h being the Planck‘s constant, c the velocity of light and G the gravitional constant. One notices the interesting interplay between the constants of quantum mechanics, relativity and gravitation in this dependence. It was obtained by Chandrasekhar while on a boat journey from India to England in 1930. Arriving there at 20 years of age he introduced his results to Sir Arthur Eddington, the leading British astronomer and director of the Greenwich Observatory, who was then working on the radiation equilibrium of stars. The young Chandrasekhar succeded in convincing Eddington about his result, and he later, in 1983, received a Nobel prize for physics.

3.2 Albert Einstein and some of his work The extraordinary contributions by Albert Einstein to modern physics are interrelated to recent research, in particular to that on Bose-Einstein condensation, suggested in 1924 and 1925 on the initiative by the Indian physicist SN Bose and finalized in publications by Bose and Einstein [3.23 and 3.24]. The experimental verification of the phenomena waited until 1995, when the American scientists EA Cornell, W Ketterle and CE Wieman succeeded in realizing the proper conditions at very low temperatures. They were awarded the Nobel Prize for Physics in the year 2001 for their achievement of Bose-Einstein condensation in dilute gases of alkali atomes and for early fundamental studies of the properties of the condensates. In fact, conditions leading to supernova-like expansions of the condensate [3.34] as well as resembling those in white dwarf stars [3.35] can be simulated in the laboratory. Another 53

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outstanding idea was launched by Albert Einstein already in 1912 namely the bending of light in a gravitational field and experimentally verified in 1919 by a group of astronomers headed by the famous English scientist Arthur Eddington on the occasion of a solar eclipse. The phenomenon has, in recent years found extremely interesting applications in astronomy for studying remote galaxies or quasars. Even to measure the weight of galaxies as well as of the whole universe!

3.2.1 From Leonardo to Einstein Leonardo da Vinci (1452-1519) described and made drawings of how light was spread among the leaves of the trees and of reflections in the atmosphere 500 years ago, unbelievably in advance of his time. He also constructed eye-glasses and simple optical instruments as precursors of the astronomical tubes a hundred years before Galilei. When he writes: «Where a flame cannot live no animal which breathes can live» he touches upon modern chemistry and the conditions of life [3.7]. Leonardos ingenious activities came to inspire generations of creative people. His vision and his ability leave the world in eternal astonishment. No words can do justice to his greatness. In the first period of 1482-1499, the period of his life most rich in activity, Leonardo lived and worked in Milan, where he painted the marvellous fresco «The Last Supper» (L’Ultima Cena) in Santa Maria delle Grazie 1495-1498, considered to be his greatest masterpiece. Interestingly enough he also worked to help improve the water system of channels in Milan, where he later returned in 1506-1507. For his hydraulic projects he made detailed studies and designs of vortices and turbulence in streaming water. Leonardo thought at the age of thirty, when he first moved from Florence to Milan, that there was little more to be learnt in Florence. The cultural climate in Milan was different from that in Florence. He thought that Milan paid less attention to «beautiful forms, words and images that hide the secrets of the 54

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universe» and started to appreciate the logical and physical culture that characterized Milan. The people in Milan appreciated him as an artist who represented the refined culture of Florence, but who had to deal also with practical problems as an engineer and inventor [3.8, 3.9] He still had a chance to deepen his knowledge in technological areas and to study physics, mechanics and mathematics, in particular from Archimedes whose work he admired. His studies became more intensified from 1496 for a number of years. He tried to understand more about Nature and the universe and he came to benefit considerably from these studies in his future work. In particular he devoted considerable interest in hydraulics and aerology. Dynamic motion often payed an essential role in his work. Leonardo saw no barriers between scientific and artistic activities but found them mutually rewarding. He had a practical experience from early days, from the age of 16 when he worked in Andrea del Verrocchio’s (1436-1488) famous workshop in Florence, and he now applied his knowledge to enrich new creative work where «time, life and space» were essential ingredients. He started to make dynamic models for many different situations: water tunneling, mechanical machines and precursors of aeroplanes and other flying objects [3.9]. It should be noted that the word machine had a wider sense in those days than it does today. It could be used for instruments, weapons and even for the human body or the whole universe. One day in the centre of Milan in the spring of the year 2001, I came across a small plate on the wall of a building in 21 via Bigli, on which an inscription said that here lived Albert Einstein from 1894 to 1900. He was 15 years old when he arrived. I was surprised and wondered what brought him here. I found out that he had left Germany to see his parents and sister, who were living in Milan, where his father had a store dealing with scientific instruments, among other things. The stay of young Albert in Milan turned out to be a wonderful time for him. He went with companions of his own age to museums and 55

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the opera and seemed to enjoy the rich culture of Milan: music (he always liked to play the violin himself), science, art and life as never before. It may be that some intellectual waves from Leonardo even stimulated him for the future. The inscription on the commemorative plate said (translation from Italian by Dott, ssa Augusta Airoldi: In this house the young Albert Einstein lived from 1894 to 1900. He often gratefully remembered this hospitable land while far away he followed virtue and knowledge. He was looking for freedom, chose the world as his homeland and recognized boundaries only of the universe. 14 March 1879

18 April 1955

E = Mc2 Later on he came to realize a dream he had, namely to enter the famous Swiss Federal Polytechnic Institute in Zürich and to devote his life to science.

Figure 3.1. Commemorative plate, remembering Albert Einstein in via Bigli, Milano, were he stayed 18941900, from the age of fifteen 56

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After many years of struggle, personal as well as scientific, he became the most outstanding scientist of the last century… In all activities his creative ability and decisive character helped him to find the solutions to problems in a modest way. It is clear that he had an extremely lively and inquiring mind. Already at an early age Albert took great interest in what happened around him. When he was five years old his father brought him a small compass. It seems to have meant almost a revolution in the life of young Albert, who was just recovering from the measles. He showed it to everybody around him and he always carried it with him. He asked questions about what it was that made the arrow move and always point in the direction of the North Pole. What kind of invisible force? What was magnetism and what was gravity? It seemed as if he was trying to understand all the secrets of the Universe at once. At a later stage of his life Albert Einstein mentioned that his acquaintence with the small compass might even have been a factor in his later studies of the gravitational field. For Albert Einstein scientific interest always had the highest priority in life. When later on he became engaged in political matters in connection with the atomic bomb and had signed the famous letter to President Franklin Roosevelt his life started as it had in fact started even before, to become split, as he said: «between politics and the equations». He was, as a matter of fact, also offered the Presidency of Israel, which he declined with reference to his naivety in politics. On this occasion the following quotation might, however, have guided him, namely: «The equations are more important to me because politics presents the presence whereas an equation is something eternal» [3.10]. The response of president Roosevelt to the letter of August 22, 1939 about the expectation: «…that the element Uranium may be turned into a new and important source of energy in the immediate future…», signed by Einstein, led on july 16, 1945 to the first test of an atomic bomb based on fission (that is based on chain reactions splitting heavy nuclei by slow neutrons). 57

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The explosion took place in a remote part of the State of New Mexico, USA The scientists waited on a platform ten miles away from the site of explosion. Among them were, besides Einstein, two pioneers in the field of atomic research, Enrico Fermi and Leo Szilard as well as Robert Oppenheimer, head of the US Manhattan project. The tremendous flash and blast wave that accompanied the explosion was followed by complete silence. Einstein then expressed himself as follows: «Our generation has brought into the world the most revolutionary force since prehistoric man’s discovery of fire». It took seven years after the first test of the nuclear fission bomb for a hydrogen bomb, based on uncontrolled fusion reactions of light nuclei to be tested in 1952 in the US as the responsibility of Edward Teller. Almost simultaneously the US Sherwood Project on controlled fusion by magnetic confinement started with its main activity in Princeton. In the Soviet Union Andrei Sakharov was the driving force behind their fusion bomb, which led to a test explosion in USSR soon afterwards. When driving in Princeton one day in the early 1960, I suddenly had to make a very quick stop coming from the small Princeton Junction Station up to the corner of Nassau Street, which passes through the center of Princeton. Somebody, quite unexpectedly, walked straight through a red light just in front of my car, whilst reading a newspaper at the same time. I immediately recognized a famous profile wearing a typical flat hat and a pipe. It was Robert Oppenheimer (1904-1967) the ingenious theoretician [3.11] (he received his Ph D in Princeton when he was 19 years old), also head of the Manhattan Project. Fortunately, the brakes of my classical 1953 Chevrolet worked well. It did not even occur to me to blow my horn. Luckily, however, I succeeded in saving Dr Oppenheimer from a fatal accident. Apparently unconscious of the risk he silently continued his walk. I do not know if he even noticed the incident. Was he reading the world news or was he occupied simultaneously with God’s equation, or was he bothered by the 58

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hydrogen bomb policy? Clearly he was determined to continue his way. The speed limit of 25 miles per hour may be fine, after all, in Princeton!

3.2.2 Albert Einstein at work Einstein’s scientific work is essentially known for his general theory of relativity of 1916 [3.17–3.18] It was however, preceded and followed by numerous important contributions by him in different fields of physics. It should, for example, not be forgotten that Einstein in 1917 introduced the concept of stimulated emission of radiation, which later on led to the development of masers and lasers, thereby creating a decisive element in modern physics and a new tool for sophisticated modern technology. The laser led to optical fibre communication, improved atomic spectroscopy and trapping and cooling of free atoms by laser as well as threedimensional imaging by holography in science and technology [D Gabor, Nobel prize 1971] Einstein’s early work in 1905, indicating that bursts of energy in the form of light quanta were responsible for the processes of transmission and conversion of light in various contexts, was indeed remarkable. It led to the rederivation of Planck’s original results, now in the new light of discrete energy packets, to the explanation of ionization of atoms by light, frequency conversion of light and the emission of electrons from irradiated metal surfaces. Einstein derived in the same year 1905 the special theory of relativity when he worked at the patent office in Bern. He, furthermore, suggested that mass and energy are equivalent, E = mc2. The equivalence, which is quite general, also governs energy production by fusion reactions, the net mass defect in the processes determining the amount of energy produced (see section 3.1.4). And all this in one year! What a splendid example of concentrated creativity. What an explosion of free energy of ideas! 59

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In the motivation for Albert Einstein’s Nobel prize in 1922, for the year 1921, it was clearly pointed out that he received the prize, independent of his general theory of relativity, «for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect. For the year 1922 the Nobel prize was awarded to Niels Bohr for «his investigations of the structure of atoms, and of the radiation emanating from them». In his work Albert Einstein (1879-1955) was highly appreciative of the work by Galilei who was the first to carry out systematic experiments to explain physical principles. Einstein often made reference to Galileian reference frames. Galileo Galilei (1564-1642) was one of the creators of modern mechanics. He introduced optical tubes in astronomy in 1609. By means of new instruments he brought a revolution to the observations and was himself the first to observe solar spots in 1610, satellites of Jupiter and the phases of Venus. He lived and worked in Arcetri, situated on a hill with a beautiful view over the city of Florence, where there was an impressive museum of science and technology, not to mention other museums and the Uffizi galleries. So it was indeed a truly inspiring experience for me to give a talk in the old Arcetri observatory in the early 1960’s. It dealt with a treatment of radioastronomical observations: An improvement of the Eddington approximation of line profiles, a technique for resolving the observed data accounting for smoothing effects by using a modified Fourier instead of Gaussion technique to solve a kind of Fredholm equation [3.12]. In particular the method was applied to the interstellar hydrogen 21 cm line radiation [3.13]. The origin of this radiation goes back to the magnetic coupling between the proton and the single electron of the atom. The spins of the electrons can undergo spin-flips to form co-linear or antilinear states with an energy split hν with ν = 1420 megacycles per second (wave-length 21 cm). It is of particular interest for cosmology since hydrogen is a building block in the universe. Doppler-shifted lines can account for motion in the interstellar gas [3.14] and of celestial objects at distances which 60

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are not easily available by optical astronomy (c.f. section 3.6). This unique transition in the radio frequency domain was discovered by the Dutch scientist H.C Van de Hulst [3.15] in 1944 at the Leiden Observatory from purely theoretical grounds during the years of German occupation of Holland and was later detected experimentally in several observatories using radio telescopes, in the USA, Australian and Europe [3.16]. It opened up a new area of interstellar and galactic studies of the universe by means of radiowaves. One day I asked a young boy, Pierre, in France: Who was Galilei? He hesitated a little. Then he said: He was the father of Einstein. My wife interjected: he was the spiritual father of Einstein, is that what you meant? Of course; so Pierre agreed to something which was not the expected answer, but truly indicative! Galilei performed a famous experiment when he let two objects, a cannon ball and a wooden sphere, fall simultaneously from the top of the leaning tower of Pisa. They reached the ground at the same time. This experiment was repeated on the moon in 1971 when D. Scott let a hammer and a feather fall simultaneously. Slowly but steadily they both reached the moon’s surface at the same instant. The two different bodies require the same time to fall in the same gravitational field, even on the moon! I remember that we learnt about the Galilei experiments at school in Sweden. The teacher in physics had a certain small piece of equipment by which, as a demonstration, he could throw two small spherical bullets simultaneously, one with a horizontal initial velocity and one falling freely vertically. He succeeded in showing that the two bullets reached the floor at the same time, and that the bullet which started out horizontally reached the floor after a parabolic trajectory with a horizontal component of the velocity which remained constant, as Galilei had predicted and verified. One day in the beginning of my physics course something unexpected happened to me whilst watching such an experiment. I was sitting in the first row of the class and 61

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suddenly felt that I had something unusual up my sleeve. It moved vividly and stung me, it was simply a wasp. It was sufficient though to disturb my attention from the very respected teacher and his experiment. He looked at me critically and asked me a little ironically to pick up the bullets, one of which had escaped my observation and rolled away under chairs and tables into the middle of the class room; clearly the one with the horizontal initial velocity! It should be mentioned by the way, that Galilei was familiar with splitting a velocity in components referring to different directions! Our teacher, Dr Y. Källén, was excellent and very demanding. He stimulated from the very beginning our interest in Physics. Later on I had the opportuneity to work with his son, professor Gunnar Källén when I was research student in Copenhagen [3.19].Gunnar Källén became famous for his investigations in quantum electrodynamics [3.20-3.21] but, unfortunately, he left the scientific scene at an early age due to his sudden death in an aeroplane accident on his way to a meeting. He was a brilliant scientist even at an early age and a devoted pilot. He had been working at the Institute for Advanced Study in Princeton, New Jersey, US, where Albert Einstein was active through many years, from 1932 until his death in 1955. When Albert Einstein died, President Dwight D. Eisenhower expressed himself as follows: «No other man contributed so much to the vast expansion of twentieth-century knowledge. Yet no other man was more modest in the possession of the power that is knowledge, more sure that power without wisdom is deadly. To all who live in the nuclear age, Albert Einstein exemplified the mighty creative ability of the individual in a free society.» The concept of a field, which plays an essential role in Einstein’s work, was introduced by James Clark Maxwell (1831-1879). Maxwell introduced a set of equations which described electromagnetic phenomena. His work challenged Einstein to study relativity as did the work by Hendrik Lorentz (1853-1928) and by several other scientists, among them the 62

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French mathematician Henri Poincaré (1854-1912), one of the foremost of all scientific theory authors. It seems that Einstein consulted a lot of literature and had many contacts with specialists in pure mathematics. He was however himself also a very skilled mathematician. He tried to treat all the subtleties of his theory in the most relevant and elegant way and to express the results in the simplest form. He attempted to extend his theory of relativity and bridge the gap to quantum theory, but such an extension still requires the missing link. Whatever will be the form of an equation for a total field, the general principle of relativity as known today and formulated by Albert Einstein, will prove a necessary and effective tool for the solution of the problem of the total field, [3.22].

3.2.3

The fifth state of matter (BEC) and related topics

In the last few years intensive experimental research has been carried out to verify the production of a new state of matter, a condensate of atoms, produced by a process named BoseEinstein condensation (BEC) in atomic gases. Convincing evidence for the existence of the new state of matter in diluted gases at extremely low temperatures was given by two groups in the US, at Boulder and MIT in 1995. They used diluted systems of alkali gases of atomic particles, 87Rb and 23Na, respectively, which offered particular advantages and provided opportunities for comparison. A number of laboratories have since then confimed the discovery of the important experimental realization of the Bose-Einstein condensation. Three representatives of the two above-mentioned groups, namely EA Cornell, W Ketterle and CE Wieman have been awarded the Nobel prize in physics «for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the 63

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condensates».They received their prizes for the year 2001, at the 100-year anniversary of Nobel prizes in Stockholm; the first prize was awarded in 1901 to WC Rõntgen for his discovery of the remarkable rays subsequently named after him. The fundamental nature of the phenomenon of BEC as well as its relations to other work by Einstein may be of particular interest here. But what is then causing the condensation, how did it come about and why is it important? In 1924 the Indian physicist SN Bose carried out theoretical investigations on light. He succeeded in proving that the Planck distribution law for photons could be derived by entirely statistical arguments [3.23] without using classical electromagnetic arguments. Bose sent a paper with his results to Einstein who immediately realized its importance and started to work on the problem himself. Einstein published two papers in 1924 and 1925 [3.24], providing the full quantum theory of particles with integer spins (bosonic particles), a considerable extension of the work by Bose who had treated only light quanta. Einstein now created the foundation for Bose-Einstein statistics. He found that a phase-transition could occur at low temperatures, and lead to the famous Bose-Einstein condensation. Bosonic particles (integer spins) have a tendency to come together at low temperatures whereas Fermions (half-integer spins) try to avoid each other in accordance with the Pauli principle. Therefore atoms of total integer spins (electrons + nucleus) like the above mentioned alkali atoms 87Rb (spin: 1/2 ± 1/2 = 0 or 1) or 23Na (spin: 3/2 ± 1/2 = 1 or 2) prefer to stay together, whereas atoms with half-integer spins avoid each other. Pairs of strongly correlated electrons with opposite spins (the separate electrons having half-integer spins) could also have total integral spins and behave like bosonic particles. As a result a superconductivity transition (vanishing resistivly in metals) or superfluidity (vanishing internal friction in liquids) 64

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can occur at low temperatures similar to a Bose-Einstein condensation. At the very low temperatures required by BEC, a tenth of a millionth of a degree above absolute zero and at sufficiently high densities, the Broglie wavelength (λ = h/p where p is the particle momentum and h the Planck’s constant) and the interparticle distance will be of the same order of magnitude. Then a favourable condition could occur for all the atoms to hook on to each other and to reach the common ground state and become a Bose-Einstein condensate. It is interesting to notice that de Broglie postulated the existence of matter waves and determined their wavelength in 1924, the same year in which the BEC was predicted. For comparison, the extremely low temperatures necessary for Bose-Einstein condensation, for which the average speed of the atoms is only about one millimeter per second, happens to be just the inverse of the temperature in the centre of the sun, where tens of millions of degrees are sufficient to balance the enormous gravitational forces from the total volume of the sun, and at the same time to support the nuclear matter to undergo fusion reactions (luckily for us on Earth). Here the corresponding fusion plasma electrons reach velocities near relativistic values. What extreme situation of states in Nature! The idea that the source of solar energy could be found in a mass transformation had been proposed by JH Jeans already in 1904.In 1919 the idea was proposed by JB Perrin [see 3.25 p.156] that solar energy came from a transformation of hydrogen into helium. It was estimated from the Einstein formula that a mass defect of 0.7% would occur resulting from a fusion of four hydrogen nuclei to become one helium nucleus. AS Eddington [3.26] took up the idea of studying the evolution of stars. As a result he found that the temperature in the centre of stars was about 10 million degrees, but not higher than 40 million degrees. His theory could, however, not be used to describe the radiation from white dwarf stars which had densities 10 5 – 10 7g /cm 3 and a weak radiation. By assuming Fermi-Dirac statistics and total degeneracy RH Fowler [3.27] in 65

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1926 concluded that the white dwarf matter was like a single, gigantic molecule in its lowest quantum state. The idea of RH Fowler was taken up by S.Chandrasekhar who extended the theory to include a relativistic mass variation at the centres of stars to obtain an equation of state for the equilibrium of the stars in their own gravitational field, and could express conditions which applied to the degenerate matter of white stars. He accordingly made the important discovery that such a white dwarf star had a critical mass, which is called the Chandrasekhar mass. For an equilibrium configuration this limit could not be exceeded. For the case of hydrogen as a main constituent B Strömgren could calculate the central temperature of a star like our sun to be about 15 million degrees [see 3.25]. It is clear that today we are in a situation where it is tempting to say that the BEC model and the model for white dwarf matter, put forward by RH Fowler two years later than Einstein suggested the BEC theory for condensation of Bose particles to a state, where all atoms will be quantum mechanically identical, and stay in the lowest energy state, could have something in common for shedding light on star formation problems with the aid of laboratory experiments. Since the experimental verification of Bose-Einstein condensation in 1995 in JILA, Boulder, Colorado and at MIT, Cambridge USA, intensive work is going on in many laboratories in the USA and Europe [3.28–3.37]. The JILA group has shown that the sign of the particleparticle interactions can be switched suddenly, leading to supernova-like expansions of the condensate [3.34]. RC Hulet’s group at Rice University, Houston, Texas [3.35] has shown that an outward pressure arises because of the repulsive nature of fermions in a degenerate atomic Fermi gas and that conditions resembling those in white dwarf stars can be simulated in the laboratory. How fascinating that the two seemingly remote states of an extremely low temperature in the BEC case, and the hot fusion plasma case can be linked as shown in the above instance [3.35]. It connects two important ideas from Einstein, the mass66

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energy equivalence relationship E = mc2 which lies behind the fusion reactions in the hot plasma, and the concept of BoseEinstein condensation near the absolute lower limit of temperature. One wonders if the related ideas could not be carried further both in theory and experiment? For the hot fusion plasma the electron velocities come close to relativistic values. Relativistic velocities are generally common both in laboratory hot fusion plasma experiments and in the cosmos. So, for example, the Crab nebula is full of relativistic electrons, which spiral around self-generated magnetic fields in the nebula. Fusion devices are also exposed to losses from syncrotron radiation. It was Hannes Alfvén and Nicolai Herlofson [3.38] who first suggested that syncrotron radiation emitted by the spiraling electrons in magnetic fields might operate in the radio universe and proposed it as the mechanism for radio stars, at a time when nobody really knew what a radio star was in 1950! Some months later Karl Kiepenheuer [3.39] independently contributed by suggesting that galactic radio emission might be regarded as a by-product of cosmic rays travelling through interstellar magnetic fields. Those early contributions have been basic to our understanding of the nature of cosmic radio waves [3.40] It has been said by Kiepenheuer (1959) that «The sun is our bridge to space. It is only star that scientists can study in detail and thus is a key to whole universe of stars». To have some idea of the situation of the abundances of stars and galaxies in the universe we can cite Eddington in his book [see 3.44]. The expanding universe, namely that there are 1011 stars in a galaxy and 1011 galaxies in the universe (1011 is one hundred thousand million) which is still a good guess. Coming back to the question of condensed equilibria, the galaxies are fairly well homogeneously distributed in the universe but show tendencies of clustering, as can be seen from recent pictures taken by the Hubble telescope. How do these clusters come about? What is the role of gravitational and magnetic fields and of the particle motions in 67

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the galaxies, setting up spiral structures in the separate galaxies, and what is the role of the intergalactic forces and angular momenta of the separate galaxies in forming the clusters? Are there correlations between the spatial orientations of the discs of the individual galaxies in the clusters, and in what state of evolution or equilibria are those clusters? Would they, for example, be in a state of condensation? Could they be discussed by means of similarity transforms? Could changes in the configurations be observed in spite of the enormous timescales, or do they have to be estimated by means of computer simulations? Could phase-transitions between different states of aggregation as concept be useful, for the description of cosmic problems, and could phenomena like internal barriers and discontinuities occur, like those which are presently being discussed in fusion plasma physics? (cf. section 4.4 and Appendix) [4.31, 4.32] There are many questions to be asked which seem to be of a classical nature, but which as we have seen, are often directly related also to quantum theory. What interesting connections remain to be scrutinized between the phenomena of Macrocosmos and Microcosmos. There remains a topic for future research to find out if similar conditions as those we have been provided with, and similar cultures, exist in other parts of the cosmos. The question is if modern information technology can help us in this respect, since «we may not be able to obtain any answers in our life time» as Academician Pjotr Kapitsa said in an interview in Stockholm, in 1978 (he was then 84 years old), when he received his Nobel Prize in physics. So where are we ourselves in this gigantic system? We could say that we are in an Intercosmos, or if one wishes, in a Biocosmos, living on Earth in our solar system, situated in a spiral arm of our Galaxy. Our planet Earth has a weight which is one third of a millionth of the weight of the sun, which in turn is 1011 or hundred billion times lighter than our Galaxy. We are situated at a distance of one hundred million miles from the sun, the 68

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mean distance between the stars being roughly one light year (1018 cm). We are fortunate to be just at the right distance from the sun to receive the correct amount of heating by its radiation (also controlled by the Earth’s atmosphere), to live in equilibrium with the conditions provided by Nature around us. One cannot help admiring how well Nature has provided the conditions for us and the human body. Think, for example, if our senses of hearing or smell, taste or touch, had been ten or hundred times more acute than they actually are. What an insupportable experience that would be to say the least!! But fortunately Nature provides restoring forces to prevent such drastic states. Here again we find similarities with what happens in a plasma. For the simplest case of a cold ionized gas already a small separation of a bunch of the electrons from their usual positions represents a perturbation which creates strong restoring electrical fields and causes plasma oscillations [2.1]. Those become damped usually because of collisions with neutral particles. As another example, during a solar eclipse the UV radiation which supports the maintenance of free electrons in the ionosphere, the ionized gas layer that surrounds the Earth and reflects radio-waves, will be dimished due to the coverage of the solar surface, the active source of the UV radiation. The change in the density of the ionospheric free electrons, as a function of time during the eclipse, can be measured by the back-scattering of radio waves from the Earth. The critical frequency then changes also as a function of time. The change of the free electron density is less pronouced than the change in time of the UV radiation; it lags behind. The reason is that the changes in the electron density do not depend linearly on the changes in the radiation but are diminished by a recombination effect ot the free electrons with the ions. The time lag can be measured and used to determine the recombination coefficient in the ionospheric E-layer [3.42]; see also section (4.2.3). In hot fusion magnetized plasma devices tendencies of nonlinear effects occur, that can control the temperature profile, 69

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which is otherwise linearly unstable, in such a way that the profile shape becomes restored. We refer to this as stiffness and profile resilience [3.43]. In the interaction of strong laser pulses with plasma there is a tendency of the plasma to defend itself by nonlinear effects to limit penetration through the plasma [3.44]. Let us now consider an example from medicine to show how modern medical electronics can help guiding the motion of an artificial hand by using signals from the brain of a patient [3.45]. When Dr Arno Penzias from Bell Laboratories, Holmdel, New Jersey, USA, together with Dr Robert Wilson from the same laboratory, (discoverers of the 3K-radiation), visited Chalmers in 1978 he expressed particular satisfaction and admiration for having seen the Institute of Medical Electronics, a unique activity at Chalmers, created during the time of Professor Henry Wallman (1915-1992), brilliant mathematician and ingenious and «broad-band» inventor of electronic equipment; from him came the «Wallman Space» in mathematics and the «Wallman Cascode» and amplifiers for TV-receivers and radars. He invented X-ray television, to be used during operations and for simultaneous demonstrations to medical students, in co-operation between Chalmers and the Sahlgrenska University Hospital in Göteborg. He came to Chalmers in 1948 as a guest professor (the same year I was lucky enough to arrive at Chalmers as a student of electrical engineering), to stay for a year, but he stayed for a lifetime there with his family. During the war this extraordinary scientist had been recruited to the Radiation Laboratory at MIT, Cambridge, Mass, USA with a braintrust of different disciplines, and made contributions of important inventions (see the Valley and Wallman book in the series from Radiation Laboratory). He was invited to come to Chalmers on the initiative of Professor Stig Ekelöf (1904-1993), the excellent teacher in electromagnetics and later on creator and director of the Institute of the History of Electricity at Chalmers, a unique and important activity. 70

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Dr Penzias, after his visit, said that the invention of the use of signals on the skin of an arm, which were transmitted from the brain automatically by the human information system to be picked up by sensors on the skin on the arm to steer small motors for control of the fingers of the artificial hand according to the indications from the brain (for example to pick up a cup of coffee, lift it and drink) was the most magnificent and impressive result he saw at Chalmers on his visit there [credits for the innovation: Professor R. Magnusson, Chalmers and Professor J.Petersén, University Hospital]. In this way modern technology can help Nature to repair the functions of our body in delicate situations. Can we do the same to achieve fusion on Earth? I would like here to make an intermediary remark, that has to do with education and with evaluation of students: It is interesting to experience how different people can look at things in different ways. I remember that our highly regarded teacher in undergraduate courses Dr Yngve Källén could be rough to students, who did not fulfil his high requirements. He could say during a lecture: you should not continue to spend time on physics, you could study geography or… On the other hand Professor Henry Wallman, who was a great mathematician, but also an expert in electronics and telecommunication as well as mechanical and electronic computers in early days, as well as an inventor said: You should not underestimate students who do not have top markes in theory. They could be the best ones in other respects. They could for example repair a watch. Henry was a passionate collector of watches himself. Or, the students could may be even be practical users of mathematics and the laws of mechanics, if they would be given a little time to contemplate. Is this discrepancy not a main point of difference between University and Polytechnic views. I remember I heard Professor Pierre Gilles de Genes (Nobel Prize for Physics 1991), say on a TV program in Paris just a couple of days before he was going to receive his Nobel Prize in Stockholm (it was a program for 71

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stars; the other star was Barbara Hendricks): «To me the enthusiasm of the French students is more important than traditional mathematics». I found this so spontaneous and at the same time deep, that I asked him, the next day in Göteborg (he had not seen the program himself since he was already in Sweden) if he could comment on it to the large audience of students (and teachers) at Chalmers and he did with pleasure. As an example: If you have a bowl full of boiled spagetti and you pick one of them and pull one strand a little, how do you estimate the effect of the perturbation in an other part in the heap of spagettis. This you cannot do by traditional mathematics, but a practical student may do something to the problem. He may even use a computer. Coming back to the main topic of this section (BEC) and summarizing briefly the main features of the phenomena of Bose-Einstein condensation as observed today we notice [3.46]: The condensation means that when the particles come sufficiently close and move with sufficiently low energies (low temperature) they will participate a phase-transition and all enter the lowest energy state, corresponding to one and the same quantum-mechanical wave-function, as Einstein predicted. It is like the transformation of a drop of liquid when cooling a gas, but more delicate! In a laser the light is coherent and the photons have the same energy. In a Bose-Einstein condensate all atoms behave in a coherent manner: they «sing in unison» as it has been said, like an atomic choir! Two individual condensates have successfully interacted with each other and formed an interference pattern, indicating phase coherence of the condensates: a little similar to the interference of water waves when two stones are dropped on the surface of water. Spectacular results of vortex formation have also been produced by several teams. Sophisticated experiments use 72

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methods of laser cooling or trapping by evaporation to cause fast atoms to leave the other atoms and the system. New possibilities are offered by the BEC to study fundamental quantum mechanical processes and to simulate conditions in astrophysics, such as occur in supernova explosions or white dwarf star formation. This can be achieved by switching between attractive and repulsive forces, corresponding to boson or Fermi-gas behaviour of the atoms as realized by laboratory experiments. Among technical applications of BEC can be mentioned new developments in nano-second technology, (a billion of a second), precision measurements and holography. The Nobel prize in physics for the year 2001 is an example of how profound and extensive the influence of Albert Einstein’s ideas has been for the entire development of modern physics.

3.2.4

The bending of light and the principle of gravitational lensing

An essential idea in the general theory of gravitation is that gravity does not act directly on an object but on space, causing deformation or curvature of space [3.10, 3.17]. Therefore, matter traversing space, behaves in a different manner than it would in the absence of gravity. For a ray of light which traverses the region of curvature it also means that its trajectory will be bent. According to the general theory of relativity it follows that light which passes close to a volume of mass will be deviated by a certain amount, small but as we shall see none the less measurable. The presence of mass deforms the geometry of space in its neighbourhood. The closer a ray of light passes the mass the more it will be bent. A total solar eclipse offers an opportunity of testing the theory. Einstein had close contacts with several groups of astronomers and was extremely eager to have his theory 73

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experimentally verified. His prediction was an angle of deviation of 1.75′′ for a ray which just passes the surface of the sun. The technique used to obtain the gravitational bending of the rays was to measure the apparent positions of a number of stars, which became visible at the eclipse, and to compare them with their ordinary positions when the rays were not affected by the solar gravitational field. In 1919 a group of astronomers headed by the famous English scientist Arthur Eddington found values which extremely well agreed to those (within the limits of experiments errors) of the Einstein predictions. The measurements were done during a total eclipse on Principe Island on the African Atlantic coast. The results clearly confirmed that the Einstein theory was the adequate one and not the gravitation theory developed by Isaac Newton two hundred years before. The Newton theory was based on the assumption that light was to be considered as a particle in the process of interaction, which could not be the case according to the results of observation. It has been said that Eddington was happy with the results of the observation, even if he was an Englishman, and that he admired the Einstein theory considerably. Still more satisfied was Einstein to whom the results ment a real break-through in the scientific world [3.10]. As Einstein had conceived in 1912 even long before the experimental verification of his theory, this could moreover possibly be considered as a base for another phenomenon namely gravitational imaging or lensing. Today the astronomers use this principle for studying extremely remote galaxies or quasars. The light observed from such objects is focused (similarly as for distributed optical lenses in space) by the gravitation (or curvature of space) from clusters of galaxies, which the light passes on its way. Naturally, it is a question of considering many tiny contributions, which have to be fitted together by computer analysis. To obtain sufficient precision it seems necessary to have an accurate determination of the details 74

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of the intermediate galaxies, such as can be obtained by means of the Hubble Space Telescope.

Figure 3.2. The «Einstein Cross» observed by the Hubble telescope. Four images of a distant quasar 8 billion light-years away confirm gravitational bending of the light. The splitting is caused by a «near-by» galaxy which deforms the geometry of space that the quasar light penetrates [2.11]

Figure 3.3. Cosmic structures (clusters or superclusters) of galaxies distributed as patterns typically some 100 millions light-years wide. How are they formed and what can they tell us about the distribution of dark matter in the universe? 75

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Gravitational imaging observations can now be used to study the distribution of matter in the universe at enormously remote distances. They have, furthermore, recently been used to estimate the weight of the universe and to bring fire to the speculations about various topics in cosmology [3.10, 3.48]. The early note-book calculatutions by Einstein about his discovery of gravitational imaging (or lensing) which were found and published only recently [3.47] have led to a new and fascinating principle for the exploration of the cosmos [3.48] (see also section 4.4.6). References [3.1]

Hawking SW 1998 A Brief History of Time (New York: Bantam Books)

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Flammarion C 1880 Astronomie Populaire (Paris: Editions du Seuil, Sciences)

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Cianchi M Leonardo da Vinci’s Machines (Florence: Becocci)

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Wilhelmsson H. 1963 Accounting for smoothing effects in 21 cm observations Ark. Astr. Vol 3 n° 16 p. 187

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Wilhelmsson H and Winnberg A 1963 Upper limit to the velocity dispersion of galactic hydrogen clouds from 21 cm observations in Perseus, Astr. Notes n° 8 Gothenburg

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Van de Hulst HC, Raimond E and van Woerden H 1957 Rotation and density distribution of the Andromeda Nebula derived from observations of the 21 cm line B.A.N. 14, n°480, pp 1-16

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Einstein A 1958 RELATIVITY the Special and General Theory (New York: Crown Publishers)

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Källén G 1958 Quantumelektrodynamik Encyclopedia of Physics, edited by S Flügge, vol V Part 1: Principles of Quantum Theory I, pp 169-364 (Berlin-GöttingenHeidelberg: Springer)

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Källén G and Pauli W 1955 Dan.Mat. Fys. Medd 30, n° 7

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Einstein A 1950 Out of My later Years (New-York: Philosophical Library) page 48

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Einstein A 1924 Kgl Preuss Akad Wiss p. 261 and 1925 p. 3 77

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[3.25]

Ryde N 1994 Development of ideas in physics (Stockholm, Almqvist § Wiksell International)

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Eddington AS 1926 The internal constitution of stars (Cambridge)

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Monroe C, Swann W, Robinson H and Wieman C 1990 Phys. Rev.Lett. 65, 1571

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Monroe C, Cornell E and Wieman CE 1992 Laser manipulation of atoms and ions Proc.Int.School of Physics «Enrico fermi» Course CVXII (Amsterdam: North Holland)

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Petrick W, Anderson MH, Ensher JR and Cornell EA 1995 Phys.Rev.Lett. 74, 3352

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Anderson MH, Ensher JR, Matthews MR, Wieman CE and Cornell EA 1995 Science 269, 198

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Ketterle W, Davis KB, Joffe MA, Martin A, Pritchard DE 1993 Phys. Rev. Lett. 70, 2253

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Davis KB, Mewes M-O, Andrews MR, van Druten NJ, Durfee DS, Kurn DM and Ketterle W 1995 Phys. Rev. Lett. 75, 3969

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Cornish SL, Claussen NR, Roberts JL, Cornell EA and Wieman CE 2000 Phys. Rev. Lett. 85, 1795

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Truscoff AG, Shecker KE, Mc Alexander WI, Partrige GB and Hulet RC 2001 Science 291 2570

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Roberts A, Sirjean D, Browaeys A, Poupard J, Nowak S, Boiron D, Westbrook CI and Aspect A 2001 Science Express 10.11 26 March 22

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Pereira Dos Santos F, Léonard J, Wang J, Barrelets CJ, Perales F, Rasel E, Unnikrishnan S, Léduc M and CohenTannoudji C 2001 Phys.Rev.Lett. 86, 3459

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[3.52]

Clayton DD 1968 Principles of Stellar Evolution and Nucleosynthesis (New York: Mc Graw-Hill)

[3.53]

Marklund M, Brodin G and Stenflo L 2003 Electromagnetic Wave Collapse in a Radiation Background Phys. Rev. Lett. Vol 91 n° 16 (163601-1-4)

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Plate 1. Cosmos: 1997 painting by Pierre-Marie Brisson. (Courtesy of Galerie Lucette Herzog, Paris.)

Plate 2. Starry Night: 1889 oil painting by Vincent Van Gogh. (Courtesy of Museum of Modern Art, New York.)



Plate 3. Path with Cypresses and Stars: 1890 oil painting by Vincent Van Gogh. (Courtesy of Kroeller-Müller Museum, Otterlo.)

Plate 4. Maximiliana: 1964 gravure by Max Ernst. (Courtesy of Hans Wilhelmsson.)



Plate 5. ‘NASA’s Hubble Space Telescope yields clear view of optical jet in galaxy M87’. The jet is 4000 light years long. (Courtesy of F Duccio Macchetto (ESA) and NASA.)

Plate 6. ‘Hubble Space Telescope resolves braided galactic jet’. The jet is 10 000 light years long. (Courtesy of F Duccio Macchetto (ESA) and NASA.)



Plate 7. Chromolithography of a prominance on the Sun at 10 a.m., 29 April 1872 in Astronomie Populaire (1880) by Camille Flammarion. The prominance extends 200 000 km into space.

Plate 8. Chromolithography of a prominance on the Sun at 10 a.m., 15 April 1872 in Astronomie Populaire (1880) by Camille Flammarion. The prominance extends 200 000 km into space.



Plate 9. ‘Photo illustration of comet P/Shoemaker-Levy 9 and planet Jupiter’. (Courtesy of H A Weaver, T E Smith (STSci), J T Trauger, R W Evans (JPL) and NASA.)

Plate 10. Comet Hale–Bopp observed on 27 March 1997. The photograph was taken over five minutes with a 200 mm tele-objective. (Courtesy of Alexis Brandeker, Stockholms Observatorium.)



Plate 11. Lightning over Bordeaux. (Courtesy of Jöel Lafon, ‘Speed Photo’, Bordeaux.)

Plate 12. The Wave: 1831 etching by Katsushika Hokusai.



Plate 13. Schematic design of a stellerator plasma and magnetic coils. (Courtesy of Freidrich Wagner, Max-Planck-Institut für Plasmaphysik.)

Plate 14. Plasma in the ASDEX Upgrade tokamak. (Courtesy of Freidrich Wagner, Max-Planck-Institut für Plasmaphysik.)



Plate 15. Plasma in START—the small, tight aspect ratio tokamak. (Courtesy of Alan Sykes, UKAEA, Culham Laboratory.)

Plate 16. Plasma in JET—the Joint European Torus. (Courtesy of Hans Lingertat and JET.)



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4.1 Around the sun 4.1.1 Plasma motion and magnetic fields Not until about 1950 cosmical electromagnetics started to be seriously applied in astrophysics at the time when magnetohydrodynamics (MHD) [4.1-4.10] was developed and the existence of a magnetic field in galactic space became confirmed. Early fundamental work by S.Chandrasekhar and E.Fermi [4.11] studied magnetic fields in spiral arms by independent methods and obtained H = (6–7.2) × 10 –6 G. Rockets and satellites opened up new possibilities of space exploration and it turned out that the universe was really an immense laboratory for Alfvén waves [4.1-4.5]. The Hubble Space Telescope which started operation in 1990 made magnificant pictures of galactic jets, many thousands of lightyears long, revealing new features of magneto-plasma interactions. 4.1.1.1 The magnetoplasma revolution Magnetic fields and electric currents play an important part in the workings of the Cosmos. It has been thoroughly settled that many significant features in the make-up of the universe, like 81

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the physics of stars and galaxies or of the magnetospheres of stellar objects, are related or even governed by the coupled electromagnetic-plasma fluid phenomena. Related questions are of vital interest in many different areas of research, for example in galactic and solar physics, as well as the physics of the magnetosphere, i.e. the physics of the magneto-plasma surrounding our planet. In the beginning the progress of cosmic electrodynamics was very slow. Only since the 1950s has it been seriously applied to astrophysics. Other classical fields of physics like classical mechanics, spectroscopy and nuclear physics had been applied extensively to the astronomical problems for many decades. As a result much was already known about the motions of stars, their temperatures and chemical composition before electromagnetic fields and plasmas were considered. Now we are in a position to take a journey around the universe, to see the impact of the plasmas in their electromagnetic fields. The fact that the Earth is a magnet has been known for some 400 years and the magnetic perturbations on Earth associated with auroras have been known for at least 200 years. Strong magnetic fields in sun spots which could only be caused by gigantic electric currents on the sun were discovered about 100 years ago. Observations of radiowaves from the sun as well as from other radio sources in the universe, in the late 1940s, marked the beginning of radioastronomy, which used wave-lengths in the atmospheric «window» of the frequency band, corresponding to wave-lengths from a few millimeters to about 15 meters. The science of radio astronomy has since then grown tremendously in importance and in scope. It has led to many discoveries about physical conditions and chemical abundances of elements in the universe. Radio astronomy has contributed important information to cosmological theories. New sources of radiation in the cosmos like quasars (1960) and pulsars (1967) were discovered and studied by radio telescopes. At the same time space technology developed enormously, offering new platforms of observation outside the atmosphere 82

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like rockets and satellites carrying instruments for detailed exploration of the Earth’s magnetosphere and its plasma surrounding. Our view of the plasma-magnetic configuration around our planet has accordingly been strongly modified and the rôle of the solar wind, i.e. the steady stream of protons and electrons from the sun, has been elucidated in a very profound way. Bearing in mind that modern plasma laboratory experiments and fusion plasma physics have developed essentially within the same period of 50 years, since the 1950s, providing today an enormous integrated knowledge of plasma physics, the fields of plasma and fusion science have had an impressive growth. As we have said it took a long time before magnetic fields and electric currents became accepted as essential ingredients in the cosmos. This is still happening now. Why so late? Astronomy had been a field of great interest since antiquity, and particular events like solar eclipses, sun-spots, auroras etc... had attracted considerable attention among people for centuries. I suggest that it was simply not natural to think of magnetic fields and electric currents as playing an important rôle in outer space. Electric currents are something that one is accustomed to think of as streaming through metallic wires, and magnetic fields as something that control the local direction of the needle of a compass. But there are no metallic wires nor compass needles out in space, so why should there be electric currents and magnetic fields there? One has no feeling for the effects of currents which are distributed in space over large volumes or for magnetic fields that they might generate. We did not consider in the passed that magnetic fields could produce electromagnetic phenomena as soon as they experienced a volume of gas in motion. Another point is that the cosmic magnetic fields are often very weak. Nevertheless, we have found that the electromagnetic phenomena often become very important, so much so that they have a decisive influence on the dynamics. This is a result of the vast cosmic dimensions and the high electric conductivity of the hot ionized gases; ordinary hydrodynamics, i.e. the 83

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dynamics of ordinary uncharged fluids, does not suffice to describe what happens. It has to be replaced by magnetohydrodynamics (MHD), a combination of electromagnetics and hydrodynamics [4.1-4.10]. We now know much more about such activities on the sun. There is lots going on there that we can observe – prominences, flares and sun-spots, for example-which all seem to be magnetohydrodynamic in nature. Closer to home we have Earth’s magnetic storms and auroras. Interstellar space is electrically conductive and exposed to electric as well as magnetic fields. And there is matter for them to act on, though not much, perhaps not more than one atom per cubic centimeter. Once we see the cosmos as space supported by particles under the influence of whatever electric and magnetic fields happen to be acting there, we can begin to appreciate the importance of the theory Hannes Alfvén developed. Recent experimental work-both on Earth and probing space - has given us an idea of the range of magnetic field interactions we have to consider. How strong then are those magnetic fields? It is not surprising that the magnetic field intensities take very different values depending on where we observe them in space, or in the laboratory, for example Interstellar medium Galactic spiral arms Solar corona Solar wind Sun-spots Earth’s ionosphere Earth’s Surface Neutron Star (pulsar) Fusion experiments (JET) Fusion reactor Small motor (vacuum cleaner)

10–6 G 6×10–6 G 10–3 G 10–4 G 3×103 G 3×10–1 G 5×10–1 G 107–1012 G 34×103 G 60×103 G 3×103 G 84

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The field imposed by a small domestic motor such as the one that drives a vacuum cleaner is a few thousand gauss. Compared with that, the field in the interstellar medium is a tiny 10–6 gauss. At the other end of the spectrum is the field imposed on a plasma in the experiments to build a source of power based on the nuclear fusion 4×104 Gauss. But even this pales beside the fields Nature creates inside a neutron star which are 100 to million times stronger. How is it possible to estimate the magnetic field strengths out in the Cosmos, for example in spiral arms and to determine the influence of the magnetic field on the dynamics of cosmic masses? These questions were addressed (in two separate publications) by S. Chandrasekhar and E. Fermi as common authors of both publications. In the first of these, two independent methods are described for estimating the magnetic field in the spiral arm in which we are located. The first method uses magnetohydrodynamic wave theory in terms of the Alfvén velocity to interpret the dispersion (of the order of 10°) in the observed planes of polarization of the light from the distant stars. The second method is based on the requirement of equilibrium of the spiral arm with respect to lateral expansion and contraction. The condition for equilibrium is obtained by equating the gravitational pressure in the spiral arm to the sum of the material pressure and the pressure of the magnetic field (H2).The first method gives H = 7.2×10–6 G, the second 6×10–6 G [4.11]. The fundamental work on Magnetic fields in spiral arms was published in 1953 by S Chandrasekhar and E Fermi in Astrophysical Journal 118 116. The paper discusses problems of gravitational stability in the presence of a magnetic field. In one example the authors consider the stability for transverse oscillations of an infinite cylinder of incompressible fluid, and for simplicity also infinitely high electrical conductivity. A uniform magnetic field is acting in the direction of the axis. It is found that the cylinder is unstable for all periodic deformations of the boundary with wave lengths exceeding a certain critical value, depending on the strength of the magnetic field. It is shown that the magnetic 85

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field has a stabilizing effect, and that for a cylinder of radius R= 7.7×1020 cm (250 parsecs), mass density = 2×10–24 g/cm3 , a magnetic field in excess of 7×10–6 G effectively removes the instability. In another example it is shown that a fluid sphere with a uniform magnetic field inside and a dipole field outside is not a configuration of equilibrium. It will tend to become oblate by contracting in the direction of the magnetic field [4.12] In spite of the simplifying assumptions these early (1953) analyses demonstrate the rôle of magnetic fields and the use of magnetohydromagnetics in cosmic applications [4.13]. Whatever the strengh of the field, there is also the question of structure. In the Cosmos and also in laboratory experiments the magnetic fields, the currents and particle densities show filaments (as in the solar prominences) or granulations (as in the photosphere). Filamentation sets up by the coupling of currents and magnetic fields in plasmas is noticed in the plasma tail of comets as well as in the tail of the Earth’s magnetosphere [4.14]. The radiation from very powerful lasers makes small parts of the target very hot and very dense. As charged particles dash around they set up electric currents that generate structured patterns of magnetic fields as high as a hundred megagauss. The vortex is another structure we often see in magnetic fields, such as that in nebulas (e.g. the Crab) and galaxies (e.g.M83). Self-induced currents generate the fields, which form the structures emitting radiation to be captured by measurements. Relativistic electrons spiralling in the magnetic field structures generate syncroton radiation spectra, as in the case of «radio stars» observed in radioastronomy. Vortices also organize themselves in auroras. The symmetries and patterns shown up in these observations provide a clue to the fine structure effects generated by magnetic fields acting in plasmas. Can Alfvén waves and magnetohydrodynamics help us to explain them? In my view the answer is in many cases yes. In fact, the universe is really an immense laboratory for Alfvén waves. The results so far clearly 86

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indicate the oustanding rôle of the new type of wavemotion that involves the coupling between charged fluids and magnetic fields. 4.1.1.2 The challenge of space plasma exploration Certain problems in space plasma physics, for example the acceleration of electrons in the solar wind and in the magnetosphere, demonstrate difficulties which are characteristic of geocosmological plasma research in general. Progress in the field of geocosmophysics has been astonishingly slow as compared to other branches of modern physics, such as elementary particle physics, atomic spectroscopy or nuclear physics. At first sight it seems, for example, quite remarkable that the acceleration mechanism of the solar wind electrons and the auroral electrons is not known. Or that the phenomena at the solar surface and their connections with the interior generation of the fusion power in the sun are, in fact, still to be explained. The difficulties of making detailed observations of particles and space plasmas by rockets or satellites should be rather obvious but are often underestimated. One important fact that one has to take under consideration is that the medium to be observed is not controlled by the observer. As an example try to relate observed data of certain phenomena, for example particle velocities or velocity distributions on a certain magnetic field line, to corresponding data observed at a later time and at a different point on the same field line. How can we be sure that it is the same field line? And how can we, therefore, be sure to have the correct basic information to use for modeling phenomena, for example the acceleration of electrons? The difficulties in space plasma exploration are indeed very severe and require extreme skill in planning and realization of the measurements. Acceleration under controlled conditions such as in huge laboratory accelerators as a rule operates satisfactorily from the outset. In space the acceleration mechanisms are not specified. 87

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The difficulties are there if one considers the phenomena on the solar surface, or on the outer portions of the solar corona from which the solar wind emanates, or if one is making observations of the magnetospheric bow shock or the magnetotail. One has to rely on measurements programmed and controlled at a remote distance with often sophisticated techniques. What a lot of difficulties to surmount and what a lot of interesting discoveries to make in the future! This is not to say that measurements and definitions of situations are not difficult in other branches of modern physics. The stochastic cooling of particles for example in large accelerators is certainly also something extremely sophisticated. In the late 1950s, when space research and space communication was just beginning I remember Niels Bohr, the father of atomic physics, expressing his admiration of the new satellites and the many possibilites they might offer. They encircled the Earth and could transmit a message instantly between any points on our planet. The master of the electron motion and radiative transitions in atoms was impressed. It was at an evening gathering in the winter garden of his home, the honorary villa of the Carlsberg brewery in Copenhagen. I remember that it was a little to my surprise that such a strong appreciation of satellites was expressed by someone who had made such profound contributions himself to physics in general. Perhaps he could already envisage what a fascinating time there was to come... 4.1.1.3 Cosmic plasma jets An extraordinary space-based telescope has provided new possibilities for studying cosmic plasma jets. The NASA Hubble Space Telescope (HST) started operations early in 1960. The telescope, which has a primary lens 2.4 m in diameter, is carried by a satellite (length 13 m, diameter 4.3 m, weight 11.6 tons) As well as two spectographs to analyse the radiation from celestial bodies, one for studying 88

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very faint objects, the other for more luminous objects but with higher resolution, the HST is also equipped with a Faint Object Camera (FOC). The FOC is capable of observing objects at least 30 times less bright than the best ground-based telescopes. The HST is ideally suited for studying extragalactic jets. The telescope’s UV sensitivity allows it to clearly separate a jet from the stellar background light of its host galaxy. What is more, the FOC’s high angular resolution is comparable to subarcsecond resolution achieved by large radio telescope arrays. A remarkable photo of a 4000 light-year long jet of plasma emanating from the bright nucleus of the giant elliptical galaxy M87 was presented on January 16th, 1992 at the 179th meeting of the American Astronomical Society in Atlanta, Georgia, USA. The ultraviolet light image was made with the European Space Agency’s Faint Object Camera. (see Plate 5). Allow me to quote the caption of the photo (Photo Release STCCI-PRC92-07), Credit: F Duccio Macchetto/NASA/ESA: «M 87 is a giant elliptical galaxy with an estimated mass of 300 billion suns. Located 52 million light-years away at the heart of the neighbouring Virgo-cluster of galaxies, M 87 is the nearest example of an active galactic nucleus with a bright optical jet. The jet appears as a string of knots within a widening cone extending out from the core of M 87. The FOC image reveals unprecedented detail in these knots, resolving some features as small as ten light-years across. According to one theory, the jet is most likely powered by a 3 billion solar mass black hole at the nucleus of M 87. Magnetic fields generated within a spinning accretion disk surrounding the black hole spiral around the edge of the jet. The fields confine the jet to a long narrow tube of hot plasma and charged particles. High speed electrons and protons which are accelerated near the black hole race along the tube at nearly the speed of light. When electrons are caught up in the magnetic field they radiate in a process called syncrotron radiation. The Faint Object Camera image clearly resolves these localized sites of electron acceleration, which seem to trace out the spiral pattern of the otherwise invisible magnetic field lines. A large 89

