Моделирование процессов регистрации космического излучения высоких энергий

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Author: Назаров С.Н.

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Ne(E > Emin) 45

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Ne(r < r0)

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Ne(E > εlim, r < r0)

Ne(E > εlim, r < r0) r0 = 25 µ

r0 = 50 µ

1

10

-1

20

20.25

20.5

20.75

21

Ne(E > εlim, r < r0) 10

r0 = 100 µ

z, cm 20 20.25 20.5 Ne(E > εlim, r < r0) 60 50

20.75

21

z, cm

r0 = 300 µ

40 30 20

1 10 9 8 20

20.25

20.5

20.75

21

Ne(E > εlim, r < r0)

z, cm 20 20.25 20.5 Ne(E > εlim, r < r0)

r0 = 500 µ

100 90 80 70 60 50

20.75

21

z, cm

r0 = 1.5 mm

40 30

10 2

20 20

20.25

20.5

20.75

21

z, cm

20

20.25

20.5

20.75

21

z, cm

1, , - ¼ - +# 2 6# , ¼ - !,9"+ ! + FG - # @ # 6 0# @+ $%&'()U V - ! ! # 26 0# @+ 7 + 6 + !+

G 7 @ 3 KG 7 -,3 KG 7 +

N(ΣEγ)

N(ΣEγ)

25

25 fixed thr X

E

KG

E

20

20

15

15

10

10

5

5

0

fixed thr =

500 MeV

0

0

2

4

N(ΣEγ)

ΣEγ3 FG 0 N(ΣEγ)

25

2

4

ΣEγ3 FG

25 fixed thr X

E

fixed thr X

MG

E

20

20

15

15

10

10

5

5

0

MG

0 0

2

4

!, !

ΣEγ3 FG

0

2

4

ΣEγ3 FG

! 2 6# 26 0# !+

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2.5 2 1.5 1 0.5 0 0.04 0.02 0 -0.02 -0.04

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$%

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εtotal 45

-1

10

-2

10

1

εcalorimeter

2

10

10

3

4

10

10

E0 3FG

0.1 0.09 0.08 0.07 0.06

4/5

0.05 0.04 0.03

0.02

0.01 1

2

10

10

3

4

10

10

E0 3FG YJJ - + !- - $%&'()U 3 -6 0 - 7 2 , - 0 * ! @ ! ! !- 6 + * 28 @

εtotal 1

-1

10

-2

10

-1

10

1

2

10

10

3

10 E0 3FG[

YJJ - + !- * @ 3 0, + 0 * -, @2 * + - $%&'()U

εtarget, εcalorimeter

-1

10

-2

10

2

10

10

3

10 E0 3FG

YJJ - + 8# * 28 @ 7 6 # * ! @ !# /

εtotal 45

-1

10

-2

10

1

εcalorimeter

2

10

10

3

4

10

10

E0 3FG

0.1 0.09 0.08 0.07 0.06

4/5

0.05 0.04 0.03

0.02

0.01 1

2

10

10

3

4

10

10

E0 3FG YJJ - + !- - $%&'()U 3 !6 7 - 8 # 6- * 28 + , 0! # 6- * ! @ 45 * !0 JJ - 3 4/5 * JJ - + 67

# /

εtotal 45

1

-1

10

-2

10

10

εcalorimeter

2

10

3

4

10

10

E0 3FG 4/5

1

-1

10

-2

10

-3

10

10

2

10

3

4

10

10

E0 3FG YJJ - + 0, + 0 - $%&'()U ./26 0 7 @3 !,,"

εtotal 45

1

-1

10

-2

10

10

εcalorimeter

2

3

10

10

4

10

E0 3FG

1

4/5

-1

10

-2

10

10

2

3

10

10

4

10

E0 3FG YJJ - + 0, @2 - $%&'()U ./26 0 @3 !,,"

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7' ( " 5 * ! ! ! ! "#QCDR *@*7> *> !*@7 -7*, )-.7> ?7*+, 7-*7, @ @-F )7> 8 .* 7D-H@*7F 75 *)A @H8 ! *-.*7* +- *G@ !6H -7F !6H @*8*8 *A @*- *HE*,!F 8 .7 !8 7* @7 )75> *G@ =75F @-F -7*, ! !**7 + HG7 + 7-*7,C 8 A*!86C -F7* +787 + -F 7 +A - > !*@*-*7F 7* EE*8!F ! ":QA+R *@*7> *> !*@7 / @-F )-.7> *A .7> ?7*+, 7-*7, @ *.7> .!85C 7 ! ""QCDR )7 8-.* 87 P*7F !*@7 !*8 > -@ )-.7>* 8*-*A ! > 8 *@75> @-F -7*, )-.7> ?7*+, @7 C .8 ?8 *-.7 !-67 @-F @*8*8 C !-67 @-*77> 8 *8-67 , - !A !8 hN}C 8 , -*G8 !6 -7F 2 P @7 >)77 * -F7* +787 + -F !G*7* QS))>7*SR !*8 + F87 **.7

7-*7

7.- @77 , D 8> > G* *- @ !88 .7 D -6P , >8 @*A - 7F .**7 ! + !*8 W ! ! -6) 7* +D@7 , *8 @C +@ 7.-67F !8@F )8F -7F @*-*8!F *8 @ 78*A- C )8* G@*77>* 7 * , !8@ .!85> )*7FH8!F ! 8*8!8HEA !*@7 !@C >.!-F*> 7-8.*! *8 @ !@A 7 , 8* D 8* T($U D>- *@!8-*7> *)-688> 7P !.*8 +A D@7> *8 @ !*@7*, / .**7 ! + !*8 W D 8 T(IC (%U >.!-F-!6 -6!> .**7 ! + !*8 W 7 )-.7> !!8 F7A F 8 ! -7F < *E* D -** @*8-67F 7= 5F Q78*+F -6!>C -.* / 8R F!6 7 *)-688> ?8 !.*8 C 8G* ! @F ) !-*@HE ! A DG*7,B R *-67 ! -6)*>* !5 / < ?! 7*78> - !8**77>* =75 Q":RC Q""RX DR )7 *@ - G86C .8 @ D7 ?-*8 77> / Q"#RC ! 8*8!8HE* =75 @-F @ -GA 7> D>86 !*8.7> 87 !8*-67 **!87 &X R !5F @ -G7 *86 !7 7>* .*8> / ?-*8 7 X > >D- !A 5H / .**7 ! + !*8 W @*B , & 9 8 ! 3 " " ! & " "-.8 " .#8 9 8

& & 9

8

Q"(R

8D-5* "& *@*7> )7.*7F *8 !5 @-F )A -.7> ?7*+, 7-*7, @ -7*, F/ !! 4 5 , N Z1

¼

R!- , ½ ½ , ½ ½ ½

J-

FG G

dN/dθ

dN/dθ

1

1

45 10

10

10

10

10

4/5

-1

10

-2

10

-3

10

-4

10

-5

10 0

θ3,

0.5

-1

-2

-3

-4

-5

0

θ3,

0.5

, # N Z1

FG# 45 G# 4/5 -3 ! #,0" #

-+ 4 5 9@+ 4 5 !- ,0 2# 6 /9, 0 28 @ 3 -, + * - - , 3 ,0 H ! @ 3 -, + * + 6 ,0 4 , 2 - 7 - - 5

73 9 " 9 & * 5& " ! / !8 *77H @*-6 !*@7*, / G7 ! -6) 86 @-F 5*7 8*A D* + 87 P*7F ! !8*, !.*8 W ! !** H+ 38 G*8 D>86 !@*-7 !-*@HE D) B & *@*-F* ?==*87H - E@6 *+!85 W @-F D 7-*7, @ D* *.7> ?7*+,X ?8 7* D A @ @-F 8 + C .8 D> +7.86 *@*-> 78*+ 7F !87!8*77> ***77> >.!-*7 ! !8 !.*8 WX ; >.!-F* ! !86 !.*8 W @-F G@ + !-.FC 78*+F 8 !.*! -.*, - E@ *+!85 7!

7-*7, @ -7*, ! .*8 8++*7 + !- FX *@*-F* 87 P*7* ! !8*, !.*8 W ! !** H+ 1/ < ; 2

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¾

F/ YJJ -0 !", +

¼

FG

R!- C3 ¾

!# -

G

1/# = 2

/ ! -6 7! 78**!*8 87 P*7* ! !8*, !.*8C 8 G7 - G86 !* 78*7!7 !8 7> & /*@ -+*C .8 7-*7F @ W !*@*-*7> ) 8 7 C 8 . @*7F -7*, 7 *76 7D-H@*7F !A *@*-*7> 7 *7 ?8 !-.* ! !86 !.*8 ( -7*, @77 , ?7*A + *@*-F*8!F !-*@HE >G*7*B & 4

( ' Q"$R & $

@*!6 "; @-F ! 8*8!8HE*, ?7*+C "-. C & < + - *G@ 7-*7* @ -7F !6H 8*-*! C < !!8 F7* *G@ 8*-*! 8 . , @*7F ! -7F 7 & 4 < 8++*7F =75FB *76 7D-H@*7FC '

*!- %

& 4

' & 4 Q"IR 87 !-.* & = & &

& C = & & < /

@*!6 %

-7FC P*@P*+ 8 . @ +- & ! 8*-*! 7A

5F =

& & 7 7*)*!87C ?8 > 7* G* F !!.886

% & .*@7 C @7 C .8 % , 8 * 8 + C ) !A @7 , 8* !-*@*8C .8 C A*>C @-F @7 @7 , !*@> D*) +787 +

C & -F > G* *7F86 *!8 +*78> = & & Q & RX A8 >C = D>!8 @*8 ! !8 & / !-*@7** )7.*8C .8 !7 7F .!86 .**7 ! + !*8 )-.*8!F 7-*7 D-) 7-*7H ! -7FC ?8 -7 ! D -6P & 7* D@8 *+!8 86!F 8*-*! A -F -7*,C @FE @ -> +- ! 8*-*! C > G* ! -6) 86 !5H , & 9 8 *!8 % & C )*7 & 9 7

& 9 8 7 8C ?8 5*7*>, ?==*8 8 -6 !-8!F 8D-5* "# *@*7> *)-688> >.!-*7F ! !8*, !.*8 W !**7 HG7 7-*7F @-F 8 77> -7*, ! ?7*+F &99

? & /? PDC *@*77>* 8D-5* "#C *@*-FH8 +*P7 !86 78*+ 7F F/ . 6 \]^

¼

FG G

6 ,0

6 ,0

8

D) C *@*77>* !.*8> )-C .8 7D-H@* * ?!*A *78* )-.* ! !8*, !.*8 W !**7 HG7 7-*7F Q ; )R 7* G*8 D>86 DVF!7*7 8 -6 -F7* +* +787 + -F 7 5*!! )8F W *DH8!F @-67*,P* !!-*@ 7F @-F 7A 7F .7> F-*7F ) G7 C ! -6) 7* !*@*-*7F **7 A @ .**7 ! = 8 7 7 *76 7D-H@*7F G*8 7F86 )75

*G@ *)-688 !.*8 ?!**78-67> @77> *C *!A - *+!8HEF !!8* 8*-*! *E*!8*77 8D*8 -7 ! D -6P 5*-67> *8 Q@-77> -6! .**7 ! A + !*8RC 8 ?8 G*8 *!8 *-.*7H ! + ?==*8 * 8 + C 7* D @ 8 .7*7* 8++*7 + !- FC ! -6)* + ":&C A 8 *C G*8!F !-P )7G*77> !7*7H ! @+ @ D7> !87

45

4/5

Q(X,Y)

Q(X,Y)

10 4

10 4

200 `3

200 200

0 -200

`3

0 -200

-200

_3 4-5

Q(X,Y)

10 6

10 6

10 5

10 5

10 4

10 4

250 0 0 `3 -250 -250 -500 _3 -500

0 -200

_3 4+5

Q(X,Y)

500 250

200

0

500

500 250 250 0 0 `3 -250 -250 -500 _3 -500

500

, # N Z1

FG# -3 ! #,0" # -+ 45 9@+ 4/5 !- 3 G# -3 ! #,0" # -+ 4-5 9@+ 4+5 !-

(Q180/Q0)-1

(Q180/Q0)-1

0.15

0.4

0.1

0.3

0.05

0.2 0.1

0

0

-0.05

-0.1 -0.1 -0.2 -0.15 300 200 100 0 `3-100 -200 -300

400 200 200 0

0 `3-200 -400

_3

-200

45

500 250 0 -250 -500

_3

4/5

. 6 8 0 , # --# -,-

FG# 45 G# 4/5 -3 ! #,0" # -+ 9@+ !- 3 - 2 6 ! ,

45 !7 7>* *)-688> > @> @!!*85 77 , D 8>B / *@*7 5- D 8 !P*7H =75 7-67 !8 +7 + -*! YZ[L\ #;&C *77 B A @ D-*7 ) G7 !86 +*7*5 @ 7AF@*7> F@ AF@*7> )A @*,!8, ?7*+F >P* I9 ? 7 7- 7 5*!!* @*- 7F F@*7 + !@ E +*7*8 F@*7 + ) @*,!8F e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v 5*7 ?==*87 !8 *+!85 F@* G*-*) )-.H8!F D -** .* 7 (9vC .8 7* G*8 D>86 DVF!7*7 )75*, @*-*, F@*7 + ) @*,!8F QgJa\aNg eY^MZ\RC DA !- -*7 @*8-F *8 @ @*- 7F !@ **

