ɆɂɇɂɋɌȿɊɋɌȼɈ ɈȻɊȺɁɈȼȺɇɂə ɊɈɋɋɂɃɋɄɈɃ ɎȿȾȿɊȺɐɂɂ ɆɈɋɄɈȼɋɄɂɃ ȽɈɋɍȾȺɊɋɌȼȿɇɇɕɃ ɂɇɀȿɇȿɊɇɈ-ɎɂɁɂɑȿɋɄɂɃ ɂɇɋɌɂɌɍɌ (ɌȿɏɇɂɑȿɋɄɂɃ ɍɇɂȼ...
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ɆɂɇɂɋɌȿɊɋɌȼɈ ɈȻɊȺɁɈȼȺɇɂə ɊɈɋɋɂɃɋɄɈɃ ɎȿȾȿɊȺɐɂɂ ɆɈɋɄɈȼɋɄɂɃ ȽɈɋɍȾȺɊɋɌȼȿɇɇɕɃ ɂɇɀȿɇȿɊɇɈ-ɎɂɁɂɑȿɋɄɂɃ ɂɇɋɌɂɌɍɌ (ɌȿɏɇɂɑȿɋɄɂɃ ɍɇɂȼȿɊɋɂɌȿɌ)
ɋ.Ʉ. ɀɞɚɧɨɜ ȼ.Ⱥ. Ʉɭɪɧɚɟɜ Ɇ.Ʉ. Ɋɨɦɚɧɨɜɫɤɢɣ ɂ.ȼ. ɐɜɟɬɤɨɜ
ɈɋɇɈȼɕ ɎɂɁɂɑȿɋɄɂɏ ɉɊɈɐȿɋɋɈȼ ȼ ɉɅȺɁɆȿ ɂ ɉɅȺɁɆȿɇɇɕɏ ɍɋɌȺɇɈȼɄȺɏ
ɍɑȿȻɇɈȿ ɉɈɋɈȻɂȿ
Ɇɨɫɤɜɚ 2000
ɍȾɄ 533.9 (075) ȻȻɄ 22.333 ɀ42
ɀɞɚɧɨɜ ɋ.Ʉ., Ʉɭɪɧɚɟɜ ȼ.Ⱥ., Ɋɨɦɚɧɨɜɫɤɢɣ Ɇ.Ʉ, ɐɜɟɬɤɨɜ ɂ.ȼ. ɈɋɇɈȼɕ ɎɂɁɂɑȿɋɄɂɏ ɉɊɈɐȿɋɋɈȼ ȼ ɉɅȺɁɆȿ ɂ ɉɅȺɁɆȿɇɇɕɏ ɍɋɌȺɇɈȼɄȺɏ. Ɇ: ɆɂɎɂ, 2000
ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɫɨɞɟɪɠɢɬ ɢɡɥɨɠɟɧɢɟ ɨɫɧɨɜ ɮɢɡɢɤɢ ɩɥɚɡɦɵ ɢ ɩɪɨɰɟɫɫɨɜ, ɩɪɨɢɫɯɨɞɹɳɢɯ ɜ ɩɪɢɛɨɪɚɯ ɢ ɭɫɬɚɧɨɜɤɚɯ, ɩɪɟɞɧɚɡɧɚɱɟɧɧɵɯ ɞɥɹ ɫɨɡɞɚɧɢɹ ɢ ɩɪɚɤɬɢɱɟɫɤɨɝɨ ɩɪɢɦɟɧɟɧɢɹ ɩɥɚɡɦɵ, ɚ ɬɚɤɠɟ ɫɜɟɞɟɧɢɹ ɨɛ ɷɦɢɫɫɢɨɧɧɵɯ ɹɜɥɟɧɢɹɯ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɩɪɢ ɝɟɧɟɪɚɰɢɢ ɩɥɚɡɦɵ, ɫɜɟɞɟɧɢɹ ɨɛ ɷɥɟɦɟɧɬɚɯ ɢɨɧɧɨɣ ɢ ɷɥɟɤɬɪɨɧɧɨɣ ɨɩɬɢɤɢ, ɨ ɮɢɡɢɤɟ ɨɫɧɨɜɧɵɯ ɜɢɞɨɜ ɝɚɡɨɜɵɯ ɪɚɡɪɹɞɨɜ. ȼ ɨɫɧɨɜɭ ɩɨɫɨɛɢɹ ɩɨɥɨɠɟɧɵ ɤɭɪɫɵ «Ɏɢɡɢɤɚ ɩɥɚɡɦɵ», «ȼɜɟɞɟɧɢɟ ɜ ɮɢɡɢɤɭ ɩɥɚɡɦɵ» ɢ «ɇɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɚɹ ɩɥɚɡɦɚ», ɱɢɬɚɟɦɵɟ ɜ ɆɂɎɂ ɫɬɭɞɟɧɬɚɦ ɮɚɤɭɥɶɬɟɬɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɢ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɮɢɡɢɤɢ, ɫɩɟɰɢɚɥɶɧɨɝɨ ɮɚɤɭɥɶɬɟɬɚ ɮɢɡɢɤɢ ɢ ɮɚɤɭɥɶɬɟɬɚ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɢɛɨɪɨɜ ɢ ɭɫɬɚɧɨɜɨɤ. Ȼɚɡɨɜɵɣ ɯɚɪɚɤɬɟɪ ɩɨɫɨɛɢɹ ɢ ɫɨɱɟɬɚɧɢɟ ɜ ɨɞɧɨɦ ɩɨɫɨɛɢɢ ɫɜɟɞɟɧɢɣ ɨ ɮɢɡɢɤɟ ɩɥɚɡɦɵ, ɨ ɮɢɡɢɱɟɫɤɨɣ ɷɥɟɤɬɪɨɧɢɤɟ ɢ ɨ ɮɢɡɢɤɟ ɝɚɡɨɜɨɝɨ ɪɚɡɪɹɞɚ ɞɟɥɚɟɬ ɟɝɨ ɭɧɢɜɟɪɫɚɥɶɧɵɦ ɢ ɩɨɥɟɡɧɵɦ ɞɥɹ ɫɬɭɞɟɧɬɨɜ, ɛɭɞɭɳɢɯ ɢɧɠɟɧɟɪɨɜ-ɮɢɡɢɤɨɜ, ɢ ɚɫɩɢɪɚɧɬɨɜ, ɫɩɟɰɢɚɥɢɡɢɪɭɸɳɢɯɫɹ ɤɚɤ ɜ ɮɢɡɢɤɟ ɝɨɪɹɱɟɣ ɩɥɚɡɦɵ, ɬɟɯɧɨɥɨɝɢɢ ɬɟɪɦɨɹɞɟɪɧɨɝɨ ɫɢɧɬɟɡɚ, ɬɚɤ ɢ ɜ ɞɪɭɝɢɯ ɨɛɥɚɫɬɹɯ, ɫɜɹɡɚɧɧɵɯ ɫ ɩɪɢɦɟɧɟɧɢɟɦ ɩɥɚɡɦɵ ɢ ɩɨɬɨɤɨɜ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɝɟɧɟɪɚɬɨɪɚɯ ɢ ɜ ɭɫɤɨɪɢɬɟɥɹɯ ɱɚɫɬɢɰ ɜ ɩɥɚɡɦɟɧɧɨ-ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɭɫɬɚɧɨɜɤɚɯ, ɜ ɩɥɚɡɦɟɧɧɵɯ ɢ ɢɨɧɧɵɯ ɞɜɢɠɢɬɟɥɹɯ ɢ ɜɨ ɦɧɨɝɢɯ ɞɪɭɝɢɯ ɨɛɥɚɫɬɹɯ.