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bright knot located midway along the jet shows where the blue jet disrupts violently and becomes more chaotic. Farther out from the core, the jet bends and dissipates as it rams into a wall of gas, invisible but present throughout the galaxy, which the jet has ploughed in front of itself.» Another extraordinary observation entiled: «Hubble Space Telescope resolves brided galactic jet» (Photo Release NO 9101) reveals new features of magneto-plasma interactions in galactic jets as described by the following presentation, Credit STSI, NASA and ESA (see Plate 6). «NASA’s Hubble Space Telescope has provided a detailed view of a ten thousand light-year long jet of plasma which has been ejected from the core of a galaxy 270 million light-years away. Observations made with the European Space Agency’s Faint Object Camera reveal that the jet has an unusual braided structure, like a twisted pair of wires.» «This is the first time that such a structure has been seen in an optical jet», says F. Duccio Macchetto, ESA’s Principal Investigator on the FOC and Head of the Science Programs Division at the Space Telescope Science Institute. The results of this observation were presented at the meeting of the American Astronomical Society in Philadelphia, Pennsylvania on January 15th, 1991. The FOC image provides intriguing new details for understanding how the core of an active galaxy generates such a narrow beam of energy and then propagates the jet across millions of light-years, at velocities approaching the speed of light. The jet appears as a bright «finger» extending in the northeast direction from radio galaxy 3 C 66 B. The FOC image has an angular resolution of 0.1 arc-seconds which is 12 times better than previous ground-based optical images, and even three times better than high resolution radio maps obtained with the Very Large Array radio telescope at Socorro, New Mexico. In addition to the unique double stranded structure, the FOC image reveals filaments, bright knots, kinks and other complex features never before seen in an optical jet. Many of these features overlay the radio structure of the jet. The jet was observed on August 28, 1990 as part of an early program to assess the optical performance of the HST. 90

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«The HST is a uniquely important instrument for studying synchroton jets», says Macchetto. Image reconstruction techniques applied to the data bring out additional detail. In addition to HST’s extraordinary resolution its ultraviolet sensitivy is ideal for studying optical jets because they are relatively bright in UV compared to their host galaxies. Once the image of the host galaxy is subtracted through computer processing, details in the jet can be traced all the way to the galactic core. The bluish, highly polarized light of the jet in galaxy 3 C 66 B is produced by electrons which are spiralling along magnetic fields at velocities approaching the speed of light. The light and radio emissions produced by the electrons are synchroton radiation – so named because similar radiation is observed in particle accelerator machines. But what is the «machine» which is the powerhouse behind the jet in 3 C 66 B? The favored mechanism is a supermassive black hole which may lie at the core of the galaxy. Stars, dust and gas swirl deep into the hole’s intense gravitational field along a broad flattened accretion disk. The hot plasma in the spinning disk creates powerful electric currents which in turn generate twisted magnetic fields which align to the black hole’s spin axis. The black hole’s spin axis is also an escape route for the high speed electrons. As the electrons spiral outward along magnetic field lines, they lose energy in proportion to their frequency and the strength of the magnetic field. In a timespan of only a few hundred years the electrons responsible for the optical emission lose much of their energy. However, the electrons which produce radio emission can survive in the same magnetic field for tens of thousands of years. Hence most galactic jets which extend for thousands of light-years are detected in radio wavelengths. In only a few cases have optical counterparts been observed. Nevertheless, the long optical jet in 3 C 66 B presents a mystery for astronomers. How do the electrons remain energetic enough to radiate visible light throughout their 10 000 year journey along the jet? 91

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One possibility is that the electrons are boosted back to higher energy levels as they move along the jet, perhaps by instabilities at the edge of the plasma flow. Another possibility, which the jet’s braided appearance suggests, is that the electrons speed along a channel which has a much lower magnetic field strength and hence lower energy loss. Two sharp bends and kinks in the strand (3,000 and 8,000 light-years out from the nucleus) are also hard to explain. They may indicate that the galaxy’s «central engine» doesn’t release energy at a steady rate but rather «hiccoughs» or fluctuates in output. The kinks may also be produced by a complex magnetic field structure along the jet, or collisions with dense regions in interstellar gas. 3 C 66 B is only the second galaxy with an optical jet which has been observed by the HST (the previous optical jet studied is in the galaxy PKS 0521-36). Both observations show a close match between the optical and radio features in the jets in each respective galaxy. However, there are significant differences between the structure of the jets of these two galaxies. This suggests that different mechanisms are at work in transporting material from the galactic core. Further observation with the HST will provide fundamental new information about the nature of galactic jets, in particular how energy is transported along the jet and the role of magnetic fields in channelling material from the core of a galaxy to intergalactic space. Attempts have been made to explain the formation of extragalactic jets by Alfvén waves. The generation of Alfvén waves is assumed to originate from the twisting and annihilation of magnetic fields, and the of the waves is provided by nonlinear, surface damping and turbulent damping. The magnetic field configurations in extragalactic jets are derived from polarization observations, which imply that the magnetic fields in the powerful jets are longitudinal. The model for the jet outflow is based on the knowledge of the magnetic structure of the sun and experience from studies of the solar wind. The jet flow velocity uj is estimated indirectly from observations, the 92

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velocities ranging from 1000 km/s to the velocity of light. The characteristic period of the Alfvén waves is from 104 s to 109 s which is in agreement with fluctuation periods for the radiation continuum of quasars and active galactic nuclei. The conclusion is that Alfvén waves with their presumed damping mechanisms can be important for the acceleration of extragalactic jets. 4.1.1.4 The all-pervasive Alfvén wave Hannes Alfvén himself regarded the space age as being a revolution in science, comparable to the introduction of the telescope by Galileo Galilei. He pointed out the ability of spacecraft to serve as platforms for instruments to observe remote objects and their advantages vis-à-vis ground-based telescopes for optical observations. It seems that we are still only in the beginning of the space age and that we can expect a continued rich harvest of new results in the future. Alfvén waves are of fundamental interest to geocosmophysics, and the field of Alfvén waves is an active area of research in all branches of plasma physics more than half a century after their discovery. As early as 1937 Hannes Alfvén suggested the existence of a galactic magnetic field. He was led to this proposal in an attempt to understand where cosmic rays obtain their energy from [4.15]. Apart from being considered as the mechanism responsible for the acceleration of particles to high energies in the cosmic rays Alfvén waves have been proposed as the source of momentum for the solar wind. Their presence has been confirmed by the interpretation of experiments by the spacecraft Mariner 2 in 1968.Particle scattering by Alfvén waves also help to maintain the isotropy of cosmic rays in space. How is it possible to identify Alfvén waves in space and to confirm the effect that they may have? A characteristic feature of Alfvén waves is that the perturbation velocity and perturbation magnetic field are parallel and proportional to each other. This is true not only for 93

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continuous, i.e. periodic, waves but also for bursts. This simple relationship presumes that the medium may be considered as incompressible, which is in general a fairly good approximation. For the solar wind one can show that a necessary condition is that the Alfvén velocity vA is very much less than vS, where vS is the sound speed. The measurements aquired by Mariner 2 show strong correlations between the velocity fluctuations and the magnetic field variations. Twenty-four hour observations of magnetic field and plasma data demonstrate the presence of nearly pure Alfvén waves. The generation of Alfvén waves presumes changes in magnetic fields which, in fact, occur frequently in space. To transfer energy from the Alfvén waves and give momentum to particles, one has to rely on processes that damp the waves. Acceleration of electrons, heating of plasmas, or current drive i.e. maintaining plasma current, may be achieved in this way. There are various processes that may cause changes in the magnetic field and thereby provide conditions for generation of Alfvén waves, for example the annihilation of twisted magnetic fields near a stellar surface. Nonlinear and turbulent damping mechanisms could transfer energy from the Alfvén waves, for example in the solar wind [4.16]. Alfvén waves have, furthermore, been considered for heating the solar corona and in modelling of an abrupt transition jump in temperature in the outer parts of the solar corona. The presence of Alfvén waves in cometary environment has been identified by observations in 1985-86. Alfvén waves in describing phenomena in planetary magnetospheres, e.g. magnetosphere-ionosphere coupling, micropulsations, aurora formation, etc. Alfvén waves also play an important role in the formation of quasar clouds and of extraglactic jets. Alfvén waves are better understood now thanks to experiments in the laboratory that use them in various ways to heat plasmas. They may also be used to maintain the plasma current in fusion plasma devices. The results obtained so far clearly indicate the outstanding rôle of the coupled systems of magnetic fields and 94

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electric currents in the cosmos as well as for fusion plasmas on Earth.

4.1.2 Transcient spectacles on the sun: The improved methods of observation have led to an increased interest in research on solar flares and prominences, which are violant perturbations on the solar surface, with an aim to find out how those are generated and what connection they many have with the solar interiour. Even here the Alfvén waves are expected to play a significant role. 4.1.2.1 The dynamic face of the sun Our sun as we know it from daily life is continuously shining with a friendly yellow-reddish color on its face. It has most likely looked the same and remained the same size for billions of years. But seen in more detail by a telescope, particulary with a high-resolution satellite-based spectroscopic instrument, things may look different. The sun bubbles all over the surface and occasionaly very dynamic phenomena may occur. Looking at these is like watching a TV camera survey a football stadium where a match is going on. Expectations have excited the atmosphere and waves of hope and dissolution wander over the stadium. And suddenly, after some dramatic preparations, it happens: a goal for the home team! Supporters suddenly throw hats and newspapers and fireworks high in the air. Applause is accompagnied by roars and howls which can be heard all over the city. The stored energy has found a way out and continues to excite the spectators as well as the players for some time. We can take another analogy from a tennis tournament at Wimbledon or Roland Garros. Mostly, conditions are calm. But once in a while the players show signs of happiness or despair, throwing their rackets and balls high in the air and shouting at the umpire for unexpected decisions. Liberation of internal energy can take many forms! 95

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As we shall see, this is just what is characteristic of the phenomena that may occur on the solar surface driven by the energy liberated from the interior of the sun. Enormous gas clouds expand outwards, carrying with them magnetic fields and currents in often twisted and filamentary structures. It is these that give rise to phenomena on the solar surface, such as sun spots, solar flares and the prominences which exhibit gigantic arcs far out of the surface [4.17]. Telescopes show us many characteristic motions and detailed traces of internal activity that occur on the solar surface. Even with the strongest optical telescopes we cannot easily see such fine details on other stars. So the sun provides a unique opportunity to study interesting phenomena which presumably also take place on other stars in the Universe. Thanks to instruments on the new satellites we can see the structures giving rise to the phenomena on the solar surface. Now we can embark on new investigations of basic features of the dynamic face of the sun. We look at how heat flows through matter and what is generating the magnetic fields inside the sun. We also have results concerning how energy is released and transported in the sun’s outer layers using the mechanisms of radiation, mass motion, heating, and particle acceleration. It is important to link together such experiences to enable us to make comparisons between results from laboratory and natural plasmas with regard to magnetic reconnection, i.e. self-induced magnetohydrodynamics, joining of magnetic field lines and, furthermore, acceleration processes. The beautiful structures of filaments and vortices we see today in prominences ejected from the solar surface demonstrate several types of plasma instability caused by magnetic field-plasma current interaction. These are already well known from laboratory experiments and are called, for example, kink, sausage and filamentation instabilities. They may be regarded as external traces of what is going on under the solar surface, a domain to be explored by future research. Galilei first noticed dark spots on the solar surface in 1610. His observations made with telescopes, which were still a 96

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novelty, were regarded with great scepticism. The sun was considered as a God which should have no imperfections. Repeated observations confirmed, however, that the spots existed and that they occurred in groups of two or more. We now know that they are regions of gas on the surface of the sun, which are cooler than the rest of the surface. They have a cycle of repetition of about 11 years. The spots consist of a central region, the umbra, plus the outer grey region, the penumbra, which shows a filamentary structure which extends into the granular structure of the solar surface. The diameter of the sun is more than 100 times greater than the diameter of the Earth and the sun spots can easily be larger than our continents on Earth. Strong magnetic fields of several thousands of gauss occur in the spots, whereas the general magnetic field on the sun has a strength of about one or two Gauss, the magnetic field on the surface of the Earth being about half a Gauss. Neighbouring spots have opposite magnetic polarities. No-one knows how these strong active fields are generated. One theory is that different layers in the sun rotate at different speeds, producing vortices in the solar interior. Maybe vortex motion carries the magnetic fields to the surface of the sun, where they can be observed by their influence on atomic spectral lines or by their interactions with ionized gas. 4.1.2.2 Solar Flares and prominences Sun spots are violent, turbulent places. For example, strong eruptions of the sun produce solar flares, bright flames from the solar surface. Energetic particles from the eruption enter the sun’s atmosphere where some of them interact to generate radiation in the optical, UV, x-ray and gamma ray parts of the spectrum. The rest of the fast particles as well as clouds of solar plasma are ejected out into interstellar space. Some reach the Earth, where they can cause magnetic storms in the Earth’s field. Solar flares occur abruptly and last as a rule 15-20 minutes, sometimes an hour or two. Sometimes they take the 97

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form of flare surges, which can reach more than one million kilometers in height, carrying plasma and magnetic fields. They are ejected with velocities of the order of 1000 kilometers per second. When they reach the Earth they generate spectacular auroras and can interfere with radio communications. Prominences are more long-lived gigantic gaseous eruptions, which may reach several hundreds or thousands of kilometers above the solar surface and stay there for long periods, sometimes many hours. It may well be the influence of magnetic fields that maintains them before they return to the solar surface. The prominences also follow the II-year solar cycle. The first publication mentioning a solar prominence had the title: Observation of a solar eclipse in Göteborg, Sweden May 2 nd 1733. It was by Birger Vassenius (1687-1771), Swedish astronomer and mathematician and was published in Transactions of the Royal Society of London Philosophical Transactions for the months of July-October 1733 n°429 pp 134-135. Here is a translated extract from Latin: During the time when the whole sun was covered, I saw, apart from a great deal of the spots on the surface, the atmosphere of the moon in a telescope of about 21 foot size: and I saw it on the west side of the moon, under the maximum position, somewhat more lumious; though without the irregularity and unsmoothness of the light-beams, which entered the eyes of a spectator without tube. Meriting not only admiration, but also a notice from the illustrious Royal Academy, seemed to be some reddish spots which were noted exterior to the moon periphery, three or four in number; among them one larger than the others, almost in the middle between south and west, as far as it was possible to estimate. It was composed of something like three parts or smaller parallel minor clouds of unequal extensions somewhat oblique with regard to the periphery of the moon. Since I was caught by admiration of the phenomenon, I gave a friend, whose eyes were very sharp, an opportunity to observe. But when it turned out that he, who was not acquainted with a tube, could not even 98

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find the moon, I was happy to continue myself for 40 or more seconds to regard the same spot, or if one so desires, cloud, which was unchanged and stayed in its old position, near the moons periphery, notwithstanding any suspicion of fault with the tube or the eye… The French astronomer Camille Flammarion portrayed prominences in his important work «Astronomie Populaire», published in 1880, which greatly stimulated the general interest in astronomy. It may be noted that even Hannes Alfvén became interested in astronomy from this work. The book contains beautiful etchings in color (Bordeaux red) of magnificent prominences observed in 1872 at Harvard College Observatory, USA with detailed descriptions and discussions of the events (see Plates 7 and 8). These plates show two magnificent prominences, the first one on 29 April 1872, the second one on 15 April of the same year and the same hour, 10 o’clock in the morning. The scale of the prominences is such that the horizontal distance amounts to 200 000 km. To give some feeling for the size we may note that this distance is about that which a modern car covers in a lifetime. To justify the natural beauty of the prominences it is necessary to reproduce those solar flares in colour. That is why the two excellent chromolithographies from Harvard College Observatory, USA, are reproduced here. There is, however, something that even the colour pictures could not reproduce, namely the impression of life and rapid changes in the pattern that is characteristic of those phenomena. It helps to think of violent flames when imagining what happens in the pictures! They really demonstrate the beauty of plasmas, and of the magnetohydrodynamics which lies behind it. In these pictures, which are artist’s impressions rather than photographic images, one can see filaments and blobs of gases forming. These indicate plasma instabilities and the presence of magnetic fields, providing curved motions of the plasma. A great variety of black and white images exist which show time99

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sequences and indicate the various shapes that have been observed in prominences, from flame-like outbursts to cloudlike shapes which sometimes approach the pattern of a woven tissue. They demonstrate the fascinating variety of ways in which energy can tunnel out of the gravitationnal field that confines it! On April 3 1873 a luminous hydrogen cloud of enormous height was observed outside the limb of the sun. It seemed like a cirrus cloud, light and filamentary; the entanglement being very difficult to grasp and changing from one instant to another. From being straight and diffuse at the beginning it ramified rapidly into branches of twisted spiral nature after twenty-five minutes to extend to a height of 322 000 kilometers, i.e. about one quater of the diameter of the sun, with an average speed of 105 kilometers per second. Once again, it may be temping to return to art. Vincent Van Gogh in his paintings emphasized sunflowers and cypresses as two types of objects that he consider as contrasts or complementary to each other. Sunflowers represented open structures catching energy from the sun to feed the plant, whereas cypresses had the form of confined, closed structures keeping their identity as they evolved. Is there not an obvious similarity between sun spots and sunflowers as there is also in between cypresses and prominences? His artist’s intuition led him to analyse objects on the artistic scene which happen to closely resemble objects of today’s solar physics research. The shape and structure of the outburst are indeed, as can be seen from the plates strikingly akin to the cypresses in the Vincent van Gogh paintings «Starry night» and «Path with cypresses and stars» (see also the smaller cypresses in the second of these paintings) (plates 2 and 3). The pictures in Camille Flammarion’s Popular Astronomy were published in 1880 when Vincent Van Gogh was 23 years old, whereas the paintings were made in 1889-1890, the last years of his life. It is not entirely inconceivable that the painter was even inspired by the unique popular astronomy book as was later, at a very early 100

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age, around 1920, the creator of magneto-hydrodynamics Hannes Alfvén If so, what a coincidence! In the correspondence with his brother Théo, Vincent van Gogh (1853-1890) mentions his interest in the stars and the sky he could see from where he stayed in Provence. In fact, his famous painting: «La nuit étoilée au-dessus de Saint-Remy» (see Plate 2) depicts a constellation of stars and planets, which from astronomical information can be related to a certain moment in time when the painting was done. It seems possible to infer that the painting corresponds to a certain time on May 25, 1889 [4.23], and that dates can be given by star information also for other paintings that he did [4.24]. With the impressive artistic production that van Gogh had in the same late period of his life the dates of certain of his paintings could be especially interesting; he finished 12 paintings in 18 months, some of them rated as his more important works [4.25]. We must hope that future research will elucidate the connection between sun spots, solar flares, prominences and vortex structures, and relate them to the energy released at the centre of the sun by the fusion reactions. Great achievements are already being made in solar observations with the new satellite-based instruments.

4.1.3 Unusual visitors on the sky Once in a while comets appear as spectacular phenomena. Again outstanding observations have been made using the Hubble telescope, which have contributed to more detailed information on the structure of the comets. Since the discovery of the Hale-Bopp comet astronomers have had the opportuneity of determining the chemical structure of its dust, rock and ice, a composition which has probably not changed much since the birth of the solar system about 4.5 billion years ago. Another particular visitor which could be seen moving on the sky like a bright source every evening for long times happened to be MIR (means peace), the Russian flag ship in 101

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space, which had been operating for 15 years in order to study the behaviour and experience of man under weight-less conditions as well as to investigate in this state: materials, chemical reactions and pharmaceutical processes. It stopped operation in 2001, in a controlled way as a gigantic fire-work of enormous ionized «falling stars» of antennas, computers and other facilities over the South Pacific Ocean. 4.1.3.1 Comets Comets are spectacular objects in the sky characterized by a head of nebulous gas surrounding the nucleus and a tail of luminous gas which can be several millions of kilometers long. The nucleus of a comet consists of small frozen particles of gas and has dimensions of several kilometers. It probably contains pieces of stone, sand and dust. Comets are part of the solar system and they often move in strongly elogated elliptical orbits. When a comet approaches the sun the material of the comet gets hot. Frozen gases, water, carbon dioxide, and ammonia evaporate and evolve to form the gaseous head of the comet which is lit by intense short-wave length radiation from the sun. Spectra of emitted light from the comet reveal the presence of hydrogen, nitrogen, carbon and oxygen, and CH, OH and CN radicals, ionized as well as neutral. Intense particle radiation from the sun, i.e. protons and electrons of the solar wind, also strikes the comet and causes an ionized comet tail, which is directed away from the sun. Experiments have been done to simulate comet tails in which plasma has been ejected from rockets at a height of about 2000 km. According to Alfvén the interstellar magnetic field from the solar wind plays an essentiel rôle in the formation of the comet tails. The magnetic field accounts for structures often observed in the tails. Spectoscopic analyses show that electrically charged particles are present in the tail. – The plasma consists of CO+, CO2+, CH , N2+, OH+, H2O+, + + and free electrons. CO and N2 are the most long-lived (106 s ) 102

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and can therefore exist at long distances from the head of the comet. The velocity of the gas particles can be 10 km/s near the gas head but can be 100-1000 km/s far out in the tail. In 1985-1986 the first observations of Alfvén waves in a cometary environment were made by satellite observations of comet Giocobini-Zinner and comet Halley. The generation of Alfvén waves near comets had been discussed in theory long before the observations, which thus confirmed the predictions of the theory. It seems that the physics of the Alfvén wave generation in cometary environments is fairly well understood by now, unlike the situation in the solar wind. It may, in fact, be so that the results of the cometary investigations might help us obtain a better insight into the corresponding solar wind problem. Let us therefore take a look at what is behind the presence of the Alfvén waves in the cometary case. In interplanetary space a certain amount of neutral particles may always exist. They could be of interstellar, planetary or cometary origin. When these particles come close to the sun they may be ionized by solar radiation. From neutrons and helium the radiation will produce protons, alpha particles and free electrons. As soon as these are produced they immediately start to interact with the fast-moving solar wind. The result will be a number of wave modes, electromagnetic as well as plasma waves. Numerical simulations have shown that all unstable modes are insignifiant except the Alfvén mode, which can increase to high levels, whereas the others become stabilized due to the low density of the newly produced ions as compared with the density of the solar wind particles. As a result of the interaction the generated Alfvén waves can also enable the solar wind to pick up the created ions. Observations have shown that comets continuously eject neutral particles and gas which become ionized immediately including heavy ions like CO+ etc. It is fascinating, at least for a theoretician, to think of how the all-pervasive Alfvén wave lies behind the spectacular phenomena of comet tails. A new area in cometary research is the observation of xrays from comets. 103

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Plasma data obtained by satellites from comet Halley, for example, suggested that comets should emit x-rays. An energetic electron population with energies up to several keV was observed. Strong plasma wave turbulence in the lower hybrid frequency range ωl h, equal to the square root of the product of the electron (ωce) and ion (ωci ) cyclotronfrequencies, was simultaneously noted. Computer simulation studies had shown that lower hybrid waves were produced when comets interacted with the solar wind. Such waves seemed to be active at accelerating electrons parallel to magnetic field lines, to energies required for x-ray generation. Recently, systematic observations where made of x-rays from comet Hyakutake. They gave the astonishing result that the observed signals turned out to be more than one hundred times stronger than the predictions. Subsequent analyses and simulations [4.18] have, however, recently confirmed the observed intensities. The studies were based on a lower hybrid instability for the interpenetrating cometary and solar wind ion gases. X-ray production should depend on the solar wind. Observations of the x-rays from comet Hyakutake indeed showed time variations of the x-ray fluxes. Comets may therefore be used as remote probes of the solar wind. Statistics about comets have been collected for many hundreds of years. Since the days of the invention of the telescope experience shows that only about one-tenth of the total number of astronomical events have been observed by the naked eye. The number of reported comets before Galilei should therefore be multipied by at least a factor of ten to yield a comparable total as related to observations with telescopes in later years. From the years since AD 1 the effective number of observed comets would then amount to several thousands in total, or several each year. When the question was raised: «How many comets are there in the sky?» the astronomer Johannes Kepler answered: «As many as there are fishes in the oceans», which was not an exaggeration. According to modern estimates the solar system 104

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is surrounded by an extended cloud that includes one hundred billion comets. Comets should be useful probes for diagnostics of the interstellar medium, for solar particle ejections and, in the case of impact, for observations on planetary crusts. They should therefore continue to be challenging objects for continued astrophysical research. Outstanding achievements in the history of cometary observations have been made by the Hubble Space Telescope. It imaged the «String of pearls comet», a train of 21 icy fragments across 710 thousand miles (1 million km) of space, or three times the distance between the Earth and the Moon. Hubble’s high-resolution image showed that the comet’s nucleus was much smaller than originally estimated from observations with ground-based telescopes. The Hubble observations showed that the nucleus was probably less than three miles (5 km) across, as opposed to earlier estimates of nine miles (14 km), (Credit: Dr HA Weaver and Mr TE Smith, STSC NASA). Image taken with the Field and Planetary Camera. The pictures discussed above were taken a year before the expected impact of the multiple comet on the planet Jupiter. On the occasion of the impact in July 1994 Hubble telescope pictures were taken with its Planetary Camera, showing eight impact sites [see Plate 9]. The comet, named Shoemaker-Levy 9 after the discoverers, attracted attention from telescopes around the world when the collision with Jupiter occurred. The extraordinary spectacle continued for several days as fragments of the comet caused a series of giant explosions including fireballs over a 1000 miles across. In July 1995 two American astronomers, Alan Hale and Thomas Bopp, simultaneously but independently discovered a new comet which accordingly has been named Hale-Bopp [see Plate 10]. The luminous head of the comet extends into two magnificant tails about three million kilometers long. The white tail, which is the more dominant and broader of the two, 105

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contains dust which reflects the solar light. The second one, which is blue and has a filamentary structure, is composed of ionized gas from the solar wind and is in the direction opposite to the sun. It is produced by the solar wind of plasma emitted from the sun. Hale-Bopp produces 250 tons of water per second. Interestingly enough, the comet exhibits all four states of matter: solid state (rock and ice), liquid (water), gas and plasma. The diameter of the head of Hale-Bopp is estimated to be about 40 km. Since the discovery astronomers have had the opportunity to study the comet and determine the chemical structure of its dust, rock and ice, the composition of which is supposed not to have changed much since the birth of the solar system about 4.5 billion years ago [4.19–4.20]. By April 1997 some 33 molecules had been detected, among them SO2 for the first time in a comet. Meanwhile European astronomers discovered that Hale Bopp also has a third tail consisting of sodium (Na). The third tail, which contains sodium in the form of uncharged atoms, is emitted in a direction close to the blue ion tail. On 22 March 1997 HaleBopp reached its closest distance to the Earth, about 200 million kilometers. It then had a velocity of 44 kilometers per second. Remember that the distance between the sun and the Earth is about 150 million kilometers, i.e. less than the closest approach of Hale-Bopp. In March-April 1997 comet Hale Bopp was visible every night. The comet's tail could be seen clearly with the naked eye. Looking at the comet with binoculars, as I happened to do against a completely clear sky on the French Atlantic coast, was an extraordinary experience of a celestial event. Comet Hale-Bopp will not come back in 2380 years. The dust lost by comets in periodic motion about the sun is distributed along the orbit of the comet. When the Earth in its motion around the sun happens to cross the orbit of a comet it attracts the dust particles, which in the Earth’s atmosphere induce bright sources of light. The particles, which may be no larger than a millimeter across, enter the Earth’s atmosphere at high velocity, for example 10 kilometers per second, and become split into atoms and ionized in collisions with air 106

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molecules in the direction of the orbit. This occurs at a height of 80-120 km above the Earth. A meteor trail is formed. On certain occasions whole bundles of meteors fall from certain directions in the sky, as in the nights around 12 August every year on the event of the Perseid showers. The meteor trails or «falling stars» of these showers have also been named «Saint-Laurent’s tears». Occasionally, the luminosity of the meteor ionized trails, or plasmas, is comparable to that of the full Moon. The plasma in the meteor trails can be studied by means of pulses of electromagnetic waves using radars. And, when you see a meteor, don't forget to make a wish, but keep your wish secret! Is it the midnight’s comb Which makes them fall the stars of spring time? Natsume Sôseki 1867-1916

Free translation from the Japanese «Kasamakura». 4.1.3.2 The extraordinary voyage of MIR (1986-2001) At night one may notice the light from aeroplanes or satellites crossing the sky. One evening at Lacanau on the French Atlantic coast where the sky is often particularly clear something that was shining like a bright star or planet and slowly moving seemed to be different. My wife said instinctively that it might be MIR; the Russian space-craft that we (sometimes) heard about on the news. Every evening for weeks early in the year 2000 I glanced at it in the sky where it moved in the same way from left to right about 30° above ground level. One night something odd seemed to happen. Unusual changes in the radiation from the object became clearly visible with the naked eye. Imagine our astonishment when the next morning it was reported on the news that MIR the day before had had two cosmonauts outside the space-craft doing important manipulations! 107

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MIR the Russian flagship in space (MIR means: peace) was destroyed on March 23 2001 as planned and executed by the space control center outside Moscow. The trajectory was guided into the atmosphere of the Earth by operation at different intervals in three steps using the rocket brakes of the space-craft at a height of about 45 kms above the surface of the Earth, the main parts of MIR transformed into a gigantic firework of enormous ionized «falling stars» over the South Pacific Ocean. Most of the 140 tons of capsules, solar panels, computers and instruments were dissolved into pieces and returned into the gaseous state of the universe. The rest of the debris plunged into the sea over an extended belt 5000 km long, 200 kms wide between New Zealand and Chile. The gigantic space-craft, the size of the Eiffel Tower in Paris, had been operating for 15 years with 104 cosmonauts. The purpose had been to study the behaviour and experience of man under weight-less conditions as well as to investigate in this state: materials, chemical reactions and pharmaceutical processes, in a long term vision preparing for colonization of the Moon and the planet Mars. From the project a total of twenty three thousand experiments were reported. The impressive conclusion marked the end of the Russian hegemony in space. Economic difficulties in obtaining continous support set a limit to the operation of this gigantic long term effort [4.26]. A new space-craft, the International Space Station ISS, a 100 billion dollar project is presently already under consideration, aiming at operation in the year 2005, a 415 ton voyager, the most complex spatial system ever envisaged (cf. Leonardo da Vinci Figure 7.4).

4.2 The sun — Earth interplay There is a wind blowing from the sun, a wind of electrons and ions, with an average velocity of 430 km s–I, which could increase to 1200 km s–I when strong eruptions occur. The 108

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energy liberated on such occasions is enormous and the consequences clearly noticible when they reach Earth after 4-10 days, causing disturbances in the radio communications. The Earth’s magnetosphere is a region in space where electromagnetic forces dominate the motion of plasmas in the magnetic field, which surrounds the planet. The effects of the solar wind on the formation of a selfconsistent magneto-plasma have been explored by satellites, which provided numerous pecularities, not at all known less than 50 years ago, e.g. a shock front, the so-called bow-shock, which forms a sharp outer limit of a region of irregular and fluctuating magnetic fields. At heights above 100 km around the Earth, UV radiation from the sun ionizes the atmosphere, which becomes electrically conductive and can serve as a reflector for radiowaves. The first studies on the propagation of radiowaves in the presence of the Earth’s magnetic field in the ionosphere were carried out by Sir Edward Appleton who was awarded the Nobel Prize for physics in 1947. The Northen Lights or the Auroras are spectacular witnesses of the solar wind electrons, which enter the Earth’s magnetic field in the polar regions. They serve as probes of disturbancies on the solar surface!

4.2.1 The solar wind During periods of strong solar activity intense bursts of plasma and electromagnetic radiation occur on the solar surface. The release of energy could be enormous. A single event can liberate energy comparable in amount to the total energy consumed by humans on Earth since the beginning of time. Consequences of such phenomena are experienced in the magnetosphere surrounding the Earth. Secondary effects can be observed, for example, in auroral activity. They can also be noted as perturbations in radio communications, or in signals guiding spacecraft and satellite performance. There is, however, 109

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also a permanent continuous flow of particles in all directions out of the sun, the solar wind, which consists essentially of protons and electrons. This wind can be influenced by solar magnetic fields, which occur in connection with sun spots. The unperturbed wind has an average velocity of about 430 km/s when it reaches the region of the Earth, a value which could increase to 1200 km/s when solar eruptions occur. At a speed of 430 km/s the solar wind reaches the Earth after about four days. The solar wind has a high electrical conductivity. Accordingly, changes in magnetic fields will be compensated by new magnetic fields accompanying induced electric currents. Solar wind electrons have thermal velocities, which are considerably higher than their drift velocity whereas the opposite is true for the ions. All stars of the same type as the sun are believed to put have flows of matter out into interstellar space, which should acordingly be filled up with intercrossing plasmas from stellar winds. The solar wind represents a plasma link plasma between the sun and the Earth. It was not until a century ago that it was pointed out more directly that beside visible radiation the sun emitted some kind of particle streams, which prevailed even in the absence of enhanced solar activity. In 1896 the Norwegian physicist Kristian Birkeland suggested that the aurora borealis might be caused by electrically charged particles from the sun which entered and were guided by the Earth’s magnetic field to regions near the poles. Electric discharge tubes had at that time been recently developed and Birkeland thought that the light from them looked similar to the aurora and that the phenomena might be of the same nature. More conclusive evidence of the solar wind came much later, in the early 1950s from studies of comets by the German scientist Ludwig Biermann. In his studies he found that the pressure of electromagnetic radiation from the sun could not be sufficient to explain that the tails of comets were always directed away from the sun. Biermann concluded that streams of charged particles from the sun were responsible for this effect and, furthermore, that the solar wind was blowing continuously. The early ideas about particle 110

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emissions from the sun were also confirmed by spacecraft and satellites in the late 1950s and in the 1960s. There remain many puzzling questions of a physical nature related to the interaction of the solar wind electrons and the magnetic fields in the magnetosphere. Electric fields are also believed to play an interesting rôle. During their long journey from the sun to the surroundings of the Earth the solar wind particles undergo many adventures. When the solar wind electrons leave the outer parts of the solar corona they are believed to have acquired high, even relativistic, velocities. The acceleration mechanism is simply not known although various proposals have been made. In passing the bow-shock the electrons seem to slow down their energy considerably, whereas for some reason they become accelerated again before entering the Van Allen radiation belts where they can have energies of some Me V and even higher. Spiralling in the Earth’s magnetic field they contribute to the radiation belts which encircle the Earth at distances of 1.5 and 6 times the Earth’s radius. When high-energy, relativistic, electrons penetrate interstellar space and encounter the magnetic fields of interstellar objects they radiate syncrotron radiation and take part in the radiation from radio sources in outer space. They form the basis of an important, relatively new branch of astronomy, namely radio-astronomy, which during the last fifty years has considerably increased our knowledge of the universe, shedding light on radiation processes and chemical abundances of elements at very remote distances in the cosmos, using Earthbased telescopes for the observations. In the meantime space technology, using satellites and rockets, developed as did also modern plasma and fusion science and technology. There are many electromagnetic processes that these fields have in common. For example, when relativistic spiralling electrons radiate in the presence of a magnetic field they also lose energy which limits the generation of syncrotron radiation. These phenomena are present also in fusion plasmas, where losses by syncrotron radiation play a rôle in magnetic confinement experiments. In laser fusion experiments, where self-generated 111

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megagauss magnetic fields could be present, the strong electromagnetic laser fields could even drive the laser pellet electrons to relativistic speeds of electron oscillation. Relativistic mass corrections then become so important that further increase in the laser intensity could become inefficient. In considering solar wind problems, the following basic properties should be remembered. In the solar wind, collisions are so rare that they can be neglected. Interaction of the solar wind with electromagnetic fields and waves thus becomes particulary interesting. The energy density of the ions is much greater than that of the magnetic field and also much greater than that of the electrons. Thus the ions, i.e. the protons, dominate the motion. As we shall see, however, the influence of electric fields set up by space-charge effects could be important. An interesting observation is that the solar wind can flow at an angle with respect to the interplanetary magnetic field without being deflected. How can this be possible? The answer lies in the influence of the space-charge, or more precisely in the strong electric fields set up when positive and negative electric charges tend to separate from each other due to an influence of a magnetic field, which would normally deviate the positive and negative charges in opposite directions if they were left alone without mutual electric field interaction. But this is, in fact, not the case and space-charge effects can prevent the separation. It seems that transverse inhomogeneities of the plasma with regard to the direction of the solar wind would increase the role of the space-charge and they would even be necessary to prevent the opposite charge particle deviations of the orbits if the magnetic field was homogeneous in space. Filamentations in the plasma flow would thus tend to keep the protons and electrons together over long distances in the interplanetary magnetic field. It is therefore interesting to notice that in fact plasma filamentations seem to be common in cosmic plasmas.

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4.2.2 The Earth’s magnetosphere The term magnetosphere was coined in 1959 by Tom Gould, an American scientist and pioneer in space and plasma astrophysics. It was introduced to give reference to the region in space where electrodynamic forces dominate the motion of plasmas in the presence of a planet’s magnetic field. Our new perception of the Earth’s magnetosphere emanates from the interaction of the solar wind with the magnetic field set up by the Earth. The solar wind is actually driving the whole structure. The result is a complex of currents, of trapped particles forming confined plasmas, of shock-fronts, plasma sheets, instabilities and turbulence, and of a magnetospheric tail stretching out on the back side of the whole structure, etc... There are currents in the ionosphere flowing into the upper atmosphere and currents linking the magnetosphere with the ionosphere in the polar regions which play an interesting rôle in the behaviour of auroras. It has been observed recently that in the magnetosphere the solar wind seems to drive surface waves on the transition region between the space plasma and free space like the wind on a water surface! The most striking evidence of the solar wind is perhaps the change in the picture of the magnetic field surrounding the Earth from the idea one had only 50 years ago. It was William Gilbert who, in the year 1600, initiated the science of geomagnetism and noted that: «The Earth globe itself is a great magnet». It has been known for 200 years that the magnetic field on the surface of the Earth can be approximated with high precision by the field of an imaginery bar magnet inside the Earth. Before the knowledge of any external influence on the magnetic field outside the Earth it was believed that a dipole structure like that from a bar magnet continued even outside the Earth into the interstellar space. Modern space research has resulted in striking evidence of a dramatic change in the picture of the magnetic structure around our planet. A beautiful demonstration of the effects of a streaming plasma, the solar wind, on the formation of a self113

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consistent magnetoplasma structure on a global scale, including many internal peculiarities. Some of these can be compared with what happens in large-scale fusion plasma experiments. As an example it may be mentioned that the problem of magnetic reconnection in plasmas where collisions can be neglected was first considered in connection with space plasma processes occurring in the Earth’s magnetotail. Later on the same problem became of interest in the research into fusion laboratory plasmas. It was found to have application to the so-called sawtooth crash of the central temperature of a Tokamak plasma. High amplitude increasing oscillations become quenched suddenly on a short time-scale compared to the average electron-ion collision time due to pratically instantaneous magnetic reconnection. Early satellites (Pioneer I, 1958, Pioneer V, 1960) observing the magnetic field around the Earth recorded a sudden decrease of the magnetic field at about 14 Earth radii. It was confirmed by further satellite measurements that the abrupt transition in the magnetic field strength to a very weak interplanetary field occurred at the position of a shock front, the bow-shock, which forms the outer limit of a region of an irregular and fluctuating magnetic field, called the magnetosheath, which contains a plasma in a turbulent subsonic state in contrast to the supersonic solar wind plasma (Mach number 8) outside the bow-shock. The origin of the bow-shock is the necessary deflection of the solar wind in front of the Earth’s magnetic field. The process of forming the bow-shock is believed to involve the interaction of waves of different types, increasing the temperature of the plasma, which forms a blanket or magnetosheath. Bow-shocks occur when a fluid or a plasma passes unmagnetized or magnetized bodies. They can be produced and studied in wind-tunnel experiments. The creation of the bowshock depends on the relative motion of the fluid and the body. Comets such as comet Halley, have bow-shocks due to their motion in the interplanetary medium. Comet Hale-Bopp exhibits two bow -shocks for reasons that so far seem to be a 114

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puzzle. The flow of the solar wind through cometary bow-shock offers interesting opportunities for future research, as does the physics behind the bow-shocks of the Earth’s magnetosphere. Inside the bow-shock of the Earth's magnetosphere there is a region of plasma named the magnetopause, and furthermore the magnetotail, a stretched-out plasma behind the Earth, with the interesting property that the magnetic field has opposite directions above and below the equatorial plane. The Earth’s magnetic field forms a closed magnetic structure and gives rise to confinement of high energy particles consisting of protons and electrons in the Van Allen radiation belts, named after their discoverer. The first observations of these radiation belts were made by means of the satellites Explorer I,II,IV and the lunar probe Pioneer III. The discovery of the Van Allen belts marked one of the great early successes of space science. From the late 1950s modern space technology thus started to provide the means for observations of detailes of the magnetosphere, such as magnetic and electric structures and of particle density and velocity distributions. As a result our modern view of the magnetosphere emerged, the strongly deformed overall magnetic structure and the complexity of the magnetoplasma and the current paths. Even more interesting from a scientific point of view is the fact that the experiments demonstrated the important influence of electrodynamics and plasma physics on the behaviour of matter and radiation in the Earth’s environment. In this context it seems interesting to remember the fact that as a rule gravitationally confined plasmas (the stars) emit visible radiation, which one can see in optical telescopes or by naked eye, whereas magnetically confined plasmas emit radio and/or microwaves, which cannot be seen visually, but can be observed by rockets or satellites outside our atmosphere or by radiotelescopes operating in «windows» of our atmosphere where the waves penetrate. This may be considered as a scientific reason for why electromagnetic knowledge about the universe advanced so slowly up until the space age. 115

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The results obtained in the space age confirm and extend the pioneering early work of many scientists e.g. Carl Størmer in Norway, at the beginning of the century, Hannes Alfvén in Sweden and Van Allen in the USA, who considered the motion and trapping of charged particles in the Earth’s magnetic field. Today magnetospheres are known to exist also on the other planets in our solar system, such as Saturn, Jupiter, Uranus and Neptune, but not on Venus or Mars. In the observations of galaxies one has found magnetospheres on a galactic scale, and a whole galaxy that shows a deformed structure with a tail due to the presence of an interstellar wind. Associated phenomena have also been studied by numerical simulations on computers and these studies have confirmed the observations.

4.2.3 The ionosphere An ionized layer surrounds the Earth at heights above 100 km. It is generated by the ultraviolet (UV) radiation from the sun, which ionizes gas in the atmosphere, which then becomes a plasma. A plasma equilibrium state is established by the balance between UV radiation, which tends to increase the number of free electrons, and the effect of recombination between free electrons and ions, which causes a loss of free electrons proportional to the square of the density of free electrons (assuming equal densities of free electrons and ions). The equilibrium and also the dynamics of the ionosphere in the presence of variations in the radiation, such as occur daily or on a shorter time scale, for example during a solar eclipse, are therefore examples of nonlinear phenomena. The ionosphere reflects radio waves in the broadcast frequency domain and allows radio communication on a global scale. The presence of a magnetic field in the ionosphere affects the radio-wave propagation and the conditions of wave reflections. When the UV radiation from the sun experiences fluctuations, or when more violent variations in the magnetic 116

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field occur, due to eruptions on the solar surface, fading phenomena or even black-outs in radio-communications may occur. Such disturbances seem to be common in connection with increased sun spot activities. They demonstrate how dependent we are on the solar-terrestrial relationships. We can hear the effects of eruptions and other enhanced solar activity! The maximum density of ionospheric plasmas is of order of 106 particles per cm3.The corresponding critical or cut-off frequency, i.e. the lowest frequency of waves that can penetrate the plasma, is 107 Hz. These figures refer to the lowest of several existing ionospheric layers, the so-called E-layer, the abbreviation for the electrically conducting layer, the others being denoted by F1, F2 etc, and having lower plasma densities and being more sensitive to perturbations. Radio waves used for communication should therefore have lower frequencies to be reflected by the ionosphere. Signals from space craft entering the Earth's atmosphere might be cut off due to the high plasma density caused by increased ionization due to frictional heating of the atmosphere during the re-entry. Localized fluctuations of the ionosphere might, furthermore, introduce structured fading in radio-communications. It has been found by instrumented rocket payloads (1986, 1992) and recently confirmed in 1994 by instruments on the Freja satellite that localized wave packets in the lower-hybrid wave frequency domain exist in the ionosphere. Local density depletions are often found to be associated with the observed wave packets. The structures can accordingly be interpreted as wave-filled cavities, which as a rule are strongly elongated along the magnetic field. The lower-hybrid frequency waves do generally depend on space-charge effects as well as on magnetic field effects. The static magnetic field introduces couplings between longitudinal plasma oscillations and transverse ion oscillations. The same type of waves has been studied in great detail in connection with fusion plasma experiments on heating and current drive. The waves have been found to be serious candidates for heating and current-drive in future fusion reactors. The structures of observed lower-hybrid 117

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wave packets often closely resembles an envelope soliton, with a characteristic bump-like shape set up by the balance between nonlinear forces and dispersion. A wavelet transform technique (see later) has been used to analyse the electric-field fluctuations. The wave-frequency in the Freja observations is centred at 4 k Hz and covers a rather narrow frequency range. The observed distributions seem to be surprisingly constant in time and vary only a couple of times during several years. The generation mechanisms of lower-hybrid waves have attracted considerable interest recently and have been summarized in the literature [4.21]. The section indicates that there are still interesting phenomena to be discovered in the ionosphere, the first space plasma to be systematically studied with regard to the propagation of electromagnetic waves in the presence of a magnetic field, studies for which Sir Edward Appleton was awarded the Nobel prize for physics in 1947.

4.2.4 Auroras The explanation of auroras is simple, in principle. They are phenomena caused by the solar wind electrons which enter the Earth’s magnetic field in the polar regions. The electrons excite the atoms in the lower part of the ionosphere from about 100 kilometers up to several hundred kilometers. When the excited atoms return to their original states they emit radiation of different colours in the spectrum There are exceedingly high powers related to the auroral radiation. The amount of power associated with an average auroral arc is comparable with the power generated by an atomic bomb. The auroras, or as they are also called, the Northern Lights, have attracted the interest of generations through many centuries from mythology to the space age. Aristoteles (384-322 BC) is said to have given the following explanation of the aurora: 118

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«The phenomena occur when air collides with fire». Changing air for gas and fire for plasma he was in fact correct! He thought that auroras resembled «jumping ghosts». To describe the exceptional beauty of the auroras is, however, less simple. They should be seen! An aurora is an enormous multicoloured dynamic firework covering a large part of the sky, a three-dimensional image of the happenings occurring on the solar surface projected on our atmosphere. As modestly expressed by Chanchal Uberoi, the famous Indian expert on geocosmophysics, the auroras are like «flying sarees in the sky». Present-day research is very much concerned with the questions of how the solar wind electrons which reach the aurora have been accelerated to the energies necessary to excite the atoms in the ionosphere and produce the aurora. There are indications from recent experiments by rockets and satellites that electron acceleration occurs during the passage of the electrons from the magnetosphere into the upper atmosphere particulary in the region covering the last 10 000 km. It sems that the acceleration occurs predominantly in the direction of the magnetic field [4.22]. There are various candidates for the mechanisms which are active in accelerating the electrons, from the possibility that they have been accelerated by potential fields, to others where resonant interaction of the electrons with waves is responsible for the acceleration. The resonant interaction of an electron with a certain type of wave, the phase velocity of which may depend on the plasma density, the strength and direction of the static magnetic field etc, could be compared with the action of a surfer riding the ridge of a water wave and choosing a certain direction for his surf board in descending the whirl of the breaking wave. A particularly interesting and promising possibility for the electron acceleration by waves seems to be the interaction with lower-hybrid waves (see section 4.2.3) or bunches of such waves. The phase velocity of the lower-hybrid wave could be in resonance with the parallel motion of the electrons and 119

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simultaneously with the ions moving perpendiculary to the magnetic field. It is interesting to notice how the lower hybrid waves, which are extensively studied and used for fusion plasma heating and current drive of fusion plasmas might play an important role in geocosmology. .Electron cyclotron waves and Alfvén waves are both also important in natural and man-made plasmas.

4.3 Far beyond the sun: superstrong emitters of radiation 4.3.1 Supernovas Heavy stars may undergo gigantic explosions and become supernovas. Though these are rare phenomena they may be the source of all the heavy elements in the universe, including those vital for life. The explosions give rise to radiation of extreme brightness, hundreds of million times the extraordinary radiation from the star. Often visible to the naked eye, the brightness of the supernova may increase at a rate of a hundred thousand times in a few hours, reaching a state which is 10 billion times brighter than our sun. Gaseous clouds are ejected from the explosion with velocities of about 10 000 kilometers per hour. They appear in the sky as expanding nebulae in white, blue and red. A supernova explosion differs from a nova explosion in that the whole star is participating, not only an outer shell. The supernovas attracted great interest as long as 2000 years ago, when they were observed by Chinese astronomers. Annals from those days recount supernova events in the year 5 BC, and the years AD 185, 369, 1006, 1054 (Crab), 1572 (Tycho Brahe), 1604 (Kepler). The most famous of these supernovas is the one from 1054, the brightness of which was so intense that it could be seen for several months even in the middle of the day. 120

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In the southern hemisphere a new supernova was observed in 1987. The first one in 383 years which could be seen by the naked eye, it was a comparatively short distance away-just 170 000 light-years. Observations of this supernova, SN 1987 A, have contributed to our understanding of the physics of supernovas. It turns out that when the fuel in the chain of fusion processes is consumed the inner part of the star contracts and finally collapses. The inner part includes elements masses which are multiples of four up to iron 56Fe; this inner part is believed to form a neutronstar. Meanwhile a shock-wave of a velocity of 30 000 kilometers per second expands and drives the explosion outwards. In the process of explosion the gas is supposed to be in a plasma state. It moves under the influence of the magnetic field of the supernova. The motion may create magnetohydrodynamic waves influencing the dynamics of the system. The nebulas, which remain as luminous gaseous clouds expanding out from the position of the supernova explosion, show a filamentary magnetic structure as determined from polarisation measurements, for example in the Crab nebula. The magnetic fields may be interpreted as extensions of the explosion. Under certain circumstances the explosion becomes obstructed and the star develops into a black hole. But most turn into neutron stars which may continue to emit regular bursts of radiation as pulsars.

4.3.2 Pulsars: lighthouses of the cosmos Pulsars are stars that generate electromagnetic radiation emitted in very short pulses with intervals which are extremely regular. Pulsar radiation comes, it is thought, from neutron stars which rotate with high velocity, in certain cases several hundred times per second. The direction of rotation of the neutron star makes a fixed angle with the direction of the strong magnetic field of the 121

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star. The rotation accelerates electrons in its neighbourhood which emit electromagnetic radiation continuously over the whole spectrum from radio to visible, x-ray and even gamma ray wave lengths. Besides, the neutron star itself emits short pulses with periods corresponding to the frequency of rotation, one pulse occuring every time the beam of radiation sweeps across the Earth. Plasma physics phenomena play a role in connection with the acceleration of electrons to almost relativistic energies. Strong magnetic fields emanate from the magnetic poles of the star and channel the radiation from the pulsar. Syncrotron radiation is produced by spiralling of the relativistic electrons in the magnetic field. A neutron star, assumed to be formed in a supernova explosion, is indeed a very strange object. It has a mass about the same as that of the sun concentrated into a sphere with a radius of only about 10-15 kilometers. It corresponds to a density of about 1014 g/cm3 or one 100 tons of superdense material in the volume of a tea spoon. The discovery of the first pulsar was, in fact, made by chance in Cambridge 1967 during the course of a study of the influence of the outer corona of the sun on the radiation from remote point sources. Subsequently, radioastronomers aimed their telescopes towards the centre of the Crab nebula, the magnificent glaring gaseous remnant of the supernova event that is known, from Chinese annals, to have occurred in AD 1054 , and found a pulsar in the centre of the nebula at the expected point of the origin of the surpernova explosion. There were early precursors to the concept of a neutron star. A paper by J R Oppenheimer and G M Volkoff: On massive neutron cores [4.27], published already in 1939, suggests that «actual stellar matter after exhaustion of thermonuclear sources of energy will, if massive enough, contract indefinitely, although more and more slowly, never reaching a true equilibrium», whereas contemporary work by 122

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G. Gamow and L.Landau discussed the formation of condensed neutron cores [4.28]. The expansion velocity of the gaseous filaments in the Crab is 1300 km/s. The time from the explosion is in accordance with the present spatial distribution of the Crab and the measured velocities. The filamentary density structure is accompanied by a magnetic field structure where the direction of the magnetic field lines follows the gas filaments, as determined by polarization measurements. Cases where two pulsars rotate around each other at close distance have also been observed. In the process of radiation they lose energy and come slightly closer on each turn, finally ending up in collision. One might expect that the two masses of superdense material join each other by gravitational effects to form a black hole. In 1974 two American astronomers Russell Hulse and Joseph Taylor detected such a double pulsar with the radiotelescope at Arecibo in Porto Rico. Following the evolution of this rare object for several years allowed them to test the theory of relativity. They were able to verify that the double pulsars, having masses 1.40 and 1.42 times the solar mass, lost energy at a rate predicted by the general theory, or with 76 m/s annual decrease of the orbital period. Their investigations simultaneously proved the existence of gravitational waves. Their discoveries led to the award of the 1993 Nobel prize for physics. The space epic Aniara by the great Swedish author Harry Martinson (1904-1978), awarded the Nobel prize for literature in 1974, recounts the fascinating observations by the space-ship Aniara. It records and predicts the evolution of the Cosmos. From Harry Martinson’s poetry may we quote the following lines «World clocks tick and space gleams everything changes place and order».