/ !!-*@ 7 -F7* ?7*+*8.*! + + 8D ?!**78-6A

7> ! D>8, 7 ?==*87 !86 *+!85 8 7 ?-6! 77 , ** ?!**78 JKLMNO &%%( + @ / )7 C .8 ! -6) 7* ?7*+*8.*A ! + + !E*!8*77 *76P*8 + H D-!86 , ?==*8A 7 !8C 7* -FF 7 D-!86 -8 C .8 ) -F*8 !E*!8*77 !7)86 .!8@7 DD8>*> ! D>8, )7.8*-67 D-*+.86 ?!**78-6A 7H D 8 1 / !8 *7 @*-6 =75 !87!8*77 A+- + !*@*-*7F .**7 ! + !*8 W ! ?7*+F ?C .8>HEF -F7* +* +787 + -F 7 5*!! )8F -7F - / !8 *77F @*-6 =75 !87!8*77 A+- + !*@*-*7F .**7 ! + !*8 W ! -6) 7 @-F 5*7 ! !8 !.*8 W .*A *7 ! 8*-*! ?!**78* T;"U / )7 ) G7 !86 7D-H@*A 7F ?==*8 -F7F +* +787 + -F 7 5*!! )8F WC @7 -.*77 * !-67 * )-.* ! !8*, !.*8 W @ 7-*A 7F 7 &9v 7* ) -F*8 DVF!786 ?!**78-67H )75 ! !8*, !.*8 8 -6 -F7* +* +787 + -F / -6)F!6 !-.*C . D-+ @86 *+ 7.7 + @8*-F -@ + *. -7 ) !8 F77 * .!8* E6 D 8*C )*@HEH -D 8 *, 8* ?-*8 77 A= 8 77> -7*, A 1 86F7 ,- 7 +7 ) 77* D 8*C D!G@*7F 5*77>* )*.7FC 8G* *!6 --*8 -D 8

.6 & & " ! " :;<.=> ?+@>@/?

-F >F!7*7F .7 )-.F 5*7 ?==*87 !8 *+!85 F@* G*-*) ?-6! 77 , * , ?!**78 JKLMNO &%%( + @C -.*77> @F )7> *8 @C D>- *@*7 !7*7* 7* 8 > 8*A !8 @*-*, F@*7 + ) @*,!8F gJa\aNg eY^MZ\ -F ?8 , 5*-C ! E6H ! 8*8!8HE +*7*8 ) @*,!8FC D>- )>+7> &999 m < r~ ) @*,!8, ?7*+ 7-*8HE*+ 8 7 &9 ? &999 gz < r~ ) @*,!8, ?7*+ 7-*8HE*+ F@ G*-*) &99

? 7-!6 7* 8 >* 8*!8 8 .7> !7 7> !8 .7 A!@ C @HE !7 7 , -@ 8*7*7*C *+!8A * * *78+*7 ! -*7 *> !7* "(QC DR *@!8-*7> !*@*-*7F 7 G*!8*77 !8 m < r~ gz < r~ ) @*,!8F @-F !!8*> @*-*, !7 "$QC DR < 7-H)7>* !*8> C "IQC DR < !*@*-*7F !*@ D>!8 8* C "%QC DR < !*@*-*7F **.7 -6! C "&9QC DR < !*@*-*7F 5-67 ?==5*78 7*+ !8 8D-5* ": *@!8-*7> !*@7* )7.*A 7F 7 G*!8*77 !8 5-67 + ?==5*78 7*+ !8 m < r~ gz < r~ ) @*,!8FC -.*77>* @-F @ @*-*, F/ 1, @ - ! JJ !+ !6 ,0 , <$aEa(< ABC'DE G2 , - K, b c b c

? * ST ABC'DE <$aEa(<

3

<; * ST ABC'DE <$aEa(<

/ *@*77 * !7*7* )>*8 7* 8 * )-.* @ @*-*,C

.!87 !8C D -6P* 7 G*!8*77 !8C 7*! -6 D -6P* ?7*+ @*A - gJa\aNg !-*@ 8*-67 D-6P* **@. ?7*+ @-F ?8 , @*- @7 C 8-.F ?8 8*!8 7* 7!8 -6 !E*!8*77>*C .8 D> DVA F!786 -.*77H )75 5*7 ?==*87 !8 *+!85 F@* G*-*A ) 8!H@ G7 !@*-86 > @ 8 C .8 )-.* 5*7 ?==*87 !8 D!- -*7 @*8-F *8 @ @*- 7F !@ **