Ɋɟɰɟɧɡɟɧɬ ɩɪɨɮɟɫɫɨɪ, ɞ.ɮ-ɦ.ɧ. ȿ.ȿ. Ʌɨɜɟɰɤɢɣ Ɋɟɤɨɦɟɧɞɨɜɚɧɨ ɪɟɞɫɨɜɟɬɨɦ ɆɂɎɂ ɜ ɤɚɱɟɫɬɜɟ ɭɱɟɛɧɨɝɨ ɩɨɫɨɛɢɹ ɋ.Ʉ. ɀɞɚɧɨɜ, ȼ.Ⱥ. Ʉɭɪɧɚɟɜ, Ɇ.Ʉ. Ɋɨɦɚɧɨɜɫɤɢɣ, ɂ.ȼ. ɐɜɟɬɤɨɜ, 2000. Ɇɨɫɤɨɜɫɤɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ ɢɧɠɟɧɟɪɧɨ-ɮɢɡɢɱɟɫɤɢɣ ɢɧɫɬɢɬɭɬ, 2000.
ɈȽɅȺȼɅȿɇɂȿ ɉɊȿȾɂɋɅɈȼɂȿ ȼȼȿȾȿɇɂȿ ȽɅȺȼȺ 1. ɈɋɇɈȼɇɕȿ ɉɈɇəɌɂə ɂ ɋȼɈɃɋɌȼȺ ɉɅȺɁɆɕ §1. Ɉɛɪɚɡɨɜɚɧɢɟ ɩɥɚɡɦɵ §2. Ʉɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɶ, ɩɥɚɡɦɟɧɧɚɹ ɱɚɫɬɨɬɚ § 3. Ⱦɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ, ɞɟɛɚɟɜɫɤɢɣ ɫɥɨɣ § 4. ɂɞɟɚɥɶɧɨɫɬɶ ɩɥɚɡɦɵ § 5. ɉɪɹɦɵɟ ɢ ɨɛɪɚɬɧɵɟ ɩɪɨɰɟɫɫɵ ɜ ɩɥɚɡɦɟ § 6. ɍɩɪɭɝɨɟ ɪɚɫɫɟɹɧɢɟ § 7. Ɋɚɜɧɨɜɟɫɢɹ ɜ ɩɥɚɡɦɟ § 8. ɇɟɪɚɜɧɨɜɟɫɧɨɫɬɶ ɩɥɚɡɦɟɧɧɵɯ ɫɢɫɬɟɦ § 9. ɉɪɨɰɟɫɫɵ ɪɟɥɚɤɫɚɰɢɢ ɜ ɩɥɚɡɦɟ § 10. ɉɪɨɰɟɫɫɵ ɩɟɪɟɧɨɫɚ ɜ ɩɥɚɡɦɟ § 11. Ⱦɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɥɚɡɦɵ ȽɅȺȼA 2. ɉɅȺɁɆȺ ȼ ɆȺȽɇɂɌɇɈɆ ɉɈɅȿ § 12. Ɉɞɧɨɱɚɫɬɢɱɧɨɟ ɪɚɫɫɦɨɬɪɟɧɢɟ § 13. Ⱦɜɢɠɟɧɢɟ ɜ ɩɨɫɬɨɹɧɧɨɦ ɢ ɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ § 14. Ⱦɜɢɠɟɧɢɟ ɜ ɫɢɥɶɧɨɦ ɦɟɞɥɟɧɧɨ ɦɟɧɹɸɳɟɦɫɹ ɩɨɥɟ. Ⱦɪɟɣɮɨɜɨɟ ɩɪɢɛɥɢɠɟɧɢɟ § 15. Ⱦɜɢɠɟɧɢɟ ɱɚɫɬɢɰɵ ɜ ɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɩɨɫɬɨɹɧɧɨɣ ɫɢɥɵ § 16. Ⱦɪɟɣɮ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜɞɨɥɶ ɩɥɨɫɤɨɫɬɢ ɫɤɚɱɤɚ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ §17. ȼɚɠɧɟɣɲɢɟ ɬɢɩɵ ɞɪɟɣɮɨɜɵɯ ɞɜɢɠɟɧɢɣ ɱɚɫɬɢɰ ɜ ɩɥɚɡɦɟ § 18. Ⱥɞɢɚɛɚɬɢɱɟɫɤɢɟ ɢɧɜɚɪɢɚɧɬɵ § 19. ɉɪɢɦɟɧɟɧɢɟ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɢ ɞɪɟɣɮɨɜɨɝɨ ɩɪɢɛɥɢɠɟɧɢɣ § 20. əɜɥɟɧɢɹ ɩɟɪɟɧɨɫɚ ɜ ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɟ ȽɅȺȼȺ 3. ɆȺȽɇɂɌɈȽɂȾɊɈȾɂɇȺɆɂɑȿɋɄɂɃ ɆȿɌɈȾ ɈɉɂɋȺɇɂə ɉɅȺɁɆɕ § 21. ɂɞɟɚɥɶɧɚɹ ɨɞɧɨɠɢɞɤɨɫɬɧɚɹ ɝɢɞɪɨɞɢɧɚɦɢɤɚ ɩɥɚɡɦɵ. ɍɫɥɨɜɢɹ ɩɪɢɦɟɧɢɦɨɫɬɢ § 22. Ɉɫɧɨɜɧɵɟ ɭɪɚɜɧɟɧɢɹ § 23. Ɇɚɝɧɢɬɧɨɟ ɞɚɜɥɟɧɢɟ § 24. Ɋɚɜɧɨɜɟɫɢɟ ɩɥɚɡɦɵ ɜ ɦɚɝɧɢɬɧɨɣ ɝɢɞɪɨɞɢɧɚɦɢɤɟ
§ 25. Ȼɵɫɬɪɵɟ ɩɪɨɰɟɫɫɵ § 26. ȼɡɚɢɦɧɨɟ ɩɪɨɧɢɤɧɨɜɟɧɢɟ ɩɥɚɡɦɵ ɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ȽɅȺȼȺ 4. ɄɈɅȿȻȺɇɂə ɂ ȼɈɅɇɕ ȼ ɉɅȺɁɆȿ. ɇȿɍɋɌɈɃɑɂȼɈɋɌɂ ɉɅȺɁɆɕ § 27. Ⱦɢɫɩɟɪɫɢɨɧɧɵɟ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɩɪɨɞɨɥɶɧɵɯ ɢ ɩɨɩɟɪɟɱɧɵɯ ɜɨɥɧ ɦɚɥɨɣ ɚɦɩɥɢɬɭɞɵ § 28. Ɇɟɬɨɞ ɦɚɥɵɯ ɤɨɥɟɛɚɧɢɣ. Ⱦɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɧɟɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɵ § 29. ɉɨɩɟɪɟɱɧɵɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ ɜɨɥɧɵ ɜ ɧɟɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɟ § 30. əɜɥɟɧɢɟ ɨɬɫɟɱɤɢ ɧɢɡɤɨɱɚɫɬɨɬɧɨɣ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɵ § 31. Ʌɟɧɝɦɸɪɨɜɫɤɢɟ ɤɨɥɟɛɚɧɢɹ ɢ ɜɨɥɧɵ ɜ ɩɥɚɡɦɟ. ɉɥɚɡɦɨɧɵ § 32. ɂɨɧɧɵɟ ɥɟɧɝɦɸɪɨɜɫɤɢɟ ɜɨɥɧɵ. ɂɨɧɧɨ-ɡɜɭɤɨɜɵɟ ɜɨɥɧɵ ɜ ɩɥɚɡɦɟ. § 33. Ȼɟɫɫɬɨɥɤɧɨɜɢɬɟɥɶɧɨɟ ɡɚɬɭɯɚɧɢɟ ɜɨɥɧ ɜ ɩɥɚɡɦɟ § 34. Ⱦɢɷɥɟɤɬɪɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɦɚɝɧɢɬɨɚɤɬɢɜɧɨɣ ɩɥɚɡɦɵ § 35. ȼɨɥɧɵ ɜ ɦɚɝɧɢɬɨɚɤɬɢɜɧɨɣ ɩɥɚɡɦɟ § 36. ɇɟɭɫɬɨɣɱɢɜɨɫɬɢ ɩɥɚɡɦɵ § 37. Ʉɢɧɟɬɢɱɟɫɤɢɟ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɩɥɚɡɦɵ ȽɅȺȼȺ 5. ɗɅȿɄɌɊɈɇɇȺə ɂ ɂɈɇɇȺə ɈɉɌɂɄȺ § 38. Ⱥɧɚɥɨɝɢɹ ɫɜɟɬɨɜɨɣ ɢ ɷɥɟɤɬɪɨɧɧɨɣ ɨɩɬɢɤɢ § 39. ɗɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɢɟ ɥɢɧɡɵ § 40. Ɇɚɝɧɢɬɧɵɟ ɥɢɧɡɵ § 41. Ɉɬɤɥɨɧɹɸɳɢɟ ɢ ɮɨɤɭɫɢɪɭɸɳɢɟ ɷɥɟɬɪɨɧɧɨ-ɨɩɬɢɱɟɫɤɢɟ ɫɢɫɬɟɦɵ ȽɅȺȼȺ 6. ȼɅɂəɇɂȿ ɉɊɈɋɌɊȺɇɋɌȼȿɇɇɈȽɈ ɁȺɊəȾȺ ɗɅȿɄɌɊɈɇɇɕɏ ɂ ɂɈɇɇɕɏ ɉɍɑɄɈȼ § 42. Ɉɝɪɚɧɢɱɟɧɢɟ ɬɨɤɚ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɦ ɡɚɪɹɞɨɦ ɜ ɞɢɨɞɟ § 43. ɉɪɟɞɟɥɶɧɚɹ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ ɩɭɱɤɚ ɱɚɫɬɢɰ ɜ ɩɪɨɥɟɬɧɨɦ ɩɪɨɦɟɠɭɬɤɟ ɜ ɜɚɤɭɭɦɟ ȽɅȺȼȺ 7. ɗɆɂɋɋɂɈɇɇȺə ɗɅȿɄɌɊɈɇɂɄȺ § 44. Ɍɟɪɦɨɷɦɢɫɫɢɨɧɧɚɹ ɷɥɟɤɬɪɨɧɢɤɚ § 45. Ⱥɜɬɨɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ § 46. ɂɡɦɟɧɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɷɦɢɬɬɟɪɚ ɩɪɢ ɬɟɪɦɨ ɢ ɚɜɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ § 47. Ɏɨɬɨɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ § 48. ȼɬɨɪɢɱɧɚɹ ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ȽɅȺȼȺ 8. ɗɅȿɄɌɊɂɑȿɋɄɂɃ ɌɈɄ ȼ ȽȺɁȺɏ ɂ ȽȺɁɈȼɕɃ ɊȺɁɊəȾ § 49. ɗɥɟɤɬɪɢɱɟɫɤɢɣ ɬɨɤ ɜ ɝɚɡɚɯ § 50. Ɍɟɨɪɢɹ ɷɥɟɤɬɪɨɧɧɵɯ ɥɚɜɢɧ
§ 51. Ɍɥɟɸɳɢɣ ɪɚɡɪɹɞ § 52. Ⱦɭɝɨɜɵɟ ɪɚɡɪɹɞɵ § 53. ɂɫɤɪɨɜɨɣ ɢ ɤɨɪɨɧɧɵɣ, ȼɑ ɢ ɋȼɑ ɪɚɡɪɹɞɵ ɋɩɢɫɨɤ ɢɫɩɨɥɶɡɨɜɚɧɧɨɣ ɢ ɪɟɤɨɦɟɧɞɭɟɦɨɣ ɥɢɬɟɪɚɬɭɪɵ
ɉɊȿȾɂɋɅɈȼɂȿ ȼ ɞɚɧɧɨɦ ɭɱɟɛɧɨɦ ɩɨɫɨɛɢɢ ɢɡɥɚɝɚɸɬɫɹ ɨɫɧɨɜɵ ɮɢɡɢɤɢ ɩɥɚɡɦɵ ɢ ɩɪɨɰɟɫɫɨɜ, ɩɪɨɢɫɯɨɞɹɳɢɯ ɜ ɭɫɬɚɧɨɜɤɚɯ ɢ ɩɪɢɛɨɪɚɯ, ɩɪɟɞɧɚɡɧɚɱɟɧɧɵɯ ɞɥɹ ɫɨɡɞɚɧɢɹ ɢ ɩɪɚɤɬɢɱɟɫɤɨɝɨ ɩɪɢɦɟɧɟɧɢɹ ɩɥɚɡɦɵ. ɉɨɷɬɨɦɭ, ɧɚɪɹɞɭ ɫ «ɤɥɚɫɫɢɱɟɫɤɢɦ» ɢɡɥɨɠɟɧɢɟɦ ɨɫɧɨɜɧɵɯ ɩɨɧɹɬɢɣ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɯ ɩɥɚɡɦɭ ɢ ɩɥɚɡɦɨɩɨɞɨɛɧɵɟ ɫɪɟɞɵ, ɚ ɬɚɤɠɟ ɫɩɟɰɢɮɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɩɥɚɡɦɵ ɢ ɩɪɨɬɟɤɚɸɳɢɯ ɜ ɧɟɣ ɹɜɥɟɧɢɣ, ɜ ɩɨɫɨɛɢɢ ɩɪɢɜɟɞɟɧɵ ɫɜɟɞɟɧɢɹ ɨɛ ɷɦɢɫɫɢɨɧɧɵɯ ɹɜɥɟɧɢɹɯ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɩɪɢ ɝɟɧɟɪɚɰɢɢ ɩɥɚɡɦɵ, ɷɥɟɦɟɧɬɚɯ ɢɨɧɧɨɣ ɢ ɷɥɟɤɬɪɨɧɧɨɣ ɨɩɬɢɤɢ ɢ ɨ ɮɢɡɢɤɟ ɧɟɤɨɬɨɪɵɯ ɨɫɧɨɜɧɵɯ ɜɢɞɨɜ ɝɚɡɨɜɵɯ ɪɚɡɪɹɞɨɜ. Ɍɚɤɨɟ ɫɨɱɟɬɚɧɢɟ ɜ ɨɞɧɨɦ ɩɨɫɨɛɢɢ ɫɜɟɞɟɧɢɣ ɨ ɮɢɡɢɤɟ ɩɥɚɡɦɵ, ɨ ɮɢɡɢɱɟɫɤɨɣ ɷɥɟɤɬɪɨɧɢɤɟ ɢ ɨ ɮɢɡɢɤɟ ɝɚɡɨɜɨɝɨ ɪɚɡɪɹɞɚ ɞɟɥɚɟɬ ɷɬɨ ɩɨɫɨɛɢɟ ɛɨɥɟɟ ɭɧɢɜɟɪɫɚɥɶɧɵɦ ɞɥɹ ɫɬɭɞɟɧɬɨɜ, ɛɭɞɭɳɢɯ ɢɧɠɟɧɟɪɨɜ-ɮɢɡɢɤɨɜ, ɢ ɚɫɩɢɪɚɧɬɨɜ, ɤɨɬɨɪɵɦ ɩɪɢɞɟɬɫɹ ɢɦɟɬɶ ɞɟɥɨ ɫ ɫɨɡɞɚɧɢɟɦ ɢ ɩɪɢɦɟɧɟɧɢɟɦ ɩɥɚɡɦɟɧɧɵɯ ɭɫɬɚɧɨɜɨɤ ɢ ɭɫɬɪɨɣɫɬɜ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɢ ɩɥɚɡɦɵ, ɢ ɩɭɱɤɨɜ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɪɚɡɥɢɱɧɵɯ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɢɯ ɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɡɚɞɚɱɚɯ. ȼ ɨɫɧɨɜɭ ɩɨɫɨɛɢɹ ɩɨɥɨɠɟɧɵ ɤɭɪɫɵ «Ɏɢɡɢɤɚ ɩɥɚɡɦɵ», «ȼɜɟɞɟɧɢɟ ɜ ɮɢɡɢɤɭ ɩɥɚɡɦɵ» ɢ «ɇɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɚɹ ɩɥɚɡɦɚ», ɱɢɬɚɟɦɵɯ ɜ ɆɂɎɂ ɫɬɭɞɟɧɬɚɦ ɮɚɤɭɥɶɬɟɬɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɢ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɮɢɡɢɤɢ, ɫɩɟɰɢɚɥɶɧɨɝɨ ɮɚɤɭɥɶɬɟɬɚ ɮɢɡɢɤɢ ɢ ɮɚɤɭɥɶɬɟɬɚ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɢɛɨɪɨɜ ɢ ɭɫɬɚɧɨɜɨɤ. Ȼɚɡɨɜɵɣ ɯɚɪɚɤɬɟɪ ɷɬɨɝɨ ɩɨɫɨɛɢɹ, ɜ ɤɨɬɨɪɨɦ ɢɡɥɚɝɚɸɬɫɹ ɨɫɧɨɜɵ ɮɢɡɢɱɟɫɤɢɯ ɹɜɥɟɧɢɣ ɤɚɤ ɜ ɫɚɦɨɣ ɩɥɚɡɦɟ ɩɪɢ ɟɟ ɨɛɪɚɡɨɜɚɧɢɢ ɜ ɩɥɚɡɦɟɧɧɵɯ ɭɫɬɚɧɨɜɤɚɯ, ɬɚɤ ɢ ɩɪɢ ɝɟɧɟɪɚɰɢɢ ɫ ɟɟ ɩɨɦɨɳɶɸ ɢɨɧɧɵɯ ɢ ɷɥɟɤɬɪɨɧɧɵɯ ɩɭɱɤɨɜ, ɞɟɥɚɟɬ ɟɝɨ ɩɨɥɟɡɧɵɦ ɞɥɹ ɫɬɭɞɟɧɬɨɜ, ɫɩɟɰɢɚɥɢɡɢɪɭɸɳɢɯɫɹ ɢ ɜ ɮɢɡɢɤɟ ɝɨɪɹɱɟɣ ɩɥɚɡɦɵ, ɬɟɯɧɨɥɨɝɢɢ ɬɟɪɦɨɹɞɟɪɧɨɝɨ ɫɢɧɬɟɡɚ, ɢ ɜ ɞɪɭɝɢɯ ɨɛɥɚɫɬɹɯ, ɫɜɹɡɚɧɧɵɯ ɫ ɩɪɢɦɟɧɟɧɢɟɦ ɩɥɚɡɦɵ ɢ ɩɨɬɨɤɨɜ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɝɟɧɟɪɚɬɨɪɚɯ ɢ ɜ ɭɫɤɨɪɢɬɟɥɹɯ ɱɚɫɬɢɰ ɜ ɩɥɚɡɦɟɧɧɨ-ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɭɫɬɚɧɨɜɤɚɯ, ɜ ɩɥɚɡɦɟɧɧɵɯ ɢ ɢɨɧɧɵɯ ɞɜɢɠɢɬɟɥɹɯ ɢ ɜɨ ɦɧɨɝɢɯ ɞɪɭɝɢɯ ɨɛɥɚɫɬɹɯ. ɇɟɫɤɨɥɶɤɨ ɫɥɨɜ ɨ ɫɬɪɭɤɬɭɪɟ ɤɧɢɝɢ. ɇɚɦɟɱɟɧɧɚɹ ɜɵɲɟ ɰɟɥɶ ɨɩɪɟɞɟɥɢɥɚ ɨɬɛɨɪ ɦɚɬɟɪɢɚɥɚ ɢ ɩɪɢɧɹɬɭɸ ɧɚɦɢ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɟɝɨ ɢɡɥɨɠɟɧɢɹ. Ƚɥɚɜɚ 1 ɩɨɫɜɹɳɟɧɚ ɤɪɚɬɤɨɦɭ ɨɛɫɭɠɞɟɧɢɸ ɨɫɧɨɜɧɵɯ ɩɨɧɹɬɢɣ, ɭɩɨɬɪɟɛɢɬɟɥɶɧɵɯ ɜ ɨɩɢɫɚɧɢɢ ɩɥɚɡɦɟɧɧɵɯ ɹɜɥɟɧɢɣ ɢ, ɩɨ ɫɭɬɢ ɞɟɥɚ, ɫɨɫɬɚɜɥɹɸɳɢɯ ɨɫɧɨɜɭ ɮɢɡɢɤɢ ɩɥɚɡɦɵ ɤɚɤ ɫɨɫɬɨɹɧɢɹ ɜɟɳɟɫɬɜɚ. ȼ ɝɥɚɜɟ 2 ɨɛɫɭɠɞɚɸɬɫɹ ɧɚɢɛɨɥɟɟ ɯɚɪɚɤɬɟɪɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɩɨɜɟɞɟɧɢɹ ɩɥɚɡɦɵ, ɩɨɦɟɳɟɧɧɨɣ ɜ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ. ȼ ɝɥɚɜɟ 3 ɢɡɥɚɝɚɸɬɫɹ ɨɫɧɨɜɵ ɦɚɝɧɢɬɧɨɣ ɝɢɞɪɨɞɢɧɚɦɢɤɢ ɩɥɚɡɦɵ ɢ ɞɚɧɵ ɩɪɨɫɬɟɣɲɢɟ ɟɟ ɩɪɢɥɨɠɟɧɢɹ ɞɥɹ ɨɩɢɫɚɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɩɥɚɡɦɵ ɢ ɞɢɧɚɦɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ ɜ ɧɟɣ. ȼ ɝɥɚɜɟ 4 ɨɛɫɭɠɞɚɸɬɫɹ ɜɨɥɧɨɜɵɟ ɫɜɨɣɫɬɜɚ ɩɥɚɡɦɵ ɢ ɭɫɥɨɜɢɹ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜɨɥɧ ɜ ɩɥɚɡɦɟ ɛɟɡ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɜ ɦɚɝɧɢɬɨɚɤɬɢɜɧɨɣ ɩɥɚɡɦɟ, ɚ ɬɚɤɠɟ ɨɫɧɨɜɧɵɟ ɬɢɩɵ ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɢɯ ɢ ɤɢɧɟɬɢɱɟɫɤɢɯ ɧɟɭɫɬɨɣɱɢɜɨɫɬɟɣ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɪɚɡɜɢɜɚɬɶɫɹ ɜ ɩɥɚɡɦɟ. ɗɬɢ ɝɥɚɜɵ ɹɜɥɹɸɬɫɹ, ɩɨ ɫɭɬɢ ɞɟɥɚ, ɪɟɡɭɥɶɬɚɬɨɦ ɨɛɨɛɳɟɧɢɹ, ɧɟɨɛɯɨɞɢɦɨɝɨ ɞɨɩɨɥɧɟɧɢɹ ɢ ɤɪɢɬɢɱɟɫɤɨɝɨ ɩɟɪɟɨɫɦɵɫɥɟɧɢɹ ɦɚɬɟɪɢɚɥɚ, ɨɩɭɛɥɢɤɨɜɚɧɧɨɝɨ ɚɜɬɨɪɚɦɢ ɪɚɧɟɟ ɜ ɩɨɫɨɛɢɹɯ [1,2]. Ɉɛɫɭɠɞɟɧɢɸ ɮɢɡɢɤɢ ɩɭɱɤɨɜ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ, ɜɨɩɪɨɫɚɦ ɢɯ ɮɨɤɭɫɢɪɨɜɤɢ ɢ ɭɫɥɨɜɢɣ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɩɨɫɜɹɳɟɧɵ ɝɥɚɜɵ 5 ɢ 6. ɉɪɨɛɥɟɦɵ ɷɦɢɫɫɢɨɧɧɨɣ ɷɥɟɤɬɪɨɧɢɤɢ ɨɛɫɭɠɞɚɸɬɫɹ ɜ ɝɥɚɜɟ 7 ɢ, ɧɚɤɨɧɟɰ, ɡɚɤɥɸɱɢɬɟɥɶɧɚɹ ɝɥɚɜɚ 8 ɞɚɟɬ ɤɪɚɬɤɢɣ ɷɤɫɤɭɪɫ ɜ ɮɢɡɢɤɭ ɨɫɧɨɜɧɵɯ ɬɢɩɨɜ ɝɚɡɨɜɵɯ ɪɚɡɪɹɞɨɜ. Ɉɬɦɟɬɢɦ ɬɚɤɠɟ, ɱɬɨ ɧɚɦɢ ɩɪɢɧɹɬɚ ɧɭɦɟɪɚɰɢɹ ɪɢɫɭɧɤɨɜ ɢ ɮɨɪɦɭɥ ɩɨ ɝɥɚɜɚɦ.