One may interpret the ticking world clocks in the gleaming space as the pulsars, rapidly rotating remnants of supernovas 123

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carrying superdense material and sending out repetitive short pulses or radiation. The discovery of the first pulsar was made much later than the poem and was recognized by the award of the Nobel prize for physics to the British radioastronomer Anthony Hewish in 1974. The dynamic structure of the universe corresponds well to the poet’s observations that everything changes place and order.

4.3.3 Quasars The Universe has never ceased to astonish us. Every now and then new objects with unexpected properties are discovered. In 1960 a new type of radio source, quasars or quasi-stellar sources, were observed for the first time. At present several hundreds of such sources are known. They seem to be sources of extremely high luminosity corresponding to hundreds or thousands of galaxies, and of cosmically seen very small dimensions, only some light-years. One believes that the most remote quasars are at distances of the order of 14 billion lightyears from us, and that they may be the central nuclei of galaxies, originating from stars and gas-clouds attracted by a black hole. They are extremely massive objects with enormous emission of energy. Studies of a particular source 3C-273 (3C notifies the third Cambridge catalogue of radio sources) in the optical domain have revealed that the anomalously large widths of the spectral lines from quasars are connected with a very strong shift towards the red part of the spectrum. This indicates that the source is moving away from us at high speed. The same source has also been studied in the x-ray part of the spectrum with a telescope on the satellite Einstein. If the spectrum is caused by the relative motion of the quasar it moves away from us at about 80% of the velocity of light. Provided the estimated distance of the quasar is correct (1.8 billion light-years) the source 3C-273 radiates an energy of 1040 joules, which corresponds to the radiation from about one thousand normal galaxies. As is sometimes the case with 124

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radiosources quasars may occur as double objects. The radiation from them, optical as well as radio, may vary in time periodically or irregulary. It has been suggested, as an alternative, that quasars are objects at relatively close distance, which have been thrown out from nuclei of exploding galaxies. Many unanswered questions still remain. So far quasars seem, however, most likely to be very remote, extremely strong sources of radiation. The most distant quasar known so far (PC 1247+3406) has been photographed with the largest optical telescope in the world with a diameter of 9.8 m, situated at the top of the volcano Mauna Kea at an altitude of 4150 m in the islands of Hawaii. The light received from this quasar was emitted when the universe was not yet one billion years old. The photo also reveald some more similar faint spots from objects at extremely remote distances. What can we say about the possible mechanisms of formation of those distant sources of radiation? Does plasma physics enter the formation of quasars and if so in what way? Even if astrophysical objects in general are formed by selfgravitation there are objects that cannot be explained by such processes. The reason is that the internal energy is larger than the gravitational energy. Quasars seem to belong to this category. Therefore one has to look for other processes of condensation than gravitation. Alfvén waves may be important in the formation of quasar clouds due to a thermal instability which may occur in the presence of Alfvén waves. It is well known that magnetic fields exist in active galactic nuclei from observations of strong emissions of syncroton radiation. The observations also show that the radiation from the nuclei is highly variable due to some strong perturbations, presumably in the magnetic field. Magnetic field perturbations create Alfvén waves. These are supposed to be damped by resonance surface damping on a thermal instability for the formation of quasar emission-line clouds. It is believed that such line-emitting clouds are small and embedded in a broad-line region, which is in pressure 125

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equilibium with the small clouds for a temperature of 2×107 degrees, [4.14]. The energy release in quasars is so enormous that, in fact, nuclear energy is wholely insufficient to explain what happens. The property of quasars to eject matter, often as jets, is an indication in favour of annihilation of matter as a source of energy. The field is open for speculation and the future may be full of surprises

4.4 The expanding universe 4.4.1

From plasmas to gravitation; The complex medium and the fields

The universe with all its twinkling stars, planets, nebulae and galaxies forms a gigantic system. When we look out in the sky it seems quite static. On a universal time-scale the pieces of the pattern are instead in continuous, systematic and often violent motion. They form all together a complex medium [4.29–4.31], resembling not so little a plasma, i.e. an ionized gas, in particular a hot fusion plasma [4.32, 4.33]. The complexity is exhibited by numerous types of phenomena, which one can observe, e.g. dynamic events like Northern lights from the Aurora Borealis or solar prominences, comets, pulsars as well as nebulae which are remnants from supernova explosions. The formation and the physics of stars and galaxies and their clusters as well as the fusion of galaxies are challenging for future observaton. The emission of neutrinos and X-rays are highlights in present day astrophysical research (see sections 4.4.4 and 4.4.5) Gravitational forces as well as forces of electromagnetic origin are governing the motions of all these celestial elements. At planetary distances the attraction by gravitational forces is 126

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active to balance the centrifugal forces to keep the moon circling around our Earth and maintain the Earth circling at a constant distance around the sun. The gravitational forces have even been responsible for forming the sun and to cluster galaxies in domains, where the intermediary space is filled with plasma, which in itself exhibits numerous pecularities. Looking at the universe at large we know, however, that there is a universal expansion everywhere, to the outer limits of observation. How do all these facts fit together? To describe the over-all motions of the galactic objects collective methods of transport might be used, accounting also for the influence of magnetic fields; filamentation and other structural phenomena like spiral motion as well as inertial effects included. One might envisage nonlinear phenomena to play a role in the universal dynamics as they do in laboratory plasmas. Recent observation by means of the Hubble telescope and by using sofisticated techniques like gravitational lensing indicate that structural patterns are present in the distribution of very remote galaxies. Similar structures often occur as a result of selfformation and self-organization in plasma physics as well as in chemical and biological systems. They exhibit features of intricate nonlinear behaviour. The universe expands equally in all directions independent of from which point the observation is made. The expansion is governed by the Hubble law, which states that the velocity of expansion is proportional to the distance between the observer and the object. The repulsion between all parts of the universe is thought to have its origin in a continuous cooling of the whole universe, slowing down the rotational motion of the galaxies as one example. This means a liberation of free energy. Transfer of a sufficient amount of free energy from the entire universe is necessary to have the expansion. The energy liberated is used to carry out work against the gravitational attraction, which would otherwise lead to a collapse of the universe. Compare shooting up a rocket in the sky. 127

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The presence of all kinds of cosmical objects in the universe, which possess free energy, e.g. energy that could be liberated to perform work, suggests that the universe might be regarded as an active medium, represented by average characteristic parameters (cf. a hot plasma in a magnetic field or a molecular medium with molecules having inverted population, e.g. astro-chemical emitters, masers or lasers! A corresponding amount of nonlinearity in the diffusion operator is likewise necessary to have the observed Hubble expansion (see Appendix). Of particular interest would be to determine to what extent the universal medium is nonlinear (cf. particle and heat transport in hot plasmas). For a subsystem of the universe, like the solar system the formation is caused by the gravitational attraction, which means that small-scale (on cosmical dimensions!) and over-all cosmical behaviour differ. On cosmical dimensions the over-all work by the liberated energy may overcompensate the gravitational contraction. The mass of the universe determines whether or not the gravitation is sufficient to balance the expansion forces. If the universe has a high mass, the gravitation could prevent the matter in the universe to escape for good and one talks about a closed Universe. In the opposite case one talks about an open universe. There is a critical mass of the universe for which there is on the average a complete cancellation between the expanding forces and the gravitation. One says that in that case one has a flat universe, a domain where it seems that our universe rests, perhaps with a slight tendency of escaping into an open state. The critical density is estimated to about a dozen nulei (protons or neutrons) per cubic meter… Measurements indicate less, but one can not be sure that all contributions from e.g. exotic objects are included. NL phenomena penetrate the whole of modern science. Consequences like self-formation and self-organization appear everywhere, and are studied in different disciplines. This has 128

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happened in less than fifty years, even if some examples where known already in the beginning of the last century. What is the reason? A crucial point is that we now have available high amounts of energy; density and temperature, even magnetic fields in limited regions of space and time. Some situations of this type was realized only recently, with lasers of high power entering on the scene. They have led to ultrafast phenomena governed by short pulses on time-scales of ten to minus fifteen, to ten to minus eighteen seconds. A new and fascinating field of laboratory astrophysics has attracted considerable interest, introducing experimental as well as theoretical simulations of cosmical phenomena [8.6, 8.7, 8.14, 8.24–8.26]

4.4.2 The nonlinear universe The question arizes if one might be able to give a large-scale NL description of the overall behaviour of the whole universe? Can we formulate a NL PDE for the whole universe like for the particle transport or temperature diffusion in a fusion plasma, where also coupled NL PDE’s for particle and transport are studied; and determine the NL coefficients from astronomical observations? And similarly describe more localized phenomena like star and galaxy formation by NL PDE’s, again using explicit physical data. One might then think of the entire universe as being described by a big matrix containing NL PDE elements related to the local situations, or by a single over-all view. What would be the use of such a way of looking at the evolution? It would give an overall unified picture. But what is more, it would provide, when the NL constants are determined, a possibility of estimating the impact of sources that may enter. To decide whether or not these would have the possibility of establishing themselves and grow, or vanish as determined by a corresponding NL PDE of reactiondiffusion type, just as in a Tokamak fusion plasma. Or, if equilibria could be established, and if they would be stable? 129

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What happens, as an example, even if it rarely occurs, when there is a supernova explosion or when a comet enters our solar system or even comes close to our Earth? Or, if stars and galaxies fuse or separate? Or even, to look closer to us, when stars are falling. By the way, why do they fall? When the moon continues to move around the Earth and the Earth around the sun? Because they do not have a rotational motion giving rize to a centrifugal force, compensating for the gravitational attraction! If the same would be true on a universal scale the universe would not expand, but contract due to gravitation. The expansion of the universe, as described by the Hubble law, requires work to be done by all the elements of the medium, provided by a tendency to calm the medium and cool the galaxies. The extent to which this is done and what effect this might have is related to the NL constant in the PDE. Now we can understand the similarity between the effect of the gravitational force fighting against the temperaturedensity pressure force on the sun, leading to an equilibrium or to compression or expansion to a red giant star, as well as the explosion of an atomic bomb as compared to an expansion of the universe. In those cases the gravitation may or may not be sufficient to confine the system. Nor is it in a fusion reactor plasma, where magnetic or inertial effects have to be added to quench the violent motions and pressure from the plasma. The difference for the universe is that there the large scale motion of all the cosmic objects are responsible for the main part of the free energy. The transfer of radiated energy may also play an important role. But now comes the real point of comparison! In the solar plasma or fusion reactor plasma the energy originates from fusion reactions and nota bene the fusion reactions are originally also responsible for the motions and energy of all the cosmic objects in interplay with the gravitation in the universe. The whole universe behaves like a fusion reactor. In conclusion it seems rather natural if similar methods 130

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of analysis could be used in solving the problems of the universe as in the fusion plasma case.

4.4.3 The small and the large; atoms and the cosmos In atomic physics the Schrödinger equation has proper (finite amplitude) solutions only for specific values of the constant E that enters the equation. Those values E = En correspond to the energy levels of the atom and to specific states of the atom. The states are related to characteristic average shapes of the distributions (wavefunctions) of the clouds of electrons surrounding the nucleus, e.g. a proton for the hydrogen atom. Transition between different states produces (or absorbs) radiation, which can be observed to have a frequency ν, determined by the relation hν = Em – En , h being the Planck’s constant and Em and En the related energy levels of the atom. Formally the energy values and the characteristic wavefunctions are determined by breaking successively the infinite series solution of the Schrödinger equation (Laguerre polynomials). This is done be choosing certain values of E=En which certify omitting all higher order terms in the spatial variable and thus automatically eliminating unphysical solutions. The experimentally observed atomic spectra can be used to determine the energy levels of the atoms or molecules and to verify the soundress of the Schrödinger equation and its theoretical solutions. The systems of stars and galaxies as well as other cosmic objects in the universe could on a large scale be looked upon as a complex system of atoms and molecules, or even a fusion plasma state. Would it be possible to find some kind of differential equation, which could be used to describe in an average way the collective motion of all the objects in the universe, and to settle certain characteristic parameters in such an equation by 131

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comparing with results of experimental observations and physically realistic requirements? In fusion plasma physics the problems of particle transport and temperature conductivity, i.e. the essential phenomena controlling magnetic fusion plasma confinement, have been successfully described by specific forms of nonlinear partial differential equations (NL PDE’s) accounting for certain types of turbulence, e.g. so called temperature gradient induced drift wave turbulence which fixes the value of a power coefficient to a certain value in the equation. Could something similar be deviced for the cosmos and, if so, what would be the choice of requirements put on the equation to determine the free constants? An attempt to introduce such a procedure of collective description for the evolution of the universe has recently been made, using the experimentally established Hubble law (expansion velocity proportional to the distance) and the assumption that the universe expands without form-deformation [4.33]. An analysis based on these ideas (see Appendix) has led the author to determine the value of the exponent for the nonlinear diffusion in the NL PDE. It turns out to be directly proportional to the Hubble constant. An interesting result of the calculation is that it seems that the restriction that the universe may have a finite extension introduces a long-term correction to the Hubble law. The established proportionality of the expansion velocity with distance seems to need a modifying factor which would introduce an extra increase (or possibly decrease) with time and in the first case, correspond to an explosive evolution in a finite time. From a formal point of view it is interesting to notice that the quantity L(t), i.e. the scale length as a function of time, often used in the PDE calculations on hot fusion plasmas, [8.23– 8.26], [A3] and in Appendix now plays the role of the Einstein radius of curvature R(t) in our gravity formulae, indeed a new connection! 132

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The results obtained are not in contradiction with the possibilities of reversed evolution or even with the ideas about an oscillating universe, a «cosmic pendulum» [4.31]. Similar considerations have also been used [4.33] to describe the star (or galaxy) formation by gravitational contraction, limited by plasma formation and fusion burn. In this case a slightly different NL exponent is required than for the whole universe (corresponding to the limited more «local» phenomenon!). What is now the motivation for a formulation of the universal expansion problem in terms of the nonlinear partial differential equation (NL PDE). The connection of the NL PDE form with the Hubble law may, in fact, be considered as a particular «check point» for a more general property of the universe to behave like a nonlinear medium with response to perturbations of localized or large-scale nature. Such a nonlinear description may be said to give a formally extended and more unified description of the cosmos. It concerns the dynamics of all types of cosmic objects and provides a simple and conform view with an analytic background to what happens or could happen! Further experimental studies of cosmic objects and events as well as patterns of remote structures of galaxies and galactic clusters, remain to be done in order to confirm a nonlinear universal dependence of the type indicated above. In this context one should benefit from the impressive development of sofisticated new tools of astronomical observations like gravitational lensing and fiberoptic techniques, X-ray and neutrino detection as well as computer simulation methods. For more information on the new fascinating tools of observation and interpretation see sections 4.4.4.–4.4.6. Extensive results in nonlinear physics and in fusion plasma theory and laboratory experiments, recently described in a survey article by V V. Parail [4.32], might also give valuable support to the development of ideas about cosmic behaviour. It seems, in fact, that the more one penetrates into the matter the closer one finds that problems are related in cosmic and fusion laboratory plasmas (see also reference [4.15], 133

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particularly on Alfvén waves). Related questions are further discussed concerning the effects of gravitation in a recent paper by the author [4.33] and in the Appendix.

4.4.4 Neutrino astrophysics Fusion reactions create neutrinos (see section 2.1). The proof that nuclear burning is the energy source of the sun came from observations of solar neutrinos. Today these tiny particles, first predicted by Wolfgang Pauli in 1930 (NP 1945) are known to penetrate the universe in enormous amounts. We do not notice them even if thousands of billions of them penetrate us every second. The reason is that their influence on matter seems to be almost absent. We now know that in the universe the ratio between the abundance of neutrinos and nucleons, i.e. neutrons and protons, is exceedingly high, about one billion. We also know that most of the neutrinos reaching the Earth come from the sun [4.42]. In early days, when the discussion about the source of energy of the sun where very lively, it was believed that gravity was responsible. Such an hypothesis could however, not explain by orders of magnitude the estimated life-time, which we now know should be counted in billions of years. Sir Arthur Eddigton, in 1920, suggested that nuclear fusion was the energy source. It was by then known from experiments that a helium atom has less mass than four hydrogen atoms, and that large amounts of energy might be gained by fusion according to the Einstein relation E = mc2. In the experimental achievements of neutrino detection Raymond Davis jr was the great pioneer. In the early 1950’ ies he made laboratory investigations on neutrino capture by chlorine in a large tank and in 1955 [4.37]; [4.38] he estimated an upper limit for high energy neutrinos from the sun considering also the possibility of detecting solar neutrinos. It was the Italian physicist Bruno Pontecorvo who had proposed that it might be possible to detect a high-energy neutrino after 134

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reaction with chlorine, producing an argon nucleus and an electron [4.39, 4.40]. Davis continued his pioneering work and succeded in 1960 for the first time in history to prove the existence of neutrinos [4.38]. He placed a tank filled with 615 tonnes of common cleaning fluid tetracloroethylene in i gold mine in South Dakota in USA. He estimated a reaction rate corresponding to the creation of about 20 argon atomes a month produced by 20 neutrinos. Davis experiments were carried out almost continuously until 1994, [4.41]. The experimental results were always below the calculated ones, causing a «solar neutrino problem», a possible consequence of the assumption that the neutrinos were massless and left-handed. An explanation might be based on the assumption that the neutrinos could have different states, «flavour states», electron-, muon-, and taon-neutrinos, being combinations of mass eigenstates, with oscillations between the flavour states. The Davis results might then be explained, since solar electron-neutrinos might be lost by oscillations. Numerous investigations are on the way concerning the neutrino oscillations. Several new and larger detectors were constructed in the meanwhile. One of them by Masatoshi Koshiba, placed in a mine in Japan was an enormous tank filled with water. The Koshiba experiments were sensitive to the direction of incidence of the neutrinos and could also account for the time of the events. They were the first observations to prove that the neutrinos came from the sun [4.42]. The same detector enabled Koshiba and his group in February 1987 to observe a burst of neutrinos from a supernova explosion, denoted 1987 A in the Large Magellanic cloud [4.42; 4.45]. Most of the enormous amounts of energy released from a neutron star in a supernova explosion will be emitted as neutrinos, from 1987 about 1058 neutrinos. Of these Koshiba observed 12 of about 1016 estimated to have passed through his detector. In 1996 Koshiba constructed an even larger detector, and with this device neutrino production in the atmosphere has 135

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been observed. Particularly important is the indication of neutrino oscillations, allowing one kind of neutrino to change to another type. A consequence of this is that the neutrinos have a non-zero mass with important implications for the role that neutrinos play in the universe as well as for the Standard Model in elementary particle physics. It would also improve the interpretation of previous neutrino observations. The new discoveries have created a new field, neutrino astronomy, of utmost importance for not only astrophysics and cosmology but also for elementary particle physics; [4.53]. For their outstanding achievements the Nobel Prize in Physics for 2002 was awarded with one half jointly to: Raymond Davis Jr, Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, USA, and Masatoshi Koshiba, International Center for Elementary Particle Physics, University by of Tokyo, Japan «for pioneering contributions to astrophysics, in particular for the detection of cosmic neutrinos».The Nobel Prize in Physics for 2002 was awarded with the other half to Riccardo Giacconi, Associated Universities Inc. Washington DC, USA «for pioneering contributions to astrophysics, which have led to the discovery of cosmic X-ray sources» (see section 4.4.5), [4.56].

4.4.5 X-ray astrophysics In 1895 Wilhelm Röntgen (NP 1901) discovered the X-rays, which were rapidly introduced for experimental and practical use in physical and medical centres, where the discovery turned out to mean a real revolution. Astronomy had to wait a long time, more than 50 years, before X-rays could give any message about what happens outside the Earth or its atmosphere, which effectively prevents the radiation to penetrate. Rocket measurements of X-rays were done for the first time in 1949 by Herbert Friedman [4.46] and his group. Their investigations were limited to phenomena on the solar surface, such as prominences and other eruptions, as well as from the solar 136

THE EXPANDING UNIVERSE

corona, which has temperatures of several million degrees. In the late 1950’s Bruno Rossi took initiative to make a more extensive effort in the US by the aid of a young scientist Riccardo Giacconi, who designed a new type of X-ray telescope, to be used in rocket experiments [4.47]. The first measurements failed to detect X-rays from the moon, which might have been induced by solar radiation. Instead unexpectedly strong X-rays were noticed from a source at much larger distance by the rotating rocket. Also, an evenly distributed background X-ray radiation from the sky was an important result in the early measurements, which were a great challenge for continued research [4.48]. In fact, they have been said even to give an impetus to the development of X-ray astronomy. Identification of X-ray sources with objects oserved in visible light followed the improvement of the directivity of the observations. This led to discoveries of sources in the Scorpio (Scorpius X 1) and Swan constellations (Cygnus X 1, X 2 and X 3). Many of the stars detected were double-stars, were one star circles around another object which might be a neutron star or even a black hole. The rockets were followed by X-ray satellites and Giacconi was again the innovator. The first was launched in 1970 from a base in Kenya and extended appreciably the observation times. It’s sensitivity was ten times higher than that of the rockets and the results gathered in heaps [4.49]. After a couple of years Giacconi constructed a new X-ray telescope, which was launched in 1979 and was babtized the Einstein X-ray Observatory, providing improved sensitivity, so high that it was possible to record objects which were a million times weaker than Scorpius X 1. A continuous stream of new discoveries came along: Xray double stars, studied in great detail, some of them believed to contain black holes; ordinary stars where studied in detail for the first time using X-ray radiation, and at distances outside the Milky Way. Distant active galaxies were observed with high resolution as well as remnants of supernovas, and even the intergalactic domains in clusters of galaxies, in search for 137

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further information about dark matter and other universal novelties [4.52] All the time Giacconi, as it seems, worked on new constructions, so also in the period after 1976, and launched in 1999 another improved and larger X-ray observatory. It was babtized Chandra after Subrahmanyan Chandraseckhar (NP 1983), (see e.g. section 3.4 and the afterword), and continued the success of X-ray observations with extraordinary resolution, in space and also in time [4.54]. The astrophysical X-ray applications may turn out to mean a revolution, a gigantic success similar to what the applications of X-rays have meant to medicine [4.55]. One day in August 1981 I came to Varenna in northen Italy from Kiruna, situated north of the Arctic Circle in Sweden. The trip ended on a small shaking train from Milan, which went along the beautiful Como lake. In Kiruna there had been the inauguration of the European incoherent scatter facility (EISCAT), a device for studying the upper atmosphere in the auroral zone (see Afterword, p 121 in the 1st edition). Now my aim was to participate in the Varenna Course and workshop in Plasma Astrophysics. There, I had the opportuneity of meeting professor Hannes Alfvén and of discussing with him problems of the plasma universe [4.4, 4.5]. He took special interest in the filamentary structures of cosmic plasmas, such that are very often observed in coronal streamers and prominences in the solar atmosphere and in galactic clouds, most likely caused by electric currents [4.4]. Furthermore, Alfvén was anxious to emphasize the important role of X-ray and γ ray observations for the modern view of the universe, and that the rays observed derived mainly from magnetized plasmas. The emission of such rays was likely to be produced by electrons having energies higher than 100 eV, sometimes even much higher, billions of eV. He therefore liked to talk about the high-energy plasma universe, or simply the plasma universe [4.58]. He pointed out the high frequency observed in intensity variations – ten orders of magnitude faster at those high energies than we see in the visual universe [4.58]. 138

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During the workshop I had the opportuneity of meeting the late Professor Bruno Rossi who gave a survey talk on «Evolution of X-ray astronomy» [4.51]; the same man who in 1959 recuited the at that time 28 – years-old Riccardo Giacconi to build up a space-research program for a company that was to make it easier for young scientists to be supported by NASA. Together Rossi and Giacconi worked out principles for how an X-ray telescope should be constructed and Giacconi carried out rocket experiments and made unexpected discoveries from the universe: the beginning of X-ray astronomy followed by X-ray Sattellites and the Einstein and the Chandra Observatories, as mentioned above. I personally learnt from Bruno Rossi about X-ray astrophysics, particularly as we made long walkes in the neighbouring mountains on the week-ends. He told me about the unexpected rapidly repetitive bursts of radiation from compact X-ray sources, for which the explanation was an open question. At Chalmers we had studied three wave interaction (see section 7.3) rather intensively, and even predicted the occurence of repetitive nonlinearly phase-shifted and nonlinearly saturted explosive instabilities [7.5] causing sharp repetitive peaks. Since the requirements for such repetitive phenomena might be satisfied by an X-ray burst I asked Professor Rossi what he thought about such a possible explanation, and instantaneously he expressed a positive interest. Stimulated by this unexpected encouragement we tried to formulate a physical model for rapidly repetitive X-ray bursts when I came back home to Chalmers after the meeting. The model we suggested included the excitation of two electrostatic modes: one electroncyclotron mode and one lower-hybrid mode (mixed electron cyclotron and plasma mode), coupled to a pure electron plasma frequency mode, driven by the accretion flow. There seemed to be qualitative accordance with observations for a magnetic field of B ~ 2.1012 G and for a frequency of the emitted radiation of 139

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an order of magnitude down to a few keV. This led us to formulate a two page paper [4.53] on the question: Is the rapidly repetitive radiation from X-ray sources due to explosive three-wave interaction? by H. Wilhelmsson, LO Pekkari and D. Andersson, with an acknowledgement to Professor B. Rossi for information on observational results on X-ray astronomy during the Varenna meeting and with references [4.50] to R. Giacconi and R. Ruffini, and [4.51] to B. Rossi and his Varenna lecture: «Evolution of X-ray astronomy». The paper [4.53] was presented at the 1982 ICPP conference in Göteborg. Since then new observational results have accumulated. These indicate that a majority of the intensive X-ray sources are double stars. One of the two is a normal star that rotates at close distance around a neutron star (density of the order of 10 1015 g/cm 3). Gravitating matter is drawn out from the ordinary star and accelerated by the strong gravitational field from the neutron star, reaching very high energy. Then follows a deceleration caused by collisions between the atoms when they reach near the surface of the neutron star, under formation of a flat accretion disk in the presence of very high magnetic fields. The violent deceleration results in very strong X-ray emission. As Professor Giacconi told me last week in Stockholm it seems that for black holes (density of the order of 10 16 g/cm 3) the corresponding process would be so powerful and chaotic that the X-ray spectrum would have an entirely white noise structure! For neutron star matter the situation is different. What a pleasure to experience, more than 20 years after I met Professor Rossi in Varenna, that Professor Riccardo Giacconi was awarded a Nobel Prize in Physics in the year 2002 «for pioneering contributions to astrophysics, which have led to the discovery of cosmic X-ray sources» [4.56] and to meet him in person for the first time on the occasion of the Nobel ceremonies. 140

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4.4.6

Gravitational lensing as a tool for cosmological observations

Einstein had the idea, sketched in his note-books almost hundred years ago, to use the bending of light by gravitation (see section 3.2.4) for lensing effects. The idea is as simple as it is revolutionary. It provides a tool for studying the outer limits of the universe, and also to measure the weights of stars, galaxies and even the whole universe. Why not determine the characteristics of supernovas, neutrons stars, black holes and other dark matter in the universe in this way? It now seems just a matter of time, skill and work..! The gravitational lensing effect means that light from far-away galaxies can be observed as it is bent around galaxies that lie closer to us. These serve as lenses or combinations of distributed lenses. The amount of bending of the light provides information on the mass of the stars or galaxies that are closer to us. It also means that those galaxies, or cluster of galaxies, which are «near by» can be used to investigate very distant objects. Compare with some imagination the early optical instruments of Galilei 400 years ago and also the radioastronomical interferometers (M.Ryle, NP 1974) and the principale of holography (D.Gabor, NP 1971) The technique of measuring masses of nearby stars has been analyzed by the Norwegian scientist Sjur Refsdal. It has been witnessed [4.59] that Refsdal thereby suggested the first practical application of gravitational lensing in the cosmos already in the 1960’ies. He analyzed originally how a series of astronomic measurements to a gravitational lens could be used for determining the mass of the lens, and showed about 15 years before any gravitational lens system was imagined or selected, how the phenomena of gravitational lensing could be used for probing the universe, thereby pioneering this important field of astronomical observations. Detailed information on the background source as well as the lens can thus be obtained, indeed a great achievement, which is now generally referred to as the Refsdal Method, used in 1964 to determine the Hubble constant. The technique may be further developed e.g. for detailed studies of the dark matter in the Halo of the Milky way. 141

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Studies of the Hubble law (see [4.33] and Appendix) have important implications for the modeling of the universe with possible consequencies for the form of the Einstein general relativity equation. It has recently been argued [3.10, p 202] that the mass of our universe is by far not sufficient (only 20% of the necessary weight) to retain the universe from continued expansion («open universe»), whereas other opinions favour the contrary («closed» universe) or an intermediary «flat» universe. Nor has the Big Bang model full support from all scientists even if it exhibits many attractive features [4.57]. It seems as if the possibility of reversed motion after an initial expansion is still an open question [3.10, 4.31, 4.57, 4.33]. The gravitational lensing technique could clearly be expected to remain an important tool for answering fundamental questions in future astrophysical and cosmological studies [4.57]. References [4.1]

Alfvén H 1942 Existence of electromagnetic-hydrodynamic waves Nature 150 N° 3805 October 3 p.405

[4.2]

Alfvén H 1950 Cosmic Electrodynamics (Oxford University Press)

[4.3]

Alfvén H and Fälthammar C-G 1963 Cosmic Electrodynamics (Clarendon Press)

[4.4]

Alfvén H 1982 Paradigm transition in cosmic plasma physics Physica Scripta Vol T2/ 1 10

[4.5]

Alfvén H 1986 The plasma universe Physics Today September 22

[4.6]

Lundquist S 1949 Experimental demonstration of magnetohydrodynamic waves Nature 164 145

[4.7]

Lundquist S 1949 Experimental investigations of magnetohydrodynamic waves Phys. Rev. 76 1805 142

THE EXPANDING UNIVERSE

[4.8]

Åström E 1950 Magnetohydro-dynamic waves in a plasma Nature 165 1019

[4.9]

Åström E 1950 On waves in an ionized gas Ark. Fys. 2 443

[4.10]

Lehnert B 1954 Magneto-hydrodynamic waves in liquid sodium Phys. Rev. 94 815

[4.11]

Chandrasekhar S and Fermi E 1953 Magnetic fields in spiral arms Astroph. J. 118 113

[4.12]

Chandrasekhar S and Fermi E 1953 Problems of gravitational stability in the presence of a magnetic field Astroph. J 118 116

[4.13]

Chandrasekhar S 1961 Hydrodynamic and Hydromagnetic stability (Oxford University Press)

[4.14]

de Azevedo CA et al (Eds) 1995 Alfvén waves in cosmic and laboratory plasmas Proccedings of the international workshop on Alfvén waves Rio de Janeiro Brazil Physica Scripta T 60

[4.15]

Fälthammar C-G 1995 Hannes Alfvén Physica Scripta T 60 7

[4.16]

Shukla PK and Stenflo L 1995 Nonlinear Alfvén waves Physica Scripta T 60 32

[4.17]

Tajima T and Shibata K. 1997 Plasma Astrophysics (Addison Wesley )

[4.18]

Dawson JM, Bingham R and Shapiro VD 1997 X-rays from comet Hyakutake Plasma Phys. Control. Fusion 39 A 185

[4.19]

Levy DH 1995 The quest for comets (Oxford University Press)

[4.20]

Huebner WF ed (1990) Physics and Chemistry of Comets (Springer-Verlag, New-York)

[4.21]

Pécseli HL, Lybekk B, Trulsen J and Eriksson A 1997 Lower-hybrid wave cavities detected by instrumented spacecrafts Plasma Phys Control. Fusion 39 1227 143

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[4.22]

Bryant D 1999 Electron Acceleration in the Aurora and Beyond (IOP Publishing Bristol and Philadelphia)

[4.23]

Guérard S 2001 Van Gogh, peintre et astronome (Ca m’interésse Paris: Prisma Press) n° 248 page 64

[4.24]

Olson D and Doescher R 2001 Sky and Telescope Avril Vol 010 n° 4

[4.25]

Bailey M 1992 Vincent van Gogh Lettres illustrées (Paris: Herscher

[4.26]

Le Monde 2001, 24 March, pages 1,19,30 and 31

[4.27]

Oppenheimer JR and Volkoff GM 1939 On massive neutron cores Phys. Rev 55, 455

[4.28]

Gamow G and Landau L 1939 Condensed neutron cores (private communication, OEH Rydbeck)

[4.29]

Al-Khalili J 1999 Black holes Wormholes and Time Machines (Bristol:Institute of Physics Publishing).

[4.30]

Reeves H 1992 L’heure de s’enivrer; l’univers a-t’il un sens (Paris: Seuil)

[4.31]

Öpik EJ 1960 The oscillating universe (New-York: Mentor Books)

[4.32]

Parail W 2002 Energy and particle transport in plasmas with transport barriers Plasma Phys. Contr.Fusion 44 A63-A85

[4.33]

Wilhelmsson H 2002 Gravitational contraction and fusion plasma burn; universal expansion and the Hubble law Physica Scripta 66, 395

[4.34]

Bethe H, Chritchfield L 1938 Phys.Rev. 54, 248

[4.35]

Bethe H 1939 Phys. Rev 55, 434

[4.36]

Fowler W 1958 Astrophys. Journ.127 551

[4.37]

Davis R 1955 Phys. Rev. 97, 766

[4.38]

Davis R et al. 1968 Phys.Rev. Lett. 20 1205 144

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[4.39]

Pontecorvo B 1946 Chalk River Nat.Lab. Report PD – 205

[4.40]

Alvarez L 1949 University of California Rad. Lab. Report UCRL – 328

[4.41]

Cleveland B et al. 1998 Astrophys. Journ. 496, 505

[4.42]

Hirata K et al. 1987 Phys Rev. Lett. 58, 1490

[4.43]

Hirata K et al. 1988 Phys. Rev. D 38, 448

[4.44]

Koshiba M 1992 Phys.Reports 220, 229

[4.45]

Suzuki A 1994 Physics and Astrophysics of Neutrinos (Eds M Fukugita and A Suzuki p.388 (New York: Springer)

[4.46]

Friedman H, Lichtman SW, Byram ET 1951, Photon counter measurements of solar X-rays and extreme ultraviolet light, Phys.Rev. 83, 1025

[4.47]

Giacconi R, Rossi B 1960 A «telescope» for soft X-ray astronomy, J.Geophys. Res. Letters 65, 773

[4.48]

Giacconi R, Gursky H, Paolini F, Rossi B 1962 Evidence for X-rays from sources outside the solar system, Phys.Rev.Letters 9, 438

[4.49]

Giacconi R, Gursky H (eds) 1974 X-ray astronomy (Dortrecht, Holland/Boston, USA: D. Reidel Publ. Co)

[4.50]

Giacconi R and Ruffini R 1980 Physics and astrophysics of neutron stars and black holes (Amsterdam: North Holland Publ.Comp.).

[4.51]

Rossi B 1981 Evolution in X-ray astronomy Plasma Astrophysics Course and Workshop 27 August - 7 September 1981, Varenna (Como) Italy esa SP-161 pp.225-249

[4.52]

Tucker W, Giacconi R 1985 The X-ray universe (Harvard Univ. Press)

[4.53]

Wilhelmsson H, Pekkari L-O and Anderson D 1982 Is the rapidly repetitive radiation from X-ray sources due to explosive three wave interaction Physica Scripta Vol. T 2/1 271 145

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[4.54]

Tucker W, Tucker K 2001 Revealing the universe – the making of the Chandra X-ray Observatory (Harvard Univ. Press)

[4.55]

Gursky H, Ruffini R, Stella L (eds) 2000 Exploring the universe: A festschirft in honour of Riccardo Giacconi, Advanced series in Astrophysics and Cosmology, Vol: 13

[4.56]

Advanced information on the Nobel Prize in Physics 2002, The Royal Swedish Academy of Sciences: http://www.nobel..se/physics/laureates/2002/phyadv02.pdf

[4.57]

Gold AP 2001 News and views Nature 414, 591

[4.58]

Shukla PK and Stenflo L 2003 Dynamics of nonlinearly coupled upper-hybrid waves and modified Alfvén modes in a magnetized dusty plasma Phys. Plasmas 10, 45 72

[4.59]

Pokhotelov OA, Onishchenko OG, Sagdeev RZ, Balikhin MA and Stenflo L 2004 Parametric interaction of kinetic Alfvén waves with convective cells, J. Geoph. Res. 109, AO3305

[4.60]

Wilhelmsson H 2005 Alfvén waves Encyclopedia of Nonlinear Science (ed. Alwyn Scott. New York and London: Routledge)

.

146

Atmospheric lightnings and auroras are among the earliest manifestations of plasma phenomena observed in Nature. Considerable damage is caused every year due to lightning strikes. They could be disasterous to space crafts and have caused numerous accidents. Rockets and missiles leave jet plumes behind them, which might cause black-outs in signal processing and communication. It may be interesting to mention briefly some fruitful practical applications of plasmas [5.1, 5.11]. Among new and promising techniques can be mentioned plasma etching for microelectronic circuit production. Plasma screens based on controlled mini-lightnings of plasma on a square flat grid are about to introduce a revolution in TV and computer presentation. The free electron laser (FEL) [5.1–5.7] generates tunable electromagnetic radiation over wide wave-length domains by letting waves on relativistic electron beams interact with periodic magnetic structures. The FEL benefits from the coupling between longitudinal plasma oscillations and transverse electromagnetic waves, and can generate pulses of very high power radiation. The free-electron laser is an exceedingly interesting device both from the point of view of its technical applications and for demonstrating interesting physical processes. It exploits the whole spectrum of electromagnetic phenomena of relativistic 147

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beams in alternating magnetic fields, wave interactions, amplitude-and phase-dynamics of waves and particles under nonlinear conditions. A free-electron laser (or maser, for microwaves) operating with collective Raman scattering (cf. section 6.2) can produce 10-100 MW with beam currents of several KA. The reader is adviced to consult the book by MV Nezlin [5.1] and also [5.2] for further details on generation and amplication of electromagnetic waves by relativistic electron beams, a technique which has developed into real art. The frequency spread of the generated radiation by a free electron laser is generally quite large. It has been suggested by H Wilhelmsson [5.3] that this drawback might be remedied by using a system, where the FEL is interacting with an active molecular medium, for example a gas having inverted population. Such a system of a FEL and a gas laser has several interesting properties. Under favorable conditions the power output of the coupled system could for example be larger than the sum of the power outputs from the uncoupled elements of FEL and gas laser, as a consequence of nonlinear effects. Due to NL coupling the frequency spread shrinks and the gain of the system increases [5.5]. References [5.1]

Nezlin MV 1993 Physics of intense beams in plasmas (Bristol: IOP)

[5.2]

Wilhelmsson H 1962 Interaction between an obliquely incident plane electromagnetic wave and an electron beam in the presence of a static magnetic field of arbitrary strength, J. Res. Nat. Bureau of Standards D Vol 66 D, n° 4

[5.3]

Wilhelmsson H 1980 Resonant interaction between an active molecular medium and a free-electron laser Physica Scripta 22, 501

[5.4]

Stenflo L and Wilhelmsson H 1981 Radiation from a relativistic electron beam in a molecular medium due to 148

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parametric pumping by a strong electromagnetic wave. Phys.Rev A 24 1115 [5.5]

Wilhelmsson H, Gustavsson H-G, Stenflo L 1983 Generation of high power, very coherent radiation by interaction of a free electron laser with a molecular (or ionic) medium, Physica Scripta 28, 374

[5.6]

Guillory J and Wilhelmsson H 1983, Ionization effects in a system of a free electron laser and a molecular medium Physica Scripta 27 374

[5.7]

Marshall TC 1985 Free electron lasers (New-York: Macmillan Publ.)

[5.8]

Wilhelmsson H 1991 Double-beam free electron laser Physica Scripta 44, 603

[5.9]

Klimontovich Yu L, Wilhelmsson H, Yakimenko IP and Zagorodny AG 1990 Statistical theory of plasma-molecular systems (223 pages, in Russian (Moscow: Moscow University Press): also 1989 Physics Reports 175 264-401 (in English)

[5.10]

Davidova I A and Wilhelmsson H 1992 Resonant and nonresonant wave excitation in a double beam free electron laser Physica Scripta 45 184

[5.11]

Root JR 2001/2 Industrial plasma engineering Volumes I-III (Bristol:IOP)

[5.12]

Bradu P 1999 l’Univers des Plasmas. Du big bang aux technologies du IIIe millénaire (Paris: Flammarion)

[5.13]

Stenflo L and Yu MY 1998 Plasma oscillons in spherically bounded magnetized plasmas Phys Plasmas 5 3122

[5.14]

Kapitza PL and Dirac PAM 1933 Proc. Cambridge Phil. Soc 29, 297

[5.15]

Rebut PH 1999 L’energie des Etoiles La fusion nucléaire controlée (Paris: Editions Odile Jacob) 149

The implosion of matter to achieve confinement for a short period of time, by means of pulses of laser radiation, is a challenging task. Conceptually, the compression of the pellets resembles not so little what happens out in the cosmos, where stars contract or where matter is collapsing in a black hole. Astrophysical systems could now be simulated in the laboratory as a result of the extraordinary power of highintensity lasers. Laboratory investigations on the magnetohydrodynamics of supernovas and radiative properties of stars and nebulae can be performed for the first time. So far, the conditions now available could previously only be obtained out in the cosmos. Thanks to new high-power, ultra-short laser technology [6.6, 6.13, 6.21, 6.26, 6.28] a new link with the physics of the cosmos has been established.

6.1 The principle of inertial confinement The idea of using micro-balloon explosions to produce fusion energy relies on the inertia of imploding targets to provide confinement. The targets are usually small spherical microballoons filled with tritium-deuterium (D-T) gas (1 mg/cm3 ). The inner part of the small pellet contains the main fuel D-T region surrounded by an ablator. When energy is supplied 150

THE PRINCIPLE OF INERTIAL CONFINEMENT

from a deriving laser the ablator heats up and expands, forcing the rest of the shell to contract inward to conserve momentum. Inertial confinement fusion uses pulsed high power lasers or ion beams as drivers. The pulses have to be so strong and short that the target does not have time to expand during the period of fusion production. The confinement time is so short, less than 10–10 s, that light does not propagate more than 1cm over the course of the explosion. The particle density in the central region, where the fusion reactions occur (radius less than a tenth of a millimetre) is extremely high at 1025 cm–3, [6.1]. The fusion reactions begin in the central part of the pellet which contains a few per cent of the D-T fuel and propagates as a fusion burn-front in the rest of the fuel to complete the process. The details of the implosion are important for the efficient operation of the fusion burn. To avoid hydrodynamic instabilities restrictions must be observed concerning the minimum pressure (100 megabars) and irradiance (1015 W/cm2 ) during the pulse. Other effects like the symmetry of the implosion are also important for the ignition.

6.2 Instabilities Hydromagnetic instabilities of e.g. Rayleigh-Taylor and KelvinHelmholz type may occur in the fuel when domains of different densities meet each other. In the nonlinear regime interaction between modes may lead to turbulence, which is studied intensively using numerical simulation methods. Parametric instabilities may occur when laser radiation interacts with the natural modes of oscillation the plasma .Nonlinear coupling with ion sound waves may generate stimulated Brillouin scattering and be accompanied by filamentation of the plasma, whereas interaction with electron plasma waves may result in stimulated Raman scattering. It may be interesting to mention that similar phenomena have been observed when high-power radio waves interact with the plasma in the ionosphere which surrounds the Earth; 151

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experiments have been carried out in the north polar region in connection with observations by means of the European. Incoherent Scatter Facility (Kiruna, Tromsø ).

6.3 The concepts of direct and indirect drive There are two different paths which have been developed for coupling the energy from the driver to the target: one is known as direct drive, the other as indirect drive. For direct drive the laser beam or ion beam is incident directly on the fusion target pellet. Indirect drive is characterized by the laser or ion beam first being absorbed in a «hohlraum», an enclosure of high atomic number surrounding the pellet. X-rays are then produced which act as driver for the implosion. Each type of driver has its advantages and its drawbacks. Direct drive transfers the energy directly to the pellet but is sensitive to the spatial quality of the radiating beams, whereas indirect drive is less sensitive in this respect and has the advantage that the implosion becomes hydrodynamically less unstable. Indirect drive is, on the contrary, more sensitive to laser-driven parametric instabilities, which may be generated in the plasma produced by the X-rays.[6.2–6.3] Active research has resulted in detailed knowledge about the requirements for efficient operation of directly [6.4] and indirectly driven inertial confinement fusion.

6.4 Laser fusion Large facilities like the Livermore experiments have used neodymium-glass lasers producing 1.05 µm radiation, which is commonly converted to 0.35 µm at the third harmonic to minimize instabilities from laser-plasma interaction. Experimental results from the Livermore Nova using indirect drive show excellent agrement with predictions from sophisticated numerical simulations of neutron yield, ion temperature and fuel density. 152

LASER FUSION

Direct drive experiments have also shown considerable progress in many laboratories all over the world. A fusion power plant based on inertial confinement consists of the following parts, namely: a driver, (laser or particle accelerator providing the fusion target with energy), a target factory, (manufacturing the targets and filling them with D-T fuel), a reactor, (the base for fusion energy generation by microexplosions) and a generator, (producing electricity from thermal energy). The inertially confined plasma stays for only an extremly short time in a burning state (10–10 s) and is very small (10–2 cm) [6.5]. The repetition rate of pulses from the driver is a few pulses per second. The repetition pulse rate can be varied as can the yield of the target. This is advantageous since in development tests the experiments can also be carried out at moderate cost by using lower powers. The targets should be prepared with a high surface finish to obtain high gain. The requirement is less for indirect drive. The targets are prepared in special drop towers which can produce hundreds of drops per second with nearly perfect spherical shells. Sophisticated techniques are developed for filling the drops with D-T fuel, using for example diffusion filling in high-pressure chambers. There are several attractive features which make inertial confinement fusion a worthwhile option to consider for a future energy producing plant. Development of megajoule lasers for experiments and tests of ignition and gain in reactor-size devices would be useful in this respect The progress of advanced research in recent years has led to plans for constructing megajoule lasers for future inertial confinement experiments. Defence applications have been a driving force for the large Mégajoule laser-fusion project now under way in Bordeaux. After years of constructive debate, during the Mitterand-Balladur regime in French politics, economic support 153

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was released by the French government to create a machine in the several billion euros (or tens of billion french francs) range. In 1995 after the end of the French nuclear explosions at Mururoa in the Pacific Ocean President Jacques Chirac himself said that the construction of the huge Magajoule laser laboratory in Bordeaux would make such tests a thing of the past. The technique of short-pulse laser radiation has advanced considerably in recent years. It has become routine to produce 10TW pulses and to focus them to 1020 W/cm2. As a result of the high power, a terawatt pulse in a plasma may produce selfchanneling and excite ultrastrong (hundred gigavolt per meter) longitudinal electric fields and multimegagauss (100 MG) magnetic fields in the wake of the propagating pulse! Not only may the electronic component be excited but also ion currents of the order of mega-amperes with ion energies of the order of 150 keV may be generated. Such energies are of interest in fusion, as the resonance peak in the cross-section of D-T reactions happens to be not far away from this value. Selfgenerated 100 MG magnetic fields could pinch relativistic electrons causing laser filamentation and self-focussing. New possibilities for simulating astrophysical systems in the laboratory are being opened up by the extraordinary power of the high-intensity lasers. For the first time laboratory investigations of the magneto-hydrodynamics of supernovas and of the radiative properties of stars and nebulae could be made under conditions which were hither to only to be found out in the cosmos. Densities and temperatures corresponding to those of stellar interiors may be achieved in the laboratory with high-power lasers and used for studies of opacity of dense matter. Relativistic astrophysical plasmas may, furthermore, be simulated with ultra-short pulse lasers. Phase-transition of ultradense hydrogen under high pressures, e.g. metallisation or magnetization, may occur in the interiors of stars and planets and may be basic mechanisms in the formation of supernovas. There are indeed many fascinating possibilities for discovery using high-power and ultra-short pulse laser technologies. They 154

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open up a new field of research - a new link with the physics of the cosmos.[6.6–6.28].

6.5 Ion beam drivers Ion beam drivers use short beam pulses from either light-ion or heavy-ion accelerators to drive the fusion target, and a variety of pulsed power techniques have been developed for each type of acceleration. It turns out that heavy-ion accelerators offer particular advantages such as high-rate pulse production and reliability. Certain ions like xenon, cesium and bismuth accelerated to some GeV are well suited for absorption infusion targets. For singly charged ions a current of about 100 k A is needed to obtain the required power of 1014–1015 W. Experiments using either radiofrequency accelerators or induction accelerators are performed to obtain such high powers with beams of required brightness. The beam intensity needed to convert the accelerated beam. energy to x-rays in indirect drive targets is about 1015 W/cm2 The focal spot should be no larger than some millimeters, which requires a spread of less than 1% in the longitudinal momentum of the beam. More experiments are needed, possibly with megajoule drivers, to provide a base for future reactor development. With regard to the targets there are many features common to the x-ray production in indirect drive experiments by lasers and by ion-beams. Heavy-ion drivers are attractive because of the high energy loss of the ions with distance of penetration into matter. To the lowest order this loss is proportional to Z2, where Z denotes the ion charge state. According to the principle of indirect drive the heavy ion beam is stopped in the converter, where its kinetic energy is transformed into x-ray radiation. The x-rays propagate through the «hohlraum» and drive the fusion target isotropically.

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Figure 6.1. Explosive cannon balls («cotombrots») ejected from cannons. Drawing by Leonardo da Vinci (Codex Atlanticus 1502 )

The interaction of the heavy ions and matter, which produces a hot plasma state of solid material density, is a complicated area. Recent measurements and simulations show deviations from the predictions of linear theory. Particle in cell (PIC) simulations made 1997 indicate that nonlinear screening of the free electrons causes the observed weakening of the stopping power. A full understanding of related problems is important for target design, a crucial point in inertial confinement fusion. Leonardo da Vinci constructed cannon balls which appear in the drawing (figure 6.1). He gave them the strange name «Cotombrots»; they were half a foot wide, and full of small projectiles producing the most disasterous effects when thrown among the enemies. References [6.1]

Lindl JD, Mc Crory RL and Campbell EM 1992 Progress toward ignition and burn propagation in inertial confinement fusion Phys. Today September 32

[6.2]

Kruer WL 1988 The physics of laser plasma interactions (Addison-Wesley, Redwood City) 156

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[6.3]

Baldis HA and Labaure C 1997 Interplay between parametric instabilities in the context of inertial confinement fusion Plasma Phys. Control Fusion 39 A51

[6.4]

Nishimura H 1997 High-convergence uniform implosion of fusion pellets with the new GEKKO laser Plasma Phys. Control . Fusion 39 A401.