dN(n) 200

45

175

- QGSJET - FRITIOF

150 125 100 75 50 25 0

0

10

20

30

40

50

60

70

n

80

dN(n) 300

4/5

- QGSJET - FRITIOF

250 200 150 100 50 0

0

200

400

600

800

1000

n !, 0 ! @ - - ?7ST -2 , - 0# ! ¼ X FG 45 <;7ST -2 , - 0# ! ¼ X

FG 4/5 ,0 , 0,+ -2 , - 0 <$aEa(< ABC'DE

dN(x)/N0 45

10

- QGSJET - FRITIOF

1

-1

10

-2

10

-3

10

0

0.1

0.2

0.3

0.4

0.5

x=E/E0

dN(x)/N0

4/5

10 2

- QGSJET - FRITIOF

10 1 -1

10

-2

10

-3

10

0

0.005

0.01

0.015

0.02

0.025

x=E/E0 I92 - ! - ?7ST -2 , - 0# ! ¼ X FG 45 <;7ST -2 , - 0# ! ¼ X

FG 4/5 ,0 , 0,+ -2 , - 0 <$aEa(< ABC'DE

dN(η)/N0 4

45

3.5

- QGSJET - FRITIOF

3 2.5 2 1.5 1 0.5 0

-2

0

2

4

6

8

10

12

14

dN(η)/N0

η

40 4/5

35

- QGSJET - FRITIOF

30 25 20 15 10 5 0

-5

-2.5

0

2.5

5

7.5

10

12.5

η

15

!, 0 ! ! -,/ - ?7ST -2 , - 0# ! ¼ X FG 45 <;7ST -2 , - 0# ! ¼ X

FG 4/5 ,0 , 0,+ -2 , - 0 <$aEa(< ABC'DE

dN(pt)/N0 10 4

10

45

- QGSJET - FRITIOF

3

10 2

10

1 0

1

2

3

4

5

pt 3 MG[d

dN(pt)/N0 10 2

4/5

- QGSJET - FRITIOF

10

1 -1

10

-2

10

-3

10

0

1

2

3

4

5

pt 3 MG[d !, 0 ! !!6 ! - ?7ST -2 , - 0# ! ¼ X FG 45 <;7ST -2 , - 0# ! ¼ X

FG 4/5 ,0 , 0,+ -2 7 , - 0 <$aEa(< ABC'DE

dN(Kπ0) 45

140

- QGSJET - FRITIOF

120 100 80 60 40 20 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Kπ

0

dN(Kπ0) 250

4/5

- QGSJET - FRITIOF

200

150

100

50

0

0

0.05

0.1

0.15

0.2

0.25

Kπ0 !, 0 ! ! JJ !+ - ?7ST -2 7 , - 0# ! ¼ X FG 45 <;7ST -2 , - 0# ! ¼ X

FG 4/5 ,0 , 0,+ -2 , - 0 <$aEa(< ABC'DE

7 T&U - C 2!87!*7 4C 3 C #" Q&%"IR ! (#"A(:9 T;U Okztu r_C [t [tm`C ;$& Q&%%#R m (:%A((& T#U nku [fC rtd &( a]J] Qb`RC I Q&%$%R m $A&; T:U O rzztC ^imm Li ]kzC &: Q&%"%R m :#( T"U H7 C *@*7 C 5*7 C ) * )C ;( Q&%(;R ! (I"A(II T(U 7)D+ > 8!, C S/ ! G@*7* !.*! -A .*,SC C &%(# T$U 7 C 2!87!*7 4C 3 C :: Q&%(#R L; ! (((A($" TIU rik q^C Ju`u ^aC }ktuukk qL z uC [t [tm`C ;(I Q&%%#R m$;(A$#" T%U M d` u [ zuzC M r` [C ( Q&%$#R m &"%: T&9U JM rtztz u [r ^u~C r` Jz _zC (% Q&%%;R m ;II" T&&U [J OzC rtd ;; a]J] Qci~kRC ; Q&%%&R m :;9 T&;U a [xtC ^imm [tm` MC %9 Q&%%:R m %#$ T&#U Lk` ^aC rtd ;: a]J] QJzRC & Q&%%"R m ;"&A;": T&:U f adkitu z uC r` JzC c:I Q&%%#R m &%:% T&"U M[]ZZ du~tukC rtd ;" a]J] Qcit~uRC : Q&%%$R m & T&(U M[]ZZ du~tukC [tm` MC "9; Q&%%IR m ;$I T&$U ar auz z uC rtd ;#t a]J] Q]uut`RC ; Q&%%#R m &$

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