[6.5]

Hogan WJ, Bangerter R and Kulcinski GL 1992 Energy from inertial fusion Phys Today September 42

[6.6]

Mourou GA, Barty CPJ and Perry MD 1998 Ultrahighintensity lasers: physics of the extreme on a tabletop Phys Today January 1998

[6.7]

Lontano M, Mourou G, Pegoraro F and Sindoni E. Eds 1998 Superstrong fields in plasmas, First International Conference, Varenna, Italy August-September 1997, AIP Conference Proc. 426 (Woodbury, New-York)

[6.8]

Siegman AE 1986 Lasers (Mill Valley, CA: University Science Books)

[6.9]

Silfvast WT 1995 Lasers Handbook of Optics, Fundamentals, Techniques & Design 2 nd edit. Chapter 11 p. 1-39 (McGraw Hill, Inc)

[6.10]

Tsytovich VN, Stenflo L, Wilhelmsson H, Gustavsson H-G, and Östberg K 1973, One-dimensional model for nonlinear reflection of laser radiation by an inhomogeneous plasma layer, Physica Scripta 7, 241

[6.11]

Gurevich A, Anderson D and Wilhelmsson H 1979 Ion acceleration in an expanding rarified plasma with nonMaxwellian electrons, Phys. Rev. Lett 42, 769

[6.12]

Wilhelmsson H 1989 Self-formation and evolution of singletons, Intern.J of Quantum Chemistry, 35, 887

[6.13]

Svanberg S 1998 High-power lasers and their applications, Advances in Quantum Chemistry 30 209-233 157

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[6.14]

Lontano M 1997 Interaction of short super-intense laser pulses with dense gases and plasmas, Proc. Journées Maxwell ’97, Bordeaux (May 97) JF Eloy, edt, Annales des Journées Maxwell’97, p.91-103 (Le Barp, France: CEA/CESTA )

[6.15]

Wilhelmsson H, Trombert J-H and Eloy J-F 1995 Dispersive and dissipative medium response to an ultra-short pulse: a Green’s function approach Physica Scripta 52 102

[6.16]

Wilhelmsson H, Trombert J-H and Eloy J-F 1995 Critical damping of wake-field oscillations in a dispersive and dissipative medium: influence of nonlinearity Physica Scripta 52 218

[6.17]

Wilhelmsson H, Trombert J-H and Eloy J-F 1996 Utrashort pulse propagation in a magnetized plasma Physica Scripta 54 305

[6.18]

Eloy J-F and Wilhelmsson H 1996, New principle of X-ray diagnostics of plasma by applying an ultra-short pulse excitation, Proc. of Progress in Electromagnetics Research Symposium, PIERS’96, Innsbruck, Austria

[6.19]

Eloy J-F and Wilhelmsson H 1997 Response of a bounded plasma to ultra-short pulse excitation, Physica Scripta 55 475

[6.20]

Eloy J-F, Gerbe V, Trombert J-H and Wilhelmsson H 1998 Experimental setup with optoelectronically pulsed antenna for giga/terahertz spectoscopy 1998 IEEE Trans. Inst. Measurements IM 47 453

[6.21]

Eloy J-F (Ed) 2001 Ultrashort Electromagnetic Pulse Science, Technology and Measurement Measurement Science and Technology Journal Vol 12, N° 11, Nov p.1747-2002

[6.22]

Eloy J-F 2001 Ultra-short Electromagnetic Pulse Technology (London and Paris: Hermes Penton Science)

[6.23]

Yamanaka C 2000 The prospect of laser fusion energy Proceedings of I st Int.Conf. on Inertial Fusion Sciences and 158

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Applications’99, Femtosecond Laser Interactions and Fast Ignition, IFSA’99, Bordeaux, France (12-17 Sept.-99), A Migus, EM Campbell and K.Mima, edts. p.19-31 (Elsevier Publ.) [6.24]

Cattani F, Kim A, Anderson D and Lisak M 2001 Multifilament structures in relativistic self-focusing Phys. Rev. E 64 016412

[6.25]

Tushentsov M, Kim A, Cattani F, Anderson D and Lisak M 2001 Electromagnetic energy penetration in the self-induced transparency regime of relativistic laser-plasma interactions Phys. Rev. Lett. 87 275002

[6.26]

Chen, P. 2002 Laboratory astrophysics using high intensity particle and photon beams. In: Superstrong Fields in Plasmas (Varenna, Italy 2001) Editors: Lontano,M, Mourou, G.,Svelto, O. & Tajima T. Melville, New York. AIP Conference Proceedings, Vol 611: 375

[6.27]

Pfalzner Susanne 2005 Inertial confinement fusion (Bristol: IOP publ)

[6.28]

Eliezer S 2002 The interaction of high-power lasers with plasmas (Bristol: IOP publ)

159

The way in which the plasma forms certain preferred shapes, and tends to remain in those shapes has sometimes been referred to as profile consistency [7.30].This tendency may be considered as an example of the means by which plasmas exploit their inherent complex features to produce particular forms or structures in the presence of the confining magnetic field. The parameters which account for particle and heat transport in the fusion plasma, i.e. the particle diffusion and the heat conductivity parameters, depend on phenomena, which may be called by the common name as dynamic fine structure of the plasma. Global dynamics of the fusion plasma, i.e. the macrobehaviour, will generally be described by a coupled system of nonlinear partial differential equations for temperature and density, which can be studied by analycal or simulation methods. The results will give information on equilibria and stability of the plasma [7.12, 7.13, 7.25, 7.30].

7.1 Waves and instabilities Why is it that the field of waves and instabilities has constantly attracted such great interest since the very beginning of fusion plasma research? One reason is that these phenomena may have very important consequences for the behaviour of fusion 160

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plasmas, and another that they offer many challenging basic scientific problems a scientific. A fusion plasma can carry a large variety of different types of waves, such as plasma waves, electromagnetic waves, ioncyclotron waves, electron-cyclotron waves, hybrid waves, magnetoacoustic waves, magnetohydrodynamic waves (Alfvén waves) etc [7.1]. From a practical point of view, certain waves are particulary important because heating of the plasma to high temperatures by external sources can be achieved by exciting the plasma at certain frequencies which are characteristic of the particular waves. As examples the low-frequency ion-cyclotron waves or high-frequency electron-cyclotron waves can be used for this purpose, the excitation frequencies being determined by the magnetic field and the masses of the particles. For hybrid waves the frequency depends on a combination of the ion and electron masses. Such waves are also candidates for practical heating of the plasma, as are Alfvén waves, low-frequency waves whose properties depend on the magnetic field and the density of the plasma. In fact, the properties of Alfvén waves can be deduced by proper modelling of this type of wave in terms of a mechanical analogy, namely a vibrating string. The mass and tension of the string, in this analogy, would play the rôle of the density and the magnetic field in the plasma. Such low-frequency waves are variously called magnetohydrodynamic (MHD), hydromagnetic or Alfvén waves. They have many interesting properties; a basic one is that in the associated motion of the charged particles, the perpendicular velocity component with regard to the magnetostatic field is approximately the same for the ions and electrons, in spite of their very different masses. As a consequence, the gas moves essentially as a whole in its motion across the magnetic field. The essence of the magneto-hydrodynamic phenomena can be traced back to the following situation: if an electrically conductive gas (a plasma) or liquid moves in a magnetic field an interaction between the magnetic field and the electric 161

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currents occurs which affects the motions of the gas or the liquid and also the magnetic field. Accordingly a coupling will be established between the magnetic and hydrodynamic phenomena thus the name magnetohydrodynamic phenomena. The Swedish scientist Hannes Alfvén received the Nobel prize physics in 1970 for his work in the field of magnetohydrodynamics. These phenomena are of vast astrophysical interest and have important consequences for laboratory plasmas. Certain phenomena like sun spots, which can be seen occasionally by the naked eye as dark regions on the solar surface, may be explained, at least partly, by the assumption that Alfvén waves are created by perturbations in the central parts of the sun and propagate to the solar surface where the spots are formed. Other characteristic types of wave, plasma waves, which may be regarded as electro-elastic types of waves are fundamental in plasmas and are of interest also in plasma diagnostics. These waves are longitudinal in nature, i.e. the particle oscillations occur in the direction of the wave motion. The way in which electromagnetic waves propagate in plasmas has important consequences for communication technology. Radio waves are scattered by the ionosphere, the electron plasma surrounding the Earth, and propagate around the Earth as a result of scattering. Electromagnetic waves, microwaves of centimetre to millimetre wave-lengths, can be used to probe fusion plasmas to determine their spatial density distribution. Such waves are transverse waves, i.e. the particle oscillations are transverse (or perpendicular) to the direction of propagation of the waves. When propagating in a plasma there are, affected by the presence of a magnetic field. If the plasma density in a certain region is high enough, i.e. if the plasma frequency ν, is greater than the frequency of the wave, then the wave can not propagate further but becomes reflected. Phenomena of this type cause interruptions to radio communications, for example when space-craft enter and ionize the Earth’s atmosphere. 162

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Figure 7.1. Waves entering shallow water Drawing by Leonardo da Vinci (Codex Madrid II 1503)

Figure 7.2. Leonardo da Vinci: Betleém’s star, drawing probably around 1480 (Windsor, Royal Library) 163

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Figure 7.3. Leonardo da Vinci: Graphical reconstruction from mural painting in Sforza Castel in Milano: Symbolic vegetative patterns (complex nonlinear structures), 1498

Among Nature’s elements none caught the interest of Leonardo da Vinci more than water. His note-books are full of sketches of waves. He studied how waves form, how they turn and whirl and create bubbles. With the same precision he drew or painted waves in human hair as in the water on the sea. The waves that he studied on the shore he connected with the motion of the wings of a bird or the breathing in a person. He devoted a lot of interest to the waves entering shallow water and becoming reflected on the shore. He made sketches of flowers and of terrifying scenes of cataclysms, i.e. the end of the world, in the same devoted way. His cataclysms resemble many active solar spots.

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Figure 7.4. Aerodynamically shaped projectiles with directional wings. Drawing by Leonardo da Vinci (Codex Arundel 1502)

He constructed artificial wings after watching the motions of flying birds, and he designed projectiles which were aerodynamically shaped and had directional wings which made them seem like modern rockets or precursors of the space age. (figure 7.4). Instabilities of waves or other perturbations may occur as self-amplifying phenomena in plasmas. They have been investigated extensively with regard to various configurations and conditions of and with regard to different kinds of wave oscillation. Such instabilities show a tendency to develop when the plasma possesses some kind of free energy, which it would 165

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prefer to get rid of and transfer to wave motion. The origin of such free energy could be an inhomogeneity in the plasma density or temperature or magnetic field. Such inhomogeneities almost always exist. The free energy could also be associated with a beam of electrons penetrating a plasma. Instabilities may affect the plasma configuration negatively and even spoil the confinement completely. An example of an instability which could have disastrous effects is one that could occur in a tokamak torus is the current in a plasma were to be driven by magnetic induction to such high values that the magnetic poloidal field became too strong for the plasma torus to be kept together causing it to break into wiggles. In limiting the plasma current to avoid the risk of such instabilities one also limits the heating due to plasma resistance, ohmic heating. Nonlinear effects are important for waves and instablilites. Nonlinearities may saturate instabilities but they can also cause or enhance instabilities. We discuss these in the next section.

7.2 Nonlinear effects For a long time nonlinear effects were considered as small corrections to the linear response of a medium to some kind of influence. It was considered natural that when an electric voltage was applied to a wire it would cause a current proportional to the voltage. Or when an electromagnetic wave launched into a medium, for example a plasma, the wave penetrating the medium, and also the reflected wave would have amplitudes, proportional to the amplitude of the incident wave. The waves should also have the same frequency. The response was always proportional to the primary source, i.e. to the voltage or the amplitude of the incident wave as long as the source was weak. For strong sources, i.e. above a certain threshold power, things change and new interesting phenomena may occur. The medium starts to react nonlinearly.[7.2–7.5]. The nonlinear response can then become larger even than the 166

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linear one, and dominate the situation. Nonlinear phenomena are becoming of growing interest in science. Historically, nonlinearities were noticed in the 1920s in the field of chemistry. At present they are studied extensively in connection with biological problems and in several fields of physics, notably in laser and plasma physics. From a mathematical point of view important developments have occurred, starting from the early work of Volterra who studied the oscillations of nonlinearly coupled systems, namely the abundance of fishes in the Adreatic sea! Milestones in nonlinear theory are the contributions of Fermi, Ulam and Pasta in 1955 on thermalization of nonlinear vibrations in a chain of periodically situated particles between which linear and quadratic forces operate [7.23], and related work by Zabusky and Kruskal in 1965 on solitons [7.24], i.e. spatially bell-shaped distributions of exceptional stability governed by the mutual influence of two phenomena: nonlinearity and dispersion. During the last decades considerable efforts have been devoted to studies of selforganization in non equilibium systems and dynamics of synergetic systems, and to the problem of chaos, for which modern computer simulation has become an essential tool. In Japanese art Hokusai (1760-1849) was one of the great masters. «The wave» one of the etchings in the suite entitled: Thirty-six views of mount Fuji is a grandiose demonstration of wave-breaking, i.e. the nonlinear effect, where the amplitude of a wave becomes so high that the top of the wave splits into separate filamentations and bubbles. The impression of the force of the wave is enhanced by the design, in which the wave, seen in the foreground, takes up an area of the design which dominates mount Fuji seen at a distance. I was told by Japanese scientists that in his lifetime Hosukai lived in about a hundred places in Japan, that he gave away everything he could spare and that he was known as a very happy man. One cannot help comparing him with creative people of our time! [see Plate 12]. In the early 1960s the principle of light amplification by stimulated emission of radiation, the laser, was discovered. It 167

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meant that high power of coherent light could be concentrated in small domains in space and also in short intervals of time. Excellent conditions for research on nonlinear effects were suddenly provided. The field of nonlinear research really exploded with the advent of the laser. The need for basic understanding of nonlinear phenomena became particulary pronounced when high power laser projects started in the US and USSR, and also in Japan, accompanied by research on laser-fusion, i.e. attemps to produce fusion reactions by microballoon explosions caused by laser pulses. Nonlinear effects were particularly important for the coupling of the laser pulse with the microballoon (pellet) and for making diagnostics of the pellet plasma. For the diagnostics of fine structure phenomena and chaotic behaviour of plasmas the use of ultrashort pulse techniques seems to become a interesting future possibility. Nonlinear effects in plasmas have been studied intensively since the early 1960s when large magnetic fusion experiments also started to be constructed. The field of reaction-diffusion problems, i.e. studies where reaction and diffusion processes occur simultaneously, and which are therefore governed by two phenomena: nonlinearity and diffusion (which is generally also nonlinear), has recently attracted considerable attention. Numerous applications of the reaction-diffusion phenomena are found in modern science, for example in fusion plasma physics, where the evolution of a burning fusion plasma is governed essentially by nonlinear diffusion and by alpha particle heating. The problems of heat and particle transport and of magnetic confinement in toroidal devices are key questions for the realization of a future fusion reactor. [7.6–7.13].

7.3 Three-wave interaction If three waves are present simultaneously in a medium, all of them sufficiently intense that each one experiences the presence 168

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of the two others, interesting things may happen. One obtains a three-waves interaction. From a nonlinear point of view the phenomenon is a particulary interesting one for the following reasons: firstly, it is complex enough to exhibit features which it may have in common with more general systems, where many waves interact, like a plasma turbulence; and secondly, it is sufficiently simple from an analytic point of view that it can be solved exactly, [7.5]. There are many different types of waves which may occur in plasmas, some closely related to the motion of the electrons, some to the motion of the much heavier ions, some determined by the presence of a magnetic field, like ionor electron-cyclotron waves; others may be electromagnetic waves etc... Therefore, it might be possible to excite a wide spectrum of waves from low frequencies to high frequencies, all fulfilling an equation of the medium, relating the wave-lenght to the frequency of the medium, the so called dispersion relation. When two waves interact to form a new wave not only the primary waves but also the produced wave should be natural waves of the medium. This means a strong selection of the possible ways of coupling. Only the right selection gives what is named a resonant interaction with a possibly strong excitation of the new wave. It should be remembered here that we are discussing nonlinear interaction of the simplest type where the excitation of each wave depends on the product of the two other waves. It is easy to imagine a simple mechanical analogy to resonant coupling. If a plate or membrane is exposed to two sources of vibrations of different frequencies a mutual coupling of these perturbations may occur. Only if the sum (or difference) frequency coincides with another natural frequency of the plate may the coupling have a noticible effect as a result of resonant interaction. The same may apply to the rotating tyres of a car, which has been tested by holography! When lasers became available in the early 1960s beautiful experiments were carried out on resonant three-wave 169

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interaction. An experiment was done in a bi-refrigent crystal which demonstrated that resonant coupling could occur only on the surface of a cone, where the matching conditions for the frequencies and wave numbers were fulfilled. The result was a beautiful luminescent conical surface in agreement with theory. Similar experiments have been performed in magnetized plasmas in the microwave domain of the spectrum. It turns out that three-wave interaction can be an unstable process, a simple example of nonlinear instability. A necessary condition for this to happen can be shown to be that the medium, for example the plasma processes free energy. This is, the case when a plasma is penetrated by an electron beam having kinetic energy. Such a combined plasma and an electron beam medium has also the interesting property that one of the three interacting waves carries negative wave energy. This means that the total wave energy (mechanical plus electromagnetic) counted per unit volume of the medium is lower in the presence of the wave than in the absence of the wave. The concept of negative wave energy has no practical sense, except when other waves are present simultaneously, which carry positive wave energy. Since this is, in fact, the case for the other two waves in the three wave interaction considered, a most extraordinary phenomenon may occur, namely that all three waves grow in amplitude simultaneously and conserve the total wave energy of the three waves in the process of growth. It turns out that the process will be an explosive three-wave interaction. All the three waves will grow explosively together to approach exceedingly high values in a finite time. A mechanical, or rather acoustical analogue, may illustrate the unstable three-wave process. Suppose that two people are getting into serious conversation and their voices are increasing in amplitude. A third person who has taken interest in the conversation wants to join the discussion. To be noticed he has to speak up loudly. This causes the others to raise their voices even more, each of them defending their opinions vis-a-vis the others, and so on, the state reaching a possibly violent collapse in a finite time! 170

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Other cases of three wave interaction may not be of the explosive type. However, it has been demonstrated that such cases may lead to other interesting situations. Imagine that one wave has linear growth (i.e. for small amplitudes), and that the two other waves are linearly damped. It turns out that if the linear growth is considerably higher than the damping, a chaotic behaviour of the system is caused as a result of the competition between the nonlinearly coupled waves, and the solution breaks into numerous new branches. The examples given here may illustrate how simple nonlinear processes may have rather remarkable effects. The dynamics of fusion plasma is governed by a set of competing processes. The change in temperature of the plasma depends on the heating from the fusion reactions, and from the other auxiliary heating processes; it depends on the heat conduction, and losses, all these processes being of nonlinear nature. They may help to set up a stable state by balancing each other, but they could also hinder the establishment of such a state were it not for the presence of the confining magnetic field and for the influence of the boundaries. In fact, even the simplest forms of reaction-diffusion equations show tendencies to self-formation, corresponding to self-organization in more complex structures, and of pattern formation as in biological and chemical systems. Profile consistency may be regarded as a consequence of such tendencies in a fusion plasma [7.25, 7.30].

7.4 Evolution of populations: explosive instabilities The problem of evolution of populations plays an important rôle in physics, chemistry, biology and several other fields of science. Studies of related questions generally lead to systems of coupled nonlinear differential equations, which are most often handled by computer analysis. 171

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A simple example could be mentioned here, which in spite of its simplicity has important consequences. It expresses how the change of a dynamic variable, let us say u, for example the density or temperature of a medium, per unit time is proportional to u squared which results in the interesting dependence of the variable on time, namely that the variable increases steadily towards very high, in fact infinite values within a finite time [7.14]. The time-dependence, therefore has an explosive trend. It might be an interesting exercise: prove that the sigular behaviour is described by (t0 –t)–I where t0 is the time of explosion. The time it takes for the variable (the temperature or density) to reach infinitely high values is shorter the larger the initial value and the stronger the nonlinear coupling is (Again readers may like to prove this statement for themselves). It has been suggested that the observed explosive increase in field energies and temperature of solar flares (pulses of hard x-rays, prompt gamma-ray lines and microwaves, simultaneous and similar in shape) is caused by current loop coalescence of two magnetic islands. As a result the magnetic field energy, which is proportional to the strengh of the field squared, the electrostatic energy, proportional to the electric field strengh squared and the temperature T all diverge explosively as a function of time [5.17]. Since the quadratic term u2 may be interpreted as a natural source term for the growth of population n (compare a sink term - ne ni for the recombination of electrons and ions in a plasma, or - ne2 for ni = ne ) it seems tempting to make some comparisons with empirical data, and possibly some predictions for the future. Empirical data for several hundreds of years show that the increase in the human population fits closely to an evolution of the explosive type. In fact the drastic increase in our population during the last decades has followed astonishingly well the predictions of a simple equation with a quadratic term, accounting for the simultaneous death-rate separately by a linear term, [7.15]. 172

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The prediction of the theory would be that, if there is no drastic change in the trend of evolution, extremely high values will soon be expected in the world population. According to United Nations estimates the world population which is today 6 billions might reach much higher values in a few decades. The asymptotic infinity is estimated to occur in the third decade of the 21st century. The only efficient way to prevent an explosion of population seems to be to control the source term, thus making the parameter a strongly decreasing function of time. A reason for discussing the population problem here at some length is that it illustrates, for a simple nonlinear case, the principle of modelling. Besides, the population problem is of vital interest for our future; the nature of population increase the required energy per capita and is thereby linked to the need of realizing fusion energy. Furthermore, if the variable u in the simple equation is chosen to represent the temperature T in a fusion plasma the term T2 could be a realistic source term for representing alpha particle heating in a fusion plasma, i.e. accounting for the contribution of helium 4 to heating in plasma fusion reactions. A full equation for the temperature evolution of a fusion plasma should include also terms, accounting for the conduction of temperature and losses by radiation as well as for the influence of the plasma boundaries. Even so, a simple nonlinear model could represent the influence of heating of the plasma by fusion energy. It might obviously lead to a strong evolution of temperature in time, and would crudely represent a model of the hydrogen bomb. A fusion reactor should make efficient use of the heating process, but should also effectively confine the fusion plasma. Intensive research on the principle of magnetic confinement using experiments, analysis and computation has resulted in clear evidence that a solution to this problem is available. Today one also has reason to be confident of the future success of efforts to reach the goal on a practical level. 173

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A question which parallel’s the fusion energy problem is then: will we be able to master the problem of controlling the evolution of the world population, which seems to be the most urgent question of all? With a comparatively short time scale? Should this problem be adressed urgently to avoid an ‘explosive’ catastrophe?

7.5 Vortices When cream is stirred into a cup of coffee, when a propeller moves in the sea or when a rocket takes off in the air, vortices are formed. They are common in the atmosphere and occur as galaxies of stars in the sky. They appear everywhere in nature and in technology, and also in fusion plasmas. Extensive studies of vortices have been made in fluid dynamics by experiments and by analyses using a set of nonlinear partial differential equations, named Navier-Stokes equations, mostly for twodimensionnal cases.[7.16–7.17]. Vortices played an important rôle in the early history of science. Cosmological vortices were thought to produce order out of the chaos. Democritus (500 BC) who also introduced the atom, made vortex motion a tool to formulate general physical laws. The concepts of the atom and the vortex motion together formed a primitive first «unified theory». Today the early ideas about vortices could be given a somewhat extended interpretation, namely that small fluctuating disturbances in the very beginning of the universe may be regarded as seed vortices from which galactic systems later evolved. There are many shapes that vortices can take, from elongated tornadoes to flat hurricanes, more commonly observable as bath-tub vortices. An interesting property of vortices is their ability to produce locally high rates of rotation. In a tornado or a bath-tub vortex a fluid element has a constant angular momentum rv, 174

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where r is the radial distance of the element from the centre of the vortex and v is the circumferential velocity. When the element is drawn to the centre of the tub the velocity increases as 1/r which explains the violent central rotation, also accompanied by a minimum of the pressure in the center. Leonardo da Vinci (1452-1519) took an active interest in making detailed designs of the phenomena which occurred when a stream of water fell into a basin filled with water or when an obstacle like a flat plate was inserted into the stream. Patterns of vortices and bubbles in Leonardo’s designs are reproduced today in numerical studies using large computers, which produce results which show detailed similarities with the original drawings. His studies were of practical interest in his own time in relation to an hydraulic project in Milan in 1507. Leonardo da Vinci’s scientific drawings of water in motion remain today as artistic works. He studied a water jet running out of a square-shaped hole down into a pond, where it causes a pattern of bubbles and whirls resembling the structure of a chrysanthenum flower. The drawing was probably made around 1507 in connection with the above mentioned hydraulic project in Milan. The water jet may be compared to a beam of neutral particles injected into a plasma where it causes vortices and turbulence when heating the plasma. Today we study such phenomena in great detail using computer simulations and the results are similar. Compare plasma streams around obstacles such as plates and wires in laboratory experiments the bow-shock and the tail of the magneto-sphere or caused by interuption of solar wind flowing around the Earth. Detailed analytic studies of vortices are simplified by the introduction of vorticity, an abstract notation in terms of which the Navier-Stokes equations can be transformed into a form which is more lucid both physically and mathematically. In terms of vorticity it can be shown that microscopic vorticity at a point in space can generate macroscopic patterns, i.e. very small-scale phenomena can develop into large-scale structures, as has been demonstrated in computer-generated images in the two-dimensional case. 175

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The origin of biological evolution can be traced back to the development of patterns due to random disturbances of the genetic code. A generalization of the dynamics of vortices to a threedimensional description of reality, which both in principle and computationally is a formidable task, may reveal deep secrets and produce new surprises. An indication of such expectations comes from daily weatherforcasts, which can easily fail to predict even certain large-scale phenomena, can may originate from small local perturbations in an atmospherically sensitive, e.g. very inhomogeneous, domain in another part of the world. How can these ideas be connected to fusion plasma experiments? Obviously, it would be disastrous if small perturbations were to develop into gigantic plasma motions and spoil the global confinement. But on the other hand, it could sometimes be useful for heating purposes if perturbations in certain domains of the plasma would spread out over the whole plasma and not stay localized. This may be the case when auxiliary heating from high-frequency waves or neutral beams is applied to heat the fusion plasma.

7.6 Wavelets and turbulence Wavelet theory is a new and interesting approach which may help improve our understanding of turbulence. Wavelets can be considered simply as mathematical tools which are generalizations of Fourier integrals. They may be used to describe the propagation and nonlinear interaction of pulses in space-time, allowing for special frequency control is necessary to screen the dependence in time of different parts of a composition (‘windowing’ by means of the pedal control of a piano). In physics, one may think that different nonlinear mechanisms or changes introduced by geometrical effects in, for example, a fluid stream can introduce effects of a similar nature. A crucial question concerning turbulent flows is how to separate coherent structures (vortices) from the rest of the flow. 176

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So far the structures responsible for the chaotic and accordingly unpredictable behaviour of the turbulent flows have not yet been identified. There are strong indications from laboratory and numerical experiments that vortices are such elements. They might form the basis for constructing a new statistical mechanics in terms of equations appropriate for fully developed turbulent flows. It seems to be necessary to develop new approaches in this direction since available theory based on incompressible Navier-Stokes equations from fluid mechanics is not adequate for turbulence at high Reynolds numbers (the ratio of the nonlinear convective motions, responsible for the flow instability, to the linear dissipative damping which converts kinetic energy into thermal energy), which cover many orders of magnitude, representing various fields from naval engineering and aeronautics to meteorology and astrophysics.[7.18–7.20]. All classical methods in turbulence are based on Fourier representation which is inappropriate for the nonlinear convection term. Wavelet theory has recently been applied to analyse for example electric-field fluctuations of observed lower-hybrid wave-packets in the ionosphere. The wavelet technique has established itself as a useful tool for studies of wave packets in various connections and should be of considerable interest also for fusion plasmas.

«When an electron vibrates the Universe trembles» Sir Arthur Eddington

7.7 From fine structure to global dynamics of fusion plasmas How is it possible that fine structure dynamics (like the motion of bubbles in boiling water) can influence the global dynamics 177

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of fusion plasmas? Do similar situations exist elsewhere in Nature? Well, it is known that dolphins make use of small vibrations in their skin to help propel their heavy bodies in water. They even jump out of water! The small vibrations in the skin lower the resistance of the overall motion of the body in the water appreciably, by as much as ten times, probably because they counterbalance the influence of water microvortices set up at the interphase between the skin and water. A similar example may be taken from naval technology. The resistance from the water, and thereby the power used to propel the ship, can be lowered considerably by shaping the underwater prow-profile in a particular way. A correctly designed «bump» immediately below the water-line in the prow-profile will cause a wave-diffraction pattern compensating for the effects of the «ordinary» bow shock waves compare this with Cherenkov radiation from fast particles in media with a velocity v greater than the speed of light c in the medium) on the surface of the wave. This artificially introduced «skin» effect lowers the water resistence and thus the power necessary to propel the ship. In a similar vein financial disturbances in one country can grew quickly and may even shake the whole world economy. A small fire can ignite explosively in the wind and may burn large forests (compare the effects of lightning). A political conflict can lead to violent agitation and may even be the origin of a world war. From ecology it is well known that small disturbances, famously from the wings of a butterfly, in the air localized under certain conditions, such as sharp temperature or density gradients, in one part of the world, could induce giant phenomena like cyclones at remote distances in the atmosphere in other places of the world. From these examples we notice that wave phenomena which may seem tiny could have a strong influence on the overall motion of large systems. With this in mind let us now see how small-scale phenomena may influence the large scale motions of fusion plasmas. 178

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It is known from laboratory experiments with fusion plasmas that plasma phenomena and the plasma structure near the plasma edge can have a decisive effect on the properties of the whole plasma, for example with relation to plasma confinement. Of the two characteristic modes of a fusion plasma, the L mode and the H mode, the H mode corresponds to steeper gradients near the edge and also provides a confinement time which could be twice that of an L mode. To study the bulk behaviour of fusion plasmas one has to consider the influence of all the various processes that contribute to the dynamics of the whole plasma. For the analysis of this problem one has to construct an equation in which the separate terms model the various processes which contribute actively to the plasma behaviour. In doing so, for example in describing the temperature evolution in a plasma, one has to model the contributions from the process of temperature conduction, as well as, from creation processes, which have a tendency to increase the temperature by ohmic, alpha particle or external sources of heating, like highfrequency or neutral particle heating. Loss processes, for example. by brems-strahlung, also have to be taken into account. Each of these processes has a particular nonlinear dependence on temperature and density of the plasma: for p example the alpha particle heating nT , where p is a parameter of the order of two for a hot plasma and n and T denote the density and temperature of the plasma. The temperature conduction process entering the equation is an even more complicated term envolving spatial derivatives. In a onedimensional model this term could take many forms, depending on what type of phenomena one assumes to be responsible for the temperature conduction. A particular phenomenon which is often considered is the temperature gradient-induced drift-wave instability, which causes turbulence in the plasma and leads to a temperature dependence of the thermal conductivity which is 179

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approximately equal to temperature (T) to the power where δ = 3/2, a characteristic value for this type of turbulent fine structure. Losses may be represented by a brems-strahlung term nTq, where q = 1/2. The equation describing the global dynamics of the plasma temperature will thus include a number of terms which depend differently on the temperature and which are all nonlinear. The sum of terms representing the individual physical processes will be equal to the rate of change of the temperature ∂T/∂t, where t is time. A similar equation in n, the plasma density, can be constructed for the particle diffusion. The global dynamics of the fusion plasma will accordingly be governed by a coupled system of nonlinear partial differential equations in T and n, which may be studied by analytical or numerical simulation methods, including the possibility of phase-plane description [7.7 – 7.9]. The results will give information on the possibilities of equilibria, and on the details of the approach of the plasma to such equilibria as well as of the stability properties [7.21]. In fact, the partial differential equations describing the simultaneous influence of reactions, for example alpha particle heating, and diffusion processes (and therefore often called reaction-diffusion equations), also have solutions with timescales characteristic not only of diffusion but also of propagating phenomena. These can be much faster than ordinary diffusion processes. The propagating solutions depend on the spatial gradient (steepness) of the pulse or the wave, which the solutions represent. In this context it should be mentioned that studies of certain perturbations of the plasma, which give almost immediate responses at a large distance from the source of perturbation, have until now lacked an explanation, [7.22]. It seems that the nonlinear plasma phenomena continuously offer new and unexpected results. 180

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A satisfactory understanding of transport processes in fusion plasmas requires detailed knowledge of the complex plasma system. In astrophysical and cosmological contexts problems, formally similar to the above mentioned, have been studied. Strong electromagnetic waves interacting with electron-positron plasmas are of interest in understanding the emission process in pulsars. It can be shown that coupled nonlinear equations, governing the propagation of finite amplitude shear Alfvén waves in such strongly magnetized plasmas, can lead to Alfvén vortex structures, which can propagate in the form of twodimensional dipolar vortices, affecting cross-field particle and energy transport in the pulsar magnetosphere [7.27]. Related phenomena may also occur in electron-hole solid state plasmas, where the electrons and holes can have similar masses, but the lattice ions are too heavy, or fixed by the lattice, to take part in the dynamic process. Other recent work by P. Shukla and L. Stenflo suggests [7.28] that the ponderomotive (self-generating) force of a nonuniform neutrino beam can generate large-scale quasistationary magnetic fields in supernovae star interiors, and neutron stars (pulsars), were intense fluxes of neutrinos exist in addition to electrons, positrons and quarks. It is shown that a random-phase nonuniform neutrino beam can create intense stationary magnetic fields that can account for the observations, indicating magnetic fields of the order of 10-100 MG. Furthermore, it seems possible that an ensemble of random phase incoherent neutrinos can generate both the inhomogeneities and magnetic fields in the early universe. «Hence, neutrinos can be considered as building blocks of the two most important astrophysical phenomena that are central to modern physics and cosmology» [7.29]. Extented observations and future analyses will tell us more about those fascinating possibilities.

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References [7.1]

Stix TH 1992 Waves in plasmas (American Institute of Physics, New-York)

[7.2]

Sagdeev RZ and Galeev AA 1969 Nonlinear plasma theory (Benjamin Amsterdam)

[7.3]

Tsytovich, VN 1970 Nonlinear Effects in plasmas (Plenum, New-York and London)

[7.4]

Davidson, RC 1972 Methods in nonlinear plasma theory (Benjamin, Amsterdam)

[7.5]

Weiland J and Wilhelmsson H 1977 Coherent nonlinear interaction of waves in plasmas Pergamon Press Oxford; Russian edition Energizdat Moscow 1981)

[7.6]

Smoller J 1983 Shock waves and reaction-diffusion equations (Springer New-York)

[7.7]

Wilhelmsson H and Le Roux M-N 1993 Self-consistent treatment of transport in tokamak plasmas Physica Scripta 48 735.

[7.8]

Le Roux M-N, Weiland J and Wilhelmsson H 1992 Simulation of a coupled dynamic system of temperature and density in a fusion plasma Physica Scripta 46 457

[7.9]

Wilhelmsson H, Etlicher B, Cairns RA and Leroux MN 1992 Evolution of temperature profiles in a fusion reactor plasma Physica Scripta 45 184

[7.10]

Wesson J 1987 Tokamaks (Oxford University Press, Oxford)

[7.11]

Krall NA and Trivelpiece AW 1973 Principles of plasma physics (McGraw-Hill, New-York)

[7.12]

Itoh K, Itoh S-I and Fukuyama 1999 Transport and structural formation in plasmas (IOP publishing, Plasma physics series, Bristol and Philadelphia)

[7.13]

Weiland J 1999 Collective modes in inhomogeneous plasmas and advanced fluid theory (IOP publishing, Plasma physics series, Bristol and Philadelphia) 182

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[7.14]

Wilhelmsson H 1972 On the analysis of the population problem Physica Scripta 5 116

[7.15]

Weiland J and Wilhelmsson H 1974 On the evolution and saturation of the world population Physica Scripta 10 257

[7.16]

Lugt HJ 1985 Vortices and vorticity in fluid dynamics American Scientist 73 162

[7.17]

Lundin R and Marklund G 1995 Plasma vortex structures and the evolution of the solar system-the legacy of Hannes Alfvén Physica Scripta T 60 198

[7.18]

Farge Marie 1992 Wavelet transforms and their applications to turbulence Ann Rev Fluid Mech 24 395

[7.19]

Farge Marie, Kevlahan N, Perrier Valerie and Goirand E 1996 Wavelets and turbulence Proc. IEEE 84 639

[7.20]

Lesieur M 1997 Turbulence in fluids (Kluver acad.publ)

[7.21]

Wilhelmsson H, Lazzaro E and Cirant S 1996 Sensitivity of fusion plasma temperature profiles to localized and distributed heat sources Physica Scripta 54 385

[7.22]

Lazzaro E and Wilhelmsson H 1998 Fast heat pulse propagation in hot plasmas Phys Plasmas 8 2830

[7.23]

Fermi E, Pasta J, Ulam S 1955 Studies of nonlinear problems 1 Los Alamos Scientific Report LA 1940

[7.24]

Zabusky NJ, Kruskal MD 1965 Phys.Rev. Lett. 15 240

[7.25]

Wilhelmsson H and Lazzaro E 2001 Reaction-diffusion problems in the physics of hot plasmas (Bristol:IOP)

[7.26]

Elskens Y and Escande DF 2002 Microscopic dynamics of plasmas and chaos (Bristol: IOP)

[7.27]

Yu MY, Shukla PK and Stenflo L 1986 Alfvén vortices in a strongly magnetized electron-positron plasma Astro Phys.Journ. 309 L 63

[7.28]

Shukla PK and Stenflo L 1998 Intense magnetic fields produced by neutrino beams in Supernovae Phys. Rev. E 57 2479 183

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[7.29]

Shukla PK, Bingham R, Mendonca JT and Stenflo L 1998 Neutrinos generating inhomogeneities and magnetic fields in the early universe Phys. of Plasmas 5 2815

[7.30]

Coppi B 1988 Profile consistency: global and nonlinear transport Phys.Lett. A 128 183; 1980 Non classical transport and the «principle of profile consistency» Comments Plasma Phys. Contr.Fusion 5 261

[7.31]

Reeves H 1986 L’heure de s’enivrer L’univers a-t-il un sens? (Paris: Seuil)

[7.32]

Reeves H, de Rosnay J, Coppens J and Simmonet 1996 La plus belle histoire du monde Les secrets de nos origins (Paris: Seuil)

[7.33]

Reeves H 1999 L’espace prend la forme de mon regard (Paris: Seuil)

[7.34]

Moestam R and Weiland J 2003 Resistive drift wave instability due to nonlinear structures, Nucl Fusion 43, 11 35

[7.35]

Zagorodny A, Zasenko V, Weiland J and Holod I 2003 Particle diffusion in random fields: Time-nonlocal description and numerical simulations Phys.Plasmas 10, 58

[7.36]

Moestam R 2003 Transport barriers in plasmas and fluids (Ph D thesis CTH)

[7.37]

Weiland j, Dastgeer S, Moestam R, Holod I and Gupta S 2004 Excitation of zonal flows and fluid closure, Invited talk, Toki Conf.2003, JPFR (Japan) vol.6

[7.38]

Moestam R, Sheikh O and Weiland J 2004 Self-Consistent theory of zonal flows in ion temperature gradient turbulence Phys. Plasmas 11, 4801

[7.39]

Holod I 2004 Statistical aspects of diffusion in turbulent plasmas (PhD thesis CTH)

184

Cosmos exhibits a whole spectrum of examples of magnetic confinement, by means of electric currents. Those currents could be due to changes in time of cosmic magnetic fields or could emanate from charge particle emissions from nuclear reactions. The examples from cosmos have given a lot of ideas for laboratory plasma experiments, and the whole field has developed into a veritable art of plasma confinement.

8.1 Toroids, magnetospheres, beams, filaments and blobs The key to the principle of magnetic confinement is that, in the presence of magnetic fields, charged particles are not free to move in directions perpendicular to the magnetic fields lines. Generally it turns out that the sum of the plasma pressure and the magnetic field pressure is a constant. In sunspots the magnetic field is high, whereas the temperature is low. They are dark and cold, as compared to the surroundings. The particles in a magnetized plasma have a tendency to spiral around the magnetic field lines, the closer the stronger the field is. The principle is used to confine fusion plasmas, in toroids like in Tokamaks, where the ratio between the plasma pressure and the magnetic field pressure is only about 5%.In 185

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such machines the magnetic field is generated by the plasma current itself, supported by a contribution from external magnetic field coils. In cosmic plasmas the magnetic field could be selfgenerated like in filaments or blobs, thrown out from the solar surface, from which the magnetized blobs can even reach the Earth’s magnetic field and enter the magneto-spheric plasma. The same is true for the enormously long galactic jets, resolved in details in the Hubble telescope pictures. It turns out that filamentation is a far more common feature in cosmos than hitherto believed. In wave-amplifiers, i.e. travelling-wave tubes, used in satellites for communication, the electron beam is confined by a longitudinal magnetic field, as in various other types of beam amplifiers. In the magnetic field system, generated around our Earth, satellite observations have revealed a detailed structure of magnetically confined plasmas, where a whole spectrum of plasma phenomena occurs, from plasma instabilities and turbulence to shock waves. The particulary interesting circumstance that there exists a pronouced asymmetry of the magneto-plasma surroundings of the Earth, caused by the solar wind, has led to new discoveries, such as the bow-shock and the magneto-spheric tail. A comparison between discoveries made in the plasma laboratories on Earth and by the satellite observations could often be helpful to reach a deeper understanding and interpretation of related phenomena. In the domain of fusion plasma magnetic confinement there are recent fundamental results from theory, which have been confirmed by detailed experiments in several laboratories, namely that plasmas which have a strongly peaked configuration, i.e. high central values in their density profiles, and also in associated temperatures, should be particulary favourable for confinement and therefore possibly for fusion burn and efficiency in a future fusion reactor. In laser fusion (cf. section 6.4), attempts to achieve, by expansion of the pellet surface, a reaction and optimum 186

TOROIDS, MAGNETOSPHERES, BEAMS, …

compression of the pellet centre for efficient fusion burn, have been made for the same purpose as in magnetic confinement. This is mentioned here for a specific purpose, namely to compare the above two characteristic features from magnetic and laser fusion laboratories with a fundamental experience from solar physics. It has been considered a paradox [3.1] that the larger a star is the faster it will consume its nuclear resources and begin to contract. It happens when the gravitational attraction is not any more in equilibrium with the pressure from the burning plasma, which starts to decrease in temperature and loose its pressure. It is estimated that our sun, will continue to burn for another five billion years, whereas there are other stars, which are more heavy, which will finish their resources in a coupole of million years, i.e. they will die at an age much less than that of the universe. This does not seem evident from an elementary consideration. Comparing with the above mentioned examples from laboratory fusion plasma experiments one may, however, remark that there seems to be no contradiction between the solar «paradox» and either of the magnetized or laser fusion plasma experiments. In the laboratory, higher contraction would lead to more efficient conditions for fusion burn. In the solar case, with the enormous gravitational contraction in the heavy stars, violent phenomena might happen and on the average favour increased burning of the nuclear fuel. As a result, the shorter life-time of the heavy stars might seem less surprising in the light of recent experiences from fusion plasma experiments [8.41–8.42] .

8.2 The principle of magnetic confinement A remarkable property of magnetic fields may be the key to the problem of fusion plasma confinement, namely the fact that free motion of charged particles is not allowed in directions transverse to the magnetic field. 187

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Instead, the particles will spiral around the magnetic field lines. The radius of the spiral, the Larmor radius, is proportional to the square root of the thermal energy and inversely proportional to the magnetic field. For typical tokamak ion temperatures T = 10 keV and magnetic fields B = 5 the ion Larmor radius is less than a centimeter. It turns out, furthermore, that the sum of the plasma pressure and the magnetic field pressure is a constant, equal to the magnetic field pressure outside the plasma. In the plasma the ratio of the plasma pressure and the magnetic field pressure, usually denoted by β, is less than unity and in tokamaks typically only about 5%. Even if elementary considerations clearly indicate that magnetic fields offer attractive possibilities for the confinement of fusion plasmas important problems remain concerning the thermal flux and the influence of boundaries. Related problems are actively being studied both experimentally and theoretically. The magnetic fields used for the confinement of the fusion plasma could be generated from outside the plasma, using a convenient set of coils, or could be produced by the plasma itself, using the magnetic field originating from the plasma current. In a tokamak, use is made of internally as well as externally generated magnetic fields, whereas in stellarators, which have no toroidal current, only externally created magnetic fields are used. As a result, tokamaks and stellarators exhibit vastly different magnetic configuration architectures, and also have alternative schemes of operation.[8.1–8.2] Before discussing related topics further, let us emphasize some of the basic questions relating to fusion energy generation and to the conditions for self-sustained fusion.

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8.3 Fusion energy generation and self-sustained fusion The reaction between deuterium (D) and tritium (T) can be illustrated as ⊕ ⊕ ⊕Ο Ο + Ο Ο → ΟΟΟ → +Ο ⊕ ⊕ Ο⊕ where ⊕ denotes a proton and Ο a neutron, or 5

4

D + T → He → He + n + 17.6 MeV As an intermediate state a compound nucleus of 5He is formed which, however, immediately splits into an alpha particle and a fast neutron, sharing the liberated energy as 3,5 MeV and 14,1 MeV, respectively. The majority of the alpha particles stay in the plasma and contribute to the plasma heating, whereas the neutrons, n , leave the plasma with enormous energy, available for useful energy production. The D-T reaction has the highest power production rate of the fusion reactions. For T about 10 keV, n ∼ 1014 cm-3 and a D-T fusion cross section of 10-26 cm, the generated power density is about 1 W cm-3. The fusion reaction rate has to be higher than the energy losses from the plasma. Denoting the ratio between the thermal energy in the plasma and the energy losses by τE, the energy confinement time, one can conclude that a condition for selfsustaining fusion by D-T reactions (the Lawson criterion ) is 14

nτE > 2 × 10

–3

(cm s)

The critical limit depends on temperature and has a maximum between 10 keV and 20 keV. The high temperature is necessary to surmount the Coulomb repulsion between the 189

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charged ions, which at those high temperatures are completely stripped of their electrons, and to penetrate into the nuclear interaction region. It should be emphasised that the fact that the cross section for the fusion reactions diminishes for extremely high temperatures (higher than the maximum) provides an inherent safety against excessive heating of the fusion plasma. Through the years there have been many debates on various schemes of magnetic confinement and many attemps have been made in the plasma laboratories to improve the performance of the machines: to increase the values of nτE to fulfil the Lawson criterion and at the same time obtain fusion temperatures has turned out to be an extremely difficult task.

8.4 The architecture of magnetic confinement The architecture of the different magnetic confinement configurations has developed into an almost sculptural art. Configurations range from the first straight pinch currents and the first toroidal stellarator (Princeton), with the figure-of-eight variant, to todays, tokamaks with D-shaped cross-section configurations like JET (Culham), new attemps with elogated D cross-section (Lausanne), and new versions of stellarators like the Wendelstein VIIX (Garching), using highly structured magnetic coil windings. Superconducting coils are used for example in Tore Supra (Cadarache). They introduce a new approach in magnetic confinement technology and are being considered for the next generation of large fusion devices.

8.5 History of alternative concepts Historically, the first experiments in the field of magnetic confinement were straight pinches, using high power current discharges to heat and to confine the plasma. The self-generated magnetic field from the current itself was responsible for the confinement. Such a system turned out to be unstable and 190

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needed an external longitudinal magnetic field combined with a conducting wall for stabilisation. In order to minimize particle losses caused by leaking along the magnetic field lines the next step was to bend the magnetic field lines to form a magnetic bottle or a torus. However, the curvature of the magnetic field lines introduced, however, new problems. Strong externally produced toroidal magnetic fields were necessary to stabilize the plasma, for example in a tokamak. As a result the beta value of the ratio between the thermal pressure and the magnetic pressure, became rather low, a drawback for tokamak plasmas. Another type of configuration, the reversed field pinch, is similar to a tokamak in that it has the shape of a torus carrying a toroidal current. It is different, however, in the sense that the toroidal magnetic field is much weaker than in a tokamak so that on average the toroidal and the poloidal magnetic fields are of the same order. In the reversed field pinch the direction of the magnetic field has a strong variation in the radial direction, so called magnetic shear. Simultaneously, use is made of conducting walls to improve stability. The toroidal field usually maximizes in the centre and reverses sign near the wall. It is characteristic for the reversed field pinch operation to first show an initial turbulent evolution of the plasma developing into a quasi-steady state in which the plasma experiences a slow temperature increase accompanied by a simultaneous decay of the density. The energy confinement time of the reversed field pinch in usually smaller than for tokamaks but the beta-values are considerably higher, of the order of 30-40%. Another concept of magnetic confinement, the Spheromac, does not use any external coils at all to enclose the plasma current. The toroidal and poloidal magnetic fields are of the same order of magnitude. The control of the plasma to establish an equilibrium is left free for the plasma itself, which results in some technical advantages. The spheromac concept may be considered similar to an astrophysical confinement system which self-organizes its plasma equilibium with a minimum amount of energy. 191

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8.6 Stellarators and tokamaks The stellarator principle which is still one of the main candidates for a future reactor was originally developed in Princeton, USA, according to ideas of the astrophysicist Lyman Spitzer [see plate 13]. In a stellarator the poloidal as well as the toroidal magnetic fields are generated by external coils. This has the advantage of giving a certain flexibility in the control of magnetic properties. A stellarator has no current flowing in the plasma which gives the important advantage that it can operate continuously. The absence of a current in the plasma also eliminates a free source of energy that could drive instabilities. Important progress in recent years has made the stellarator concept a possible candidate for a future reactor. Two large machines are in early phases of operation: the Wendelstein VII– X in Garching, Germany, and the Large Helical Device (LHD) in Toki, Japan (see plate 13). The tokamak concept has, however, provided the base for the most important developments in recent years and has become the greatest hope for realizing a fusion reactor (see plates 14 and 16). The important results in JET (Joint European Torus, Culham, UK) and TFTR (Thermonuclear Fusion Test Reactor, Princeton, USA) and many other tokamaks in the world have considerably advanced our level of understanding of the properties and behaviour of fusion plasmas and have increased the technological experience to such an extent that hopes are high that fusion power plants producing electricity may be realized in the next century. Significant and extensive monographs on the development of fusion resarch during half a century have recently been produced by Bo Lehnert [8.3] emphazing the Stockholm activities and by Kuus Braams and Peter Stott [8.4] covering essentially European activities. For additional information has 192

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here been included a continued list of references to work on nonlinear plasma and fusion physics problems [8.5-8.42],a field where a lot of pioneering work has been carried out at Chalmers in Göteborg. The magnetic confinement principle has established itself as a useful method to substitute the gravitional fusion plasma confinement that the rest of the universe exploits for its power generation.

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8.7 The struggle for life: Electrodynamics in the laboratory and in the cosmos

«A Glimpse into the Theatre of Science and Technology» (Play in seven scenes S1-S7)

Scene 1 (Göteborg 1951-1955) So, how did it start then? For us students in the electrical engineering department at Chalmers radioelectronics and radio wave propagation were attractive fields. They stimulated to further studies and research even after the EE degree. The perceptive and efficient guidance by professor Olof Rydbeck led some of us to enter these activities, and even to become pioneers of different branches rather soon. There are many stories about the struggles in the beginning. The Research Laboratory of Electronics at Chalmers had two facilities for radioobservations outside Göteborg, one at Råö on the west coast (later named Onsala Space Observatory) and another one at Kiruna, north of the polar circle (which developed into Kiruna Geophysics Institute and later on became the Institute for Space Physics).Kiruna has excellent conditions for observing Aurora Borealis (the Northen Lights) particularly in the darkness of the year which lasts there from October to March, when however temperatures often comes down to – 20 °C and even more. 194

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In the winter of 1951 two young men in their last year EE studies, Bert Almqvist and Lars Olsson set out for Kiruna on the suggestion of professor Rydbeck. They brought with them receivers, which they had put together in the laboratory in Göteborg from used pieces of other old equipment and with elements of directional rotating (Yagi) antennes to be assembled up in Kiruna. The purpose was to use pulsed radiowaves of 10 m wavelenght from an emitter of about 100kw to find out if they could have radio-echoes from the Aurora Borealis. Dream of their satisfaction when they discovered beautiful echoes after only a few days work up in Kiruna. That compensated for all their struggles of planning and building devices as well as for the, at that time, almost endless and inconvenient travel by third class railway train (no sleeping wagons!) from Göteborg to Kiruna. Even more astonished became professor Rydbeck when the observers phoned him telling about the echoes. That was more than I had expected, he said! The success was total and the pioneers could return home with a great memory for life. In recent years auroral structures have been studied by means of satellites, revealing for example interesting features of vortex motion [cf. section 7.6]. My first real scientific experience was the work for the degree of Electrical Engineering at Chalmers, with the examination in the spring of 1952. That work was an extensive one, experimental as well as theoretical. It took nine months, which means that it started after the summer vacation in 1951 just 50 years ago. My collaborator was Vidor Westberg, who was ingeneous, practical and had a lot of patience, which was a good thing. The topic of our investigation was: «A method for oscillographic studies of the electron velocity distribution in a gas discharge plasma exposed to rapid changes» (in Swedish). It gave us a time of intensive, very constructive work and good possibilities of feeling electricity in our fingers. For me it was the beginning of a continuous interest in experiments, even if my future happened to be in theory. 195

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For studying gas discharges it is important to have a measurement technique available, which can quickly deliver information about the fundamental, characteristic quantities of the discharge. The famous probe method developed by Langmuir [8.34] assumes that the electrons have a Maxwellian velocity distribution, which however is not always true. In parts of the discharge, for example near the cathode, the deviations can be appreciable. For a general case, the velocity distribution of the electrons can be described by the product of the probe voltage and the second derivative of the probe current with respect to the probe voltage. Accordingly, a particular cathode ray tube was constructed with a multiple electrode lens system controlling the electron beam, by means of which the above mentioned product, and then also the electron distribution function could be displayed instantaneously on the screen. The topic of this early work is, interesting enough, still very up-to-date. It resembles in not a little way the studies made to day, with much more sophisticated tools of ultra-short pulse techniques using high-power lasers. For these modern techniques the reader is recommended to study the informative new books by Jean-François Eloy [6.21, 6.22]. After my Electrical Engineers degree I went immediately into military service as a radar technician in the Swedish Air Force Defence in Stockholm for a year, where again I was exposed to the secrets of the military radar electronic equipment, after which I was transferred in my military service to become a research technician at the Research Institute of Swedish National Defence, where later on I held a position for three years as Director of Research with the rank of full professor. It was a good school of training in applied electronics. I had decided to embark on a possibly long-time effort in the domain of physics and electronics, so I applied to Chalmers to be considered as a student for the degree of licenciate of technology in electronics (main topic), where a thesis had to be produced, and in physics. It was accepted and my advisors were 196

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Professor Olof Rydbeck and Professor Nils Ryde. I was offered the chance to work as assistent with each of those very respected scientists. I started straight after my military service in Stockholm to work at the Institute of Electronics with Professor Rydbeck. He himself had a Doctor of Science degree from Harvard, from where he came back in 1940 to start up an activity in the propagation of radio-waves and electronics at Chalmers. With his entusiasm and intellectual strength it must have been almost a revolution at Chalmers. An important part of the research in the new institute was devoted to experiments and theory of electron-beam amplifiers, such as travelling-wave tubes, double stream amplifiers, voltage step tubes, etc. All of these amplifiers were based on physical principles, where static electron beam energy was transformed into wave energy of a signal to be amplified. The travelling-wave tube uses a spiral helix around the electron beam to bring down the velocity of the electromagnetic signal to about one tenth of the velocity of light, since the light velocity will be projected on the axis of the beam to a part determined by the pitch angle, or the slope of the helix. Thus the speed of the electron beam and the electromagnetic wave in the axial direction of the beam will be of the same order, and a strong coupling may occur to take energy out of the beam and achieve an amplification. Amplifiers of this type have been used for years in satellites. Excellent experimental and theoretical work was performed on this artistic idea, which in fact came from an Austrian architect by name Rudolf Kompfner. One of my closest collegues was Sven Olving; we started and graduated from Chalmers, 1948-52, in the same years; he developed a very elegant and sophisticated theory and guided detailed experiments on the performance of the travelling wave tube. It led not only to a Doctor of Technology Degree in 1960 and a full professorship in 1964, but in 1974-1989 he held the position as the President of Chalmers. A rather admirable triplejump! Even more admirable if one knows that Sven Olving came from Estonia at the time of the Russian invasion. He escaped on 197

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a small boat over the Bothnics towards Stockholm, not yet eighteen years old, and when in the morning he saw land and several other boats arriving the same way, he saw the rest of the family, who came on one of the other boats. After some months in Sweden he went to Göteborg and to Chalmers to ask the President Gustav Hössjer, the mathematician, if he could arrange for Sven to start electrical engineering studies. It turned out to be impossible, since Sven had no documents with him, everything was left in Estonia, and besides, the requirements to enter Chalmers were very high and many Swedish applications were also refused. So Sven went home and thought over what to do. He decided to approach the President again and ask if he could be accepted for the first year (out of four) to show what he could really achieve. Gustav Hössjer understood that this was an unusual case, and exceptions are never excluded. He agreed to give Sven a chance. The results were very good, I believe better than for most of the Swedish students. Besides he did not tear out the benches in the lecture halls, but simultaneously worked most of the time in an electric company, and thanks to Siemens he could then earn a living, soon becoming married and having a family. I remember the many discussions we had when later on we were both assistants, often rather short, but always efficient and creative. When later on Sven was President, I was Dean of the Electrical Engineering Department, and Sven’s decision makings were extremely time-saving. The result of a demand could be yes, immediately, or no, in the latter case with an advise to go home and think it over. I remember that our meetings did not take more than three minutes on average. Sven tried to teach me the principles of management which I certainly appreciated. It meant simply finding out what was wrong and then improving things in the best way. I often applied this simple rule, the application of which was not always easy, but as a rule everything turned out well. I left lots of freedom and responsability to my collaborators. But I had decided to go for research and to direct research myself, with all that meant beside research; also committée meetings, research councils, conferences at home 198

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and abroad and Academies, whereas Sven became a member of the boards of several important Swedish industries. He also became the President of the Royal Swedish Academy of Engineering Sciences, a very prestigeous Academy (IVA). The early activities of the Research Laboratory of Electronics at Chalmers developed into a modern and internationally recognized activity specializing in several directions. The Onsala Space Observatory (Råö) on the coast near Göteborg was created by Professor Olof Rydbeck. Antennas and sophiscated receivers were constructed to make observations in the dm, cm and possibly even shorter wavelength domains. Maser amplifiers were developed in the laboratory to study the distributions of molecules in galactic clouds, radicals of OH, CH and magnetic hyperfine structure of nitrogen had been on the program for some time and were finally discovered at Onsala thanks to new electronics and new high precision telescopes. What paradise to work in for young electronics engineers and what a fascinating atmosphere for the students at Chalmers. Atomic clocks were installed which enabled measurements on different continents to be correlated. Intercontinental drift motions could then also be measured whith astonishing precision (accuracy in the domain) (see also section 7.67) Just as I write this on Wednesday, November 28, 2001 official news arrived that for the first time ever the existence of an atmosphere, a mixture of gases, around a distant planet, which is situated outside our solar system, 153 light years from us, has been observed in the constellation of Pégasus. The planet is a giant planet (HD 209458) larger than Jupiter but less heavy (69%). It is a sphere of gas with a temperature of about 1200 °C. The scientists plan to study the presence of sodium (Na), carbon dioxide (CO2) These investigations have probably to wait, however, until new telescopes will be ready by 2004 and later by the end of this decade. 199

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The new planet seems though to be far too close to its sun to support life. The discovery made by David Charbonneau from California Institute of Technology and Timothy Brown from the National Centre of Atmospheric Research (Colorado) may be considered as a decisive new step in the exploration of the universe. One is looking forward to determining the «chemical finger print» of the new planet. This may be the way to decide if conditions for life on other planets exist. To come back to the research in the Laboratory of Electronics I remember Olof Rydbeck being enthusiastic about a new type of electron-beam amplifier, namely «the voltage step tube». It consisted simply of an electron beam which on its way passed a plane where the electrons were exposed to a sudden voltage drop. A signal, let us say a small oscillatory motion, could here be amplified or damped, depending in what phase the electrons happened to pass in their motions. A simple analogue would be to ride a bicycle with a small swinging pendulum in your hand, if you apply the break suddenly, then the pendulum will swing out if, when the breaking occurs, the pendulum is on its way out in the direction of the bike, but its motion will be diminished if the breaking occurs when the pendulum motion is already in the backward direction. «Nature’s simplest amplifier», was Rydbeck’s reaction. In his coarses, which were exciting to follow, Olof Rydbeck always stressed the physical meaning of the different parts of the mathematical description. He was internationally known for his fundamental contributions to radioscience: An important contribution of his in this field was: «On the Propagation of Radio Waves» which contained a thorough mathematical description of how an electromagentic wave propagates around the Earth making use of the ionosphere, under general conditions for the dielectric properties of the Earth. He was awarded the Polhem gold medal for his contribution in 1945 (Polhem was a great Swedish inventor two hundred years before; one of those who started the Royal Swedish Acadmy of Sciences). Rydbeck’s work was very 200

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up to date; Sir Edward Appleton was awarded a Nobel Prize in Physics in 1947 for his investigations of the physics of the upper atmosphere especially for the discovery of the so-called Appleton layer (E-layer). Olof Rydbeck, when I started as his assistant in the autumn of 1953 stimulated me to do theory. It so happened that in the Summer of 1954 there was going to be a solar eclipse over Göteborg and the Onsala Space Observatory, or Råö as it was simply called in those days. OR as he was often nicknamed, prepared to make observations on different wave-lenghts. The eclipse was a partical eclipse from our site of observation. A theory had to be worked out for how the density of free electrons changed in the ionosphere, i.e. about 140 km above the surface of the Earth. With an ionospheric recorder this variation should be observed by measuring the critical frequency of the E-layer (see 4.2.3. page 61). Accordingly, such a theory was worked out by OR and myself. Essentially, it amounted to solving a first order nonlinear equation in time for the free electron density with a time-dependent source term. The source term came from the UV radiation from the sun, which varied with time, according to the eclipse geometry (assuming a constant radiation density over the visible part of the sun). The nonlinear term described the effect of recombination with ions, and the loss of free electrons by recombination with ions (as numerous as the free electrons) was then proportional to the free electron density squared. The loss of free electrons by attachment to neutrals could be neglected as well as diffusion effects. The result was that we could express analytically the time of occurrence of the minimum in free electron density during the eclipse as well as the expected value of the minimum value of the density. Comparisons with the measurements done during the eclipse gave us the value of the recombination coefficient in the ionosphere for the E-layer at hand. The time-lag of the minimum density point as compared with the symmetry point of the UV-radiation change, came from the nonlinear term 201

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proportional to the recombiantion coefficient [3.42]. It gave me my first experience in nonlinear physics and its relation to experimental observations. As an assistent I was suggested by Olof Rydbeck to consider the problem of scattering of an electromagnetic wave by an electron beam of cylindrical cross section of the beam and for an oblique angle of incidence of the wave. This was beside the work on the theory for the solar eclipse problem [3.42], already discussed here. OR looked at my paper on the theory for scattering of a wave by an electron beam, which was assumed relativistic with a strong magnetic field in the axial direction of the beam. He said to my surprise: «I had not written a work like this when I was 24, In fact, it would be foolish of you not to extend it to a Doctor of Technology thesis». This was not so evident nor expected to me, particularly since nobody in the electrical engineering department at Chalmers had ever defended a doctoral thesis at Chalmers.. I saw some possibilities of extension of the work myself and wrote four more papers on the topic in the years to come and a complete dissertation publication which was ready in the fall of 1958 (n° 18 in the history of Chalmers, all departments counted). In the meanwhile I had spent, however the years 1955-1958 in Lund and Copenhagen, where as we shall see in the next scene also other things were going on.

Scene 2 (Lund and Copenhagen 1955-1958) I spent more than three years in Lund and Copenhagen, 19551958. In Lund I was associated with the university, where I studied quantum mechanics, quantum electrodynamics, nuclear theory and took a degree of Licenciate of Philosophy at the Institute of Theoretical Physics, the Director of which was Professor Torsten Gustafson. During this time I got to know in Lund particularly Sven Gösta Nilsson and Torleif Ericson, both active in the theory of atomic nuclei, and real pioneers in this 202

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field, with an enthusiasm that encouraged me. They became both internationally famous, Sven Gösta for his treatment of nuclei of ellipsoidal shape and Torleif for the Ericson Fluctuations which occur in nuclei. Torleif got a position at CERN in Geneva, where he came to spend the rest of his active career after his dissertation. Torsten Gustafson was a man of high qualities, who took a personal interest in his students. He had an extensive net-work of contacts, was a good friend of Niels Bohr and of Tage Erlander, then Swedish Minister of State, as well as of Ernst Wigforss, then Swedish Minister of Finance, the last two former students of the Lund University at the same time as TG, as he was always called. Once in a while they came to the Institute in Lund and had a small hearing what was going on in research and in Lund in general. It was good for the Institute, good for the University and naturally very interesting for us who stayed there to do research. I was told that TG himself was offered the post of Minister of Education in Stockholm, which however he declined. Lund was a lovely city, and its nearness to Copenhagen very attractive. Gunnar Källén, already at that time, by the age of thirty, an international authority in quantum electrodynamics, who had taken his doctorate in Lund for Torsten Gustafson, was now permanently in Copenhagen as a research professor, but had close contacts with Lund, where he guided several graduate students. He also worked with Wolfgang Pauli from Zürich (Nobel Prize in Physics 1945 for the discovery of the Exclusion Principle also called the Pauli principle). At that time a new Scandinavian research organisation was established, namely NORDITA (The Nordic Institute of Theoretical Atomic research) with its centre in Copenhagen, the aim of which was to improve the interrelation between scientists visiting Copenhagen and Nordic scientists working in different Scandinavian institutes, and also to offer possibilities for scientists in «external» institutes to come and work in NORDITA. Torleif Ericson and I had the opportunity of going to NORDITA as the first research students in 1956-57 and I was 203

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proud when the first paper in the new series of publications from NORDITA came out by H Wilhelmsson and P. Zielinsky (also in Nucl. Phys. Vol 6 n° 2, 1958). There were many talks by visitors of NORDITA, often by top scientists of different nationalities. One day there came Professor Victor Weisskopf, Director General of the European Organisation for Nuclear Research (CERN) in Geneva. He started his talk by saying that he got a letter of invitation from NORDITA. He did not know what it was, but as he said: « I thought it was a beautiful girl!» And his talk was really very charming. Before my doctoral dissertation I had the opportunity to go to some international courses and conferences. In the spring of 1957, when in Copenhagen, Torleif Ericson stimulated me to go the French summer course (arranged by the University of Grenoble) in Les Houches in Savoie, where he had once participated. I followed his advise, applied and was accepted. The summer 1957 the topic of the course was elementary particle physics, a new and fascinating field, which was new to me. It became an extraordinary experience, with very good participants, and in the fabulous nature of the French Alps around the Chamonix valley. We could see Aguille de Midi and part of Mont Blanc from where we stayed in small cottages. There came Professor Chen Ning Yang, Princeton, who later on the same year was awarded the Physics Nobel Prize together with Professor Tsung Dao Lee, Columbia University, NewYork, NY for their penetrating investigations of the so-called parity laws, which has led to important discoveries regarding the elementary particles. They were only a little more than thirty years old then. When they were interviewed in Stockholm in connection with their prize, and were asked by the journalists what real use there could be of their work, they said, with an excuse that: we are so impractical that we can not even play the gramophone! Then came Professor O. Chamberlain, Berkeley, Cal. with his whole family. He was going to share the 1959 Nobel 204

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Physics Prize with Professor Emilio Segré, also from Berkeley, for their discovery of the antiproton. There came also Dr Jack Steinberg from Geneva who was going to share the 1988 Nobel prize in Physics with Dr Leon Lederman, Batavia, Il. and with Dr Melvin Schwartz, Mountain View, Ca, for the neutrino beam method and the demonstration of the doublet structure of the leptons through the discovery of the muon neutrino. Then there was Professor Leon Rosenfeld from the Niels Bohr institute, and he gave a series of lectures on the principle of quantum theory. He incouraged me to give a talk on photodisintegration of nuclei, which I also did. From Sweden was also Dr Ulf Uhlhorn from Lund, from France and from other countries a number of students, who stayed for a long time, four or six weeks. It was an unbelievale experience, and together with some French students and a professional guide we climbed the tope of Aguille du Tour in beautiful weather (about 2.800m). Next year I participated a Varenna course 1958 on plasma physics at Varenna, on Lago di Como with about fifty participants, my first international course on plasma physics with many good speakers: professor VCA Ferraro from England, professor HC van de Hulst from Holland, Dr Tom Gould from the USA, and Dr Bo Lehnert from Stockholm, whom it was my great pleasure to meet almost for the first time, and further professor Karl Kiepenheur, the famous solar physic expert from Germany. The first results from the so called ZETA-machine for future fusion energy were presented by Dr Peter Thonemann from Oxford and gave good hopes that fusion was perhaps not so far away…[7.4]. This was at the time of the Geneva Conference in 1958. Professor Righini, who was the director of the Varenne course, had arranged for me on request of a calm room for work, one of the two rooms in Villa Monastero (the other one had professor Kiepenhauer). It meant that at night I could work with the last part of my thesis with open window toward the Como lake, watching the stars and listening only to the waves on Lago di Como.What a wonderful 205

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experience! About ten years later, in 1969, Nils Robert Nilsson and I had the opportunity of visiting Florence and the Museum of the History of Sciences there, and who was the director if not Mrs Righini, the wife of Professor Righini, whom I knew from Varenna. She was astrophysicist, and if I remember correctly also responsible for the Observatory in Arcetri, the old home of Galilio Galilei. The world is small! At the Varenna School in 1958 I also gave a lecture on my thesis work, and I had, I remember also some questions from professor van de Hulst. Later on the same year I was invited to a Telecommunication Conference at the World Exibition in Bruxelles in the fall of 1958, where again I talked on the topic of my thesis. So I was quite well prepared when I was going to defend my work on February 14 th 1959 at Chalmers! It was decided that I should work with Gunnar Kãllen on a project during my time in Copenhagen, and that was really challenging for me. It should be said from the very beginning that research is like almost everything else in a dynamic society: it falls between opportunity and risk. Quantum electomagnetics (QED) was some of the most challenging but also most risky studies that one could imagine. It dealt among other things with how one could, in a logic way «renormalize» or eliminate parts of a theoretical expression ,that were unnatural, or «pathological», mathematically speaking singular (with infinities) from a theory to obtain something realistic, which had a final form in terms of finite measurable quantities. By means of QED one might hope to express the magnetic moment of the electron, accounting for the magnetic properties of the particle related to its spin, in terms of the electric charge of the electron. The result might be possible to express in a converging series of consecutive terms in orders of e2 , that is e4, e6, e8, etc…of which the e2 – term was known, and also verified by us, whereas the next one, or better the coefficient of the next one was not, nor apparently the other ones [cf..3.20]. Practically, the exercise consisted in calculating all matrix elements between quantized fields and particles, governed by 206

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coupled differential equations, which contributed to the order e4. This work occupied me for more than half a year. Gunnar Kâllén followed me with great interest and verified if the forms I found were reasonable. Finally, however, it became clear that a complete treatment of the problem, as I estimated it, might require an appreciable part of my time left before retirement, and we stopped the approach. Gunnar looked at me with a profound expression that I recongnized from his father [see section 3.5] and said with the same ironic humour: «It is better to hear the breaking of a string than never to drew the bow»

«Det ãr skõnare lyss till den strãng som brast ãn att aldrig spãnna en båge»

(Free translation from the Swedish National poet Esaias Tegnér from Lund) There have been calculations carried out much later to higher order in e2 by means of computers, and besides methods exist now for graphic systematization of the contributions by means of Feynman diagrams (The 1965 Nobel Prize in Physics was awarded to Professor Sin-itiro Tomonaga, Tokyo, Professor Julian Schwinger, Cambridge, Mass., and Professor Richard Feynman, Pasadena, Cal. for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles). Still I think that the approach to the problem in terms of a series expansion in e2 is an awkward one. Gunnar and I then tried to find integral representations of solutions to the set of QED equations. A necessary requirements was to carry out the integration over four fourvectors (three spatial coordinates and time) so that only one integration was left, which enabled a study of the analytic properties of the solution. It meant that we had to carry out fifteen of 4×4 = 16 integrations over different variables in order to succeed. It was necessary to choose the right order of integration in the sequence of variables, otherwise we got stuck 207

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after only a few integrations. We worked at the black board and found after much effort that we could do fourteen integrations. Then I was happy to discover that the integrand that remained could be transformed by means of a Bessel transform, which I happened to know, and after inverting the order of the two remaining integrations it was possible to find the desired form of the final solution in terms of only one integral, which allowed further analytic studies [3.19]. I would say that was an achievement. Gunnar was happy, and we were complimented by Professor Arthur Kerman, Princeton, NJ who was in Copenhagen once in a while. Many years later, when I gave a seminar in Kiev about solutions to reaction-diffusion problems in the physics of hot plasmas, one visiting scientist in the audience asked me if I was the Wilhelmsson who worked out the general singular functions with Kãllén. I was astonished, but happy to admit. Gunnar had been to Moscow after we had done the work and talked about the solutions. The man from Moscow told me that in Russia they were called the Kãllén-Wilhelmsson functions. He later sent me a photo to Sweden that he had taken of Gunnar, when he was lecturing, keeping an atomic model high in the air. At the time when I got the photo Gunnar had already passed away in the airoplane crash. I still have the photo. There were two young scientists Drs Trehan and Pradan from Chicago, originating from India, recent students of Professors Chandrasekhar and Fermi, who used to come to the Institute in Copenhagen. Dr Trehan had written the published lecture notes by Enrico Fermi. He told me that Fermi was very demanding with regard to time. When he gave lectures he closed the doors at the precise starting time and kept the doors closed intil the lecture was finished. He did not want to be disturbed! Dr Pradan was staying for an extensive period, when I was also there, and he had an interest in QED and nuclear physics. Once I asked him what he thought about QED. Did he think it was challenging? Knowing the background of his education I was a little shocked when he answered: «Not to a 208

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crazy extent!» At the time I was not tempted to defend the QED. I decided to return to Chalmers and to finish my doctoral thesis, writing up the final parts in a couple of months. But before we return to Chalmers let me describe a little bit more about the physics of nuclear structure and the collaboration between Copenhagen and Lund, which was very active in those days. The contacts between Copenhagen and Lund I had found very rewarding and interesting from the research as well as educational point of view. There was a small ferry to connect Copenhagen with Malmõ on the Swedish coast, and a short trip by train from Malmõ to Lund, which made the exchange convenient, except when the water was frozen which happened once a while. I remember when I crossed the frozen belt with Sven Gõsta Nilsson for the first time in a small aeroplane. That was my first ever flight! Sven Gõsta told me about his calculations of energy states in strongly deformed nuclei [3.25, 7.35]. For the individual nucleons characterized by a certain quantum number he was able to find the variation in energy as a function of the excentricity of the nucleus. The level diagrams, soon called Nilsson diagrams, or more popular: the smørebrød list (the list of sandwiches), could be used to classify the energy levels found by experiments. They turned out to be extremely useful and were refered were to frequently in the literature. His interest was very near the problems which Aage Bohr, the son of the Niels Bohr, and Ben Mottelson studied. In the year 1975 the Nobel Prize in Physics was awarded to Professor Aage Bohr, Copenhagen, to Professor Ben Mottelson, Copenhagen, and to Professor James Rainwater, New-York, N.Y for the discovery of the connection between collective motion and particle motion in atomic nuclei and the development of the theory of the structure of the atomic nucleus based on this connection. I remember the satisfaction Sven Gõsta expressed when he could predict the spin of the Hafnium nucleus to 7/2 which was 209

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just what the experimentalists found to their astonishment, since it fell a little outside the sequence of neighbouring nuclei. The element Hafnium was detected for the first time by a young X-ray spectroscopist Dirk Coster and George de Hevesy in 1922. They wrote: For the new element we propose the name Hafnium, after the Latin name of Copenhagen: Hafnia. It was number 72 on the series of elements in the periodic table and had been found in quite high abundances in minerals containing circonium. Niels Bohr mentioned the discovery in his Nobel lecture in Stockholm in 1922 I remember from Copenhagen when I first met Bob Schrieffer. He was sitting with his feet on the desk at the Institute with a very complicated matrix, all lines and rows written out explicitly, on a sheet of paper in a form which had many non-diagonal elements, more or less discouraging if not impossible to interpret. What he did was to neglect all the nondiagonal elements, somewhat arbitrarily, and keep only the diagonal terms, which simplified things appreciably. And, what a miracle, he found that the result agreed nearly with what was observed in the experiments on superconductivity. He paved the way to a famous theory: In 1972 Professor John Bardeen, Urbana, Ill., Professor Leon N. Cooper, Providence, R.I and Professor John R. Schrieffer, Philadelphia, Penn. were awarded the Nobel Prize in Physics for their theory of superconductivity, usually called the BCS-theory. This is an example of a method of working out difficult problems, a technique which Sven Gõsta Nilsson stressed for me. It sounds simple, but nontheless it could help significantly in difficult situations: (i) given the difficult problem which you find you cannot solve (ii) define a simpler problem which is sufficiently close to the original problem not to lose essential features of the physics of the original problem (iii) try to solve the new variant, and if you succeed, try to improve your approximate solution, and if you are 210

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lucky: find, with your new experience, may be a closed form solution to your original problem. This is a technique which could often be useful and which is stressed in a famous little book: «How to solve it» by Polya. I used it myself a number of times on problems which were, not always so complicated, but which seemed so. It was, in fact, stressed on seminars in the fusion theory group in Princeton in the 1960’s, by Nandor Balazs. I remember that Sven Gõsta and I played doubles tennis with Schrieffer and Wataghin (with whom I was writing up lecture notes from a series of lectures by Professor Abraham Pais on Dispersion Relations; he was a frequent visitor to the Institute). We probably lost, even if Schrieffer sometimes was as careless with the balls as he had been with the non-diagonal matrix elements! Games as well as films were very much appreciated among the scientists in Copenhagen and in Lund. I remember that Sven Gõsta Nilsson and I played the game of ice-hockey in his home in Lund with Aage Bohr and Ben Mottelson on the occasion of Sven Gõstas doctoral dissertation. Among the scientists at the Institute in Copenhagen it was a habit to watch Charlie Chaplin films. It might have helped to imagine the single particle coupling to collective motion whilst enjoying «Modern times». Copenhagen is a city where bicycles and tramways are important ingredients in the city life. Even Niels Bohr made use of them once in a while. One day when he was sitting in one of those nice ancient shaking tramways, which are running in all directions at the Triangle near the Institute, a lady with a boy entered and sat down. After a while the boy whispered to his mother: «Do you know mother that the gentleman sitting there is the most famous football player of Denmark?», what a compliment for the world-famous scientist! It was certainly worth a great Danish smile from everybody who heard it, Niels Bohr included. In explaining scientific matters, Niels Bohr liked to be very precise and clear and he could spend a long time to describe a certain point, to be sure that a collaborator or an 211

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audience really had understood his point of view. Some of his early drawings are extremely detailed. Once he gave a talk about theory of electrons and he made just one point with the chalk on the black board, which he repeatedly returned to in his presentation. He was, in fact, very anxious of being well understood! It should be added that he often spoke with a rather soft voice. Which kept the audience very silent. There were some signs of his profound wishes of being understood already in his early days. A story tells about Niels and his brother Harald when they were boys: One day their father came and found them wrestling, and apparently Niels seemed to treat his brother a little hard, sitting on him. On his fathers question why he was doing that, Niels answered: He does not understand what I am saying! Then I am sure that they all smiled: a Bohrish smile. Great scientists like Niels Bohr are often thought of not as formalists but rather somewhat magic. One day a journalist visited Niels Bohr at his house on the contryside and found that there was a horseshoe hanging over the entrance door. A little astonished the journalist could not resist mentioning to Bohr that he had seen the horseshoe and that he did not find it possible to believe that such a great scientist could be supersticious. The reaction of Bohr was immedite: «no, no certainly not, but after all one never knows! Coming back to Polya and the question of «How to solve it» we consider the following application [8.5]. An example from basic fusion plasma physics, where physical insight could be gained without solving the whole problem, is the stationary nonlinear waves in hot plasmas. It is well known that if the plasma oscillation in a cold plasma (negligible temperature effects) has nonlinear amplitude, the frequency of free oscillations is still the same as for small amplitudes. What happens when the plasma becomes hot? The form of the oscillations will change with a tendency of «overtaking» that is to tip over, like a wave on the shore before it dissolves into bubbles. But also, it becomes a wave with a given wave-number k = 2π/λ, λ being the wave-length and ω 212

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the angular frequency. To solve this nonlinear problem explicitly is difficult if not impossible. However, we might be interested in finding out the relation between ω and k without enquiring about the detailed shape of the wave-form (or the «bubbles») simply by asking how often the wave goes through zero when it propagates. This can be determined directly from the nonlinear equation by inspection.[8.5] The result obtained seems to be one of the first solutions to a NL wave problem for a plasma with temperature. I was told by Oscar Buneman, pioneer in computer plasma simulations, when I met him at a conference, that many people had tried to solve this problem! The result was verified experimentally by R. Stern at Bell Lab. Interesting physical insight had thus been obtained without solving the full problem. The details may be obtained by computer, and the analysis may be generalized to other cases considering for example the presence of magnetic fields. Similar approaches have recently been applied to the study of problems in the field of ultrashort pulse electromagnetics in dispersive and dissipative media [6.15-6.22] and in the research on reaction-diffusion problems in the physics of hot plasmas [7.25]. In Lund I got interested in the nuclear photo-effect. More precisely it amounted to studying what happens when nuclei are irradiated by high-energy photons in the γ-ray range. This offered one way to investigate the structure of nuclei, or to make models of nuclei, which could be compared with experiments. Now, as far as modelling goes one could use a nuclear shell model, where every nucleon moves in a potential which is caused by the motion of all the other nucleons in the core of the nucleus, or one can devise other models for the purpose, as we shall see. Experiments had shown that the nuclear photo-effect exhibits cross-sections with giantresonances in the region of about 16-20 MeV energy of the gammas, with different positions and widths. One might imagine that well-organized collective effects lie behind this. 213

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The experimental groups in the physics department in Lund had an interest in these problems with graduate students. Since, for some reason, I was interested in α-particles we looked into the nuclear photo-disintegration of alphas and tried to relate the results of this to the corresponding problem for oxygen 16, considered as a nucleus, consisting of four αparticles interacting with each other or regarding each αparticles bound in a core representing the influence of all the other particles. We could integrate this problem and obtained agreement with experimental results from which a kind of interparticle force could be determined [8.36]. Naturally, we had to be a little imaginative and used some approximations. One was somewhat more imaginative than the others, but probably having Bob Schrieffer in mind and his approximation of the giant matrix element for BCS (it was the same year) we wrote: «This approximation is not worse than any other approximation used in this paper». It gave physical insight into the problem and it passed the referee in Nuclear Physics and made the paper famous, at least in Lund! I was asked to be the candidate’s (Nils Svanteson’s) referee in a doctors dissertation in Lund on the nuclear photoeffect and also to be a speaker at one of the weakly meetings of the «circus» in the Bohr Institute in Copenhagen. The alpha particles play an important role in physics in general and in the universe. Oxygen is decisive for life. It seemed natural that the associated nuclear photo-effect could have some general interest. That was why I thought it interesting to study in particular problems of the giant resonance in connection with alpha particles. Alpha particles turned out to be extremely important in relation to the fusion problems. The alphas are products of the nuclear fusion protonproton reactions in the sun (see sections 2.3 and 3. 1.4), where γ-rays are also generated. They are generated when deuterium and tritium nuclei react to produce fast neutrons and alphas in fusion devices in the laboratory (see section 8.1). For a future fusion reactor they are expected to be unavoidable to maintain 214

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the energy in the plasma in the form of a hot gas. Continuous heating by alpha particles in the plasma is thus the important process to be used to have a continuously operating reactor [8.16], and it has to be sufficiently strong to balance the losses. Thus, it should be of the utmost importance to understand everything that has to do with the alphas in the extremely complex physical system of, for example, a Tokamak plasma [8.1]. Not very many years ago, say only a dozen years, which is a short time in fusion time scales, the behaviour of the alphas in a Tokamak was poorly known, if not unknown. There were no available diagnostics. It was when I spent a couple of weeks JET at Culham that I got the idea that perhaps one could use the giant resonance to help the diagnostic of fusion alphas in Tokamaks. However, there was a need then to have available γradiation of an energy of the order of the giant resonance to do something useful. It was not encouraging to build an electron syncroton, or something like that, around the Tokamak to provide the γ’s! But may be one could arrange to provide some sufficiently high energy γ’s produced in the machine for our purpose? It was then that I consulted some experts in JET to get to know if there was something known or done in this direction. It came to my knowledge that a certain dr Ed Cecil in Boulder, Colorado had even made some measurements to find out that certain effects could be observed from γ’s produced in the plasmas, even if they were rather tiny statistical effects on the curves. When I talked with Peter Stott the other day he told me that one might use γ’s produced either by the neutron beam heating or by Lithium in the plasma to produce the γ’s. At least this demonstrates how useful it can be to have at hand knowledge about particular phenomena like photo-nuclear processes for unusual diagnostics. The experimental site was very active in Lund, with a rich tradition from the days of Manne Siegbahn who made his important discoveries and researches in the field of γ-ray spectroscopy in Lund, where he became professor by the age of 36 in 1923 and then professor in Uppsala, by invitation, the same year. He was awarded the Nobel Prize in Physics for 215

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1924, received in 1925. An elegant and impressive triple-jump! In Uppsala he stayed until 1937 when he became Director of the Nobel Institute of Physics at Frecasti (Stockholm), with an extremely flourishing group of experimentalists. In those days atomic spectroscopy offered a very broad and rich field of research and numerous spectra were registered for the different elements of the periodic system. A certain JR Rydberg (1854-1919) originally mathematician; dr at the age of 26, had a hard time to keep order in all the multitude of spectral lines produced. I was told later in Lund that he measured by hand and a ruler the distances between levels, often from measurements or figures published by other scientists. He helped to work out the corresponding rules for the frequencies of transitions. He found a quantity that the frequencies of the transitions had in common which was called the Rydberg constant after him. Furthermore, I was also told that every evening when he went home after work, down the small hill from the Physics Institute at Sõlvegatan, he stopped at the Lund Saving Bank, where he had an appointment to make up the daily accounts of the bank to earn his living, counting money instead of spectral lines. And, finally after many years of very important and highly qualified active work of interpreting spectra he became professor in Lund (1909) In the year 1922, Albert Einstein and Niels Bohr received their Nobel Prizes in Physics, Einstein for 1921 and Bohr for 1922. At the banquet in Stockholm after receiving the Nobel Prize (december 1922) Niels Bohr gave the following speech (here in parts) «That it has been my undeserved good fortune, to be a connecting link at a stage in this development is only one piece of evidence among many of the fruitfulness, in the world of science, of the closest possible intercommunication of research work developing under different human conditions. However, when a Danish scientist is here in Stockholm, on an occasion such as this, he must not only think of the international character of science but fully as much of the intellectual followship among the Nordic countries which we all 216

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feel, not least in the realm of science. It would be tempting to try to describe the great debt which science, and, hence, also Danish research work, owes to Swedish scientists in old and recent times. However, that would take us too far, even if I should limit myself to describing only the most important contributions of the eminent representatives of Swedish natural Science present here tonight, whose work in various ways has been of fundamental significance also for atomic research. Hence, I shall call to mind only a single Swedish physicist, the late Professor Rydberg in Lund, whose ingenious work on unravelling the spectral laws has been of such great importance for deepening our knowledge of atoms and, not least, for the contribution that it fell to my lot to make…. After the ceremonies in Stockholm, Bohr wrote to Einstein on November 11, 1922 telling how much he appreciated receiving the Prize at the same time as Einstein. Einstein received Bohr’s letter on a trip to Japan and he answered it thus on January 10, 1923: «Your cordial letter reached me shortly before my departure from Japan. I can say without exaggeration that it pleased me as much as the Nobel Prize. I find especially charming your fear that you might have got the prize before me-that is truly «bohrich». Your new investigations of the atom have accompanied me on the trip, and they have made my fondness of your mind even greater…» [8.40]. In this connection I also find particularly interesting the following excerpt of a letter from Niels Bohr to CW Oseen on August 30, 1922 after «an interesting and successful conference in Uppsala I cannot say how great a joy it is for me every time we meet to feel how close we are to each other in our general view of the fundamental problems of physics»… [8.37, 8.39, 8.40]. In the domain of electromagnetic phenomena Oseen should certainly be considered as one of the great innovators concerning the theoretical description, particularly with regard to connecting the atomic properties of matter and the radiation 217

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field. Allow me to quote Born and Wolf on those fundamental aspects. Oseen adopted an alternative point of view than the conventional Maxwell’s equations for describing the interaction of electromagnetic radiation with matter [8.37, 8.39]: He introduced «two new vectors for the purpose, namely: the electric polarization P and the magnetic polarization or magnetization M. This led to a new conception of the propagation of an electromagnetic wave in matter. An electromagnetic field produces at a given volume element certain amounts of polarization P and M, which, in the first approximation, are proportional to the field. Each volume element then becomes a source of a new secondary or scattered wavelet, whose strength is related in a simple way to P and M. All the secondary wavelets combine with each other and with the incident field and form a total field… By expressing this identity formally, we obtain two integral equations, which may be shown to be equivalent to Maxwell’s differential equations, but which describe the propagation of the electromagnetic field in a manner more clearly related to the atomic constitution of matter. The too main results which will be obtained from the theory are: (1) The Lorentz-Lorenz formula, which relates the macroscopic-optical properties of the medium to the number and the properties of the scattering particles, and (2) the socalled extinction theorem of Ewald and Oseen, which show how an external electromagnetic disturbance travelling with the velocity of light in vacuum is exactly cancelled out and replaced in the substance by the secondary disturbance travelling with an appropriately smaller velocity». Oseen’s points of view are behind many new developments in for example solid state physics and have been applied also in the field of plasma physics. How should one, for example, calculate the scattering of an electromagnetic wave by an object of such a form that it can not be described by any geometrical coordinates in which the 218

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wave equation is separable? For example in a form of a pear or more detailed structures. By chance we happened to live in Gõteborg as next-door neighbours to someone who had lived in Uppsala next to Oseen. He told us that Oseen for some time used to walk around muttering to himself: What happens with the incident wave, what happens with the incident wave…? What happend was that Nature and mathematics took care of it in a very simple and elegant wave, just by cancelling it by a part of the total wave field set up in the medium by the atoms, the remaining part being the new wave, propagating with a velocity c/n where n is the refractive index of the medium (cf. the Fresnel formulae). One of the beautiful contributions to electromagnetic field theory! One has the feeling that the atoms react collectively to defeat the incident wave and to dominate the situation in a way that suits them! Similar processes occur frequently in nonlinear laser-plasma interactions [3.44] and generally in processes which disturb the plasma.

Scene 3 (Gõteborg 1959-1960) The final date to defend my doctoral thesis was settled by Chalmers to be the 14 th of February 1959. The first (external) referee (opponent) was Professor Leon Rosenfeld from the Niels Bohr Institute in Copenhagen. The second referee (the candidate’s choise of opponent) was Sven Olving, my collegue from the Research Laboratory of Electronics) and the third my friend and school-mate through about 20 years, Per Granholm, who was expected to joke about the work. The topic of the thesis was: «The scattering of electromagnetic waves by an electron beam and a dielectric cylinder.» As early as 1881 Lord Rayleigh (Phil.Mag. p.81) studied the scattering of a perpendicular incident wave by a cylinder 219

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with an arbitrary refractive index. Other work done at the beginning of the last century are useful for practical calculations only when the wave-length is long compared with the diameter of the cylinder, with the exception of the work made by P. Debye 1908 (Physik. Z. 9 775), who suggested a method for treating the case of a cylinder having a large diameter compared with the wave-length. All these studies, however, were confined to perpendicular incidence. The scattering of electromagnetic waves by an electron beam had not been studied theoretically before the work presented in the thesis. The purpose of the thesis was to find the formal solution in the more general case of oblique incidence. This was achieved by combining a mode-matching treatment, developed by the author, for the scattering of obliquely incident waves by cylindrical obstacles, with the method of obtaining the wave functions suitable for describing the wave propagation properties of an electron beam. The dynamic equation for the cylindrical electron beam structure in the presence of an axial magnetic field of arbitrary strength and assuming an arbitrary velocity were given and discussed in some detail. The static magnetic field introduces a coupling between the transverse magnetic and the transverse electric oscillatory fields, which vanishes only in the limits of infinite or zero magnetic fields. Even in those limits the modes are coupled through the boundary conditions at the surface of the beam (tangential components of the oscillatory magnetic and electric fields required to be continuous through the boundary), when the beam is excited by an obliquely incident wave. For such an excitation there should be a mixed kind of coupling between the beam surface and the internal «bulk» dynamics to account for the total scattering and the beam plasma effects. Applications of the theory are found in microwave electronics, for millimeter wave generation, in astrophysics or geo-cosmophysics, e.g. scattering by meteor trails and in the diagnostics of electron beams or plasma devices. 220

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The complete formal solution of the scattering problem for oblique incidence in the case of an axial magnetic field of arbitrary strenght was outside the scope of the thesis, and thus left open for further consideration [5.2]. The dissertation could start as was announced by the President of Chalmers Professor Lennart Rõnnmark (who stayed through the whole performance). It became a rather lively spectacle, with many questions and remarks from the audience; a real chance to see the great elephants dancing! It went well in the general defence which was indeed very thorough and official with about three hundred people in the audience. I do not remember all questions and the details of the discussion. After all I was well prepared! Professor Rosenfeld was in general very positive and appreciative. Sven Olving made some very original comments, and particularly pointed out that a resonance I had found in the scattering by the cylinder could be related to the Brewster angle for the plane case. Professor Rydbeck made some nice comments, for example that my conclusion in the discussion, that for collisional damping to play a role the beam would have to be at least as long as the distance between Copenhagen and Gõteborg, was not relevant for cosmical physics, where the distance between those two cities was indeed negligible! So I learnt something. Then I got some questions about the convergence of the series expansions, which I had already tested numerically, and so on. The spectacle went on for five hours, in fact little more, said the president Lennart Rõnnmark, who was instructed to brake the ceremony with this time limit. The third referee, Per Granholm, remarked that the thesis started with something that was called abstract but he had found it was the only part of the work that was not abstract. Later on I learnt that the local evaluation committee in the Department could not agree about the note since there were no experiments in the thesis! However, it was clear that it claimed a theoretical work and should be judged as such. Besides professor Leon Rosenfeld, for many years a close collaborator of Niels Bohr, had told the committee that his opinion was that 221

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the theory was writter like music and poetry. The faculty of Chalmers finally agreed to give the note six for the thesis, with the competence of Docent, an old fashioned title which formally means that you are entitled to teach at the university. So I was very satisfied and happy to continue my research. Besides, I got among many telegrams one from Margrethe and Niels Bohr: (see the original telegram, in Danish) «Congratulations to the doctor’s degree and best wishes for the future». Dissertations were considered important occasions in the academic life in those early days, besides rather rare, and it is not surprising that the principles of judging the work were open to uncertainties. In Lund, the famous University in the very South of Sweden Helmuth Hertz defended a thesis in the 1950’s considering the penetration of discharges through matter, and the faculty referee (opponent) was Professor Hannes Alfvén. Hertz had done excellent experiments appreciated by Alfvén. But Alfvén said he could not find any theory whatsoever in the thesis. The candidate could do nothing but agree. But Alfvén said, that at least the candidate had been consistent! Hertz got the top mark, seven. It has to be said that the requirements to obtain a doctors degree in Scandinavia were not the same as in the USA or England for a Ph D, which is more like a Scandinavian licenciate degree. Now, since the 70’s the Doctors Degree in Sweden is not awarded any more, but is substituted by a Doctors Examination, for which there is no particular note given, but just: passed or failed. This may be more practical even if it does not measure the quality. It saves time and effort!

Scene 4 Astro and fusion plasma physics 4.1 Princeton 1960-61 In July 1960, after my promotion to Doctor of Technology at Chalmers, I started as Post-Doc at Princeton Plasma Physics 222

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Laboratory at Forrestal Research Centre at the invitation of Professor Lyman Spitzer, which was the beginning of my research in fusion plasmas. It was extremely hot and humid; a good time to stay indoors and work in an air-conditioned office, which was something quite new to me. I was introduced by Professor Edward Frieman, head of the theoretical department, and later Scientific Advisor to President H Jimmy Carter (Nobel Peace Prize 2002). We discussed together the problem of temperatur gradient induced drift wave instabilities in fusion plasmas. I started to work on my first nonlinear problem concerning nonlinear stationary oscillations in a plasma with temperature. It was a generalization of the so-called Bernstein-Green-Kruskal solution for the corresponding cold problem from 1957 (Phys. Rev.108 546). To me, as a beginner, the temperature effects seemed essential if one was going to achieve fusion! I introduced a new technique which enabled me to obtain a dispersion equation including a nonlinear term (in amplitude of the electron oscillations), proportional to temperature, and presented the results in a seminar in Princeton with many questions from the audience, particularly from Martin Kruskal. Ed Frieman approached me afterwords and said I should send the results to Physics of Fluids, where it was published in half a year [8.5], and I also talked about the work in September at a Sherwood Meeting in Gatlinburg, Tennesee. I was complimented for the work at the meeting by Martin Kruskal and Oscar Buneman, the pioneer of using computers to simulate plasma dynamics. It was a good beginning I thought after one month’s work. I went to graduate seminars by Professor EP Wigner and Professor JA Wheeler on Saturday mornings in Palmer Laboratories. It was most of the time a small group present, about a dozen people. The seminars were on different topics and rather informal. The speakers enjoyed answering questions. I was told that Professor Wheeler used to prepare his seminars during his morning walk from his home to Palmer Lab. 223

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Since my dissertation at Chalmers I often thought of how one could generalize the treatment I had presented in my thesis to include the effects of a static magnetic field of arbitrary strength, assuming still an arbitrary angle of incidence of the external wave and allowing for relativistic velocities of the electron beam. A question was to satisfy the boundary conditions for the external field (incident plus scattered wave) and the wave solutions inside, which were split up by the arbitrary strong magnetic field in the axial direction; in experiments used to confine the beam. It did not seem very encouraging, from the rather complicated forms of the solutions that I already had for the cases of an infinitely strong magnetic field or no magnetic field in the axial direction, and with arbitrary polarizations of the obliquely incident wave. It was a problem of practical interest for diagnostics of the electron beam, e.g. by changing the angle of incidence, and also for the possibilities of frequency multiplication by the Doppler effect or by nonlinear processes. But the solution had to come and it did rather unexpectedly. At Christmas we went to church at the University Chapel for a ceremonial, filled with glory and Christmas songs, which I deeply admired. But then in the middle of the prayers it suddenly became clear to me, without intension, how I could solve the whole problem. It was unbelievable but it must be true, it seemed to come from God. What a Christmas gift! What Devine inspiration – or could it have come from Einstein? I was sure immediately, and I later checked up everything. It was possible to express the solution in exact form, in welldefined pieces of combinations of Hankel and Bessel functions of functional arguments with all boundary conditions and wave equations satisfied. It was certainly the most complicated problem I had ever treated and it was, under the conditions given, an exact solution bridging the particular cases obtained before. The complicated expressions for the field (external as well as internal with respect to the cylindrical beam surface, can be split up in parts, or packets, which can be used to define 224

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coefficients of partial reflections and transmissions, at the boundary of the beam. They correspond to reflections of the waves (or rays) at the surface of waterdrops in the sky in forming a rainbow. One here approaches the points of view of C.W Oseen [8.39]. All the dynamics of the beam in a magnetic field is included, for arbitrary direction and arbitrary polarization of the incident wave, in closed form in those expressions. I spent several months with the people from the computer department, who were very helpful to unravel the complications of resonant excitation, angular resolutions etc. as functions of all the parameters describing physical and geometrical quantities. I was invited to Los Alamos, to the University of California, Los Angeles (UCLA), to Berkeley, and to the National Bureau of Standards in Boulder, Colorado, where I gave talks. The work was published in their Journal of Research [5.2]. I drove all over the United States and visited many different Universities, research laboratories and also national parks. After one year in the USA I returned to Chalmers, by ship; with many remembrances and a new car in my luggage. I had expected a relaxed and calm time on the boat, where I could breathe a little after a very active year in the USA, something like on arriving, also by ship, reading among other books one that I liked a lot, namely the autobiography by Norbert Wiener: I am a mathematician, 1956 (London: Victor Gollancz Ltd) famous Professor of Mathematics of the Massachusetts Institute of Technology (MIT), the creator of Cybernetics.I just have the book in front of me, signed by the author, when he visited Chalmers in the spring of 1960, before I left for the USA. But the adventures on the trip had not come to an end. The Norwegian liner Bergensfjord had a voyage rather north to reach Kristiansund on the Norwegian west coast and continue to Copenhagen. In the early morning, I believe south of Island, we woke up by a terrible noise and shaking of the whole ship. The machine had done full stop and reverse. I almost fell out of my bed, and went up on deck immediately to discover, first of all, 225

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that the radar was pointing in the reverse direction, apparently without tracking in the fog. The watch in front of the boat had visually discovered objects directly ahead: iceberg and fishing boats, that was the reason. Fortunately we had no direct encounter, and the voyage could slowly continue. But it was, I can tell you, a rather refreshing experience in the morning. The captain invited everybody for champagne! 4.2 (Gõteborg 1959-64) When I came back from Princeton to Chalmers and Gõteborg in the Summer of 1961 I had been appointed associate professor, in fact: «Observator», which is and old- fashioned title and meant a certain responsability also for work on radioastronomy and the Onsala (Råõ) Space Observatory. I gave courses in wave-propagation, antenna-and diffraction theory, advanced electronics for undergraduate students and on superconducivity and maser theory for the graduate students. The early research had been on Dynamic nonlinear wave propagation in ionized media, a series of investigations carried out on contracts with the US Air Force Research Centre, Bedford, Mass. It was on the initiative of the US Air Force that I had my first trip to the USA already in December 1959. Olof Rydbeck came to me telling that it was arranged for me to go to a conference in Boston and I should talk about my theoretical work. MATS Airlines (Military Air Transport Services) will take care of you from Paris to the USA. You will go tomorrow, 2 nd of December and back on the 17 th. The day after I was sitting on the plane from Paris among US soldiers in grey coats, going home from Germany, via Paris over Christmas. A propeller plane over the Atlantic, with an intermediary landing in Prestwik, Scotland for tanking then a very long trip to Labrador, again for tanking, and then reaching the finite destination at Mc Guire Air Port in New Jersey. I immediately phoned Professor Mimno at Harvard (Olof Rydbeck’s former 226

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teacher there) who invited me to his home the next day and arranged my stay in Harvard Faculty Club. There was an informal faculty meeting in the evening in Professor Mimno’s house and I remember that I met professor Nicolaas Bloembergen and his wife there for the first time, and he hold me about his very active research. In parenthesis it may be mentioned that, much later, in 1981 Professor Nicolaas Bloembergen, Harvard University and Professor Arthur L. Schawlow, Stanford University were awarded the Nobel prize in Physics, for their contributions to the development of laser spectroscopy, with the second half of the Prize going to professor Kai M. Siegbahn, Uppsala University, for his contribution to the development of high-resolution electron spectroscopy. In 1993 Professor Bloembergen participated the «Maxwell Days» conference here in Bordeaux and gave an invited lecture on nonlinear effects, theory and experiments, and I had again the opportuneity of meeting him and his wife, this time at «Cité Mondiale du Vin». In the United States I had two weeks of extreme activity. I gave a talk at the Conference in Boston, another at the Air Force Research Centre in Bedford, Mass. visited MIT and Harvard, saw the Museum of Fine Arts in Boston, before, I went to New York and the Courant Institute to see Professor Morris Kline and Professor J B Keller, theoretical experts on electromagnetic theory. Klein had finished a book on the History of Science then, and JB Keller his exceedingly elegant Geometrical Theory of Diffraction. From there I went to Princeton and the Plasma Physics Laboratory there to see Lyman Spitzer, Ed Frieman, Ira Bernstein (whom I had met in Uppsala at the Conference on Ionized Gases in the spring the same year 1959), John Dawson and many others. Finally I went to Washington DC and National Bureau of Standards, where they did interesting experiments on turbulence in plasmas. I followed the advice of Olof Rydbeck who said to me before I departed from Gõteborg: In Washington you should 227

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stay in Statler Hilton; I want you to get a good impression of America when you come there for the first time; and don’t forget to ask for a faculty discount! I followed his advice, enjoyed my stay and went home by MATS airlines; I remember the 17 of December 1959. When I met Olof again, and I was full of impressions to tell him about what I had seen and done, he very rapidly interfered: You gave a nice talk at the conference in Boston, they sent it over to me on a tape! He knew a lot of things beforehand as it often happened. On the radioastronomy side (1962-1963) a problem which attracted a great deal of my interest was the smoothing, or rather de-smoothing, of radioastronomical observations [3.12– 3.14]. The problem, which is of general interest to many fields of science and technology amounts to the following: The problem of finding the real form of a source, from the result of a measurement given in an observed form (or frequency distribution), which is then a modified version of the real source due to smoothing effects (atmospheric disturbances etc…), the form of the smoothing process given or estimated. The results obtained were used to modify or even omit the reduction techniques for observed measurements in several observatories, even in Holland. I remember that I heard that seven thousand profiles had been observed and analysed before. Often the so-called Eddington approximation had been used, which does not take into account correctly more detailed changes in the density profiles, due to omission of higher order terms in a series expansion. With this technique negative values of interstellar particle densities were even obtained after reduction. This being obviously unrealistic the de-smoothed profiles were sometimes quite arbitrarily rounded off, by pencil, to become positive, but what was seriously wrong, the peak values (which had no similar reference level as the minimum levels) were kept high as they were. The new technique [3.12– 3.14] indicated correctly to what levels the peak values should be adjusted as a result of the de-smoothing. 228

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I was happy to see that the new technique was given complimentary remarks in one of the proceedings of the Bonn Conference on measurement techniques in radio-astronomy, 1962 [3.15] by Dr A. Ollongren from Leiden, Holland and by Sir Martin Ryle from Cambridge. The result is not unimportant since it should provide the correct top values of the radiation sources in the cosmic interstellar matter. At the Onsala space observatory (Råö) the interstellar density distribution of hydrogen atoms was studied rather routinely in those days by observing the 21 cm spectral line emitted by the hydrogen atoms. The radiation was detected by radio telescopes, equipped with sensitive maser amplifiers, constructed at Chalmers. In the united states, particularly at the Green Bank radioastronomy observatory in West Virginia, serious systematic search for signs of possible extra-terrestrial civilizations was carried out. A very large (140 feet in diameter) parabolic telescope and ultra-sensitive receivers were constructed, providing opportuneties for looking further out in the cosmos than ever before. Even so no sign of life has been obtained so far. One day in June 1963 I happened to sweep the frequency spectrum by means of an ordinary radio receiver out at Onsala, when I came across some unexpected sounds. To my surprise I suddenly heard foreign words which, when I tuned the receiver, turned out to come from a women’s voice which spoke Russian, repeating the name Terechkova as well as words like space and satellite etc. It turned out that what I had come across was nothing but the voice of the first woman in space, the Russian cosmonaut Valentina Terechkova, who was on her satellite trip around the Earth, which she circled 48 turns in June 16-18, in 1963. I phoned up my director Olof Rydbeck at once saying that I had Terechkova on line from the Cosmos. He could not find his words to repond, which did not often happen. Then he said: what kind of material is the antenna made of? May be he 229

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thought that my call was a joke. In any case the antenna was just an ordinary copper wire but Terechkova was really the first women in space. Quite often in those days Olof Rydbeck and also Sven Olving used to amuse themselves with what they called practical jokes. One afternoon Olof Rydbeck phoned me; he was on summer vacation and said: «Professor and Mrs Charles Townes will arrive in the evening at the airport. They will stay at the guest house of the Institute. You take care of them! Hour and flight number given. That was it. In the summer of 1963 I believe it was. Townes was already a world authority after his discoveries of masers and lasers. I went to the airport, not absoluty sure if this was a joke or not. But there came Dr and Mrs Townes from MIT, Boston and I took them to the Institute and offered them, if they so wished, to have a dinner with us at home. We had been out sailing the whole day in the archipelago of Gõteborg, but as always we had fresh fish available, and dinner was prepared. Our guests were very satisfied, indeed, and we had a delightful evening. When leaving them at the Institute I asked them if they were interested to come again to us in the morning to have breakfast. And they would be very pleased (luckily since the Institute had no regular breakfeast service). They went with me back home and we had a leasurely pleasant Swedish breakfeast. Everybody seemed satisfied and Mrs Townes wrote in the guest book: « Swedish hospitality is wonderful!» Then I took Professor Townes to our space observatory at Onsala (Råõ) situated on one of the most beautiful parts on the Swedish west coast. The weather was beautiful and I was driving my new Chrysler Valiant which I had brought from the USA. Onsala what not of the size of the Goldston Observatory, where I had just been before, landing in the desert, directly on the sand with a sportplane, but it had some attractions like maser amplifiers built in our own laboratory and I told him everything of the little I knewn including my own theory. Professor Townes seemed very satisfied, pleased but also astonished. Then he said, when we drove home: Isn’t this a very 230

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great responsibilty for a young man like you? I had not expected such a comment by a man of his capacity, and I just wondered what Olof Rydbeck would have thought if he had heard it! Then came the next surprise. Townes wanted to by a Volvo car. Those are produced in Gõteborg. And he had a partiular color that he wanted. I do not remember what color it was but let us say violet. Which was not a very common color on cars then, at least not in Gõteborg. Townes said he was going to Stockholm and coming back on Wednesday, which was within less than a week. I contacted Volvo, telling that it was from Chalmers (which is very popular in Gõteborg) and that we had a very famous scientist Professor Townes with us, who invented the laser, for which, I judged he would certainly have the Nobel Prize. He wanted to by a violet Amazon, and to have it available next Wednesday. The answer was that they did not have that color, and that they could not arrange for it Wednesday even if the gentleman was Emperor of China! This needed some diplomacy. It so happened that the father of one of my school makes Mr Larsson was one of the two engineers who built the very first Volvo in a barn in Gõteborg; the other engineer was Mr Gabrielson, who was next neighbour of our summer house, whom I met with my father, I remember, when I was nine years old. The influence of my connections made the negociations quite simple and when Townes came back from Stockholm on Wednesday the new car was ready in the color he desired. This might have been a good demonstration of the efficiency of organization in Swedish industry; and at Chalmers! I got to know that several of the other professors at MIT, for example SC Brown, head of the electronics laboratory also bought Volvos. I met Professor Townes later, in 1964, in Stockholm, where I then lived, and he was coming to receive his Nobel Prize, together with the Russian scientists NG Basov and AM Prokhorov from Moscow, for fundamental work in the field of quantum electroncis, which has led to the construction of 231

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oscillators and amplifiers based on the maser-laser principle. He still had his Volvo! We had quite a number of scientists visiting Chalmers in those days. One day came a young gentlemen on a stipendium from NORDITA to visit us. He came from Paris and I was asked to take care of him. His name was Dr Claude CohenTannoudji. I remember him as a very polite, rather silent young man with an interest in quantum physics, possibly also in lasers, with a face which I remember well through the years. This was almost fourty years ago. I drove him up to Chalmers from the university and out to Onsala. Through the years I saw a lot of his publications and I was also at the Prize Ceremony in Stockholm and at the banquet in 1997, when he was awarded the Physics Nobel prize for development of methods to cool and trap atoms with laser light. He was now professor at College de France and Ecole Normale Superieure, Paris. He shared his Prize with Professor Steven Chu from Stanford University and dr Willian D.Phillips, National Institute of Standards and Technology, USA. The importance of this Prize for Physics in general became evident very soon when it turned out that cooling of atoms with laser light was an essential ingredience in achieving Bose-Einstein-Condensation, suggested by Einstein in 1924, and awarded the Nobel Prize in Physics in 2001 for its experimental verification (see section 3.2.3) Some of the early papers from this period (1959-64) on nonlinear effects and velocity distributions of electron beams, are here listed as selected references, e.g. Rydbeck OEH and Wilhelmsson KHB 1959. The influence of the electron velocity distribution on space charge waves, Res. Rep n° 1, Research Laboratory Electronics, CTH Wilhelmsson H 1960 On the problem of overtaking in a velocity distributed electron beam, Res. Rep. N° 19 Research Laboratory of Electronics, CTH Wilhelmsson H 1961 Stationary nonlinear plasma oscillations, Phys Fluids 4, 335 232

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Wilhelmsson H 1963 A nonlinear coupling mechanism for generation of very low frequency waves, Astronomical Notes 8 3 Wilhelmsson KHB and Thomasson AR 1964 Cerenkov effect in a pre-oscillating medium, Res. Rep. N° 46, Research Laboratory of Electronics, CHT Wilhelmsson KHB 1964 The magneto-ionic theory for «massanisotropic» electrons RES. Rep. N°47, Research Laboratory of Electronics, CTH

They mark early pioneering contributions, mathematically not complicated but physically illuminating in a field, which was going to explode in a few years. They were precursors to the evolution of nonlinear waves in plasmas.

Scene 5 Personalities Chalmers and its Presidents The name Chalmers has already been mentioned frequently in the text and the reader may wonder where it comes from and what it is. Chalmers is from 1994 the foundation Chalmers University of Technology, a private state supported university in Gõteborg, situated on the west coast of Sweden. The school from which the university grew, called a handicraft school (1785-1875) was founded in 1829 with Carl Palmstedt as its first «Rector», or President. He had already from the beginning high ambitions concerning science, and he was a near friend to Jõns Jakob Berzelius (1779-1848), the famous chemist, who discovered numerous elements of the periodic system and who was also an important and enlightening man in science administration. Three volumes about the letters of exchange between Berzelius and Palmsstedt have been published by the Royal Swedish Academy of Sciences, through Jan Trofast (Lund 1981, in Swedish) All together more than one thousand pages. 233

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William Chalmers (1748-1811) was born in Gõteborg. His father also by name William, came from the area of Aberdeen in Scotland and moved to Gõteborg in 1722. William Chalmers started already in 1773 his own buisiness and by foreign travels he aquired lots of experience and a good reputation among valuable acquaintencies and friends. In 1783 he traveled to China and returned in 1793 bringing with him a considerable fortune, aquired within the East India Company. William Chalmers wanted to increase the standard of living in the Society and he wanted to take particular care of poor people, as explained in his testament, which he signed in Gõteborg only a few weeks before he died in July 1811. His fortune went to the «Industry School for poor Children», now Chalmers, and with an equal part to the Sahlgrenska Sjukhuset (hospital), now the University Hospital, Gõteborg. It took a long time before all the donated money could be liberated in 1821. Then the sum for the «Industry School» could be settled to 109.050 «rdrks mynt», which was an appreciable amount of money in those days. On July, 1st 1828 a contact between Carl Palmstedt and the economic less became settled. Palmstedts enthusiasm to take on the responsability was great and he spent the winter 1928-29 in Stockholm to plan the activities for the «Chalmers Handicraft School» as it was now called. On June 7, 1829 Carl Palmstedt moved to Gõteborg to take on his duties. (My sincere thanks Mr Palmstedt, says the author, who was born in Gõteborg just hundred years later and spent about fifty years with Chalmers) He took on an enormous amount of work and struggled intensively, but with good advise from Berzelius and others he managed to make progress in spite of many difficulties like cholera etc… Today Chalmers is one of the most active polytechnics in the country with thousands of research projects and about twenty principal educational programs. The yearly budget is about 1.7 billion SEK, of which two thirds, 100 million dollars, for research and research education. Chalmers has about 5000 students for engineering degrees and about 1000 graduate students, about 2400 employes of which nearly 1500 are 234

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teachers, scientists or graduate students (figures from the Chalmers Catalogue 2000). There is a saying that «The history of Sweden is the history of the Swedish kings». That makes me suggest another, namely: the history of Chalmers is the history of the Chalmers‘ Presidents. I will present here a brief history of Chalmers from the presidents I met, and I will take this opportuneity to say that they were all extremely important and encouraging for the activities we represented. During the time when I have been associated with Chalmers it had five consecutive presidents, namely the following professors:, (with accompaning periods of service ): Gustav Hõssjer

(1943-1958)

Lennart Rönnmark (1958-1966) Nils Gralén

(1966-1974)

Sven Olving

(1974-1989)

Anders Sjõberg

(1989-1998)

Who were they and what did I learn from them? Gustav Hõssjer was a skilled mathematician. My personal acquaintance with him came from the Astronomical Club in Gõteborg, where I was first secretary and then president. Most members were graduate or undergraduate students, but also some very qualified persons, among them Professor Niles Ride, the physics professor at Chalmers used to come to the meetings. We invited scientists from different observatories: Stockholm, Uppsala, and Lund and from Osaka (Rio) to give accounts of their latest research or about astronomy. I remember that Hössjer took a particular interest in the possibility that the Planck’s constant could be multivalued. In general Professor Hõssjer showed a keen interest in astronomy and appreciated the presence of the young students. We could talk about astronomy or about almost everything. It was a fascinating and fruitful experience. In his administrative duties at Chalmers 235

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Hõssjer was very efficient and prepared to find the best solution in any situation. It was said that Bismark had defined politics as the art of the possible. Hõssjer could therefore be considered a great politician! Chalmers was about to experience a considerable growth and the next president, Lennart Rõnnmark was a civil engineer experienced in construction of buildings, a very open and humorous personality, who had good contacts with the authorities of the city of Gõteborg. He continued the success in the evolution of Chalmers. We had one rather unusual interest in common, namely rifle shooting. He was a master and his brother as well, who had represented Sweden in many competitions even in Olympic games. I was not more than ten years old when I first met Lennart Rõnnmark. From him I learnt a particular trick in rifle shooting, which I came to apply, namely to fire not with the index finger but with the middle finger. In this way I could keep my middle finger along the the direction of the barrel to help the direction and stabilize any unnecessary vibrations. (It has a similar effect as taking a glass of beer before a competition, which is not allowed; olympic masters lost their medals, when such tricks were discovered). The Rõnnmark method was like stabilizing a hot plasma equilibrium against undesired oscillations with control mechanisms! Twenty years later it so happened that the Swedish Academic Shooting Competitions were going to be held in Göteborg and in spite of the fact that I had not been training for a long time, except in my military service, I decided to participate for fun accompanying Lennart Rönnmark. I was then new Docent and Rõnnmark new as President of Chalmers. I had no expectations and was completely relaxed when I fired my shots. But believe it or not, in the general competition a won a silver-plated rifle. Naurally using the Rõnnmark technique! But the more interesting competition was follow, entered by about a dozen of us. The game was to fire from a standing position at a distance of 200 meters at targets where the central 236

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usually black part had been covered in the very middle with white paper so that only the ring nr 7 (out of 10), about 5 cm wide with a diameter of may be half a meter was visible as black. Then the competition started, almost like Russian roulette; only those who had hit the ring in the first shot were allowed to continue. After a few shots only Rõnnmark and myself were left. The difference in our techniques was however (and here comes the point) that he probably aimed at the ring, whereas I tried to aim at the centre of the ring with a natural spread by chance of the order of magnitude of the diameter of the ring. Rõnnmark won with his last shot. It was great fun! In his administrative duties at Chalmers Rõnnmark was as far as I experienced a very friendly personality who liked to arrange things for the students. Personally, there is one thing among many that I learnt from him: to see a problem from different angles which sounds trivial but which is not always evident. Nils Gralén, who became the next President was a chemist, who had textile chemistry as his speciality. Only 32 years of age he became Director of the new Swedish Institute of Textile Research. During his time as President of Chalmers, from 1966 the research facilities at Chalmers grow enormously. He was the first president of a university in Sweden to let the students be represented on the board of the University. Gralén was an excellent lecturer and teacher and a good director of research, which in 1960 produced the first woman Doctor of Technology at Chalmers, Marianne Kãrrholm, with a thesis on Solver-Assisted Dying of Wool. Later on she also became professor at Chalmers. Nils Gralén had a lot of administrative responsabilities on the boards of research laboratories and research councils. He became President of the Royal Swedish Academy of Engineering Sciences. In 1971 he arranged a Nobel symposium on «The changing Chemistry of the Ocean». Nils Gralén was not only a skilled scientist and teacher, as well as a good organiser, but an exceedingly pleasant 237

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personality with a strong interest in music, who liked to play the piano and loved student theater (spex). Sven Olving was the President whom I got to know best of all and with whom I had numerous encounters in scientific as well as administrative matters. There had been one President of Chalmers before with the name Sven, namely Sven Hultin, a beloved President, appreciated by the students as well as by the staff. He got the nick-name Sven the Great..., or Great Sven (Stor-Sven). Had he not been there before certainly SO would have been Great Sven. However, SO did not need the epithet as President; it was clear that he was Great. SO did a lot to inspire the students and the staff at Chalmers in many respects, including contacts with Swedish industry. In fact, he participated in early days, very actively in establishing TV in Gõteborg. He wanted to see and hear everything. He taught practical management, the golden rule of which was to find out what was not so good, and to improve the situation or change it. He was a practical man in everything, looking at realities. I think he considered too much knowledge a burden if you were going to do something. For practicle reasons he went to very few lectures when a student, however, he used his time properly. He was keen to make contacts with the outside world. SO had his own points of view about lecturing, and he was an excellent, clear lecturer. A teacher, who did not tell at least one good story per lecture he probably considered not very appropriate, not to say useless. He himself lived up to his high requirements. He wanted his lectures to be considered important, and taken seriously even with the humor included. Once in a lecture in electronics he said: «This will be useful for you not only in life but for eternity!» SO became President of the Royal Swedish Academy of Engineering Sciences and was on the board of a number of important Swedish industries, like Ericsson, Electrolux, Chairman of Volvo Finance etc… 238

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He liked playing golf and eating shrimps. He loved listening to opera, and once he invited Birgit Nilsson from the Metropolitan in New York to sing at the Theater in Gõteborg on the occasion of a promotion of the young Doctors of Technology at Chalmers. What a rare event, what a President and how well forseen by Gustav Hõssjer when he gave Sven a chance and accepted him as a student of Chalmers without formal merits. In fact, SO chose to take mathematics for Gustav Hõssjer in his Technical Licenciate Degree and I know that he took it very seriously! During the period of Sven Olving there was a quality evaluation of the Polytechnique Schools or Universities in Europe. It rated Chalmers and the Swiss Federal Polytechnique Institute in Zürich at a shared first place, indeed a very honorable result! The Polytechnique Institute in Zürich was where Albert Einstein studied in early days [see section 3.2]. Anders Sjõberg was the next President to arrive, and he came, like Lennart Rõnnmark from the Civil Engineering Department. I knew him before since we had been simultaneously Deans of our different Departments of Chalmers. During the period of Anders Sjõberg as President an important step forward in the history of Chalmers was taken. Chalmers became the Foundation Chalmers University of Technology, that is a private university supported by the Swedish Governement the only university of this type in Sweden. The decision was taken by the Governement after thorough evaluation of various possibilities, the Royal Institute of Technology in Stockholm being another candidate. The election of Anders Sjõberg as President went through a new process then before in which five candidates had been chosen to be evaluated in a final vote after official public hearings. Quite unexpectedly for me, I was one of the five, which gave me an interesting experience. Our international co-operation in the field of plasma and fusion research had been extremely successful and thanks to the Exchange Program with the Soviet Union organized by the 239

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agreements between the Swedish and Russian Academies of Sciences, as well as our association with Euraton Fusion and an organized cooperation with the Laboratory of Energy Research in the University of Maryland, represented by Professor Chuan Liu, our research capacity had increased considerably. To such an extent that international scientists said that the scientific efforts would lead the way to open the doors between East and West. In appreciation of the fruitful collaboration Professor Vadim N Tsytovich, Lebedev Institute, Moscow, and Professor Chuan S Liu, University of Maryland where both awarded Honorary Doctorates at Chalmers in 1982 and 1994, respectively. Then came Michael Gorbatchev as the new President of the Soviet Union which really opened the way on a political level. A result was that a stream of the best Russian scientists went to the USA, Europe or elsewhere, but then the whole internal economic situation in Russia collapsed. With this in mind on a large scale one can easily understand the opinion that caution should also be observed with international collaboration on a university level. And what happened with the young scientist I met the first day in the Institute of Theooretical Physics in Kiev, on my first visit in Kiev in 1971, who came to my office and said that he would like to work with me, and we had no language in common so instead communicated in mathematics. He not only made a career in plasma physics but made an impressive improvement linguistically and became a real polyglot. He now speaks not only Ukrainian, but good English and also Swedish! He lives with his family in Sweden and he became Professor of space plasma physics at the University of Uppsala, the oldest University in Sweden from 1477, the University of Carl von Linné (1707-1778) and several Nobel Prize winners like The Svedberg, Arne Tiselius and Kai Siegbahn, and his own name is Vladimir P. Pavlenko [8.7, 8.11]. I met him recently at a European Fusion Theory meeting in Elsinore in Denmark, and two years ago at the same type of meeting in 240

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Como, Italy. And he told me with his typical broad smile: you see Hans, to get along with languages is like science-you must love them…! A deep experience but a rich reward. From Pole to Pole; the two Roalds An ancestor on my mothers side emmigrated as a young man with his parents from the place on the Swedish west-coast, where my mother was born, to Oslo, where he was going to study medicine. Very soon he discovered that he preferred to do other things; he wanted to go to sea and make new discoveries. His name was Roald Amundsen the first man at the South Pole 1911, in competition with Scott, and later on at the North Pole, where however he dissappeared with his expedition (1925) During my first visit to the Soviet Union arranged by the Academies, NAUK and KVA I came to the large center of research in Novosibirsk (with the ancient city Academgorodok), where I met the Director Professor GI Budker and professor RZ Sagdeev, the ground-breaking theoretician in plasma physics, particularly in nonlinear theory with its applications to fusion and space physics. They took very well care of me, together with doctors DD Ryutov, BN Breizman, AA Galeev and several others. I remember that we discussed shock-waves, and various approaches to nonlinear interaction of waves, such as the random phase approximation, a Russian speciality taken over from Solid State physics, coherent wave interaction and many other things. Everybody called Professor Sagdeev: Roy, and when I met him, I could not help asking him once about his first name since Roy did not sound very Russian to me. He said it was Roald and I was told that he was baptized in this way since Roald Amundsen was so popular and admired in Russia when young Sagdeev was born that his parents chose to give him the name Roald. It was an interesting coincidence, and he became as successful in setting out flags for his discoveries and 241

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achievements in science and in life as the other Roald had been on the globe. He was very young as Academician and became member of the highest authorities in Moscow, Director of the Space Science Institute in Moscow with several thousand employées, then Scientific Advisor to President Michael Gorbatchev.(Nobel Peace Prize 1990) He visited us several times in Gõteborg. At the ICPP conference in 1982 he was the first chairman of the introductory talks by professor Dirk ter Haar (Physics of hot plasmas) and by Professor Hannes Alfvén (Cosmic Plasma Physics). He was a good friend of Hannes Alfvén and he was happy and honored to meet King Carl XVI Gustaf at our conference. Today Academician Sagdeev is at the University of Maryland, Department of Physics and the EastWest Space Science Center, College Park, Maryland, where he is now living with his wife, who’s grandfather, by the way, was President Dwight D Eisenhower (p.62).

Scene 6 L as ers , hol ography, rock et f l ames (Stockholm 19641967) In 1964 I was appointed Director of Research at the Research Institute of Swedish National Defense (FOA) with the rank of full professor, and only research duties. It became a very rewarding time from the physics and technology points of view. The contacts with the physics department at Uppsala University were strong. A section of the FOA activity was actually within the university under the supervision of Dr Nils Robert Nilsson, who came to be one my nearest collaborators and closest friend for many years. We did not only have science and technology as a common interest, but to an equal extent: art. There is no question about the fact that the laser meant a revolution to science when it was discovered in the early 1960’s. I remember how surprised and astonished I became when I heard for the first time that one had succeeded in 242

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amplifying light, and coherent light; that was when I stayed in Princeton. The step from microwaves to lasers was unbelievable, it was like night and day. It certainly meant new activities at the research establishment (FOA) which I now boarded. The secrecy laws imply that I am not allowed to write about any details of what was going on in the laboratories, but I can say so much that what took up my interest, and I was perfectly free to choose, was Lasers Nonlinear interaction of lasers with matter Holography Laser imaging and optical communication The physics of rocket flames and practical applications All these topics rapidly became an important part of modern science and technology I stayed with FOA and Uppsala University for seven years, and as a consultant much longer. My interest in art was really created at the same time, thanks to the impressive activities and exhibitions in Stockholm and to the contacts with people I met , apart from Nils Robert Nilsson; Gert Marcus, Arne Jones, Piotr Kowalsky and Carl Fredrik Reuterswãrd. With CFR we arranged the first LaserHolography exhibition ever (Galerie Burén, Stockholm 1969). The same year Gert Marcus had a laser-exhibition and demonstrated among other novelties how a ray of light from a ruby laser can be captured and contained in a curved plexiglass cavity (Galerie Doctor Glas, Stockholm). Also the same year in July the astronauts made the first moon-landing. What a demonstration of technical achievements! An optical phenomenon which has attracted considerable intrest in the development of science is the process of bending of light rays. Already Leonardo, who considered light as the most fascinating phenomenon of all in Nature, made drawings of how light was spread among the leaves of the trees and reflected in the atmosphere. We are now used to think of how light rays are reflected and refracted at surface boundaries, where discontinuities in the 243

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index of refraction occurs, or in media, where the refractivity changes continuously. Optical communication uses fibre optics to guide light waves in optical tubes, by repeated reflections at the fibre surface or by continuous internal reflection in fibres where a smooth radial change in the refractivity occurs. Similary, radio waves are bent in the ionosphere due to variation of the index of refraction with height, and can provide radio communication around the Earth. More sophisticated forms of the deviation of light are caused by gravitational bending or lensing as used in modern astrophysics. There the explanation of this delicate phenomenon can be understood on the basis of the curvature of space, associated with the presence of a gravitational field, according to Einstein. The bending effects there are small, but the distances enormous, causing noticable results. Bending of light can therefore occur as a result of a gravitationl field in Cosmos as well as by boundary effects in optical waveguides. Invisible light from a ruby laser can be used to excite a confined optical wave-field inside a curved section of plastic material as shown in the optical sculpture by Gert Marcus.

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Figure 8.1. Gert Marcus: Laser light confinement in a plexiglas rod Galerie Doktor Glas, Stockholm 1969 (Photo Gert Marcus)

In the spring of 1967 I was introduced to Piotr Kowalsky, a sculptor of Polish origin with an American education, who had just represented France at the International Venice Festival (Biennale de Venice). He was an interesting artist who had studied at MIT, Boston, Mass, mathematics as well as cybernetics for Norbert Wiener. He had large sculptur projects going on in California with elements of steel plates which were formed under water by mean of distributed explosive strips. He had students to calculate how those strips should be positioned on the plates to receive the desired shapes .I heard him give a seminar on his work in the Academy of Arts in Stockholm, which attracted a lot of attention. In any case, he had got to know that I had an interest in holography, which I then explained to him. He found this attractive, and since he was a co-editor of the journal Leonardo he invited me to write an article on holography, which I also did: Allow me to cite here the abstract of the paper, which serves as a short introduction to the field of holography, a principle that elucidates the internal features of light, and introduces a new dimension of image presentation: Wilhelmsson H. 1968, Holography: a new scientific technique of possible use to artists, Leonardo Vol. I, pp 161-169 (Oxford: Pergamon Press) Abstract. The possibility of using in art a new optical technique-called holography-is pointed out and the basic principles of the method are discussed. Although invented by D Gabor some twenty years ago, the real possibilities of the method have become more gnerally realized only recently, when lasers became available. The reason for this is that the success of holography depends to a large extent on the coherence of the light used. By utilizing coherent light from a laser, it is possible to store information about a three-dimensional object on a flat plate-the hologram. 245

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On a hologram an interference pattern is recorded. This pattern is produced by mixing the incident undisturbed laser light with laser that has been scattered by different parts of an object. Information on the relative phase-shifts of the scattered waves is then transmitted from the object to the hologram and stored in the form of interference patterns on the developed plate. By illuminating the hologram only by an undisturbed laser beam, it is possible to reconstruct the original scattered waves. To an observer this means that he sees a three-dimensional object in exactly the same way as if the real object were present. Parallax effects are preserved and the observer also must change the focus of his eyes regarding different parts of the objects in the hologram. The technique thus provides a third dimension to a two-dimensional presentation. The same part of the image of the object can be seen in different parts of the hologram when viewed from different angles. This means that each small area of the hologram plate contains information about the whole object. A number of experiments, aiming at technical and scientific applications of holography are discussed. Some aspects of the impact of the field of holography on present day scientific research are mentioned, as well as future possibilities of the new technique. The question of how holography may be used by artists is left open.

In 1948 D Gabor invented the new method to record lightwaves from an object without the use of lenses. In fact, Gabor originally developed his method for electron-waves, aiming at avoiding errors of aberration in electron microscopy. Four important publications should here be emphasized, namely: Gabor D 1948 A new microscopic principle* Nature, London May 15 Gabor D 1949 Microscopy by reconstruced wave-fronts Proc. Roy. Soc. A, 187

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Gabor D 1951 Microscopy by reconstructed wave-fronts proc. Phys. Soc.B, 64 Gabor D 1966 Holography – The reconstruction of wave-fronts, Electronics & Power, July

In 1971 Professor Dennis Gabor was awarded the Nobel prize in Physics for his invention and development of the holographic method. I had an opportuneity to meet Professor Gabor together with Professor Nils Gralén President of Chalmers at a dinner in Gõteborg when Gabor returned from the ceremonies in Stockholm. It was a great experience to meet this gentlemen, an inventive geneous with more than 250 patents quite apart from holography. Before 1948 he had been working in information theory at Imperial College, London. I remember that I asked him the question if his work in information theory had been essential for his invention and development of holography, which to me did not seem unlikely. And he said: may be unconsciously. A diplomatic anwer from a great thinker. Holography has been applied in various contexts where high precision is required, for example in measuring deviations of rotating parts in mechanical engineering, for dynamic changes in gas-streams, for structure variations in threedimensional interferometric patterns, introduced by perturbations, e.g. when a bullet traverses a gas volume. Furthermore, for studies of turbulence patterns in gases and plasmas, e.g. diagnostics of fusion plasmas. Even if the principle of holography can be expressed in simple terms it should not be hidden that, in essence, it is of an exceedingly complex structure which should be used to study detailed structures, where high precision is needed. The problem of transmitting the enormous quantity of information hidden in the structure of a hologram, requires electronic systems with very high capacity, which makes something like holography television difficult, may be even unrealistic. The possibility of using holography for artistic purposes came to my mind since for such purposes high accuracy might play a less 247

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dominant role and require less resolution as I explained in a seminar which Arne Jones invited me to give at the Art Academy in Stockholm. The article I wrote in Leonardo on holography had stimulated Carl Fredrik Reuterswãrd to an interest in using holography and lasers in art and to make the exhibition in Galerie Burén with the generous technical assistance of Nils Robert Nilsson. Carl Fredrik soon left his professorship in the Academy to set up his own laser laboratory for art in Switzerland. As a curiosity I got to know that Dennis Gabor happened to be honorary editor of the journal Leonardo in which I wrote the paper on holography! Piotr Kowalski had a separate exhibition of his work at the Museum of Modern art in Stockholm, arranged by Pontus Hultén, the creator of the museum beautifully situated on an island, Skeppsholmen, in Mãlaren, the lake joining the city of Stockholm with the Baltic See. It was a great event. Pontus Hultén was not only the creator of the museum at Skeppsholmen, one of the best museums of modern art in the world; he was artistically responsible also for the new Pompidou museum in Paris the most debated monument there, due to its architecture, and furthermore later for the . I think one could say that he has been really the world exhibitor of modern art, now living in the Loire valley in France. I got to now him throught Piotr Kowalsky, and met him several times later. He and Piotr came to visit us in our house in Uppsala. They even enjoyed our sauna! Holography, as a principle, has certain similarities with other methods of analyses used in astrophysics, such as the aperture-synthesis technique (M.Ryle, NP 1974) for studies of the distribution of matter in the cosmos. It has even been proposed that the entire universe may be regarded as a hologram. The human brain will help to decipher the information contained in the structure. The brain itself can also serve to capture the details of the information stored in the human memory, indeed a hologram in itself, so why not of the memory of the cosmos. 248

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But the list of fundamental applications of holography can be further extended. For the attempts to obtain a combination of classical gravitation and quantum mechanical gravity effects when describing the universe it has been noted that the string theory in a certain sense includes the holographic principle. The disorder (entropy) in a black hole, which controls the quantum effects and therefore the possibilities of having radiation from a black hole is recorded on an area defined by the horizon around the hole, which serves as a hologram. The two-dimensional surface mirrors all information about the three-dimensional internal structure of the hole. Similarly everything that happens in the entire universe is coded in an interference pattern of a remote fictitous surface, a universal hologram. In this connection one cannot help noticing that already the poetry of Harry Martinson «captures the dewdrop and mirrors the cosmos» (citation from the Nobel Prize motivation for literature in 1974), as mentioned at a symposium in May 2004 on the occasion of the 100 anniversary of his birth. E l ect rodynami cs , pl as mas , f u s i on; Techni cal phys i cs edu cat i on and t he U S A agai n (Uppsala 1967 – 1971) After three years at the Research Institute for National Defence in Stockholm I decided that I wanted to contribute to teaching. I came to Uppsala in 1967 as associate professor in Electromagnetics and Plasma Physics. The students were good, thanks to a hard selection process. There were two coarses for the undergraduate students of Technical Physics: One in Electromagnetics and one in Plasma Physics. We used good books: Panofsky and Phillips (and Feynmann lectures) in Electromagnetics, and Clemmow and Dougherty in Plasma Physics. I tried to explain the essential points in as great detail as possible, the students having the books available. But I did not fill the blackboard with equations from top to bottom. Olof Rydbeck at Chalmers had instructed me: you should explain the physics of all parts of the equations 249

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and motivate how these are formed, and why they are important. Probably he learnt this himself from Harvard, where he graduated. It was nice to lecture in this way, and the interaction with the students was good. They even gave practical remarks. I remember, for example, one day Tord Ekelõf asked me to show more slides and use more the technical facilities. He should get more of that later on in life, when he became a great man in CERN in Geneva! I had very good help of my colleages Lennart Stenflo an Bo Kjellmert in those days. Lennart became very soon professor at the University of Umeå, at the very north of Sweden, and also member of the Academy (KVA) in Stockholm. Jan Weiland, one of the students then, became professor of fusion plasma physics at Chalmers in Gõteborg. One day Nils Robert Nilsson, my good friend and collegue came and listened to one of my lectures. Afterward he said that it was OK but something puzzeled him: He was surprized what a resemblance one student in the front row had to Professor Kai Siegbahn! Nils Robert had been wondering before why Kai, as he said, knew so much about my teaching. It turned out that the student was Per Siegbahn, a son of Professor Siegbahn! Besides, I was pleased to get to know that Per was interested in the lectures and at the end of the coarse took an extra examination on Feymann’s book. In 1981 his father was awarded the Nobel prize in Physics, as had his grandfather, professor Manne Siegbahn been 1924, Per Siegbahn is nowadays professor of theoreitical physics at the University of Stockholm and a member of the class for chemistry in the Academy (KVA). Nils Robert Nilsson was busy building surge generators to produce short energetic pulses in a hall of the Physics Institute. He had been an enthusiastic collaborator with Professors Kai Siegbahn and Per Ohlin in building the first fusion oriented device in Uppsala, a toroidal pinch, somewhat like today’s Tokamaks. The Uppsala machine got the name Fyrisatorn (from the river Fyris which traverses the city of Uppsala). 250

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Nils Robert had also been responsible for arranging the International Conference on Ionized Gases in the Spring of 1959, which became a great success, in the most beautiful weather. It was my first international conference and I gave several talks on wave propagation in plasmas. I remember Uppsala, when I came to live there for more than three years in 1967-71 a delightful period in my life, a city where the snow was always white several months of the year and one could make long tours on skis. Even before then I had given courses at Husbyborg, a centre for High Tension Research near Uppsala. It was there, I introduced a graduate course teaching, where I was sitting with half a dozen students around a table to discuss the literature, a method which I later introduced at Chalmers. At Husbyborg Professor Stig Lundquist was the scientific leader, famous for his early experiments on magnetohydrodynamic waves (MHD), and for the Lundquist number, i.e. the magnetic Reynolds number, referring to situations where the characteristic plasma velocity is equal to the Alfvén speed. The Institute was based on a donation from two ladies who were afraid of lightning. Nils Robert Nilsson and I went on several international conferences and visits to laboratories together, and it was certainly always useful that we could represent both experiment and theory. In 1965 we went on a long tour around the USA, visiting laboratories, all over the states, among them Princeton, (where we visited RCA and saw holography for the first time), Los Alamos, Berkeley etc… We had decided also to visit Boeing Company in Portland, Ca, where interesting experiments on solid states plasmas were going on. On the way we had a flight from Albuquerque to Denver with connection in Denver to reach Portland. We entered a morning flight in Albuquerque which turned out to be very bumby in hard winds. We were served champagne, probably in order to calm the passengers. I remember that Robert and I had a competition who could best fetch the content of our glasses when the liquid suddenly jumped up. We reached 251

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Denver in hard winds and changed plane for Portland. On the way there I looked down on the landscape which had abundant steep montains, and I remember, funny enough, that I thought it would not be nice to land there. And, suddenly it became dark in the cabin and we got to know that one of the two jet generators had gone on strike. The plane changed immediatly direction, and we were informed that we were going to return to Denver. We did not understand how serious the situation was, but clearly it would not be easy to make an emergency landing under the prevailing conditions. When we landed again in Denver the platform was full of ambulances and fire equipment but all went well and we could make a new attempt 3 hours later. We were lucky to conquer the Rocky Mountain this time and land in Portland. The next day we got to see not only the plasma laboratory and the experiments on solid state plasmas, but also the production analysis of the big aeroplanes Boeing 747, which was indeed an interesting experience. How they did detailed surface testing of the wings and how they bent the top of each wing about ten meters up and down to down ascertain that they should resist heavy forces from winds. When the visit was over we got informed that the next day we were booked on a test flight; we felt that was not exactly what we had expected! They said that as a rule there were no problems, but once recently they had petrol leaking out in one of the wings, but they thought they had mastered that problem now. The next day, we were informed the test-flight had been postpened. We felt quite happy with the experience we already had gotten, and which we could report on as representatives of the Research Institute of Swedish National Defence! At a conference in Stockholm in 1967 arranged by Professor Bo Lehnert, I met Professor Folker Engelmann from the fusion laboratory in Frascati (Rome), and we discussed nonlinear problems. I was invited next year to visit the laboratory in Frascati and work there for three months in Summer of 1968 with Folker Engelmann as my host. It was a pleasant and active time which resulted in a publication joint on «Phase effects in the nonlinear interaction of negative energy 252

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waves» Zeitschr. Naturforsch. 24 a, 206 (1969) and in the paper: Wilhelmsson H 1969 Nonlinear coupling of waves in a magnetized plasma with particle drift motions J. Plasma Physics 3, 215, which led to a sequence of related papers. Sweden was not associated with Euratom at that time and I learned a bit about the Italian association. Later on, I remember that a Chinese delegation visited Frascati and studied the experimental facilities. They became interested in a proposal for a new medium-size Tokamak in Frascati and were allowed to see and copy the drawings for the construction. The machine finally did not get approval to be built in Frascati, possibly because it did not fit the overall planning. When some French scientists in a delegation visited China a year or two later they found that the machine had been built in China. By the end of the 1960’s I wrote my first application to a research council. It was to the Swedish Technical Research Council (there were going to be many!). I for mulated it as follows: With the event of the newborn laser the nonlinear effects were going to be of paramount importance for many technical applications. The simultaneous focussing in both space (narrow pulses) and time (short pulses) was going to produce very strong not to say explosive effects. I got the money I was asking for and payed a young very good associate with it: Kjell Õstberg, who finished his doctorat with me in Gõteborg when I moved there. When later on I met Professor N.G Basov from Moscow, who received the Nobel Prize in Physics together with Professor CH Towns and AM Prokhorov; he told me that now they had so strong fields from lasers that the field tore all the electrons away from the atoms in a solid pellet and the remaining positive nuclei just exploded due to their positive charges, as a result of Coloumb repulsion. It did not contradict my proposition to the Council! Another conference which Nils Robert Nilsson and I participated in was the European Physical Society Conference 253

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in Florence in 1969, which was held in Palazzo Veccio. In his introductory address Professor Victor F Weisskopf said: «An account of physics in the XX-th century would be very incomplete whithout mentioning astrophysics. It is a science born in this century. It is the frontiers of physics at extremely large distance in contrast to particle physics, which is the frontiers of extremely small distances. There is good reasons to believe that the two are intimitely related». At the same conference Professor Antony Hewish presented the situation in the field of pulsar research (when this had gone on for only one year).His talk was entitled «Pulsars»: «The discovery of pulsars by radio astronomers at the Cavendish Laboratory just over one year ago was precisely one of those lucky accidents… It would be satisfying to report that we were seeking them at the time, but this was not so. We were, in fact, engaged upon a study of distant radio galaxies far beyond the confines of our own galaxy when the first pulsar placed its faint signature on our record. Since that time astronomy has witnessed an almost explosive growth of interest in pulsars and they therefore provide a topic entirely in keeping with the theme of this conference (the Growth Points of Physics). Pulsars are important, not only for themselves, but because they focus attention on some unsolved problems in physics – problems in which the state of matter is far removed from conditions which can be reproduced in terrestrial laboratories, yet which ultimately depend upon fundamental particle interaction. As concerns the interferometric methods of measurements, developed for radioastronomy, these may be considered new and principally interesting ways to obtain information about remote sources of radiation under often extreme physical conditions. They could thus be considered as tools for penetrating new domains of physics. To furthermore elucidate the general role of such techniques of measurements it should be mentioned that Professor Hanbury Brown developed the technique of intensity 254

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interferometry to measure star diameters, but according to information from CERN, the European Center of Nuclear Research, with the large accelerators in Geneva, the technique mentioned can also be used to measure particle dimensions». The main part of the activity of the Physics Institute at Uppsala was the development of the high resolution electron spectroscopy by Professor Kai M Siegbahn. The activity had an impressive configuration like the form of a tree with the Master in the top and many fruits and grooth-points on the branches, signifying the large school of physicists that grew up under his direction. The acronym ESCA, Electron Spectroscopy for Chemical Analysis was coined when it became clear that the chemical shift effect offered interesting applications for chemistry and that electron spectroscopy was applicate to the analysis of all elements in the Periodic System. In 1981Professor Kai Siegbahn was awarded the Nobel Prize in Physics. Half of the Prize was awarded jointly to Professor Nicolaas Bloembergen, Harvard University, and Professor Arthur L Schawlow, Stanford University, for their contributions to the development of laser spectroscopy and the other half to Professor Kai M Siegbahn, Uppsala University for his contribution to the development of high-resolution electron spectroscopy. In the spring of 1971 I had left Uppsala to become Professor of Electromagnetic Field Theory at Chalmers University of Technology in Gõteborg.

Scene 7 (Gõteborg and the world 1971-2003) It was a time full of activities of different kinds: Research, teaching, meetings in research councils, in academies, a lot of travelling to Stockholm and abroad to meetings and conferences, but in a way: to make a good soup, none of the ingrediences could be neglected. It meant new 255

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impressions, new acquaintencies in science and art, new ideas and a lot of pleasure. To be fair, I would say that during the time as full professor at Chalmers (1971-1994) I did not spend more than part of the time at Chalmers, which gave possibilities of keeping an objective view on the base activities at Chalmers. It also motivated, two new extra professorships to the fusion plasma physics group, and later on another two! It moreover gave a chance for the young members to develop independently, in research and in teaching, and it gave me an opportunity to increase considerably our external contacts and activities. This could not have been done without efficient help, first of all from my teaching personnel for the undergraduate courses: Hans Desaix and Eva Palmberg, and from my very skilled secretaries Monica Hansen and Bente Larsson, and the departmental secretariate when at the same time I was Dean of the Electrical and Computer Engineering Department of Chalmers (1983-1987). The association of the Swedish fusion activities with Euratom Fusion in the 1970’s opened the windows for extended collaboration with activities in the other member states, but that was not the only thing. The collaboration with the Soviet Union and the USA were also considerably increased. Thanks to the scientific exchange of the Academies of Sciences in Sweden and the Soviet Union close agreements on collaboration in the field of plasma physics and fusion were established in Moscow, and almost simultaneously, the activity at Chalmers signed an agreement of collaboration with the University of Maryland USA, in the same field. This led to a lot of activities with symposia and exchange visitors from both sides. In part it was not until the 1970’s that Soviet scientists were allowed to travel outside the USSR. Those exchanges had also synergetic effects, in the way that when we had visitors at Chalmers of active scientists from the Soviet Union or the USA, or both, this was a further attraction for scientists from the other European member states and even Japan to come also, and the wheel turned around and much information was dropped at Chalmers to the benefit of the 256

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scientists and the graduate students. In the beginning it was just a different world then before. And the number of graduate students increased and contributed to the examination rate for young doctors. In the long run this was important and increased also the number of scientists working in our activity, motivating new extra professorships. It is not the purpose here to comment on all the work published in this period of more than thirty years, and the author lets the reference list with explicit titles talk for themselves. A few books and some collected papers and proceedings are, however, mentioned separatly, namely: I.

WILHELMSSON H (Ed.) 1977 Plasma Physics: Nonlinear theory and experiments Nobel Foundation Symposium 36 th, Gõteborg, June 1976, Sweden, pp I-XIV and 1 – 513 (NewYork, London, Washington DC, Boston: Plenum)

II.

WEILAND J and WILHELMSSON H 1977 Coherent nonlinear interaction of waves in plasmas (Oxford: Pergamon press; Moscow: Energizdat, russian edition)

III.

WILHELMSSON H (Ed) 1979 Solitons in physics Chalmers Symposium (150 th Anniversary of Chalmers) Physica Scripta Vol 20, n°3/4

IV. WILHELMSSON H (Ed) 1982 The physics of hot plasmas International conference on plasma physics (ICPP), Gõteborg, Sweden, Part 1 Vol T 2/1 pp 1-274, Part 2 Vol T 2/2 pp 275-600 V.

LISAK M and WILHELMSSON H (Ed) 1986 The role of alpha particles in magnetically confined fusion plasmas Physica Scripta (1986/87)

VI. WILHELMSSON H 1994 Global dynamics of thermonuclear fusion plasmas: Self-consistent treatment of diffusion-reaction equations (selected publications 1987-1994) (26 publications) CTH-IEFT/PP-1994-01 ISSN 0281-1308

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VII. WEILAND J 2000 Collective modes in inhomogeneous plasmas (Bristol and Philadelphia: IOP publ.) VIII. WILHELMSSON H 2000 FUSION: A voyage through the Plasma Universe (Bristol and Philadephia: IOP Publ.) IX. WILHELMSSON H and LAZZARO E 2001 Reaction-diffusion problems in the physics of hot plasmas Bristol and Philadelphia: IOP Publ.)

I am proud and lucky to be a member of the following academies: •

The Royal Swedish Academy of Sciences (the Class for Physics) Stockholm (since 1974)

•

The Royal Swedish Academy of Engineering Sciences Stockholm (the Division for Basic and Interdisciplinary Engineering Sciences (since 1978)

•

The Royal Society of Art and Sciences in Göteborg (the Class for Physical Sciences) (since 1983)

•

The Ukrainian Academy of Sciences (foreign member) (since 1991)

•

The National Academy of Sciences, Literature and Arts in Bordeaux (resident member since 1999 foreign member 1995-1999)

In the academies one can sometimes be inspired to new thinking and new activities, both in scientific matters and in organization. When I was new in the Royal Swedish Academy of Sciences in Stockholm, I happened to be next to a fine gentleman at the buffet after a wednesday reunion. He was quite entertaining and he spoke with a beautiful Finish singing accent. He said to me when he heard that I was starting a new activity: you should aquire excellent collaborators, that is the most important point, he had tried this himself, and then he took another «snaps» (aquavit). I learnt that the name of this 258

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charming gentleman was Ragnar Granit. And apparently he had been successful with his method; he had received a Nobel Prize in oftalmology! I took him rather seriously and tried to do the best of my situation. I think his advise was good, and I thought of it many times later. May be that was one reason that I came to travel so much and have such a lot of collaboration! From the Russian side there are many stories. In fact, I think the Russians are very good at telling stories, and very appreciative of good stories. The Russian stories as a rule are quite simple but at the same time deep, which to me is a real sign of art, in stories like in physics. In Russia, may be more than anywhere else, the Academies play an important role. Academician is used as a title, you have advantage, for example not to wait in a line, not to pay entrance fee, to have an extra salary, or in short to be regarded as a particularly respected person The Academies also do a great work to promoting sciences, for scientific collaboration with other countries e.g. Sweden etc. They are also pioneers in Fusion Sciences. So, naturally there are stories also about the Academies and the Academicians. In the city of Gorki (nowadays Nijni Novgorod, («the new St-Petersburg») there has been for long times a strong radio transmitter (Gorki was the city of Russian military research) which had daily programs telling stories to amuse people. The following two examples come from this source: There was a young lady whose boy friend for some reason became interested in the Academies: The young lady contacted the President of the Academy and said: My boy friend would like to become a member of your Academy (may be the boy thought that is was as easy as to become a member of the communist party; the author’s remark) the problem is that he can not write nor read. The answer from the President was direct and decisive: It is OK, but he cannot be a corresponding member! The other story of a similar kind from the same source goes like this: A gentleman who had been offered to become a foreign member of the Academy, and who knew that the Academicians 259

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had certain advantages, asked about what advantages he would have as a foreign member, if they would be the same as for an ordinary member. The President said that there were no such advantages. The gentleman, slightly disappointed, then asked what was the meaning to become a foreign member. The President said: as a foreign member you do not have to stay in the country. The research council meetings every spring were indeed very tough, going on often from early morning to sometimes late in the evening. There were in Sweden two different research councils: The Natural Science Research Council (NFR) and the Atomic Physics Research Council (AFR) covering essentially all research projects from expensive experiment to salaries for research personal. The projects were examined in delegations, for example the physics delegation of NFR. For a number of years I was a member of both councils which covered all plasma physics, and before the European association also fusion, and chairman of the AFR delegation. The work gave certainly a very good insight in what was going on, and the limited amount of money available required as a rule rather severe cuts. Out of the many interesting projects I will here only as an example, refer to an application from Professor O. Rydbeck to build a one hundred meter diameter parabolic, fully steerable radio telescope at Onsala (Råõ) Space Observatory Gõteborg. The budget was estimated to thirty million SEK in the year 1968/69, possibly amouting to a corresponding value of the same amount in Euros or Dollars today. This was an extremely costly investment for Swedish research standards which needed careful judgement. The German radioobservatory in Effelsberg had already such a telescope and was continuously making discoveries. New result almost every day. The instrument was constructed by the Krupp Company. Constructing large telescopes is a science in itself (cf. the work by Sir Martin Ryle, Cambridge, N.P 1974). The «efficient» focal point, for example, of the paraboloid changes with orientation of the instrument. When the heavy mass of the 260

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antenna experiences the gravitation, the parabolic form changes and there is a tendency that the instrument will incline, in such a way that it bends over differently for different orientations. This has to be accounted for in the observed data for all directions. It is thus not possible to make a stiff paraboloid of this size, which should also have a good surface accuracy of the order of a part, say one tenth of the wavelength of observation. Those were just some but important questions to consider. The situation, from the economic point of view, did not become simplified by the fact that the Kiruna Geophysics Institute (nowadays the Swedish Space Research Institute in Kiruna) also came with a very expensive proposal from Kiruna, for ionosphere measurements, however, whereas the Onsala observations were aiming at spectral line measurements of molecules, radicals and atoms of galactic gas studies, objects much more remote than the ionosphere studied at Kiruna. It seemed difficult to realize anyone of these antennas, and even more so, both of them. In the discussion there came up, however, a new idea, launched by Dr Per Maltby (invited consultant) from Norway, motivated by a physics point of view, that should help the whole situation. The tendency in short wave radio astronomy was to approach the millimeter wave-lengh domain, where new interesting lines might be expected. The idea was therefore to abandon the very huge paraboloidal antennas and to construct something smaller for which several of the mentioned drawbacks could be avoided, namely a stiff construction which avoided the bend-over effects and kept the focal point stationary during the operation of the antenna, furthermore which could have an extremely high surface accuracy, thereby allowing for millimeter waves without «blurring», and finally having a sheltering condome all around the antenna to help avoiding wind disturbances. That would be a really new facility with exceptional possibilities, and besides with a reduced cost. This was an intelligent solution, which was after further detailed considerations decided upon. So much the better it provided 261

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possibilities also for the Kiruna project to be realized, and Sweden got two new instruments to enter on the scene. And the results and discoveries came also very soon from the 20m diameter supersensitive telescope at Onsala. The observed magnetic hyperfine structure splitting of Nitrogen into 17 lines was remarkable. These could not be seen in the laboratory, since there the necessary abundance for observation would introduce interactions, broadening and overlapping of individual lines. Space provided sufficient distance between the particles and integrated numbers of molecules to provide the necessary intensity of radiation without interference of the separate contributions. Today, as an example, not less than 170 radio-frequency lines from 24 different molecules have been identified in the Orion nebula by the Onsala telescope, 32 of these lines essentially rotational transitions from one single type of molecule namely CH3COOH. One could say that there are similarities between radioastronomy and fusion plasma diagnostics. Radio astronomy could be regarded as diagnostics in the Universe, looking at clouds, nebulae, galaxies and at details in those, whereas diagnostics in fusion, seems clear what it means, determining densities, temperaturs, the presence of different kinds of particles their energy relationships and the nature of occuring physical phenomena. More than so the astronomical objects could, like the fusion plasmas offer states which can not easily, if not at all so far, be produced in an ordinary spectroscopic laboratory. JET has provided excellent opportunities of spectroscopic studies for the atomic spectroscopists. They have for example seen new excited states and forbidden transitions, similar to those which can be observed at short instances in exploding wires. And, as we just discussed, cosmos could provide conditions to see, in diluted states, a large number of non-interacting atoms or molecules, with resolved spectra. Global dynamic states can also be said to prevail in, for example, nebulae like the Crab nebula exhibiting also syncroton radiation as in fusion plamas. 262

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When the Nobel Prize for physics was awarded in 1974 it was for work in the field of astrophysics. I may be allowed to cite here the adress I gave on behalf of the Royal Swedish Academy of Sciences on the occasion of the presentation in the Stockholm Concert Hall.

THE NOBEL PRIZE FOR PHYSICS The Work of Sir Martin Ryle (Great Britain) And Professor Antony Hewish (Great Britain) presented by Professor Hans Wilhelmsson Chalmers University of Technology Prize citation:

«for their pioneering research in radioastrophysics»

(Ryle)

«for his observations and inventions, in particular of the Aperture-synthesis technique»

(Hewish)

«for his decisive role in the discovery of pulsars».

Your majesty, Your Royal Hihnesses, Ladies and Gentlemen, The subject of the Nobel Prize in Physics this year is the science of Astrophysics, the Physics of the stars and galactic systems. Problems concerning our Universe on a large scale, its constitution and evolution, play an essential role in present-day scientific discussions. We are curious about the behaviour of our Universe. In order to draw reliable conclusions regarding cosmological models it is necessary to gather detailed information about conditions in the remote parts of the Cosmos. Radio-astronomy offers unique possibilities for studying what is taking place, or in reality what occurred very long ago, at enormous distances from Earth, as far out as thousands of millions of lightyears from us. The radio waves now reaching us have been travelling for

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thousands of millions of years at the speed of light to reach our Earth from those very remote sources. It is indeed a thrilling fact that the radio signals we record today here on Earth left their cosmic sources at a time when hardly any flowers or living creatures, and certainly no physicists, existed on Earth. New and epoch-making discoveries have been made in the field of Radio-astrophysics during the last decade, discoveries that are also exceedingly important contributions to modern Physics, for example in establishing through radio-astronomical observations the presence of matter in a superdense state. One single cubic centimeter of this superdense matter has a weight of thousands of millions of tons. It consists of tightly-packed neutrons. A neutron star appears as a consequence of a star explosion, a so called supernova event. Neutrons stars, with a diameter of about 10 kilometers, are from a coscmic point o view extremely small objects. They represent the final state in the evolution of certain stars. This year’s Nobel Prize winners in Physics. Martin Ryle and Antony Hewish, developed new radio-astronomical techniques. Their observations of cosmic radio sources represent extremely noteworthy research results. In order to collect radio waves from cosmic radio sources on utilizes radio-telescopes. It is important that a radio telescope should have a large area, both for highest possible sensitivity and for the high angular resolution that is needed to discriminate among the various cosmic sources of radio radiation. For observation of exceedingly small sources it is, however, no longer possible to build a single radio-telescope of sufficient size. Ryle and his collaborators therefore developed the method of aperture synthesis. Instead of making one huge aerial, a number of small aerials are used in this method, and the signals reived by them are combined in such a way as to provide the necessary extreme accuracy. Instead of many small aerials, Ryle in fact made use of a few aerials that could be moved successively to different positions on the ground. Ryle also invented the extremely elegant and powerful technique utilizing the rotation of the Earth to move his radio264

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telescopes. With this technique he obtained a resolution in his observations that corresponded to an aerial of enormous size. Ryle’s measurements enable us to conclude that a steady-state model of the Universe can not be accepted. The Cosmos on a large scale has to be described by dynamic, evolutionary models. In his latest construction in Cambridge, Ryle obtained an angular resolution permitting the mapping of cosmic radio sources with an error of only few seconds of arc! The radio-astronomical instruments invented and developed by Martin Ryle, and utilized so succefully by him and his collaborators in their observations, have been one of the most important elements of the latest discoveries in Astrophysics. Antony Hewish and his collaborators in Cambridge, in the Autumn of 1967, made a unique and unexpected discovery that has revolutionized astrophysics. They had constructed new aerials and instruments to study the influence of the outer corona of the sun on the radiation detected from remote point sources. A special receiver capable of extremely rapid response had been built. The fast receiver provided a result quite different from its intended purpose. By chance the receiver detected short pulses of radio signals that were repeated periodically about every second, and with exceedingly high precision in the pulse repetition rates. It was concluded that the radiation originated from cosmic sources of previously unknown type. These sources were subsequently named pulsars. One has come to the conclusion that the central part of a pulsar consists of a neutron satr. The pulsars are also accompanied by magnetic fields many millions of times stronger than those found in laboratories on Earth. The neutron star is surrounded by an electrically-conducting gas or plasma. Each pulsar rotates and emits beams of radiation in the Universe, resemblig those from a lighthouse. The beams strike the Earth periodically with high precision. The pulsars are indeed the world clocks which our Nobel Prize winner Harry Martinson mentions in his poetry. Allow me to quote this poet of space: «World clocks tick and space gleams Everything changes place and order». 265

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Early in the history of pulsar research it was suspected that neutron star matter existed in the centres of supernovas. Radiotelescopes were aimed towards the centre of the Crab nebula, a magnificant glaring gaseous remnant of a supernova event that is known, from Chinese annals, to have occurred in 1054 A.D. This pulsar emits not only radio pulses, as expected from a pulsar, but pulses of light and x-rays as well. It is comparatively young, rotates rapidly and is in fact exceptional among pulsars. Antony Hewish played a decisive role in the discovery of pulsars. This discovery, which is of extraodinary scientific interest, opens the way to new methods for studying matter under extreme physical conditions. The contributions of Ryle and Hewish represent an important step forward in our knowledge of the Universe. Thanks to their work new fields of research have become part of Astrophysics. The gigantic laboratory of the Universe offers rich possibilities for future research. Sir Martin, Some of the most fundamental questions in Physics have been elucidated as a result of your brilliant research. Your inventions and observations have brought new foundations for our conception of the Universe. Professor Antony Hewish, The discovery of pulsars, for which you played a decisive rôle, is a most oustanding example of how in recent years our knowledge of the Universe has been dramatically extended. Your research has contribued greatly to Astrophysics and to Physics in general. On behalf of the Royal Academy of Sciences I whish to express our admiration and to convey to you our warmest congratulations. The Royal Academy of Sciences regrets that Sir Martin Ryle is not here today. May I now ask you, Professor Hewish, to receive your prize and also the prize awarded to Sir Martin Ryle from the hands of His Majesty the King. 266

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‫٭٭٭٭٭٭٭٭٭٭٭٭٭٭‬

It is fascinating to notice that pulsars have indeed stimulated the whole field of astrophysics in a significant way since the time the prize was awarded thirty years ago. The most frequent and continuous visits abroad I had to Oxford, where in the neighbourhood, the JET establishment was situated at Culham. I went there regularly at least four times a year during 1979 to 1994, that is for fifteen year, as a member of the JET Scientific Council or for the last five years of the JET Council, the highest authority of JET. There were about twenty people in the Councils, representing the various European countries, and all significant decisions were taken in the JET Council with JET Scientific Council as the advisory board. It was an impressive organisation, to coordinate in particular technical and administrative questions among the different countries with professor D Palumbo as the Director General of the European Fusion activities. Each meeting lasted in general for two days, in general with very detailed discussions on a broad spectrum of questions. I know that from the American side that the JET organization has been considered as ideal. In the evening between the two meeting days a dinner was always organized in one of the many oldfashioned restaurants in the Cotswald area around Oxford, which gave rich opportunities to continued, more relaxed discussions. The extraordinary technical accounts of the progress of the whole project, which were given every time, often with visits to the sites, was a great stimulous for the participants and confirmed successively the great success of JET. Often, I took the opportuneity of combining my visits to JET with my interest in art, going to exhibitions in Ashmolean Museum of Art, the oldest museum in England, to the Museum of Modern Art, or to the Oxford Gallery of Modern Art. That was how I got to know about Stanley William (Bill) Hayter (1901-1988), who has been characterized as the greatest 267

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and most original print maker of the twentieth century. He attracted many hundreds of artists to work in Atelier 17, (from 1933), which he founded in Paris, and later, during the war times, in New-York. He was a friend and inspiration of many famous artists, among them Miro, Chagall, Picasso and others. I phoned him up in Paris, and he invited me to come to his atelier in 12, rue Cassini Arr.14. near the Observatory, a Saturday afternoon. He was trained originally as a chemist and had been a teacher before. In 1926 at the age of 24, he arrived in Paris and enrolled at the Academie Julian having decided to study painting and print making. He enjoyed Paris and the company of artists, writers and photographers. In 1921 he had accepted a three year contract with an Anglo-Iranian Oil Company (North British Petrolium) and stayed in Iran (Abadan), where he sometimes had responsability for as many as 5000workers He arrived in Paris after his Iranian adventures in 1924, which was when the surrealist movments started and his new atelier became popular to artists like Miro and Giacometti as well as Arp and Max Ernst. Hayter himself was particularly close to Miro and to Masson. He became very friendly with me, showed me many of his etchings, which were really fabulous. I liked a lot several of his early works on interferometry of water waves, and I asked him to put some aside for me if he could. He sayed: with pleasure, if I have more than one of them left. He phoned me later and said that it was O.K. I came again to his atelier, and he painted at the same time as we talked about lasers, holography and others things in science. Then the telephone started to call. It was some galleries which were interested in his work. Then another call, and I understood that it was something important: It was the British Museum which called and wanted to buy a copy of each one of all his work, from the very beginning, that must have been several hundreds. He seemed very happy about the appreciation from such an important museum, and said: I was always rather poor, now I may become rich. And then he continued to paint and we talked about art and science. 268

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He also told me stories about famous artists, among them Picasso 1881-1973, he said: I never tell stories about him, which he did not tell me himself! Then he showed me numerous small paintings he had on his walls by Miró and also drawings by him and other artists like Giacometti. He told me a story about a young architect by name Roberto Matta, who by the age of 21 came to Paris, from Santiago in Chile, in 1922, and who got a job to work for Le Corbusier 1887-1965 (the famous French architect, urbanist, theoreticien and painter of Swiss origin) to help him in his work for the Large World Exhibition to take place In Paris in the near future. Le Corbusier who found Matta not only artistically gifted by also useful for practical arrangements, and asked him to inspect a little how different works were coming along in different sections of the exhibition. In particular, he wanted him to look for a man, who should work with a mural sculpture, but as Le Corbusier said, did not seem to progress very much and that he might be even lazy. Roberto Matta went away to try to find the man, but it took quite a long time, before he returned, and as it turned out, he had in the meanwhile become a good friend with the suspected figure, who happened to be Pablo Picasso! I happened to meet Roberto Matta himself on several other occasions in Paris and he was a very inspiring man, very timid about himself. He presented himself as an architect and a mathematician who also did some painting and graphics. In reality he was the only great surrealist still alive. His daugther, Frederica, is also a top-star artist of her own, who by the way recently won a world competition in designing a new logo for NASA. I knew her and her husband Peter Fletcher, a very interesting artist, active also in optical art, and we met in Paris several times. Roberto Matta had some gigantic exhibitions in Paris some years ago, when he was more then eighty years old. In the «young» generation that I know, I would particularly also mention Eliane Larus, Christine Pichette, Michel Potage, among the thirty thousand artists active in Paris. One day in 1988 I was going to give a seminar on plasma physics in Paris University for a public audience and I had 269

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invited Bill Hayter to attend. I was surprized and a little disappointed that he did not appear until I understood the reason. The day after (May 4, 1988) I received a short note with the following content: «I was told by Bill that he enormously enjoyed all the discussions that you had together. But I have to inform you that Bill died». Sincerely, Désirée, his wife. (The letter still remains with me, in French). A short time later there was a retrospective exhibition of the graphic works of Stanley William Hayter, which had been planned for a long time, in Ashmolean Museum in Oxford. It was a fascinating, extremely beautiful exhibition, demonstrating with his sophisticated technique in color, and with his concepts, a most interesting and beautiful part of modern art. In 1992 Peter Black and Désirée Moorhead published «The prints of Stanley William Hayter», a complete catalogue which includes many masterpieces which may be given a plasma or astrophysical interpretation, such as Constellation (1987), Downward (1987/88) Black Hole (1978) and Magnetic Field (1966). They demonstrate Hayter’s greatness as an artist and as a technical inventor of color engravings (London: Phaidon Press), (see figures 9.3–9.5). Of the many exotic countries that I visited, Japan remains the one, which most frequently comes back to my mind. The first time was in 1974 when I visited Tokyo and Kyoto, where I took part in a US-Japan workshop. I remember that in Tokyo I stayed in the Tokyo Tower Hotel, which was very practical, since the Tokyo Tower was visible all over Tokyo. Since there were no names on the streets this helped greatly the orientation in the city and certified a happy return to the hotel. The visit gave a first glimpse into the Japanse fusion activities. In the Kyoto hotel there was an extremely careful security gard already along the street which led up to the hotel. When I got into the lobby I could see why, because the former US President Lyndon Johnson and Henry Kissinger were there. The visit to the laboratories was well arranged and the immediate impression was that Fusion was taken very seriously 270

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in Japan, with many research centers located in various places along the Shinkansen fast railway train. I met many of the scientists and responsible directors of the institutes, and was asked if I would be interested in a longer visit to Japan, supported by the Japan Society for the Promotion of Science (JSPS). That was the beginning of a long a fruitful scientific exchange, which continued over an extensively period of time, and which took me to Japan again the next time in september 1976, for three months, just after a sabbatical year in Grenoble, France, and a Nobel symposium at Chalmers which I had arranged in the spring the same year 1976.It became one of the most educative and valuable experiences that I had so far, not only from the scientific point of view, where I worked with Professors Yoshi Ichikawa and Haru Obayashi in Nagoya, and during part of the time with Professor Kyoji Nishikawa in Hiroshima on nonlinear effects in plasmas, and space and time evolution of explosive instabilities, but also from the point o view of organization. In particular the close coordination of the fusion plasma physics activities with the interest of Japan industries and Japan banks. I remember that when I was in Japan on another occasion (1980) Professor John Dawson and I were invited to take part in a meeting in Ueno Hotel in Tokyo to discuss with representatives of the Japanese industry, the Tokyo Bank and leaders of the Japanese Fusion research such as the Director of the Institute in Nagoya, professor Kayuo Takayama the future prospects of cooperation between Governmental supported Research Industry and Banks in the field of Fusion. Japan was far ahead there and had already experience from such cooperation. I had very good contacts with the graduate students in Nagoya and sometimes I used to go to their seminars. In the young generation of scientists I met Kimataka Itoh and Sanae Inoue who later became his wife. They were delightful representatives of their generation, Sanae even prepared Japanese green tea in the old traditional way. They are now top scientists in Japanese fusion, and I am very glad to have a new book by them in front of me: K Itoh, S-I Itoh and A Fukuyama 271

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(1999) Transport and Structural formation in plasmas (Bristol: IOP Publishing) and another one even more recent: A Yoshizawa, S-I Itoh and K Itoh (2003) Plasma and Fluid Turbulence Theory and Modelling Bristol: IOP. I had also cultural experiences from visit to theatres such as Noo theatre in the company of Professor K Takayama and professor K. Husimi, the grand old man in Japanese fusion research. A visit was arranged for me to Hiroshsima were Kyoji Nishikawa was my host, and to Hagi, on the Japanese Sea side, the centre of Japan’s most famous ceramicists where three of them had their ateliers, one of them Sakata, who took care of not only me but also of Professor Obayashi, Professor Nishikawa, Dr Narumi, labrarian of Hiroshima University and his secretary, who had become interested when they had heard that I was going to see the Master Sakata (Sakatasen). He was the third generation of ceramicist in the family, working according to traditional methods, burning the ceramics directly in the wood. I remember Sakata writing calliography, when he had an exhibition in Nagoya, where I first met him. He was a representative of Japanese splendor both in his way of writing calliography and as a personnality, with a profile like an ancient God. In 1980 the International Conference on Plasma Physics was arranged in Nagoya and there was time again to meet old Japanese friends and to learn about new developments. In the beginning of the banket, which was a huge ine with more than 500 participants from many nations, professor Yoshi Ichikawa, the main organizer of the conference asked me if I could give a speech as a representative of the foreign guests at the banquet. I accepted with pleasure, and in a short break I went up to my room in the hotel and sketched a few lines on paper. I happen to still have them and it is my great pleasure to add them here: Honoured Hosts, dear Friends! we were invited to come to Nagoya in the best season of the year in Japan to discuss new results and new trends 272

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in plasma physics. We now have enjoyed the pleasure of tasting the fruits of an extremely well organized conference. We have experienced an overwelming hospitality from our Japanese hosts. We are totally impressed by the sophistication and the strength that characterizes the Japanese people and the Japanese efforts. It is remarkable, we find, how efficient and successful the Japanese plasma physics efforts have been during the last decade. This has been a challenge to the international development in plasma physics. It has meant a lot to the international collaboration and evolution in the field of plasma physics. This international collaboration, we believe, is very important not only for the progress in scientific matters but for the understanding of different cultures and various problems of the countries involved, and for their interrelations. Thus this world-wide scientific collaboration may help us to solve international problems quite apart from the pure scientific ones. Concerning Japan, we think that this is a country where things really happen. My own experience when arriving here for a 3 months stay 4 years ago was to land at Haneda in the worst typhone (nr 17) of the year 1976, and to take shelter immediately in Tokyo Green Hotel. The next day when most transportations were broken, I was lucky to have a 273

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very pleasant 6½ hours bustrip from Tokyo to Nagoya along the coast. On my arrival at Nagoya, Professor and Mrs Takayama greeted me welcome in the most charming way. During my stay in Nagoya that time I learned indeed how delightful it is to work and what happiness it means to stay in Nagoya and in Japan. The same great Japanese hospitality has been extended to us this time again at this conference. On behalf of the foreign scientists I would like to thank our hosts most cordially for everything they have done that has made this conference such a great success, and to congratulate all the responsible Japanese representatives to this success in their work. Domo-arigato-goh-sai-mashta

When I came back to Sweden I reported to the Swedish Research Council that if fusion will not be realized as an energy producing reactor elsewhere, it seems to me that it will be in Japan. Nothing has changed my points of view in the meanwhile. At the ICPP Conference in Nagoya 1980 there was a meeting of the organization committé discussing the format of the conference and the responsability and place for the next conference. Gõteborg had been mentioned as a candidate and it was formally decided at the meeting that the next ICPP would be in Gõteborg, Sweden in 1982 and the author was suggested and elected as the responsible organizer. It should be mentioned that the ICPP conferences are within the realm of the 274

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International Union of Pure and Applied Physics (IUPAP), of which the author had for several periods of three years been the secretary and then the Chairman of its Commission of Plasma Physics. I went back home with lots of work in front of me. A couple of years ago the ICPP conference was again held in Nagoya. The ICPP 96 had the same splendid organization as the last one there, and at this time the participants were given the possibility to visit the new Fusion centre in Toki-city outside Nagoya with a really impressive staff and new technical facilities. In 1984 the International Conference on Plasma Physics was held in Lausanne, Switzerland. During the conference François Troyon, head of the Swiss Fusion research, informed me that there had been considerations to start a new type of conferences in Europe, devoted to the theory of fusion, but that Euratom Fusion in Brüssels had to take the decision. I was informed a little later that Brüssels had decided to introduce and support the European Fusion Theory Conference to be held every second year, and that I was appointed chairman of the program committée for these conferences, and stayed on this duty for more than sixteen years. The first conference was going to be held in Namur (Brüssels) in 1985 with Professor Radu Balescu responsible for the local arrangements. When the conference was held recently in Elsinore, Denmark, 2001 Professor Balescu and I had participated as members of the program committée in all the previous conferences, and we both resigned from our duties after appointing Finland to be responsible for the next meeting in 2003. In the meanwhile the conferences had been held in Namur (Belg.), Varenna (Ital.), Oxford (Engl.) Gõteborg (Swed.) Escorial (Madrid, Spain), Utrecht (Holland), Jülich (Germ), Como (Ital.) and Elsinore (Den.), with about one hundred participants every time. It has formed a base for the accounts of the European progress in the field of fusion theory. The intention of the initiator of the conferences Professor D. Palumbo to encourage students and young scientists to 275

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continue in the field of plasma physics has been greatly appreciated. The scientific activities took me to many different countries in the world, in addition to more than a dozen visits to the United States, in particular to Univ of Maryland and as many to the Soviet Union, in particular to Moscow, Kiev and Tblissi, also to South America and Mexico. It started with that in 1988 I was invited to the 100 th Anniversary of the Catholic University of Santiago de Chile to give five lectures for the association of plasma physicists in Chile and to participate during another week with a contribution to a Plasma Conference arranged for the Jubilee of the University. I did this with great pleasure, an discovered a young and appreciative audience of about hundred participants from different part of South America and Mexico. Afterwards I was asked if I wanted to become a member of the Committée of Plasma Physics in South America, and to participate in future conferences, which I accepted. This took me to another meeting by invitation to Mexico the some year thanks to Dr Julio Herrera, Mexico City, and then later in 1990 to Buenos Aires, and in 1992 to Mexico city, and a couple of years laters ,in 1996, to a Magnetospheric Plasma Conference in Rio de Janeiro. I learnt a lot myself from these meetings, which also resulted in several publications. India I found to be a fascinating country which I visited twice, once in 1993, for a conference in New Dehli, with a trip to Nepal, where I gave a seminar in Katmandu; very primitive equipments but well informed scientists. The other visit was to a Nonlinear Dynamics Conference in Bangalore in the very south and to Amedabad, where is located the National Centre for Fusion Research, with professors P. Kaw and A. Sen as my hosts, and where by the way the Movements of Indira Gandhi started, further to New Dehli and to Poona, were Gandhi had been kept in prison until he died. In all places I gave talks on differents topics, as had been planned before. In Europe I had active collaboration with France and frequent visits to Ecole Polytechnique (Palaiseau) and Université VII Paris during the years 1987-1993. Those were 276

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some of my scientifically most productive years, when I worked on reaction-diffusion problems, free-electron lasers, and global dynamics of fusion plasmas. I still remember the 300 steps to mount and descend from the Metro Lozère to the laboratory on the hill in Palaiseau. What a refreshing and necessary exercise! Fondation de France in Paris gave me opportuneities of meeting outstanding personalities: The distinguished physicist Louis Leprince-Ringuer, and equally famous Georges Duby, the great specialist in the history of medieval times. Collaboration with CESTA of the French Atomic Energy Commission and with Professors Marie-Noëlle and Alain Le Roux brought me to Bordeaux. The excellent conferences: Maxwell Days in 1993, 1995, 1997 arranged by Dr JeanFrançois Eloy played an important role in this connection as did also L’Academie National des Sciences, Belles – Lettres et Arts de Bordeaux, where I became a foreign member in 1995 and a resident member in 1999.Jean-François and myself did some pioneering work on the dynamics of ultra-fast pulses in 1994-95 [6.15–6.20]. During 1994-2001 I was frequently in the Plasma Institute in Milan on the initiative of its Director Professor Giampietro Lampis and did innovative research on among other things: propagation of fast pulses in plasmas with Professor Enzo Lazzaro [7.22, 8.33]. In the meanwhile my former associates at Chalmers did outstanding progress. As an example the «Weiland Model» for heating and confinement of a hot fusion plasma was developed and refined during several years [7.13, 8.41] and reached a high degree of sofistication. «The model succeeds in simultaneous reproduction of the steady state as well as the transient transport in a variety of experimental conditions [7.42]», as recently demonstrated by numerous tests in the ASDEX Upgrade machine in the Max-Planck-Institute für Plasmaphysik, Garching, Germany. These and other contributions, among them the continued experiments on JET, are now paving the way for the realization of the large international thermonuclear 277

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reactor-ITER. Based on toroidal magnetic confinement ITER is over all a prolongation of the successful JET principles. At present it seems that the original four member blocks of collaboration on ITER, namely Europe, Russia, possibly US and Japan will have a new attached member: China. In parallel with the magnetic confinement fusion activities the Megajoule laser facility in Bordeaux is near full operation with new means of electromagnetic high power interaction for fusion energy production (see section 6,4 [6.22]. What future possibilities! Reference [8.1]

Kadomtsev BB 1992 Tokamak: a Complex Physical System (Bristol: Institute of Physics Publishing)

[8.2]

Wagner F 1997 Topics in toroidal confinement Plasma Phys.Control. Fusion 39 A 23

[8.3]

Lehnert B 1999 Fusion Plasma Physics During Half a Century TRITA – ALF-07 Report ISSN 1102-2051 ISHN KTH/ALF/R-99/7-SE

[8.4]

Braams CM and Stott PE (2002) Fusion Research: Half a century of scientific development (Bristol: IOP)

[8.5]

Wilhelmsson H 1961 Stationary oscillations Phys. Fluids 4 335

[8.6]

Wilhelmsson H 1972 Evolution of explosively unstable systems Phys. Rev. A 6 p. 1973

[8.7]

Oraevskii VN, Pavlenko VP, Wilhelmsson H and Kogan E Ya 1973 The stabilization of explosive instabilities by nonlinear frequency shifts Phys. Rev. Letters 30, 49 (1973)

[8.8]

Wilhelmsson H (Ed) 1977 Plasma Physics: Nonlinear theory and experiments Nobel Foundation Symposium N°36 (513 pages) New York and London: Plenum Press)

[8.9]

Wilhelmsson H (Ed) 1979 Solitons in Physics Chalmers Symposium, Physica Scripta 20, N°3/4 278

nonlinear

plasma

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[8.10]

Anderson D, Lisak M and Wilhelmsson H 1979 Anomalous heat transport through a cold turbulent plasma blanket, Nucl. Fusion 19 1522

[8.11]

Nakach R, Pavlenko VP, Weiland J and Wilhelmsson H 1981 Nonlinear stationary interchange modes in plasmas Phys. Rev. Lett. 46, 477

[8.12]

Wilhelmsson H (Ed) 1982 Proc. of the International Conference on Plasma Physics, Invited papers, Gõteborg June 1982 Physica Scripta T 2: 1, T2:2 600 pages

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Lisak M, Anderson D, Hamnén H, Tendler M and Wilhelmsson H 1982, Effects of velocity space loss regions on the alpha-particle distribution function and collisional alpha-particle losses in tokamak reactors, Nucl. Fus. 22, 515

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Weiland J and Wilhelmsson H 1983 Transition to chaos for ballooning modes stabilized by finite Larmor radius effects, Physica Scripta 28, 217

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Anderson D, Jancel R and Wilhelmsson H 1984 Similarity Solution of the evolution equation describing the combined effects of diffusion and recombination in plasmas, Phys. Rev A 30, 2113

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Kolesnichenko Ya I, Anderson D, Lisak M and Wilhelmsson H 1984 Bootstrap tokamak reactor driven by fusion produced alpha particles. Phys. Rev. Lett. 53, 1825

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Shukla P, Anderson D., Lisak M and Wilhelmsson H 1985, Shear Alfvén vortices in a very low beta plasma Phys Rev. A 31, 1946

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Weiland J, Lisak M and Wilhelmsson H 1987, Excitation of global Alfvén modes by trapped alpha particles, Physica Scripta T 16 , 53

[8.19]

Lisak M and Wilhelmsson H (Eds) 1987 The role of alpha particles in magnetically confined fusion plasmas Physica Scripta T 16 3 279

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[8.20]

Wilhelmsson H 1987 Evolution of burning fusion plasma density and alpha particle production in approaching ignition Physica Scripta T 16 176

[8.21]

Wilhelmsson H 1987 Explosive instabilities of reactiondiffusion equations Phys. Rev. A 36 965

[8.22]

Wilhelmsson H 1990 Equilibria and dynamics of temperature in a fusion reactor plasma, II nd International TOKI Conference: Nonlinear Phenomena in Fusion Plasmas-Theory and Computer Simulation (invited paper) TOKI, Japan

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Wilhelmsson H 1990 Diffusion, creation and decay processes in plasma dynamics: evolution towards equilibria and the role of bifurcated states Nucl. Phys. A 518 84

[8.24]

Elicher B and Wilhelmsson H 1990 Dynamics of coupled reaction-diffusion systems, Physica Scripta 42, 81

[8.25]

Wilhelmsson H and Jancel R 1990 Self-generation and nonlinear diffusion An analytic approach Physica Scripta 42 81

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Jancel R and Wilhelmsson H 1991 Quasi-linear parabolic equations: some properties of physical signifiance, Physica Scripta 43, 393

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Wilhelmsson H , Etlicher B, Cairns RA and Le Roux M-N 1992 Evolution of temperature profiles in a fusion reactor plasma Physica Scripta 45 184

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Wilhelmsson H and Lisak M 1993 Influence of alpha particle thermalization on oscillations of a burning fusion plasma Proc. IAEA Work-shop on alpha particles in fusion research, May 10-14 Trieste, Italy

[8.29]

Persson M, Nadeem M, Lewandowski and Gardner HJ 1999 Drift waves in stellator geometry Plasma Phys. Control. Fusion 41 203 280

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[8.30]

Uddholm P, Nadeem M and Persson M 2000 Approximate localization and dispersion curves of drift waves in straight stellarators Plasma Phys. Control. Fusion 42 501

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Nadeem M, Rafiq T and Persson M 2001 Dissipative electron drift modes in H-1NF stellarator Physica Scripta 63, 1

[8.32]

Ödblom A, Anderson D, Lisak M and Tendler M 1999 Analysis of nonlinear diffusion equation describing the formation of transport barriers in fusion plasmas Phys. Plasmas 6 3521

[8.33]

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[8.34]

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The sky exhibits some extraordinary examples of superstrong emitters of radiation. (cf. section 4.3). Among them are supernovas with their luminous remnants, e.g. the Crab nebula. Even if the supernovas occur with long time intervals, they may be the source of all the heavy elements in the universe including those vital for life. They are the result of gigantic star explosions and represent objects of extreme brightness. There are lighthouses in the cosmos called pulsars. They sweep beams of electromagnetic radiation around them, which an observer experiences as very short, extremely regular pulses. The radiation contains contributions from the entire spectrum: visible, x-ray and even gamma ray wave-lengths. The British radioastronomer Antony Hewish was awarded the Nobel Prize for Physics in 1974 for the discovery of the first pulsar, interpreted to be a neutron star. A new type of radio sources, quasars or quasistellar sources was discovered in 1960. They seem to be of cosmically very small dimensions, only some light-years, but extremely massive and with a luminosity corresponding to hundreds or thousands of galaxies. The most remote quasars are believed to be situated at about 14 billion light-years from us, and constitute the central nuclei of galaxies, formed by stars and gas-clouds attracted by a black hole. The quasars have large red-shifts, they move rapidly away from us. 283

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Figure 9.1. Cosmic panorama of our expanding universe; stars and galaxies 810 billion light-years away seen by the Hubble telescope

Figure 9.2. André Masson: Les oiseaux sacrifiés (aquatint 1954)

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Figure 9.3. Stanley William Hayter: Constellation; structural formation in the early universe (color etching 1987)

Figure 9.4. Stanley William Hayter: Downward; formation of a black hole (color etching 1987/1988) 285

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Figure 9.5. Stanley William Hayter: Black Hole, cosmical cubism; synthetic holography (color etching 1978 )

Figure 9.6. Roberto Matta: Fields and gadgets facing towards Big Crunch (color etching, EA about 1980) 286

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Looking at the universe at large we know that there is a universal expansion everywhere, to the outer limits of observation. In order to describe the over-all motion of the galactic objects collective methods of transport may be used, accounting for all the individual structure phenomena. One might expect nonlinear phenomena to play an essential role in the universal dynamics as they do in laboratory plasmas. Recent observations indicate that structural patterns are present in the distribution of very remote galaxies. Similar structures often occur as a result of self-formation and self-organization in plasma physics as well as in chemical and biological systems. They exhibit features of intricate nonlinear behaviour. Hubble’s law itself, which states that the velocity of expansion is proportional to the distance between the observer and the object, is a simple example. In conclusion, it seems rather natural if similar methods might be considered for the whole universe as for the fusion plasma case (cf. Appendix). As a result it seems possible to relate the value of the nonlinear coefficient of the partial differential equation (NL DPE) to the Hubble constant, and furthermore to generalize Hubble’s law. It is interesting here to refer to the new extraordinary methods of cosmical observation. In the universe the ratio between the abundance of neutrinos and nucleous, i.e. neutrons and protons, is exceedingly high, about one million. We also know that most of the neutrinos that reach us on Earth come from the sun. They are generated by solar fusion reactions. It was the pionneering work by Raymond Davis and Masatoshi Koshiba, which resulted in the first measurements of neutrinos and could confirm that the neutrinos were of solar origin. Davis and Koshiba were awarded Nobel Prizes for Physics in 2002. Bursts of neutrinos from a supernova explosion 1987 A in the Large Magellanic cloud were a great challenge for the new techniques. A new field of neutrino astronomy now exists of utmost importance for cosmic investigations, even for elementary particle physics, due to the role that neutrinos play for the Standard Model. 287

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The field of observation of rays from the cosmos experienced an important development thanks to the rockets and satellites and in particular to the patient and ingenious work by Riccardo Giacconi (Nobel Prize for Physics in 2002). The Einstein and Chandra space observatories became equipped with ray telescopes which led to a great number of new discoveries. Distant active galaxies were observed with high resolution, as were also remnants of supernovas and, furthermore, intergalactic domains in clusters of galaxies, in attemps to obtain information about dark matter. Plenty of new observational results accumulated, e.g. on double stars, where a normal star rotates at close distance around a neutron star. X-ray astronomy was established as a new discipline. The gravitational lensing technique, as used in cosmical observations, means that light from far-away galaxies is observed as it is bent around galaxies that lie closer to us. These serve as lenses or combinations of distributed lenses. Those galaxies or cluster of galaxies, which are «near-by» can be used to investigate very distant objects. The bending of light also provides information on the mass of the stars or galaxies that are closer to us. The technique has been used to determine the Hubble constant and to study e.g. dark matter in the Halo of the Milky way, or the structure of distant quasars. How fortunate for us that Einstein saved the notebooks with his ideas from 1912! The gravitational lensing technique could clearly be expected to remain an important tool for answering fundamental question in future astrophysical and cosmological studies. Among the mysteries when describing the universe there are some outstanding ones, namely the Big Bang, the Big Crunch and Black Holes. These have been hot topics of speculation and debate for quite some time, [9.1–9.5]. The Big Bang and the Big Crunch can formally be defined as follows: Big Bang: singularity at the beginning of the universe Big Crunch: singularity at the end of the universe 288

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The notation of singularity, referring to a particular event, is related to Einstein’s general theory of relativity, which prescribes that space-time started at a singularity of the Big Bang type and will finish in a catastrophe or Big Crunch (if the universe is recontracting, or «closed»). The singularities exist if the general theory of relativity is correct as pointed out by Stephen Hawking and Roger Penrose. The gravitational field might, however, be so strong that gravitational quantum effects could not be negligible. It was in the late 1940’s that the British cosmologist Fred Hoyle coined the term «Big Bang» to describe the gigantic explosion that started our universe and its expansion. He also pioneered the theoretical description of the problem, using Einstein’s general theory of gravitation. About 15 billion years ago the creation of the universe happened as an enormous concentration and liberation of energy («singularity»). In the beginning all places, that today seem separate, were one and the same place. Space and mass exploded instantaneously! After an exceedingly short time, in Planck’s time 10–43 seconds, the temperature is estimated to have been about 1032 Kelvin, many, many billion higher than the temperature of our sun. The discovery of the cosmic background radiation in 1965 by Arno Penzias and Robert Wilson, along with Hubble’s law from 1929, is considered one of the most important astronomical findings of the 20th century, and supports the big bang theory. Stars and galaxies and clusters of galaxies are all believed to have formed from the ripples in the early universe and the big bang. The uniformity of the radiation is believed to lend support to the inflationary universe theory invented by Alan Guth in 1979. Guth’s theory [9.1] tries to explain what happened in the first fraction of a second after the big bang in a way that offers solutions to two big puzzles in cosmology: the flatness problem and the horizon problem, i.e. the universe looks the same in all directions and from everywhere. 289

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A black hole can be defined as a region in space-time from which nothing, not even light can escape because the effects of gravity are too strong. John Archibald Wheeler suggested, as early as in 1939 the name «Black Hole» as a result of his studies in general relativity, which showed that the objects given the name were stable. The continued work by Stephen Hawking and Roger Penrose have established and extended the early results, considering also the combined effects of general relativity and quantum physics. In a sense the problems of black holes have much in common with the big bang and the early formation of the universe, which can be said to resemble an inversion of the appearance of a black hole. A black hole is not entirely black. It radiates due to quantum effects, and may be more or less grey, depending on its mass, which could be exceedingly high, thousands of millions of tons, even with a total size which is not larger than a nucleon. It seems as if black holes could be responsible for the observed radiation from active galatic nuclei and a key to the problem of quasar emission. For the observations of black holes x-ray astrophysics has contribued significantly. Speculations have been going on if small black holes and elementary particles could have a similar nature. The missing link turned out to be the incompatibility between general relativity, the base in the description of black holes, and quantum mechanics. This link seems now to have been found in terms of the string theory, a multi-dimensional generalization of the description, unifying the general theory of gravitation and the quantum theory. The architecture of this common theory forms a structure of visualized concepts, which as the most enthusiastic scientists say could describe not only the big bang and the black holes but the evolution of everything. It provides a new langage and a new unifying alphabet combining and extending previous forms. From a layman’s point of view one might say that it resembles the Japanese language composed of the original Chinese «ideograms», the kanji in simplified version (which 290

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can also be written in hiragana letters) and another alphabet of katakana letters (which is used more for foreign language, in particular for American words). With this combination of very different alphabets one can penetrate the old and the new secrets of Japanese culture, as one penetrate the deepest questions of physics with the string theory, a combination of gravitation and quantum theory. Einstein suggested a unified field theory, considering gravitation, electromagnetism and quanta, such that a fundamental field is determined by a set of equations which relate the characteristics of the separate fields. The hope is to finally realize a theory capable of describing the creation and evolution of the universe in all details. According to Einstein reality is composed of fields and has been so from the very beginning. Even particles, as we are used to regard them, are fields. They are located in regions of intense fields, strong enough to penetrate space surrounding them. Strictly speaking independent particles can exist separately only approximately as specific limits. Such a view might even offer attractive features if one would like to construct a general field theory related to holographic imaging [see chapter 8] or string theory. In the string theory particles are represented by minuscule strings which have particular vibration patterns described by ten or eleven dimensions in order to realize the great unification of physics. When Einstein formulated general theory of gravitation he introduced a new and more profound way of looking at gravity. It meant that the presence of a gravitational field changed space. This change had an effect on other fields or masses which penetrated space, which now would be considered curved. In order to give a mathematical description of his physical ideas, which indeed meant a revolution in physics, he had to use a suitable formalism. He was fortunate enough to find that the geometry constructed by Riemann for curved spaces was, in fact, what was needed, nota bene, when classical gravitational fields were considered, i.e. when no quantum effects were considered for the gravitational field. 291

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When quantum gravity is introduced, the general theory of relativity has to be modified, in particular to give a correct description for very small distance (10–33 cm). This is where the string theory enters the scene. For very small distances this requires the development of a new formalism based on quantum geometry, which is at present being seriously studied by a great number of scientists. It is believed that the presence of violent quantum fluctuations, occurring over very small distances, could have important consequences for the physics of black holes and the big bang. Even for the structure and evolution of the whole universe the quantum fluctuations should supplement the description in a profound way. A suggestion by Stephen Hawking in 1974 was one of major consequence. It meant that a black hole has entropy (disorder) and an associated temperature under exceptional gravitational conditions. The prediction was, however, based on primitive considerations in the absence of a strict reliable theory combining general relativity with quantum mechanics. Still, the consequence was that a black hole radiated, causing its mass to diminish slowly and the hole finally to disappear. Einstein liked to say that if an ultimate theory of Nature exists one of the most convincing arguments in favour of it would be that it could not be different. Hawking’s theory says that black holes are not completely black. A theory based on the general theory of relativity but neglecting quantum effects does not allow anything, not even light to escape gravity and return from a black hole. Quantum mechanically this may, however, occur. To understand how this is possible we can observe that the Heisenberg uncertainly principle tells us that even the vacuum is filled up by virtual particles, whirling around in violent motion. They are repeatedly created and annihilated. Hawking understood that such a behaviour might occur just outside the horizon of a black hole (separating effectively the outside from the inside of the black hole). Besides, gravity from a black hole can provide energy for a pair of virtual photons and also to separate one 292

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from the other in such a way that one of the photons will fall into the hole whereas the other will escape. Repeated separation of virtual photon pairs near the horizon of the black hole can lead to a continuous out-flow of photons, i.e. the black hole radiates. Differencies in opinion exist about what happens when a black hole evaporates. Even if the theory by Hawking tells that the hole radiates, it seems as if this continues to the very end with full disintegration of the black hole. The total process thus seems to violate the basic principles of quantum mechanics. It seems, however, that this contradiction is now on its way to be overcome. Another outstanding question is how to explain the presence and the role of “dark matter” in the universe? Matter that seems to be there because of its consequences but without direct evidence. The future theory of everything should naturally provide an answer to this question. It may be appropriate to finish these speculations here and remember that the dream of Leonardo da Vinci 500 years ago was to represent the invisible. The string theory seems to offer a theoretical basis for relating black holes and elementary particles. It should therefore provide a natural link between the description of the fundamental elements of fusion and the cosmos [9.7, 9.8]. If one prefers to compare with the imagery of music one could say that the universe is a symphony, and the heavenly strings are there to bring out its force and beauty! The first extra-solar planet (51 Pegasi) was discovered by Michel Mayor and his team of the Department of Astronomy, University of Geneva in October, 1995 [9.6]. Since then more than 100 such objects (the size of Jupiter) have been discovered, many of them by the same team and by the technique developed by them. Several features of the extra-solar planets have been discovered as a result of their measurements. It turns out that the metallic content has an influence on the formation of planets. This circumstance is an important factor for the possibility of life in the universe. The planets also have a 293

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tendency to perform radial movements of an oscillatory type with regard to the central star, as indicated by using the gravitational lensing technique. On the general problem of the origin of life, recent analyses have shown that self-organization of certain elements into water automatically leads to self-complexification of the system, on the way towards proto-cells. These and similar questions are becoming all the more attractive in the search for the possibilities for life in the universe.

Figure 9.7. Cosmic large-scale structures enlarged view [3.48] (cf. section 3.2.4)

On our voyage, the details and also the main features of our new atlas of navigation become more and more faint the further we travel. The guidance offered by the network of strings and knots entering the description appears less clear. The messages from home become less frequent. At the same 294

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time the challenge for discoveries increases. We start to feel more free to make new and detailed observations of objects neither seen nor predicted before. References [9.1]

Guth A 1997 The inflationary universe (Reading, Ma, Addison Wesley)

[9.2]

Schatzman E 1992 Our expanding universe (New York: Mc Graw Hill)

[9.3]

Rees, M 1997 Before the beginning: our universe and others (New York: Helix Books)

[9.4]

Weinberg, S. 1972 Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity New York: Wiley

[9.5]

Einstein A 1961 Relativity: The special and the general theory (New York: Crown)

[9.6]

Mayor and Queloz D 1995 Nature 378, 355

[9.7]

Hawking S 2001 The Universe in a Nutshell (New York: Bantains Press)

[9.8]

Green B 1999 The Elegant Universe: Superstrings, Hidden Dimensions and The Quest for the Ultimate Theory (Vintage Books: Random House), and in Swedish translation (Stockholm: Nordstedts).

[9.9]

Chandrasekhar S 1975 lecture reprinted in Truth and Beauty, University of Chicago Press 54 (1987)

[9.10]

Hawking SW 1975 Particle Creation by Black Holes, Commun.Math.Phys. 43, 199

[9.11]

Penrose R 1965 Gravitational Collapse and Space-Time Singularities, Phys.Rev. Lett. 14, 57 295

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[9.12]

Hawking SW and Pensrose 1970 The singularities of Gravitational Collapse And Cosmology, Proc.Roy.Soc.Lond. A 314, 529

[9.13]

Penrose R 1969 Gravitational Collapse: The role of General Relativity, Riv. Nuovo Cim 1 252 [2002 Gen.Rel.Grav. 34, 1141]

[9.14]

Hawking SW 1971 Gravitational Radiation from Colliding Black Holes, Phys. Rev. Lett 26, 1344

[9.15]

Hawking SW Black Holes in General Relativity, 1972 Commun. Math Phys 25, 152

[9.16]

Ghez et al. 2004 Variable Infrared Emission from the Supermassive Black Hole at the Center of the Milky Way, Astrophys. J. 601, L 159

[9.17]

Wang Y and Tegmark M 2004 New Dark Energy Constraints from Supernova, Microwave Background, and Galaxy Clustering, Phys. Rev. Letters 24 13 02-(1-4)

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10.1 Reactor requirements What can we say at present when it comes to the real goal of the efforts: a fusion reactor or a fusion plant to produce electricity? What are the predictions and how can we formulate the requirements for a first reactor? There has been a lot of consideration of these questions for the different schemes of magnetic confinement fusion and in inertial confinement fusion. Since the most advanced plans have been developed for the tokamak reactor concept of magnetic fusion, let us take this as an example and summarize the conclusions. Self-sustained fusion (ignition) requires the fusion triple product n τE T > 5 × 1015 (cm–3 s keV) Separate requirements for the factors in the fusion triple product emanate from conditions on the individual processes of: fuelling a sufficiently dense plasma of deuterium and tritium: Density: n ∼ (2-3) × 1014 cm–3 heating to a sufficiently high temperature o

Temperature: T ∼ 20 keV (200 M C ) achieving sufficient thermal insulation Energy confinement time: τE ∼ (1 – 2) s 297

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Even if in various experiments each of the conditions have been fulfilled separately the simultaneous fulfilment of the three of them, necessary for ignition, still lies in the future.

10.2 Reactor design The first reactor is likely to be a high power device, producing a few gigawatts electric energy, opearting with full ignition. It will be equipped with auxiliary heating and plasma control. It will also have exhaust for helium ash and impurities. It may have a major radius R of about 8 meters and a minor radius of 3 meters. The toroidal magnetic field at the major radius should be of the order of 6 Tesla and the plasma current 25-30 MA. Simulations by computer have been done for such a reactor and show that ignition can be obtained. Strict requirements are, however, necessary for the efficiency of the exhaust and impurity control systems. An enormous number of data based on technology and physics predictions are collected and prepared for the design of ITER International Thermonuclear Reactor; this will be capable of producing tokamak physics data regarding confinement properties, disruptions, beta-limits, divertor performance, and particle heating and confinement for reactor scale devices and will be able to conduct nuclear testing at neutron wall loading of about 1 MW/m2.

10.3 Heating and confinement The next generation of large machines is being designed for auxiliary heating and current drive systems: Neutral Beam Injection (NBI), Ion Cyclotron Resonance Heating (ICRA), Electron Cyclotron Resonance Heating (ECRH) and Lower Hybrid (LH). Since none of these systems can fulfill all the requirements of operation one tries to increase the flexibility by using combinations of the auxiliary systems in order to study different scenarios for optimizing the performance. 298

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The use of external heating has a tendency to lead to a degradation of plasma confinement. It has been found that such effects are extremely sensitive to the plasma conditions near the plasma external boundary. Detailed studies of related phenomena led to the discovery of a new mode, the so-called H-mode, (high mode) of operation in the ASDEX machine (Garching) which was later confirmed in other machines. Experiments with the H-mode, which was associated with steep gradients near the boundary, showed that heating could be obtained without degradation of the confinement. In fact, the Hmode could typically have twice the confinement time of that with an L-mode (Low mode) operation. The discovery of the H-mode may be seen as an example of how important improvements and new openings in science often come in steps. One reason for building larger and larger tokamaks is that the confinement time crudely depends on the minor radius a and the diffusion coefficient D as a relation, which applies for energy as well as for particles and indicates that larger machines should provide better confinement. For practical and economic reasons one might, however, envisage other lines of development using stronger magnetic fields leading to higher densities n in more compact machines. One might even for such devices eliminate or diminish the external heating using essentially ohmic heating produced by the plasma itself. There are obviously numerous of scenarios possible to exploit, and the last word has by far not been said as to the optimum line for construction of a future reactor. Reference [10.1]

Zweben SJ et al 1997 Alpha particle physics in the tokamak fusion test reactor DT experiment Plasma Phys. Control Fusion 39 A275.

[10.2]

Ono M et al 1997 Plasma transport control and selfsustaining fusion reactor Plasma Phys. Control fusion 39 A361 299

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Fusion will continue to be the energy source of the whole universe. The stars, among them the sun, will continue to shine for billions of years. In the centre of the sun the average time for a proton to undergo a fusion reaction with another proton to produce a deuterium is of the order of 1011 years, which makes the whole proton cycle extremely slow and the time scale for the consumption of the proton fuel immensely long. On a related time scale new stars will be born under the influence of gravitational forces, creating new systems of planets and in the process of formation possibly also new life. It should not be forgotten that it is and will continue to be the sun, by its own fusion processes, which continues to support the energy for life on our planet. Modern society may, however, affect the situation in our atmosphere by changing its composition in such a way that appreciable effects may be felt for life on Earth. In our everyday life one encounters urgent questions about energy and one is even reminded that very serious energy problems may arrive in the near future. The problems may seem more or less serious depending on where on Earth one is living, in one country or another, rich in resources or not, in a highly developed state or on developing continents, in highly populated areas or in areas which are scarcely populated. However, when serious energy needs are faced, they will soon be felt all over the world, demanding common efforts and requiring global solutions. 300

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It should be emphasized that in a world with rapidly increasing population and developing societies, with increasing living standards, ecological problems will strongly influence the course of the future. From extensive studies of the global ecology it has been reported that the greenhouse effect, which results in successive increases in atmospheric temperature, above what would normally be expected, could become a serious global problem. This effect is due to increasing quantities of CO2 and other gases in the atmosphere which prevent escape of excess heat from the Earth. The greenhouse effect may be responsible for «global warming» which could cause increases in sea level of several meters, due to melting of the polar caps, causing population redistribution from low-lying areas. There is indeed real need for the future for the development of an energy source which solves the large-scale energy problems of the world with due regard to possible ecological problems and damage. Fusion would provide a large-scale energy source for the production of electricity to mankind without the risks of explosion or other damaging effects and without negative ecological consequences. It does not give rize to any products that would contribute to an increase of the greenhouse effect. The advantages of having fusion available as a power source on Earth would in fact be so immense that they would motivate all the necessary scientific, technological and economic support required for realization. Great efforts will be needed to achieve the «goal of fusion» in the time we have available before other options begin to run down. Science, technology and economics as parameters are all powerful tools enabling us to reach the goal. The question of when a fusion reactor plant for the production of electricity could be expected to operate for the first time is often raised. The response could be: 301

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When do we need it? It depends on the balance between the expected consumption and the available sources. The question of the necessary economic support to realize the construction of a fusion reactor is relevant, but not in fact decisive, since if it became urgent the necessary amount of support would almost certainly be provided. The development cost would necessarily depend on the risk one would be prepared to take with respect to successful operation of the reactor, i.e. to what extent the reactor would be optimized. It is estimated that the next generation of large fusion experiments can be regarded as an extrapolation of previous experiments of the tokamak type, in particular of the JET (Joint European Torus), which in 1991 was the first machine in the world to demonstrate nuclear fusion reactions in a large scale plasma. JET has been considered a great technological success as well as one of international collaboration. How large will an operating fusion plant be? The power production is planned for about 1500 MW which is higher but not extensively higher than an ordinary nuclear reactor plant. It can well be incorporated in the power grids of, for example, the EU. The technological and scientific success of fusion energy programmes has been achieved by international collaboration, in Europe as well as at the intercontinental level. One should not forget that sometimes technical innovations and technical efforts proceed faster than expected. So, for example, the first moon landing was accomplished earlier than projected. It was, however, even if very spectacular and impressive, a technical achievment less complex and less far-reaching for mankind than the realisation of a fusion reactor would be. The reason for the complexity of a fusion experiment is the element of the plasma, the «enfant terrible» of the experiment, which makes the design of a fusion machine much more difficult than that of a particle accelerator for example. 302

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It is, in fact, an inherent property of plasmas that they refuse to be governed by external forces. As an example, if ultra-high power radiation in a laser fusion experiment is focussed on a pellet the created plasma immediately, due to strong nonlinear effects, tries to prevent the radiation from penetrating. One should, accordingly, not expect the plasma in nuclear fusion reactions to be particulary easy to handle, as is indeed the experience with fusion plasma. However, when the game comes to an end the benefits will be enormous and Nature will help to provide a peaceful source of energy as it has done for all times in the rest of the universe.

303

Conclusions — the great fusion plant A tour of the universe has made it evident what a decisive rôle fusion energy plays on a large scale. Studies of the sun, the solar wind, comets, the magneto-sphere around our Earth as well as astrophysical and astrochemical observations of remote sources by means of optical instruments and radio telescopes have revealed many events and interrelations between phenomena which occur in the cosmos. We still do not know anything about the conditions of stellar objects belonging to planetary systems of other stars. Perhaps there are many more planets apart from our Earth where life exists and societies prosper from fusion energy produced by their «mother stars» which could deliver heat by radiation to their planets as our sun does to the Earth. Or maybe fusion energy plants have long since been developed on other planets by ingenious principles and skilful engineering. As far as our own future is concerned it would not be surprising if most of the electrical power on Earth, let us say by the middle of the next century, would be provided by fusion reactors. It should be emphasized that all alternative methods of generation of electricity on Earth, wind energy, wave energy from the sea, solar radiation converted by solar cells, etc... are all indirectly derived from the energy emitted by the sun, i.e. they originate from the solar fusion energy. Even the atmosphere, the rivers and the forests providing other energy alternatives for electric power are driven by heat from the solar fusion. With a large-scale view of the cosmos as a whole one may simply conclude that not only are the sun and all stars fusion reactors but that the entire universe is a great fusion plant. 304

Afterword I spent my student years at Chalmers University of Technology in my home town of Göteborg in Sweden, where I also prepared my doctoral thesis on «The Scattering of Electromagnetic Waves by Electron Beams» (1959) under the direction of professor Olof Rydbeck, founder of the Onsala Space Observatory. Among his numerous pioneering scientific contributions he discovered the CH radical line radiation in galactic clouds at centimeter wavelengths. For many years he was a great stimulus to me in my scientific efforts. My interest in fusion plasma physics was very much stimulated by my stay, in 1960-61, as a post-doctoral fellow in the Plasma Physics Laboratory in Princeton USA, headed by Lyman Spitzer the famous astrophysicist. I met many of the leading plasma physicists in the US and I also wrote my first paper there on nonlinear waves in hot plasmas. That was the beginning of what came to occupy me for many years and to bring to me many happy episodes in life. Of the many personalities that I met in connection with fusion plasma activities the memory of Hans Otto Wüster (Director of the Joint European Torus, JET, from its very beginning) remains with me; he was a man of outstanding quality. In the early days of JET the USA was ahead of Europe in fusion research; this however, did not scare Wüster who said that we could do it even better in Europe ourselves. Not very many years later experience proved that his prediction was correct. He was a genius coordinating technical science and human relationships, a partnership which carried JET to the top of fusion activities. He made me and many others believe in Europe and in the advantage of coordinating the activities of the European countries. 305

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The contacts with scientists from different fields who I met in the Royal Swedish Academy from of Sciences in Stockholm (as a member since 1974) have always been of particular interest to me. His Majesty King Carl XVI Gustaf of Sweden takes a particular interest in the activities of the Royal Academy, being also the Protector of the Academy. His presence at meetings and conferences in natural sciences, for example in ecology or plasma physics has always been highly appreciated by the members. Through the years I have had several opportunities to participate in such conferences where the King was present. In 1981 the European Incoherent Scatter Facility (EISCAT) based in Kiruna, Sweden, north of the Polar Circle, and with collaborating stations in Tromsø, Norway and Sodankylä, Finland, was inaugurated by King Carl Gustaf in the presence of Professor Bengt Hultqvist, the Director of the Swedish Space Center in Kiruna (formerly named Kiruna Geophysics Institute, KGI, of which the author was a Board Member for many years), and many scientific reperesentatives. The King was also on the morning plane from Kiruna to Stockholm the next day. I had a connecting flight in Stockholm to Italy for the Varenna conference on plasma physics. The connection between the flights was very tight and the arrival in Stockholm late. I did not know how to manage to get on the plane to Italy in time. An unexpected source of help solved my problem. Did it come from God, from the King or from the air company? I got a message, however, that I could be taken by the King’s escort car directly on the runway from the plane from Kiruna to the Alitalia plane. Avoiding all formalities saved my time and I took off for Italy, where in Varenna at Lake Como the same day I had the opportunity to discuss problems on the plasma universe with Hannes Alfvén and furthermore to consider the planning of the 1982 International Conference on Plasma Physics to be held in Göteborg the next year. On that occasion King Carl Gustaf gave an inauguration address, as did Professor Kai Siegbahn from the Uppsala University, President of the International Union of Pure and Applied Physics, and Nobel Prize winner in Physics in 1981. 306

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Hannes Alfvén gave an invited introductory talk, addressing the problems of the plasma universe. The conference was attended also by several of the top scientists from the Soviet Union, among them RZ Sagdeev, VL Ginzburg, and AG Sitenko, visitors rather uncommon in those days and by about one hundred participants from the USA among them MN Rosenbluth, JM Dawson and A Hazegawa together with more than 500 participants from 40 countries. When a similar conference was held in Prague, Czech Republic in the summer of 1998 the number of participants had more than doubled, which indicates the intermediant trend in the field of activity. In the year 1989 King Carl Gustaf attended the promotion ceremony when the new doctors from Chalmers University of Technology were given their diploma and doctor’s hats. As promotor I gave a lecture entitled: «Fusion: dream and reality?» I remember the performance well since it was in May 1989, only a couple of weeks after the propaganda for «cold fusion», a misleading annoucement that, nevertheless, for some time seriously disturbed the reputation of fusion research in hot plasmas. The King got to know not only about the recent progress in magnetic confinement fusion, but was also informed about the misleading concept of cold fusion at this early stage, by the limerick I dedicated to the «inventors», Two chemists from Salt Lake City Who wanted to be thought very witty Said they had the solution By means of cold fusion But it didn’t work out – what a pity!

(freely translated from the original Swedish) And the King commented on it humorously at the banquet, when he talked about «fusion» and «not fusion». In 1974 the first Nobel prize related to astrophysics was awarded to the British scientists Martin Ryle and Antony Hewish for investigations on radioastronomy antenna systems with cosmological implications, and on pulsars, respectively. The same year the Swedish authors Eivind Johnson and Harry 307

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Martinson received the Nobel prize for literature for their novels and poetry. The Academy had given me the responsibility for introducing the work of the physics prize winners to the audience in the concert hall in Stockholm. I remember that I asked Harry Martinson, who was sitting next to me behind the curtains just before the opening of the ceremony, if he would agree to my quoting in my physics presentation his poetry on the world clocks from his great epos «Aniara» in connection with pulsars. I was pleased to be told that he would be delighted. What a coincidence between physics and poetry! In 1983 the physics of stars and the elements in the universe were topics for which Nobel prizes were awarded to S Chandrasekhar and WA Fowler. In his Nobel lecture at the Academy Professor Fowler, with his special humor, said: «Those of you who heard me in Göteborg the other day can go home. I will give the same lecture here». I happened to come across Fowler on the campus after his lecture and told him: «I heard you give the same lecture more than 25 years ago at the Bohr institute in Copenhagen, in 1957, when I was a student there. Fowler responded with a big friendly smile: «With Niels Bohr sitting in the front row puffing his pipe!» Fowler invited me to lunch together with Chandrasekhar. Chandrasekhar was going to come to Göteborg in the next few days, giving a lecture there and visiting our institute at Chalmers. From conversation with Chandrasekhar I learnt how as a young student he came to England and informed Sir Arthur Eddington, the leading British astronomer about his own work on the critical solar mass. He said that Eddington had been nice and had accepted his ideas, which were in fact revolutionary. Chandrasekhar came to Chalmers and spent a whole day there. His general lecture had the title: «Newton, Shakespeare and Bach». I remember that I introduced him to the audience by telling the story that as a Professor of the University of Chicago he drove a long way every week from the observatory to give lectures to only two graduate students. However, one day he was greatly rewarded when his two students TD Lee and CN Yang, in 1957, shared the Nobel prize in physics. Now, their 308

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master got his award! By the end of his visit to Chalmers Chandrasekhar was interviewed by the editor of the monthly student journal of the physics department.Chandrasekhar apparently enjoyed the interview. At the very end of it the student said that he knew that Chandrasekhar spent four years writing his last book on black holes (he had by the way then already written six other books and about 600 scientific publications), and the question was if it was really worth it. Chandrasekhar hesitated a little then he said: «I can tell you that it gave me even more pleasure than this prize». He was a real scientist! Every year in December when the Nobel prize winners of the year come to Stockholm to receive their prizes they present their work in Nobel Lectures. As a rule the lectures cover the highlights of their discoveries for which they have been awarded the prize. One year, in 1978, Academician Piotr Kapitza at the age of 84, already then a legend among physicists, came from Moscow to receive his prize. That year, the physics prize was, by the way, shared between him and two other physicists from the US, namely Arno Penzias and Robert Wilson, who received their prizes for the discovery of the 3K background radiation in the Universe. Before coming to Stockholm Kapitza had already informed the perpetual Secretary of the Academy that he was not going to talk about his work on extremely low temperature physics and his discovery of superfluent liquid helium, the topic of his award. The reason was, as he said, that he had done this work already 40 years ago, and that he had forgotten everything about it. So he was going to talk about his current interest in research which was fusion. He started his lecture a little hesitantly in a rather timid voice, and I may not have been the only one in the audience to wonder how this would end up. But after a few minutes he apparently felt more and more at home and as time went on he became even enthusiastic. His point of view was that thermonuclear fusion research had entered a state where there was not much hope of reaching 309

AFTERWORD

a final solution. He said that a lot of effort in magnetic confinement was going on in the direction of tokamak experiments but, as he explained, tokamaks were too complicated and would not reach the goal. The other alternative with laser fusion was not very encouraging to him either, since the power of the available lasers was much too low to be attractive for fusion energy production. However, he himself had recently developed a new scheme for plasma fusion experiments and that was what he was going to talk about! And it was here that enthusiasm entered his talk. He emphasized that one should use the same process for confining the plasma and for heating the plasma. The idea he launched was to use microwaves for both purposes. His new experiments were already showing promising results! A couple of years later I visited Moscow and the Kapitza Institute, where I had discussions with Professor Pytaevsky, Kapitza’s theoretician during many years of work. I was told that Professor Kapitza himself was not available. However, I would be welcome to visit the magnet laboratory. On my way there I happened by chance, as it seemed, to come across him in the corridor. He invited me to accompany him to his office, where he, sitting at his desk, very kindly informed me about his interests and his work. When he asked if there was something I wanted to have from him in particular I asked him if he could offer me a reprint of his Nobel Lecture. Immediately, an assistant came from an other room with a copy which Kapitza kindly signed. He then said: «This afternoon we shall do an experiment together!» He instructed his assistant to switch on the power for the microwaves. I got to see the bluish (as far as I remember!) faint plasma, only some centimeters wide, through a hole for diagnostic measurements. His experimental equipment was spread out on two floors of the laboratory, joined by a narrow spiral staircase. I shall never forget his enthusiasm, running up and down the stairs and trying not to stumble on the many wires that were on the floor! How different a scene from the computerized fusion machines operating today in the modern plasma 310

AFTERWORD

laboratories. I remember Paul Henri Rebut, former head of the JET project once saying: «Plasma physics is not so nice anymore when we cannot see the plasma». But remember: There will always be stars, stars, stars wherever we look throughout space...

Scholar on the prayer’chair praying force and inspiration from Leonardo (by Carl Fredrik Reuterswärd).

*** The very purpose of this book has been to reach an audience with an inquiring mind, in particular young people attracted to fusion and plasmas, an area of science the nature of which is truly interdisciplinary. On our voyage through the universe we have encountered a number of Nobel Prize winners and seen many events which have already been awarded prizes. When I tried to make a selection among Nobel Prize winners in physics and the related 311

AFTERWORD

Prize Motivations, in the list covering the whole century, with the object of collecting those which had direct or indirect relations to fusion plasmas, I found that there were an astonishing number, but the word fusion was not even mentioned in any of them! Why is that so? On the one hand the field of fusion contains almost all parts of modern physics, and one talks or thinks about the differents parts separately. On the other hand fusion has been given an image which denotes the final goal of a very long-term process of reaching the state of an operating fusion reactor: the ultimate goal unlimited energy production with its possibly immense consequences. And we are simply not there yet! «Fusion is all a question of time» (Dr Roy Bickerton, former head of JET). In this situation I came to the conclusion that it might be of interest to make reference here to the whole list of Nobel Prize winners in physics from the first prize in 1901 up to this year 2002 including Prize motivations and photographs of all the Laureates as well as color pictures of their artistic diplomas, as available on the internet! Information on the Nobel Prizes is nowadays announced on the internet Nobel Website (http://www.nobel.se). The Nobel Foundation has also recently created the Virtual Internet Museum of the Nobel Fondation (www.nobel.se and www.nobelprize.org) the aim of which is to provide information about the Nobel prizes, to interested students in the work of the Prize winners, and to promote public understanding of science, literature and peace work. It covers not only Physics but also Chemistry, Physiology or Medicine, Literature and Peace as well as Economic Prizes. It tells the story of the life and work of Alfred Nobel (1833-1896), his inventions, patents and industrial activities etc… as well as the work in the Prize-Awarding Institutions. What a rich source of inspiration this is, both now and for the future! 312

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The reader is invited to view for himself the Nobel Website. He may be surprised to discover a great deal of interest! For example: Who won: the Physics Nobel Prize and which were the Prize motivations in the years: 1901, 1902, 1906, 1918, 1921, 1922, 1924, 1938, 1945, 1947, 1964, 1970, 1971, 1972, 1981, 1983, 1987, 2001, 2002, 2004. The chemistry Nobel Prize etc…in: 1903, 1934, 1936, 1944, 1954, 1964, 1977, 1993, 1999, 2002, the Nobel prize in Physiology or Medicine in 1914, 1962, 1969, 1982; The Nobel prize in Literature, etc… in: 1909, 1951, 1953, 1974, 1997, 2001, 2002 The Nobel prize for Peace in 1906, 1962, 1990, 2002.

313

Epilogue Our book has a message. It serves the purpose of defending a great promise: that fusion will become the large scale energy source of our society on Earth. It explains fusion and its relations to all parts of the universe as well as to laboratory experiments. Historically, it surveys the development from the very beginning to the present day achievements, including a number of proper anecdotes from the struggle of life, introducing numerous personalities from science and culture. It uses simple manners of explaining essential things, avoiding formal complications. Conclusively, the book has a second message. It proposes a new and original way of looking at gravitation and the expansion of the universe [4.33]. This is inspired by global dynamics of fusion plasma evolution [7.7, 7.25] and is related to the so called principle of «profile consistency» [7.30], i.e. the plasma has a tendency to ajust itself to find and possibly remain in a certain shape or distribution, in which it likes to stay. It seems to the author, that this may happen for matter in the universe under gravitational influence, as well as in a laboratory fusion plasma with magnetic or inertial confinement. The two should therefore have common tendencies of «selfformation» of over-all structures as well as «self-organisation» of internal small-scale structures. The Gordian knot of such a comparison is resolved by considering a certain nonlinear partial differential equation (NL PDE) defined in Appendix, in combination with the experimental observation of an extended form of the Hubble law (the mutual expansion velocity being proportional to the inter-galactic distance). And here the rules of Nature conclude our voyage in the plasma universe for eternity or with a possible return back! 314

Appendix In the following pages we present a new approach to the expansion of the universe. Formally the technique developed relies on our experience from treating hot fusion plasmas. We account for the possibility that the universe, as it seems, could have a finite life-time (even if it is counted in billions of years), and combine this assumption with the experimental observation that the velocity of separation of distant galaxies is proportional to the distance between the galaxies (the Hubble law). By analysis of a NL PDE (nonlinear partial differential equation) we succeed in proving that the crucial value of an exponent has a simple linear relationship with the Hubble constant. It is recognized that the scale-length that we use as a measure of the expansion is equivalent to the Einstein radius of curvature. The final results suggest that the Hubble law should be extended by a factor, which could have an explosive tendency of growth in time (open universe), or a decaying character (closed universe). The possibility of reversed expansion or an oscillating universe («cosmic pendulum») is also discussed. UNIVERSAL EXPANSION AND AN EXTENDED HUBBLE LAW A1. Basic NL PDE and solutions It would be temping to try a nonlinear diffusion type of description for the expanding universe similar to the one successfully used for particle transport and temperature conductivity in fusion plasma physics. A formal study could be done in terms of a quantity u, representing the local density variation in space and time, u=n (x,t), where u = A (1 – x2 /L2 + ηx4 / L4 )

(1)

with A = A(t), L = L(t) time-dependent quantities, representing amplitude, scale-lenght, and where η = η(t) is a time-dependent form factor. As a rule it is sufficient to keep terms only up to the fourth order in x. 315

APPENDIX

An expression for the quantity of flow could then be written F = auα ∂u (x, t) / ∂x

(2)

where a and α are constants. The form of the nonlinear partial differential equation (NL PDE) governing the universal expansion can accordingly be expressed

∂u / ∂t = ax-γ ∂ / ∂x (xγ uα ∂u / ∂x)

(3)

where γ is related to the dimension d as γ = d – 1. Introducing the expression (1) for u into Eq. (2) and matching increasing orders of x2 – terms (x0, x2 , x4 ) one obtains the following set of ordinary coupled nonlinear first order differential equations for A, L2 and η, namely dA/ dt = – 2a (γ + l) Aα + l / L2 , 2

(4)

α

dL / dt = 2a Γ A ,

(5)

dη / dt = a Λ Aα / L2 .

(6)

If one assumes that the universe expands without large-scale deformation one has dη / dt= 0, and Λ = 0 in Eq. 6. Solutions to Eqs (4) and (5) can be expressed in the form A / A0 = (1 + t / t´) µ,

(7)

(L / L0)2 = (1 + t / t´)ν

(8)

where, for a spherically symmetric universe (d = 3, γ = 2)

µ = – 3 (3α + Γ )–l ,

(9)

ν = Γ (3α + Γ )–l ,

(10)

and Γ = 5 (α + 2η ) – 3.

(11)

It should be noted that the quantity L(t) may be interpreted as a scalelength of the distribution of matter in space, or as the forward base-point of the distribution (1) with u = 0 and η = 0, describing the evolution of the 316

APPENDIX

temporal outer limit of the universe. It can, however, also be recognized as an equivalent to the Einstein radius of curvature in space (see references [A1 – A2]. It is important to emphasize, in this connection, that the particular positions of stars and galaxies etc., i.e. their specific x-coordinates, are now relaxed in the description, which accounts only for the expansion of a smooth distribution, as a celestial fluid, averaged everywhere over a large number of objects. The characteristic time t’ in the relations (7 – 8 ) can be expressed as t´ = L02 / 2aA0 (3α + Γ ).

(12) 2

One notices from Eqs. (7) and (8) that A and L obey the following constant of motion relation, namely (A / A0 )Γ/3 (L / L0 )2 = 1

(13)

where in Eqs. (12) and (13 ) A0 and L0 denote initial conditions, related if one so wishes to an instant of the early phases of the Big Bang (t=o, L = L0 ). It follows from Eq (5) and the solutions (7) and (8) that one may express

V = dL / dt = ( aΓA0α / L20 ) L ( L2 / L20 )αµ / ν −1

(14)

where αµ/ν – l = – (3α + Γ) / Γ

(14a)

which can easily be compared with the Hubble law V = dL/ dt = H L

(15 )

i.e. dL / dt = H L0 exp (H t )

(15a)

where H denotes the Hubble constant. One notices that one has to impose the condition αµ / ν – l = 0 or (3α + Γ) / Γ = 0 in Eq (14 ) to obtain the characteristic linear dependence of the expansion velocity V on the distance L expressed by the Hubble relation (15 ). As a result one obtains from the expressions (9 – 11) the remarkably simple relation 3α + Γ = 0

(16)

and from the Eqs. (14–16)

α = −Γ / 3 = − HL20 / 3aA0α

(17) 317

APPENDIX

which settles the value of α to be α = 3 / 8 = 0.375 and Γ = – 9 / 8 = – 1.125 for dη / dt = 0 with Λ = 0 and η = 0, using the expressions (11) and (16). From the expression (17) we notice the interesting linear relationships between α and H and also between α and Γ, as well as the dependence of α on the initial values of L and A, which agrees with the dimensional form of the Eq. (3 ). A2. Extended formulation The relation (16) corresponds, in fact, to a solution, for which the parameters η and ν as well as the characteristic time t´ reach unlimited values, according to the expressions (9), (10 ) and (12 ). From the formulae (7 – 12 ), and considering 3α + Γ approaching zero, the values of A(t) and L(t) can, however, be obtained for small values of t (Ht << 1), namely A / A0 = l – 6Γ–l Ht

(Γ < 0)

(7a)

L / L0 = 1 + Ht

(8a)

as well as from Eq (14) V = dL / dt = HL0 (1 + Ht)

(14a)

To obtain a consistant and physically meaningful description by means of the Eqs. (4 – 6 ) with (7 – 12 ), and to use the proper direction of time, related to the sign in the Hubble law (15), one has to avoid the singularity by an amount ε such that 3α + Γ = –ε

(18)

or αµ / ν – 1 = ε / Γ, µ = 3/ ε , ν = – Γ / ε,

(18a)

where ε < 0 or ε > 0, corresponding to an open or closed university, respectively. One notices from the expression (12 ) with the relation (18 ) and T = –t´ > 0, ε < 0, Γ < 0, a < 0 that (19)

ε = L20 / 2aA0α T = Γ / 2 HT

and L / L0 = (1 – t / T )–H T,

(t < T )

(20) 318

APPENDIX

or V = dL/ dt = HL (l – t / T )– l = HL (L / L0 )1/ HT

(21)

where the Hubble constant, from the relations (14) and (15) is H = aΓA0α / L02,

(a < 0, Γ < 0 )

(22)

and T = Γ/ 2Hε

(Γ < 0, ε < 0)

(23)

As a result one notices that the expansion velocity V in the Eq. (21) includes an enhancement factor of explosive character, namely (1 – t / T) – 1 with respect to the conventional Hubble law. For finite T, i.e. non-zero ε the critical time t = T, is finite whereas for ε = 0, T becomes infinite. It is interesting to notice that the scale-lenght L(t) here used (1), (4 – 6), (8), (13 – 15), (21) turns out to be equivalent to the Einstein radius of curvature R(t), (see references [A1, A2] and cf [A3]. The restriction (16), i.e. 3α + Γ = 0 is not consistent with the requirement that T could be finite since from the expression (12 ) T would be proportional to (3α + Γ)–1 and therefore infinite. The origin of this discrepancy is that the classical Hubble law has the precise form V = HL. Slight changes in the form-parameters η, etc. would essentially not change this discrepancy, but only introduce small relative changes in α versus Γ, which would seem non-consistent with shape-preservation, i.e. dη / dt= 0, and may be considered more a question of informatics. The conclusion would be that one has to make an extension of Hubble’s law according to the relation (21), corresponding to an open universe (or for ε > 0 to a closed universe), or to change the form of the NL PDE equation, which does not seem attractive! A3. Conclusions and discussion It seems that the NL PDE has support from many corners of science, and besides is more general and possibly more far-reaching than the specific Hubble form. Further detailed measurements may provide an answer or at least an indication on this subtle but principally important point. What would finally be the value of the coefficient α and how would it be related to the time T? From the Eqs. (11, 18, 19) the simple form for α in the NL PDE (γ =2; d=3) becomes 319

APPENDIX

α = –(HL02 /3aA0α) (1 + 3 / 16HT),

(24)

where the second term in the parenthesis accounts for the influence of a finite value of T, which also influences Γ, namely Γ = (HL02 / aA0α ) (1 + 5 /16 HT)–1:

HT > 1

(25)

with HL02 / aA0α = – 9/8

(26)

from the relations (11) and (16) for (1 / HT) = 0, ε = 0. For an infinitely large value of T one recovers in (24) the value α = 3/8 from Eq. (17). The relations (24) and (26) are particularly interesting since they link together α with Hubble’s constant H, with T, and with the initial values of L0 and A0 as well as with the linear diffusion coefficient a, see expressions (2 – 3). The relations (24 – 25) refer to an open universe (ε < 0). For a closed universe the signs in the parentheses of (24 – 25) should be changed. One might imagine to use our formulation to model even how a turning, i.e. a reversal of the expansion, could be described. Before reaching a critical domain, or a crunch, we could assume that the universe did not change in shape with time, which meant that dη / dt = 0, with η = 0, corresponding to Λ = 0 in the expression (6) and Γ = – 9/8, α = 3/8 from the relations (11) and (16). Now approaching a crash this can not possibly be true. The conditions have to be changed.One would near the «turning» expect not only ε = 0 in (18) but also Γ = 0 and α = 0 from the relations (14 – 16), which happens for a particular value η = 0.3 in (11). The turning would then be described by a transition from d η / dt = 0 with η = 0 (Γ = – 9/8; α = 5/3, ε different from 0) to dη / dt different from 0 with η = 0.3 (Γ = 0; α = 0; ε = 0 ), and with a reversal in time to return to the previous shape and distribution (backwards in time!), not a detailed one of course, but an average one. That means to return by contraction and compression, and by heating up the matter to the state of the original Big Bang from the intermediate Big Crunch! Enormous amounts of matter may be concentrated, in both or either of these limits, forming a hot plasma, ejected particles and radiation of X-rays, neutrinos etc. Perhaps, it would mark the beginning of a new phase in the motion of the «cosmic pendulum», an oscillating universe, where the masses 320

APPENDIX

of ejected dust and crashed matter would again form new galaxies and stars to be thrown out in space, with enormous forces to later on contract again into a small total volume and form the beginning of the next universe and so on. But that is another story! One may, however, consider the Hubble expansion as a specific manifestation of what could be considered, in a more general sense, nonlinear cosmodynamics (NL CD). The above analysis may be seen as an attempt to approach such a description by means of a certain form of nonlinear partial differential equations (NL PDE). It extends ideas based on a recent paper by the author [A2], relating fusion plasma physics and gravitation. References [A1]

Einstein A 1921 The meaning of relativity (the Stafford Little Lectures of Princeton University May 1921), (Princeton University Press, Princeton NJ 1955).

[A2]

Wilhelmsson H 2002 Gravitational Contraction and Fusion Plasma Burn; Universal Expansion and the Hubble Law, Physica Scripta 66 395.

[A3]

Wilhelmsson H and Lazzaro E 2001 Reaction – Diffusion Problems in the Physics of Hot Plasmas (Bristol and Philadelphia: IOP Publishing).

321

Acknowledgement It was a great challenge for me to write this book after many years of interest in geocosmic plasma physics as well as in fusion plasma physics. The outstanding recent developments in these fields provided strong motivations. I was also particularly stimulated by discussions and questions raised when I gave talks in various places. The beginning of the story was that Gerard Bonneaud invited me to give a talk on fusion to the elementary particle physics group at Ecole Polytechnique, Palaiseau, Paris. He stimulated me considerably in the early phases of the work. Several visits to the « Istituto di Fisica del Plasma, Milan and its Director Giampietro Lampis became exceedingly fruitful for developing the contents of the book. I also greatly appreciated the comments from the audience at a talk in «l’Academie Nationale des Sciences, Belles Lettres et Arts de Bordeaux». Without my wife Julie the book would probably never had been finished. Her continuous encouragement and help with the word processing of the ever changing manuscript has been invaluable. Nils Robert Nilsson has been a never failing supporter of my work. Our discussions on scientific, artistic as well as editorial questions have been more than appreciated and sometimes gave me courage to continue the writing of the book. For the final form of the work the generous and highly competent linguistic aid by my friend John Allsop has been particularly appreciated. He transformed my text into something that came as near as possible to his own Oxford English. He also made valuable constructive comments on the outline of the book. Ros Herman on her side kindly helped me to improve the style of certain sections. 322

ACKNOWLEDGEMENT

Alexis Brandeker provided me with the beautiful picture he took of the Hale Bopp comet in March 1997. An original photo of the recent painting «Cosmos» (1997) by Pierre-Marie Brisson was kindly put at my disposal by the artist. Madame Evelyne d’Alblousse, Fondation Peter Stuyvesant, kindly offered me to use a photo of the extraordinary etching by André Masson, «Les oiseaux sacrifiés» (1954, aquatinte). The Hubble Telescope and the JET contributed with some outstanding photos from their activities; Garching from ASDEX Upgrade and of stellarators, Culham Laboratories from START. Joël Lafons, Laboratoire Photographie «Speed Photo», Bordeaux, provided me with some delicate photos of lightnings taken accross the sky of Bordeaux, one of them hitting the top of the cathedral spire! I am greatful to Professors E. Infeld, C. Alejaldre, P. Michelsen and A.P Grecos for their kind and constructive remarks. It is my pleasure to acknowledge Mrs Agnese Mandrino, Librarian of the Brera Astronomical Observatory, Milan, and Professor Maurizio Lontano, for their generous aid in confirming the reference to Birger Vassenius from 1733. I would like to express my cordial thanks to my colleage Professor Bo Lehnert [1.5–1.7, 2.5–2.7, 4.10, 8.3] (i) for his paramount example as a scientist, active both in experiments and theory – a spiritual father for the young generation, a true Galilei of our time, (ii) for good co-operation in creating the Swedish Association with the European FUSION Community (EURATOM-FUSION) and (iii) for his unfailing good spirit. It is a pleasure for me to acknowledge Monsieur et Madame Roland Flak, for encouragement and advise throughout the work, particularly on Iliazd and Max Ernst. Monsieur Pierre Rosenberg de l’Académie Française, President-Directeur du Musée du Louvre, Paris kindly confirmed to me some rules of copywrite for the Leonardo da Vinci and Vincent van Gogh artistic works, on the occasion of 323

ACKNOWLEDGEMENT

his reception as an associate member of l’Académie Nationale des Sciences, Belles-Lettres et Arts de Bordeaux in June 1999. I would like to express my sincere appreciation to Monsieur Denis Mollat for allowing me to have a presentation of the first edition of this book in his famous «Librairie Mollat» in Bordeaux, and to Monsieur François Dumont for arranging the accompanying exhibition of graphic art related to science in connection with the presentation of the book in November 1999. It is also, in particular, my pleasure to extend my highest appreciation to all my colleages at Chalmers, and to many research centres and universities abroad, for fruitful and enjoyable collaboration through many years.

324

Short gravitation-fusion-plasma dictionary This «dictionary» contains explanations of certain commonly used terms in the field of gravitation-plasma and fusion physics. Indications are also given where those terms most frequently occur in the chapters of the book. Alpha particle An alpha particle is a helium nucleus consisting of two protons and two neutron bound together by nuclear forces. Alpha particles are produced by fusion reactions between, for example, deuterium and tritium isotopes of hydrogen at the same time as high energy neutrons are generated (chapters 2, 6 and 8). Auroras are spectacular coloured phenomena observed at high latitudes caused by the particles which enter the Earth’s magnetic field from the Solar wind (sections 4.2.1 – 4.2.4). Black hole Sufficiently massive stars may undergo gravitational collapse and become black holes which are even denser than neutron stars. One may imagine that nuclear matter has become completely crashed. In black holes the gravitational force is so large that not light can be emitted from them. The density is estimated to be 16 g/cm3 or about one hundred times higher than that of a neutron star. Already by the end of the 18th century Laplace, the French mathematician and physicist, proposed that heavenly bodies with the same density as the Earth and with a radius of 250 times the solar radius would have such a strong gravitational attraction that light could not escape from them and that the largest stars in the Universe would remain invisible to us. Laplace, in his considerations, assumed, long before the concept 325

SHORT GRAVITATION FUSION-PLASMA DICTIONARY

of a «photon» had been adopted, that «light particles »could be attracted gravitationnaly according to Newton’s law. Bose-Einstein Condensation (BEC) A process which can occur near the absolute zero temperature in sufficiently dense atomic gases, obeying Bose-statistics (integer spins of the atoms), for which the matter wave length (λ = h/p), i.e. the de Broglie wave-length, is of the order of magnitude of the distance between the atoms in the gas. Atoms in different quantum states can then coupole mutually to form a Bose-Einstein condensate and occupy a common lowest level state forming a «superatom», characterized by a single wave function. One talks about «coherent matter» as of «coherent light» for lasers (see section 3.6). Chaos Chaos is a state of dynamic motion where chance enters but where certain regularities may remain. (chapter 7). Coherence The property of a set of vibrations or waves for which the mutual phases remain constant in time, a state of «ordered motion». The principle of lasers (light amplifications by stimulated emission of radiation) is based on coherent light (chapter 6). Comets Comets are objects in the solar system which often move in strongly elongated orbit. They consist of a nucleus of pieces of small frozen particles of gas and of stones, sand and dust. The nucleus is only some kilometers large. When comets approach the sun evaporation occurs and forms a gaseous head of the comet and a tail of luminous gas several millions of kilometers long and often very spectacular. Plasma phenomena which occur in the ionized gas play an important rôle. Observation of radiation from comets, even recently observed X-rays, can give us information about the chemical structure of the dust, rock and ice which cannot have changed much since the birth of the solar system 4.5 billion years ago! 326

SHORT GRAVITATION-FUSION-PLASMA DICTIONARY

Creation Process of generating particles and radiation. It could increase the temperature of a plasma as expressed by a nonlinear term in the rate equation for the temperature in a plasma (T p, where p is approximately 2) (chapter 7). Density Characterizes the numbers of particles, for example electrons or ions per unit volume in a plasma. Deuterium Hydrogen isotope which consists of one proton and one neutron bound together by nuclear forces. Diagnostics Measurements and evaluations of the plasma parameters (density temperature, current) as well as of phenomena occurring in the plasma (instabilities, fluxes of temperature and particle densities, radiation and particle emission, e.g. fast neutrons). Methods of electron-cyclotron emission (ECE) and Thomson scattering of laser light are used to determine the electron temperature profiles in fusion devices. Diffusion In a system of charged particles which collide with each other there will after many collisions, be a net migration of particles in space. The accompanying diffusion of energy and particles is a main problem in fusion research. The observed diffusion is generally much higher, about a hundred times higher, than predicted by a classical collision model. The diffusion may be caused by collective oscillations associated with microinstabilities, for example temperature-gradient-driven drift-wave turbulence, leading to a particular temperature-dependence of the thermal conductivity and particle diffusion coefficients, and D proportional to T 3/2. The diffusion of the plasma determines the energy confinement time.

327

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Earth Our planet, a very particular planet due to the presence of an atmosphere which we can breathe, and water in combination with temperatures which provide conditions for life. So far it is the only planet known to us which has these advantages! Electric field Electric field originates from charged particles and affects the motion of other charged particles. An electric field always accompanies time-varing magnetic fields, for example those responsible for the toroidal current of interest in magnetospheric plasmas (chapter 4). Electron Elementary particle with negative charge and mass 1/1836 of the proton mass. The electrons occupying different energy levels in the atoms are associated with different quantum numbers of spin and angular momentum determining the frequency of radiation from transitions in the atomic structures. The free electrons in a metal are responsible for its electrical conductivity. Energy Capacity of a system to produce work. For any system there exists an equivalence between mass and energy shown by the Einstein equation E=mc2 where E is the energy, m the mass and c the velocity of light (3×1010 cm/s).The equation tells us that one gram of mass is equivalent to 25 million kilowatt hours. The liberation of energy by the transmutation of protons and neutrons to helium is accompanied by a mass defect which multiplied by c2 gives the energy. Equilibrium Balance of a system, which could be stable or unstable according to the consequence of a perturbation. A fusion plasma could exhibit several types of instability but might also stay sufficiently long in an equilibrium state for fusion reactions to produce useful energy (chapters 7 and 8). 328

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Eruption Phenomenon where energy is released as a result of available free energy. Volcanic activities are perhaps the most spectacular example of eruptions at close distance. Eruptions associated with sun spots generate various types of prominence. These are enormously energetic and spectacular phenomena. The spots occupy local domains on the sun as large as the continents on Earth. They carry complex interweaved structures of magnetic fields and currents. The prominencies could extend above the solar surface to heights up to one-quarter of the solar diameter (chapter 4). Evolution Development in time and space of a system in general, for example the state of meteolorogic conditions, or the human population on Earth.The evolution of a hot fusion plasma to the burning plasma state in a fusion reactor under controlled conditions is a topic of considerable interest in fusion research. So is the evolution of the universe for the cosmologists, or the evolution of laser communication by optical fibres, or of the Internet system for consumers in general (chapters 7 and 8). Explosion A state where a certain quantity, e.g. temperature grows nonlinearly in space and time to reach unlimited values in a definite time. This is what defines an explosive instability, a self-creating nonlinear effect. It is believed that prominences on the sun are affected or even caused by such effects, which are also driving sources in a thermonuclear bomb explosion. For the theoretical description of a future fusion reactor the source terms will be balanced by terms describing diffusion processes and losses to result in an equilibrium operative state (chapter 7). Flame

A white-hot stream of luminous gas produced by combustion.

Rocket flames are weakly ionized gas of electron densities about 1012 per cubic centimetre and temperatures of near 1000 °C. If they are sufficiently large they can be classified as plasmas (Debye length λD proportional to (T / n)1/2 less than the 329

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cross-section of the flame). A rocket flame can cause black-out of a microwave signal of three centimeters wave-length and disrupt signal communications (chapter 4). Future It is said to be difficult to make predictions, in particular about the future! The future is, in fact the open domain in the direction of which everything evolves and where all is as yet unknown. It is the area for speculation for which unexpected happenings and unknown trends, which change all deterministic expectations. It is a higly nonlinear domain! «Future cannot be predicted it has to be invented»

Dennis Gabor (Nobel prize for physics in 1971 for holography which he invented in 1948) Fusion Nuclear reactions between light atomic nuclei such as isotopes of hydrogen from which heavier elements are produced with generation of large amount of energy. Fusion is the source of energy in the universe and the origin of ultimate goal of present day fusion research (chapter 10). Galaxies Large-scale structures of the universe containing on average 100 billion stars each and extending about 100 000 light-years, often in spectacular forms of flat spirals (chapter 3). Gravitational lensing The bending of light in a gravitational field, in accordance with the curvature of space, gave Einstein the idea to predict lensing effects from gravitational bodies. These are recently applied in astrophysics, where nearby galaxies are used as gravitational lenses to study very remote objects like quasars. Instabilitiy Instability occurs in a plasma driven by some energy-releasing source whichcould be inhomogenity in the temperature and /or 330

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density of the plasma or in the magnetic field as well as drift energy of a charge particle beam in the plasma. Different types of Interacting waves can give rise to new waves for which the plasma provides conditions for growth and instability; one talks of nonlinear instabilities which can lead to turbulence where a large number of waves participate (chapter 7). Ions Ions are the charged particles that remain when the atoms have lost or gained electrons, e.g. by radiation or collisions. They respond to low-frequency electromagnetic oscillations and to ion cyclotron wave magnetic oscillations and to ion cyclotron wave magnetic fields (chapter 2). Jet A plasma formation that may occur under different circumstances, from jet burners for the preparation of metal surfaces to elongated galactic jets which could have extensions over distances of many thousands of light years (chapter 4 and plates 5 and 6). JET Joint European Torus (Abington, UK) .The large fusion plasma experiment based on the tokamak principle (chapter 8). Laser Light amplification by stimulated emission of radiation has provided a new tool to be used in almost all branches of science and technology. Laser fusion is being investigated as one option for future energy production. Optical communication by fibre techniques is being revolutionized thanks to the advantages of using coherent light from lasers (chapter 6). Life The origin of life and the biology of interstellar matter may be connected with suitable conditions created in mixtures of gas and dust. Radioastronomy attempts to analyze the presence of heavier molecules and their formation in the cosmos. The 331

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search for the presence of life on other planets than the Earth is a gret challenge of future research (chapter 9). Light The carrier of information in the universe which from ancient times has provided us with all the information we have about astrophysics and astrochemical phenomena and the rules governing the cosmos (chapter 4). Magnetic Field Magnetic fields are very important for confinement of fusion plasmas. As well as for cosmic plasma phenomena in general (solar, galactic, magnetospheric, pulsars, comets, quasar physics).The magneto-hydromagnetic plasma phenomena (MHD) are essential in laboratory fusion experiments as well as in cosmic plasmas (chapters 4 and 8). Matter In the conventional sense the states of matter are solid, liquid and gaseous, these states being acquired at different levels of increasing temperature. For temperatures sufficiently high to cause ionization the plasma state is reached, the fourth state of matter (chapter 2). Nebula A luminous cloud of gas and dust occurring in interstellar space. The clouds which most often have a dimension of some tens of light-years often exhibit polarized magnetic fields generated by currents in the nebula. Neutron Elementary particle carrying no net charge, which together with protons form building blocks of the atoms. Neutron star Assumed to be formed by the collapse of a star and to be the final state of a supernova explosion. A neutron star may be as heavy as the sun small size, only 10–15 cm. The density is enormous, about 1014 g/cm3. A teaspoon of neutron star matter would have a weight of 100 million tons. The central 332

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temperature is exceedingly high, about 10 million degrees. Pulsars are believed to be rotating neutron stars, emitting repetitive signals of radiation. Nonlinearity A phenomenon related to a high concentration of energy (particle or radiationdensity) in space and time. A wave of high amplitude could change the medium locally to such an extent that the wave propagates differently for example with different speed and shape from how it would have done in the absence of the self-induced conditions ofpropagation. The presence of other waves occurring simultaneously in the medium could change the conditions for a particlar wave and they could also provide possibilities for the particular wave to create new waves due to mutual interactions.The advent of the laser in the early 1960 provided an excellent opportunity to create and also to study nonlinear phenomena in plasmas as well as in solids. Nonlinear effects play an important role not only in physics but in most modern fields of science as well as in the dynamics of our society (chapter 7). Origin A point or region in space-time where a source of events is to be found. It might be possible to localize the origin of a fire but not the origin of the universe. One may say that it is everywhere (chapter 4). Oscillation Vibrational motion of a charge particle, for example an electron in a periodic electromagnetic field, a radiofrequency wave or an optical frequency field from a laser (chapter 6). Photon A light-particle or quantum of radiation of energy E= hν, where ν is the frequency and h the Planck’s constants. Plasma A gas where the atoms are ionized, i.e. where the electrons are separated from the ions by the influence of, for example 333

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radiation or particle collisions. A plasma is electrically conductive, i.e. currents may occur in the plasma as a result of electric fields. Plasma is the most abundant state of matter in the Universe. The word plasma is of Greek origin and means a state of matter with plastic properties (chapter 2). Plasma currents may generate magnetic fields, and magnetic fields may also influence the currents and control their motions (chapter 8). Population Number of constituents in a state which is often in time dependent evolution. A quadratic source dependence could generate «explosive» tendencies (chapter 7). Power Electrical energy generated per unit of time, for example in units of watts = joule/s. Future fusion reactors are expected to operate in the range of 3000 megawatt or three billion watts, which could be compared the power of ordinary lamps of 60 watts with home electric radiators of one thousand watts, or 4.1023 kilowatts continuously emitted by the sun in the form of light as electromagnetic waves (chapter 4). Prominence Enormous luminous gas clouds ejected from the sun demonstrating several types of plasma phenomenon such as instabilities, filamentation and blob formation, influence and generation of magnetic fields etc... (chapter 4). Propagation The process of continued change of position in time of a certain wave or packet of waves or pulses in a medium, for example a plasma. The speed of propagation is defined by the density and temperature of the plasma and by the presence of a magnetic field (chapter 7). Proton Elementary particle with a mass 1836 times that of an electron and of positive charge.

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Pulsars Sources of rapidly repeated pulses of radiation of frequences from radio to visible and even X-ray or γ-ray waves. The generation comes from neutron stars, objects of very high density of matter, which rotate with high velocity sometimes several hundred times per second, and have strong magnetic fields, sometimes thousands of billion gauss. A pulsar exists in the center of the Crab nebula generating pulsar radiation in the plasma from a supernova remnant (chapter 4). Quasars Quasi-stellar radio sources at enormous cosmic distances from us, possibly 10 billions of light-years or more away (chapter 4). Radiation All charge particles which change their velocity, its absolute value in rectilinear motion (special relativity) or in direction (general relativity), produce electromagnetic radiation. Relativistic electrons which have a circular motion radiate electromagnetic radiation (syncrotron radiation) in their instantaneous direction of motion, which provides the radiation from all radio stars. Syncrotron radiation also occurs in fusion plasmas when the fast electrons move in the magnetic field. The term radiation is often used to notify the corpuscular motion of particles (chapter 7). Reaction Process of mutual direct influence between different elements, for example particles or molecules, to produce new elements. Nuclear fusion in stars is an example of reaction which produces energy and alpha particles from protons. The hydrogen isotopes deuterium and tritium can react with one another to produce alpha particles and energy in a sufficiently hot gas mixture of these isotopes; this is the reaction process offering most efficiently fusion energy for future energy production (chapters 2, 3, 4, 8 and 10).

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Sky Synonymous with cosmos or univers but usually imagined as the blue or starry half-sphere which hangs over our heads, reminding us of mythological or magic views of ancient times. Solar wind The permanent continuous flow of particles out of the sun, predominantly electrons and protons, which reaches the Earth after about four days. It represents a link of plasma between the sun and the Earth and has an important influence on the magnetospheric structure of the Earth in feeding the magnetosphere with charged particles (chapter 4). Source Origin of available free energy of any kind. As regards plasma and fusion physics it could be a laser source for laser-plasma interaction, resulting in forming small dense, high-temperature domains by inertial confinement; or it could be a particle injection source of neutral beam heating of a magnetized fusion plasma (chapter 7). Space Infinitely extended domain of which the center is unknown. Space-time Concept in the general theory of relativity based on four dimensions, i.e. the ordinary three space dimensions and in addition the time dimension. Stellarator Toroidal confinement system where the toroidal drift of particles is compensated by external helical magnetic fields. In a stellarator there is no induced toroidal current flowing in the plasma. Unlike a tokamak a stellarator can therefore operate continuously. The absence of plasma current also limits the possibilities of undesired instabilities. Stars Luminous points in the sky which can be seen at night. They produce and emit energy and are born by contraction of 336

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interstellar matter. In the process of collapse the temperature rises to 10 million degrees, sufficient for the hydrogen nuclei to produce fusion energy and helium (alpha particles) (chapter 3). State Physical system, for example solid, liquid, gas or plasma, or energy level of a particle or atom, for example ground state, where the electrons populate the lower levels of the atoms, or excited state where electrons populate higher energy levels defined by quantum the numbers, or ionized (plasma) state where the atoms have been split into free electrons and ions. Sun Our nearest star where fusion reactions are continually liberating large amounts of energy from which the Earth captures one part in 2 billion on the average. It seems that the sun’s energy production has remained about the same for the last three billion years. The sun is the most important element in our solar system since it supplies the energy necessary for life (chapter 4). Sun-spots Dark spots occuring on the sun’s surface often in groups. They are centres of magnetic activity with characteristic values of about 3000 Gauss, cooler than the rest of the surface. Noted by Galileo even in 1610, sun-spots have still not been fully investigated as far as their electromagnetic properties are concerned (chapter 4). Supernovas Sources of extreme brightness which occur when heavy stars undergo gigantic explosions (chapter 4). Temperature Characterizes the heat of matter, for example of a plasma, where the temperature T is a measure of the disordered motions of the charged particles expressed in terms of their thermal velocity υt , i.e. kT = mυt2, where m is the particle mass and k the Boltzmann constant. 337

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Time A concept that helps us to find out a succession of events. Tokamak A toroidal chamber with magnetic coils. The tokamak magnetic confinement system consists of a toroidal field combined with a poloidal field produced by the current flowing in the plasma. The plasma current is produced by a large transformer, which of necessity has to operate intermittently. Coils around the central limb of the transformer core form the primary winding and the torus of the plasma itself is the secondary winding. Tritium Hydrogen isotope which consists of one proton and two neutrons bound together by nuclear forces. Turbulence Disordered motion among elements in, for example a fluid where filaments and vortices become mixed instead of conserving their identity. Turbulence in a plasma may be regarded as a state composed of a large number of waves of different frequencies and wave-lengths (chapter 7). Universe The totality of space where all stars, galaxies, interstellar matter and magnetic fields are distributed. The universe is the gigantic laboratory where all the astrophysical and cosmological phenomena occur, and offer possibilities of observation from Earth or from remote space observatories. The possibility of realizing fusion energy on Earth encreases as we obtain more information about plasma-fusion phenomena in the universe (chapters 4 and 9). Wave Systematic propagating undulatory motion characterized by a wave-length determined by the distance between two successive equal phases of the repetitive motion, for example two minima or two maxima. Waves could be of acoustic, optical or radio types. In plasmas a large number of waves of a different nature, 338

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e.g. longitudinal plasma waves, transverse electromagnetic waves, magneto-hydrodynamic waves, cyclotron waves etc.. Can exist and can be used for heating or diagnostics of the plasma (chapter 7). White dwarf star Stars with the size of our Earth and weight comparable to that of the sun. The mean density of a Dwarf star can be as high as 105 – 107 g/cm3, occasionally even higher. Matter in degenerate states caused by gravitational collaps, i.e. completely «crashed» by sudden failure of the thermal pressure of the nuclear reactions to balance the gravitational forces, the collapse being accompanied by a considerable contraction of the size of the star. They could collapse again to form a «neutron star», which might collapse even further to produce a «black hole». The white dwarfs exhibit a weak white radiation. They are abundant and estimated to be about five billions in our galaxy (chapter 9).

339

Character index Brahe T, 120 Brandeker A, 322 Breizmann B, 241 Brisson P-M, 13, 322 Budker GI, 241 Brown SC, 231 Buneman O, 213, 223

Airoldi A, 56 Alejaldre C, 322 Alfvén H, 25, 30, 67, 78, 84, 93, 101, 102, 116, 138, 142, 162, 222, 305 Allsop J, 321 Andersson D, 79, 140, 159, 279-280 Appleton E, 109, 118, 201 Aristoteles, 118

King Carl XVI Gustaf, 242, 305, 306 Cecil E, 215 Chalmers W, 70, 233 Chamberlain O, 204 Chandrasekhar S, 53, 66, 81, 85, 143, 208, 294, 307 Chaplin C, 211 Charbonneau D, 200 Cherenkov PA, 178 Chirac J, 154 Chu S, 232 Cohen-Tannoudji C, 232 Columbus C, 38 Cooper LN, 210 Cornell EA, 78 Coster D, 210

Bahcall Neta, 17 Balescu R, 275 Bardeen J, 210 Basov NG, 231, 253 Bernstein IB, 223, 227 Berzelius JJ, 233, 234 Bethe H, 34, 144 Biermann L, 110 Bickerton R, 311 Birkeland R, 110 Bloembergen N, 227, 255 Bohr A, 209, 211 Bohr N, 8, 13, 14, 28, 32, 60, 88, 203, 205, 209, 211, 216, 219, 221, 307 Bonneaud G, 321 Bopp T, 101, 105,106, 114 322 Bose SN, 53, 64, 77 Braams CM, 192, 278

Da Vinci L, 29, 54, 108, 156, 163, 175, 292, 322 Davis R Jr, 18, 78, 134, 135, 144, 286 340

CHARACTER INDEX

Dawson JM, 143, 227, 271, 306 De Broglie L, 28, 65, 325 Debye P, 35, 220, 328 De Hevesy G, 210 Democritus, 174 Desaix H, 256 Dirac PAM, 149 Dumont F, 323

Fukuyama A, 182, 271 Gabor D, 8, 59, 141, 245-247, 329 Galeev A, 182, 241 Galilei G (Galileo), 54, 60-62, 93, 96, 141, 206 Giacconi R, 18, 136140, 145, 146, 287 Gilbert W, 113 Ginzburg VL, 306 Gorbatchev M, 240, 242 Gould T, 113, 205 Gralén N, 235, 237, 247 Granholm P, 219, 221 Greene JM, 223 Grecos AP, 322 Gulliver, 45 Gustafson T, 202, 203

Eddington A, 18, 53, 54, 60, 65, 67, 74, 78, 177, 228, 307 Einstein A, 7, 17-19, 5367, 73-77, 141, 216, 217, 224, 232, 239, 244, 291, 294, 320 Eisenhower DD, 62, 242 Ekelõf S, 70 Ekelõf T, 250 Eloy J-F, 158, 196, 277 Engelmann F, 252 Ericson T, 202-204 Erlander T, 203 Ernst M, 46, 47, 268, 322

Hale A, 105 Hayter SW, 267, 268, 270, 284, 285 Hazegawa A, 306 Herlofson N, 67,78 Hertz H,222 Hewish A, 124, 254, 263-266, 282, 306 Hokusai K, 167 Holgersson N,45 Hubble E, 15, 40, 46 Hugo V, 47 Hulet RC, 66, 78

Fermi E, 58, 65, 81, 85, 143, 167, 183, 208 Ferraro VCA, 205 Feynman RP, 207, 249 Flack R, 322 Flammarion C, 76, 99, 100 Fowler RH, 65, 66 Fowler WA, 308 Friemann E, 223, 227

Hulse R, 123 Hultqvist B, 305 Husimi K, 271 341

CHARACTER INDEX

Lederman L, 205 Lee T-D, 307 Lehnert B, 38, 39, 143, 192, 205, 252, 278, 322 Leprince-Ringuet L, 277 Le Roux A, 277 Le Roux M-N, 182, 277, 280 Lisak M, 79, 159, 257, 279-281 Liu C-S, 240 Lontano M, 157-158, 322 Lorentz H, 62, 218 Lundquist S, 31, 142, 251

Hössjer G, 198, 235 Ichikawa Y, 271, 272 Iliazd, 46, 47, 322 Infeld E, 322 Itoh K, 39, 182, 271, 272 Itoh S-I, 39, 182, 271 Jancel R, 279, 280 Jeans J-H, 65 Johnson E, 306 Johnson L, 270 Jones A, 243, 247 Kapitza P, 8, 149, 309 Kaw P, 276 Keller JB, 227 Kepler J, 104, 120 Kerman A, 208 Ketterle W, 53, 63, 78 Kiepenheuer K, 67, 79 Kierkegaard S, 28 Kjellmert B, 250 Koshiba M, 18, 135, 136, 145, 286 Kowalsky P, 243, 245, 248 Kruskal MD, 167, 183, 223 Kãllén G, 62, 206, 208 Kãllén Y, 62

Magnusson R, 71, 79 Mandrino Agnes, 322 Marcus G, 243-244 Martinson H, 44, 123, 249, 265, 307 Matta R, 269, 285 Maxwell JC, 62, 218 Michelsen P, 322 Mollat D, 323 Mottelson B, 209, 211 Nezlin MV, 148 Newton I, 21, 22, 74, 308 Nilsson Birgit, 239 Nilsson NR, 206, 242, 243, 248, 250, 251, 253, 321 Nilsson SG, 202, 209211, 281

Lampis G, 277, 321 Langmuir I, 29, 196, 281 Laplace PS, 324 Lazzaro E, 183, 257, 277, 281, 320 Le Corbusier J, 269 342

CHARACTER INDEX

Nishikawa K, 271, 272 Nobel A, 311

Rosenberg P, 322 Rosenbluth MN, 306 Rosenfeld L, 205, 219, 221 Rossi B, 137, 139, 140, 145 Rydbeck O, 79, 144, 194, 197, 199-202, 221, 226-232, 249, 260, 304 Rydberg JR, 216, 217 Ryde N, 78, 197, 235 Ryle M, 141, 229, 248, 260, 263-266, 306 Rõnnmark L, 221, 236239 Rõntgen WC, 64

Obayashi H, 271, 272 Ohlin P, 250 Olving S, 197, 219, 221, 230, 235, 238 Ollongren A, 229 Oppenheimer JR, 58, 76, 144 Oseen CW, 217-219, 225, 281 Pais A, 211 Palmstedt C, 233, 234 Palumbo D, 267, 275 Pasta J, 167, 183 Pauli W, 77, 134, 203 Pavlenko VP, 240, 278 Penzias A, 44, 70, 71, 288, 308 Phillips WD, 232 Petersén I, 71 Petit R, 31 Picasso P, 268, 269 Pierre, 61 Poincaré H, 63 Polhem CHR, 200 Prokhorov AM, 231, 253 Prometheus, 13 Pytaevsky LP, 309

Sagdeev RZ, 146, 182, 241, 307 Sakharov A, 58 Sakata D, 272 Schawlow AL, 255 Schrieffer JR, 210, 211 Schwartz M, 205 Schwinger J, 207 Scott D, 61, 241 Segré E, 205 Sen A, 276 Siegbahn K, 227, 240, 250, 255, 305 Siegbahn M, 215, 250 Siegbahn P, 250 Sitenko AG, 306 Sjöberg A, 239 Spitzer L, 8, 32, 38, 192, 223, 227, 304

Rainwater J, 209 Rebut PH, 149, 311 Reuterswãrd CF, 243, 247 Roosevelt F, 57 343

CHARACTER INDEX

Van Gogh V, 46, 100, 101, 144, 322 Vassenius B, 98, 323

Stenflo L, 79, 143, 146149, 157, 181, 183, 250 Steinberg J, 205 Stott P, 192, 215, 278 Strõmgren B, 66 Svedberg T, 240 Swift J, 45

Wallman H, 70, 71 Weiland J, 79, 182-184, 250, 279 Weisskopf V, 37, 204, 253 Westberg V, 195 Wieman CE, 53, 63, 78 Wigner EP, 223 Wheeler JA, 223, 290 Wiener N, 225, 245 Wigforss E, 203 Wilhelmsson H, 38, 77, 79, 140-149, 157, 158, 182, 183, 204, 208, 232, 233, 245, 252, 263, 278281, 320 Wilson R, 44, 70, 288, 308 Wüster HO, 304

Takayama K, 271, 274 Taylor J, 123 Teller E, 58 Tempel G, 47 Thonemann P, 205 Tomonaga S, 207 ter Haar D, 242 Tiselius A, 240 Trofast J, 233 Tsytovich VN, 79, 157, 182, 240 Uberoi C, 119 Uhlhorn U, 205 Ulam S, 167, 183

Yang CN, 204, 307 Zabusky N, 167, 183 Zagorodny A, 149, 184 Zdanevitch I, 46 Zielinsky P, 204

Van Allen, 111, 115, 116 Van de Hulst HC, 61, 77, 205, 206

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