ȼȼȿȾȿɇɂȿ ȼɫɟɦ ɢɡɜɟɫɬɧɵ ɬɪɢ ɚɝɪɟɝɚɬɧɵɯ ɫɨɫɬɨɹɧɢɹ ɜɟɳɟɫɬɜɚ - ɬɜɟɪɞɨɟ, ɠɢɞɤɨɟ, ɝɚɡɨɨɛɪɚɡɧɨɟ. ɉɥɚɡɦɭ ɱɚɫɬɨ ɧɚɡɵɜɚɸɬ ɱɟɬɜɟɪɬɵɦ ɫɨɫɬɨɹɧɢɟɦ ɜɟɳɟɫɬɜɚ - ɫɚɦɵɦ ɜɵɫɨɤɨɬɟɦɩɟɪɚɬɭɪɧɵɦ, ɢɦɟɹ ɜ ɜɢɞɭ ɰɟɩɨɱɤɭ ɩɪɟɜɪɚɳɟɧɢɣ: ɬɜɟɪɞɨɟ ɬɟɥɨ ɠɢɞɤɨɫɬɶ - ɝɚɡ - ɩɥɚɡɦɚ, ɢɦɟɸɳɭɸ ɦɟɫɬɨ ɩɪɢ ɩɨɜɵɲɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ (Sir William Croocus , 1879). Ƚɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ ɤɨɥɢɱɟɫɬɜɚ ɷɧɟɪɝɢɢ, ɫɨɞɟɪɠɚɳɟɣɫɹ ɜ ɧɟɤɨɬɨɪɨɣ ɦɚɫɫɟ ɜɟɳɟɫɬɜɚ (ɧɚɩɪɢɦɟɪ, ɜ ɨɞɧɨɦ ɝɪɚɦɦɟ), ɨɬ ɟɝɨ ɬɟɦɩɟɪɚɬɭɪɵ ɩɨɞɨɛɟɧ ɝɪɚɮɢɤɭ, ɩɨɤɚɡɚɧɧɨɦɭ ɧɚ ɪɢɫ. ȼ.1. ɉɪɢ ɞɨɫɬɚɬɨɱɧɨ ɧɢɡɤɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɥɸɛɨɟ ɜɟɳɟɫɬɜɨ ɧɚɯɨɞɢɬɫɹ ɜ ɬɜɟɪɞɨɦ ɫɨɫɬɨɹɧɢɢ; ɩɨ ɦɟɪɟ ɩɨɜɵɲɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɟɝɨ ɷɧɟɪɝɨɫɨɞɟɪɠɚɧɢɟ ɪɚɫɬɟɬ - ɷɬɨ ɭɱɚɫɬɨɤ ɚ-b. ɇɚɤɥɨɧ ɨɬɪɟɡɤɚ ɩɪɹɦɨɣ ɚ-b ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɟɩɥɨɟɦɤɨɫɬɶɸ ɜɟɳɟɫɬɜɚ, ɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɭɱɚɫɬɨɤ ɧɚ ɲɤɚɥɟ ɬɟɦɩɟɪɚɬɭɪ ɞɨ ɬɨɱɤɢ b ɦɨɠɟɬ ɛɵɬɶ ɢ ɨɱɟɧɶ ɦɚɥɵɦ (ɞɥɹ ɜɨɞɨɪɨɞɚ 13,9Ʉ) ɢ ɜɟɫɶɦɚ ɛɨɥɶɲɢɦ (ɞɥɹ ɜɨɥɶɮɪɚɦɚ 3643 Ʉ). ȼ ɬɨɱɤɟ b ɧɚɱɢɧɚɟɬɫɹ ɩɥɚɜɥɟɧɢɟ, ɞɥɹ ɱɢɫɬɵɯ ɜɟɳɟɫɬɜ ɬɟɦɩɟɪɚɬɭɪɚ ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɨɣ: ɷɧɟɪɝɢɹ ɡɚɬɪɚɱɢɜɚɟɬɫɹ ɧɚ ɪɚɡɪɭɲɟɧɢɟ Ɋɢɫ. ȼ.1. Ɂɚɜɢɫɢɦɨɫɬɶ ɷɧɟɪɝɨɫɨɞɟɪɠɚɧɢɹ ɫɜɹɡɟɣ, ɨɩɪɟɞɟɥɹɸɳɢɯ ɭɩɨɪɹɞɨɱɟɧɧɨɟ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɪɚɫɩɨɥɨɠɟɧɢɟ ɱɚɫɬɢɰ ɜɟɳɟɫɬɜɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɪɭɝ ɞɪɭɝɚ. ȼɟɥɢɱɢɧɚ ɭɱɚɫɬɤɚ b-c ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɚɤ ɧɚɡɵɜɚɟɦɨɣ "ɫɤɪɵɬɨɣ" ɬɟɩɥɨɬɨɣ ɩɥɚɜɥɟɧɢɹ. ɉɪɢ ɞɚɥɶɧɟɣɲɟɦ ɩɨɜɵɲɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚ ɭɱɚɫɬɤɟ c-d ɜɟɳɟɫɬɜɨ ɨɫɬɚɟɬɫɹ ɜ ɠɢɞɤɨɦ ɫɨɫɬɨɹɧɢɢ, ɪɚɫɬɟɬ ɷɧɟɪɝɢɹ ɞɜɢɠɟɧɢɹ ɟɝɨ ɦɨɥɟɤɭɥ. ɇɚɤɥɨɧ ɨɬɪɟɡɤɚ ɩɪɹɦɨɣ c-d ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɟɩɥɨɟɦɤɨɫɬɶɸ ɜɟɳɟɫɬɜɚ ɜ ɠɢɞɤɨɦ ɫɨɫɬɨɹɧɢɢ. ȼ ɬɨɱɤɟ d ɧɚɱɢɧɚɟɬɫɹ ɤɢɩɟɧɢɟ, ɢ ɜɟɳɟɫɬɜɨ ɩɟɪɟɯɨɞɢɬ ɜ ɝɚɡɨɨɛɪɚɡɧɨɟ ɫɨɫɬɨɹɧɢɟ. ɇɚ ɨɬɪɟɡɤɟ d-c ɬɟɦɩɟɪɚɬɭɪɚ ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɨɣ, ɷɧɟɪɝɢɹ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ ɪɚɡɪɭɲɟɧɢɟ ɫɜɹɡɟɣ ɦɟɠɞɭ ɦɨɥɟɤɭɥɚɦɢ. ȼɟɥɢɱɢɧɚ ɭɱɚɫɬɤɚ d-ɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɚɤ ɧɚɡɵɜɚɟɦɨɣ ɬɟɩɥɨɬɨɣ ɢɫɩɚɪɟɧɢɹ. ɇɟɨɛɯɨɞɢɦɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɷɬɢ ɪɚɫɫɭɠɞɟɧɢɹ ɜɟɪɧɵ ɩɪɢ ɧɟɤɨɬɨɪɨɦ ɡɚɞɚɧɧɨɦ ɞɚɜɥɟɧɢɢ. ɇɚ ɫɚɦɨɦ ɞɟɥɟ ɢ ɧɚɞ ɬɜɟɪɞɵɦ ɬɟɥɨɦ ɜɫɟɝɞɚ ɢɦɟɟɬɫɹ ɧɟɤɨɬɨɪɨɟ ɞɚɜɥɟɧɢɟ ɧɚɫɵɳɟɧɧɨɝɨ ɩɚɪɚ, ɜɟɫɶɦɚ ɦɚɥɨɟ ɞɥɹ ɛɨɥɶɲɢɧɫɬɜɚ ɜɟɳɟɫɬɜ. Ɉɞɧɚɤɨ ɧɚɞ ɧɟɤɨɬɨɪɵɦɢ ɜɟɳɟɫɬɜɚɦɢ ɨɧɨ ɜɫɟ ɠɟ ɜɟɥɢɤɨ (ɧɚɩɪɢɦɟɪ, ɭ ɣɨɞɚ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ 387 Ʉ ɨɧɨ ɫɨɫɬɚɜɥɹɟɬ 90 ɦɦ ɪɬ. ɫɬ.). ɉɨɷɬɨɦɭ ɩɪɢɜɟɞɟɧɧɵɟ ɜɵɲɟ ɪɚɫɫɭɠɞɟɧɢɹ ɢɦɟɸɬ ɯɚɪɚɤɬɟɪ ɢɥɥɸɫɬɪɚɰɢɢ ɢɡɦɟɧɟɧɢɹ ɩɪɢɜɵɱɧɵɯ ɞɥɹ ɧɚɫ ɚɝɪɟɝɚɬɧɵɯ ɫɨɫɬɨɹɧɢɣ ɜɟɳɟɫɬɜɚ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ. ɉɨ ɦɟɪɟ ɪɨɫɬɚ ɬɟɦɩɟɪɚɬɭɪɵ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɷɧɟɪɝɢɹ ɦɨɥɟɤɭɥ, ɭɦɟɧɶɲɚɸɬɫɹ ɫɜɹɡɢ ɢ ɩɨɫɥɟ ɢɫɩɚɪɟɧɢɹ ɜɫɟ ɦɨɥɟɤɭɥɵ ɫɬɚɧɨɜɹɬɫɹ ɫɜɨɛɨɞɧɵɦɢ. ȿɫɥɢ ɩɪɨɞɨɥɠɚɬɶ ɭɜɟɥɢɱɢɜɚɬɶ ɷɧɟɪɝɢɸ ɷɬɢɯ ɫɜɨɛɨɞɧɵɯ ɦɨɥɟɤɭɥ (ɧɚɩɪɢɦɟɪ, ɧɚɝɪɟɜɚɬɶ ɝɚɡ), ɬɨ ɩɪɢ ɜɡɚɢɦɧɵɯ ɫɬɨɥɤɧɨɜɟɧɢɹɯ ɦɨɥɟɤɭɥɵ ɧɚɱɧɭɬ ɪɚɫɩɚɞɚɬɶɫɹ ɧɚ ɚɬɨɦɵ. ɇɨ ɷɬɨ ɭɠɟ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɧɨɜɵɣ ɩɪɨɰɟɫɫ − ɱɚɫɬɶ ɷɧɟɪɝɢɢ ɡɚɬɪɚɱɢɜɚɟɬɫɹ ɧɚ ɩɪɨɰɟɫɫ, ɤɚɱɟɫɬɜɟɧɧɨ ɦɟɧɹɸɳɢɣ ɫɨɫɬɚɜ ɝɚɡɚ. ɏɨɪɨɲɨ ɢɡɜɟɫɬɧɨ, ɱɬɨ ɝɚɡ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɨɜɨɤɭɩɧɨɫɬɶ ɫɜɨɛɨɞɧɵɯ ɱɚɫɬɢɰ − ɦɨɥɟɤɭɥ (ɨɛɵɱɧɨ) ɢɥɢ ɚɬɨɦɨɜ (ɪɟɠɟ). ɗɬɢ ɱɚɫɬɢɰɵ ɫɬɚɥɤɢɜɚɸɬɫɹ ɞɪɭɝ ɫ ɞɪɭɝɨɦ, ɫɨ ɫɬɟɧɤɚɦɢ ɫɨɫɭɞɚ, ɢ ɜ ɪɟɡɭɥɶɬɚɬɟ ɫɬɨɥɤɧɨɜɟɧɢɣ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɜɩɨɥɧɟ ɨɩɪɟɞɟɥɟɧɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɱɚɫɬɢɰ ɩɨ ɫɤɨɪɨɫɬɹɦ. ɉɪɢ ɤɚɠɞɨɣ ɞɚɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɨɫɧɨɜɧɚɹ ɱɚɫɬɶ ɱɚɫɬɢɰ ɢɦɟɟɬ ɧɟɤɨɬɨɪɭɸ ɨɩɪɟɞɟɥɟɧɧɭɸ (ɧɚɢɛɨɥɟɟ 1
ɜɟɪɨɹɬɧɭɸ) ɫɤɨɪɨɫɬɶ, ɧɨ ɜɫɟɝɞɚ ɟɫɬɶ ɢ ɛɨɥɟɟ ɦɟɞɥɟɧɧɵɟ ɱɚɫɬɢɰɵ ɢ ɛɨɥɟɟ ɛɵɫɬɪɵɟ. ɑɟɦ ɞɚɥɶɲɟ ɨɬ ɧɚɢɛɨɥɟɟ ɜɟɪɨɹɬɧɨɣ ɫɤɨɪɨɫɬɢ (ɢ ɜ ɫɬɨɪɨɧɭ ɭɦɟɧɶɲɟɧɢɹ ɢ ɜ ɫɬɨɪɨɧɭ ɭɜɟɥɢɱɟɧɢɹ), ɬɟɦ ɦɟɧɶɲɟ ɱɚɫɬɢɰ, ɢɦɟɸɳɢɯ ɬɚɤɭɸ, ɞɚɥɟɤɭɸ ɨɬ ɧɚɢɛɨɥɟɟ ɜɟɪɨɹɬɧɨɣ, ɫɤɨɪɨɫɬɶ. ɇɚ ɪɢɫ. ȼ.2 ɩɪɟɞɫɬɚɜɥɟɧɨ ɜ ɤɚɱɟɫɬɜɟ ɢɥɥɸɫɬɪɚɰɢɢ ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɱɢɫɥɨ ɱɚɫɬɢɰ dn/ndv, ɩɪɢɯɨɞɹɳɟɟɫɹ ɧɚ ɢɧɬɟɪɜɚɥ ɫɤɨɪɨɫɬɢ dv, ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɜɟɥɢɱɢɧɵ ɦɨɞɭɥɹ ɫɤɨɪɨɫɬɢ v. ɗɬɨ − ɢɡɜɟɫɬɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ Ɇɚɤɫɜɟɥɥɚ. ɇɚɢɛɨɥɟɟ ɜɚɠɧɨ ɬɨ, ɱɬɨ ɩɪɢ ɥɸɛɵɯ ɬɟɦɩɟɪɚɬɭɪɚɯ ɜɫɟɝɞɚ ɢɦɟɸɬɫɹ ɛɵɫɬɪɵɟ ɱɚɫɬɢɰɵ, ɩɪɢɱɟɦ, ɱɟɦ ɜɵɲɟ ɬɟɦɩɟɪɚɬɭɪɚ, ɬɟɦ ɢɯ ɛɨɥɶɲɟ. ȼ ɨɛɵɱɧɵɯ ɭɫɥɨɜɢɹɯ, ɧɚɩɪɢɦɟɪ ɩɪɢ ɤɨɦɧɚɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ, ɞɨɥɹ ɬɚɤɢɯ ɱɚɫɬɢɰ ɤɪɚɣɧɟ ɦɚɥɚ, ɬɚɤ ɱɬɨ ɷɧɟɪɝɢɹ ɩɨɞɚɜɥɹɸɳɟɝɨ ɱɢɫɥɚ ɱɚɫɬɢɰ ɧɟɞɨɫɬɚɬɨɱɧɚ ɞɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɪɚɡɪɭɲɢɬɶ ɦɨɥɟɤɭɥɭ (ɢɥɢ ɬɟɦ ɛɨɥɟɟ ɚɬɨɦ), ɩɨɷɬɨɦɭ ɩɪɚɤɬɢɱɟɫɤɢ ɩɪɟɨɛɥɚɞɚɸɬ ɬɨɥɶɤɨ ɬɚɤ ɧɚɡɵɜɚɟɦɵɟ ɭɩɪɭɝɢɟ ɫɬɨɥɤɧɨɜɟɧɢɹ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɤɨɬɨɪɵɯ ɩɨɥɧɚɹ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɨɛɟɢɯ ɫɬɚɥɤɢɜɚɸɳɢɯɫɹ ɱɚɫɬɢɰ ɨɫɬɚɟɬɫɹ ɧɟɢɡɦɟɧɧɨɣ. ɗɬɨ ɬɢɩɢɱɧɨ ɞɥɹ ɨɛɵɱɧɨɝɨ ɝɚɡɚ, ɬɚɤɢɟ ɫɬɨɥɤɧɨɜɟɧɢɹ ɢ ɩɪɢɜɨɞɹɬ ɤ ɭɫɬɚɧɨɜɥɟɧɢɸ ɦɚɤɫɜɟɥɥɨɜɫɤɨɝɨ Ɋɢɫ.ȼ.2. Ɏɭɧɤɰɢɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ. ɪɚɫɩɪɟɞɟɥɟɧɢɹ (ɩɨ ɫɤɨɪɨɫɬɹɦ ɢɥɢ ɷɧɟɪɝɢɹɦ, ɬɚɤ ɤɚɤ ɩɪɢ ɞɚɧɧɨɣ ɦɚɫɫɟ ɱɚɫɬɢɰɵ ɟɟ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɨɞɧɨɡɧɚɱɧɨ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɤɨɪɨɫɬɶɸ: ȿ=mv2/2; ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɝɚɡ ɜ ɰɟɥɨɦ ɩɨɤɨɢɬɫɹ). ɂɦɟɸɳɢɟɫɹ ɜɫɟɝɞɚ ɛɵɫɬɪɵɟ ɱɚɫɬɢɰɵ ɪɚɡɛɢɜɚɸɬ ɦɨɥɟɤɭɥɵ ɢ ɞɚɠɟ ɚɬɨɦɵ, ɧɨ ɢɯ ɧɢɱɬɨɠɧɨ ɦɚɥɨ, ɟɫɥɢ ɬɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ ɧɟ ɜɟɥɢɤɚ. ɉɪɨɰɟɫɫ ɪɚɫɩɚɞɚ ɦɨɥɟɤɭɥ ɧɚ ɚɬɨɦɵ ɧɚɡɵɜɚɸɬ ɞɢɫɫɨɰɢɚɰɢɟɣ, ɩɪɨɰɟɫɫ ɨɬɪɵɜɚ ɷɥɟɤɬɪɨɧɚ ɨɬ ɚɬɨɦɚ − ɢɨɧɢɡɚɰɢɟɣ, ɚ ɚɬɨɦ, ɩɨɬɟɪɹɜɲɢɣ ɨɞɢɧ ɷɥɟɤɬɪɨɧ (ɢɥɢ ɛɨɥɶɲɟ),- ɢɨɧɨɦ. ɉɪɢ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ɜ 1 ɫɦ3 ɜɨɡɞɭɯɚ ɫɨɞɟɪɠɢɬɫɹ 103 - 105 ɢɨɧɨɜ, ɱɬɨ ɧɢɱɬɨɠɧɨ ɦɚɥɨ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɱɢɫɥɨɦ ɦɨɥɟɤɭɥ 2.7⋅1019 ɜ ɤɚɠɞɨɦ ɤɭɛɢɱɟɫɤɨɦ ɫɚɧɬɢɦɟɬɪɟ. Ɉɞɧɚɤɨ ɩɪɢ ɩɨɜɵɲɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ ɜɫɟ ɛɨɥɶɲɟ ɫɬɚɧɨɜɢɬɫɹ ɛɵɫɬɪɵɯ ɱɚɫɬɢɰ, ɜɫɟ ɱɚɳɟ ɩɪɨɢɫɯɨɞɹɬ ɩɪɨɰɟɫɫɵ ɞɢɫɫɨɰɢɚɰɢɢ ɢ ɢɨɧɢɡɚɰɢɢ. ȼ ɷɬɢɯ ɩɪɨɰɟɫɫɚɯ ɱɚɫɬɶ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɱɚɫɬɢɰ ɡɚɬɪɚɱɢɜɚɟɬɫɹ ɧɚ ɜɧɭɬɪɢɦɨɥɟɤɭɥɹɪɧɵɟ (ɢɥɢ ɜɧɭɬɪɢɚɬɨɦɧɵɟ) ɩɪɨɰɟɫɫɵ; ɩɨɷɬɨɦɭ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɫɬɚɥɤɢɜɚɸɳɢɯɫɹ ɱɚɫɬɢɰ ɞɨ ɫɨɭɞɚɪɟɧɢɹ ɭɠɟ ɧɟ ɪɚɜɧɚ ɢɯ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɩɨɫɥɟ ɫɨɭɞɚɪɟɧɢɹ. Ɍɚɤɢɟ ɩɪɨɰɟɫɫɵ ɧɚɡɵɜɚɸɬ ɧɟɭɩɪɭɝɢɦɢ. ȼ ɨɛɵɱɧɨɦ ɝɚɡɟ ɪɨɥɶ ɧɟɭɩɪɭɝɢɯ ɩɪɨɰɟɫɫɨɜ ɩɪɟɧɟɛɪɟɠɢɦɨ ɦɚɥɚ, ɧɨ ɩɪɢ ɞɨɫɬɚɬɨɱɧɨ ɜɵɫɨɤɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɨɧɢ ɩɪɢɨɛɪɟɬɚɸɬ ɫɭɳɟɫɬɜɟɧɧɨɟ ɡɧɚɱɟɧɢɟ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɨɛɪɚɡɭɸɬɫɹ ɧɨɜɵɟ ɱɚɫɬɢɰɵ: ɩɪɢ ɞɢɫɫɨɰɢɚɰɢɢ − ɚɬɨɦɵ, ɩɪɢ ɢɨɧɢɡɚɰɢɢ − ɢɨɧɵ ɢ ɷɥɟɤɬɪɨɧɵ. ɉɨɫɥɟɞɧɟɟ ɨɫɨɛɟɧɧɨ ɜɚɠɧɨ. Ⱥɬɨɦɵ, ɤɚɤ ɢ ɦɨɥɟɤɭɥɵ, ɷɥɟɤɬɪɢɱɟɫɤɢ ɧɟɣɬɪɚɥɶɧɵ, ɚ ɜɨɬ ɢɨɧɵ ɢ ɷɥɟɤɬɪɨɧɵ ɢɦɟɸɬ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɡɚɪɹɞɵ. ɇɚɥɢɱɢɟ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɡɚɪɹɞɨɜ ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɹɟɬ ɯɚɪɚɤɬɟɪ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ. ȼɟɞɶ ɧɟɣɬɪɚɥɶɧɵɟ ɱɚɫɬɢɰɵ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ, ɝɪɭɛɨ ɝɨɜɨɪɹ, ɬɨɥɶɤɨ ɩɪɢ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨɦ ɫɬɨɥɤɧɨɜɟɧɢɢ, ɩɨɞɨɛɧɨ ɭɩɪɭɝɢɦ ɛɢɥɶɹɪɞɧɵɦ ɲɚɪɚɦ, ɬɚɤ ɤɚɤ ɩɨɬɟɧɰɢɚɥ ɩɨɥɹ ɫɢɥ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɧɟɣɬɪɚɥɶɧɵɯ ɱɚɫɬɢɰ (ɫɢɥɵ ȼɚɧ-ɞɟɪȼɚɚɥɶɫɚ) ɛɵɫɬɪɨ ɭɛɵɜɚɟɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ. Ɍɨɝɞɚ ɤɚɤ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ ɫɨɡɞɚɸɬ ɜɨɤɪɭɝ ɫɟɛɹ ɩɪɨɬɹɠɟɧɧɵɟ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɩɨɥɹ, ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɞɥɟɧɧɟɟ ɭɛɵɜɚɸɳɢɟ ɫ ɪɚɫɫɬɨɹɧɢɟɦ, ɚ ɩɨɬɨɦɭ ɢ ɫɢɥɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɟɠɞɭ ɡɚɪɹɠɟɧɧɵɦɢ ɱɚɫɬɢɰɚɦɢ (ɫɢɥɚ Ʉɭɥɨɧɚ) ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɞɥɟɧɧɟɟ ɭɛɵɜɚɟɬ ɫ ɪɨɫɬɨɦ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ. ɂɦɟɧɧɨ ɞɚɥɶɧɨɞɟɣɫɬɜɭɸɳɢɣ ɯɚɪɚɤɬɟɪ ɫɢɥ ɦɟɠɞɭ ɡɚɪɹɠɟɧɧɵɦɢ ɱɚɫɬɢɰɚɦɢ ɢ ɩɪɢɜɨɞɢɬ ɤ
2
ɤɚɱɟɫɬɜɟɧɧɨ ɧɨɜɵɦ - ɩɥɚɡɦɟɧɧɵɦ - ɷɮɮɟɤɬɚɦ ɜ ɝɚɡɟ, ɫɨɞɟɪɠɚɳɟɦ ɫɜɨɛɨɞɧɵɟ ɡɚɪɹɞɵ. ɗɬɨ ɤɚɱɟɫɬɜɟɧɧɨ ɧɨɜɵɣ ɝɚɡ: ɝɚɡ, ɫɨɞɟɪɠɚɳɢɣ ɜ ɡɚɦɟɬɧɨɦ ɱɢɫɥɟ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ. Ɍɚɤɨɣ ɝɚɡ ɢ ɧɚɡɵɜɚɸɬ ɩɥɚɡɦɨɣ. ɋɚɦ ɬɟɪɦɢɧ “ɩɥɚɡɦɚ” ɩɨɹɜɢɥɫɹ ɜ ɨɛɢɯɨɞɟ ɧɚɭɤɢ ɩɨɫɥɟ ɪɚɛɨɬ Ʌɟɧɝɦɸɪɚ ɢ Ɍɨɧɤɫɚ ɜ 1928 ɝ., ɢ ɛɵɥ ɜɜɟɞɟɧ ɞɥɹ ɨɩɢɫɚɧɢɹ ɫɨɜɨɤɭɩɧɨɫɬɢ ɹɜɥɟɧɢɣ, ɫɨɩɪɨɜɨɠɞɚɸɳɢɯ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɪɚɡɪɹɞ ɜ ɝɚɡɟ. Ʌɟɝɤɨ ɩɨɧɹɬɶ, ɱɬɨ ɦɟɠɞɭ ɝɚɡɨɦ ɧɟɣɬɪɚɥɶɧɵɯ ɱɚɫɬɢɰ ɢ ɝɚɡɨɦɩɥɚɡɦɨɣ ɧɟɬ ɱɟɬɤɨɣ ɝɪɚɧɢɰɵ: ɨɛɵɱɧɵɣ ɝɚɡ ɫɬɚɧɨɜɢɬɫɹ ɩɥɚɡɦɨɣ, ɤɚɤ ɬɨɥɶɤɨ ɪɨɥɶ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɫɬɚɧɨɜɢɬɫɹ, ɟɫɥɢ ɧɟ ɨɩɪɟɞɟɥɹɸɳɟɣ, ɬɨ ɫɭɳɟɫɬɜɟɧɧɨɣ ɞɥɹ ɩɨɜɟɞɟɧɢɹ ɞɚɧɧɨɣ ɫɭɛɫɬɚɧɰɢɢ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɷɬɚ ɝɪɚɧɢɰɚ ɞɨɜɨɥɶɧɨ ɪɚɡɦɵɬɚɹ, ɜ ɨɬɥɢɱɢɟ ɨɬ ɪɟɡɤɢɯ ɮɚɡɨɜɵɯ ɩɟɪɟɯɨɞɨɜ, ɢɦɟɸɳɢɯ ɦɟɫɬɨ ɫ ɩɨɜɵɲɟɧɢɟɦ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɫɨɩɪɨɜɨɠɞɚɸɳɢɯ ɩɪɟɜɪɚɳɟɧɢɟ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ɜ ɠɢɞɤɨɫɬɶ, ɚ ɡɚɬɟɦ ɠɢɞɤɨɫɬɢ ɜ ɝɚɡ. ɇɟɤɨɬɨɪɨɟ ɪɚɜɧɨɜɟɫɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ (ɨɩɪɟɞɟɥɹɟɦɨɟ ɮɨɪɦɭɥɨɣ ɋɚɯɚ) ɩɪɢɫɭɬɫɬɜɭɟɬ ɜ ɝɚɡɟ ɩɪɢ ɥɸɛɨɣ ɬɟɦɩɟɪɚɬɭɪɟ, ɧɚɩɪɢɦɟɪ, ɫɜɨɛɨɞɧɵɟ ɡɚɪɹɞɵ ɜ ɩɥɚɦɟɧɢ ɨɛɵɱɧɨɣ ɫɜɟɱɢ. ɇɨ ɜɪɹɞ ɥɢ ɫɬɨɥɶ ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɵɣ ɝɚɡ ɦɨɠɧɨ ɧɚɡɜɚɬɶ ɩɥɚɡɦɨɣ. ȼɦɟɫɬɟ ɫ ɬɟɦ, ɜ ɞɚɥɶɧɟɣɲɟɦ ɦɵ ɭɜɢɞɢɦ, ɱɬɨ ɬɢɩɢɱɧɨ ɩɥɚɡɦɟɧɧɵɟ ɩɪɨɰɟɫɫɵ ɧɚɛɥɸɞɚɸɬɫɹ ɜ ɝɚɡɟ-ɩɥɚɡɦɟ ɞɚɠɟ ɬɨɝɞɚ, ɤɨɝɞɚ ɢɨɧɢɡɨɜɚɧɵ ɬɨɥɶɤɨ ɞɨɥɢ ɩɪɨɰɟɧɬɚ ɜɫɟɯ ɱɚɫɬɢɰ. Ɇɨɠɧɨ ɪɚɫɫɭɠɞɚɬɶ ɢ ɨɬ ɨɛɪɚɬɧɨɝɨ: “ɢɫɬɢɧɧɚɹ” ɩɥɚɡɦɚ ɫɨɫɬɨɢɬ ɢɡ ɫɜɨɛɨɞɧɵɯ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɢ ɨɫɬɚɟɬɫɹ ɩɥɚɡɦɨɣ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɩɪɢɦɟɫɶ ɧɟɣɬɪɚɥɶɧɵɯ ɱɚɫɬɢɰ ɧɟ ɢɡɦɟɧɢɬ ɫɭɳɟɫɬɜɟɧɧɨ ɟɟ ɫɜɨɣɫɬɜ. ɇɨ ɜɨɡɧɢɤɚɟɬ ɜɨɩɪɨɫ ɦɨɠɧɨ ɥɢ, ɧɚɩɪɢɦɟɪ, ɧɚɡɜɚɬɶ ɩɥɚɡɦɨɣ ɧɟɫɤɨɦɩɟɧɫɢɪɨɜɚɧɧɵɟ ɩɨ ɡɚɪɹɞɭ ɩɭɱɤɢ ɭɫɤɨɪɟɧɧɵɯ ɱɚɫɬɢɰ, ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɟɦɵɟ ɜ ɮɢɡɢɱɟɫɤɢɯ ɷɤɫɩɟɪɢɦɟɧɬɚɯ? Ɇɨɠɧɨ ɥɢ ɧɚɡɜɚɬɶ ɩɥɚɡɦɨɣ ɜɟɫɶɦɚ ɪɚɡɪɟɠɟɧɧɵɣ ɦɟɠɡɜɟɡɞɧɵɣ ɢɥɢ ɦɟɠɝɚɥɚɤɬɢɱɟɫɤɢɣ ɝɚɡ, ɢɨɧɢɡɭɟɦɵɣ ɢɡɥɭɱɟɧɢɟɦ ɡɜɟɡɞ? Ɉɱɟɜɢɞɧɚ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɤɨɥɢɱɟɫɬɜɟɧɧɨɝɨ ɤɪɢɬɟɪɢɹ, ɩɨɡɜɨɥɹɸɳɟɝɨ ɨɩɪɟɞɟɥɢɬɶ, ɹɜɥɹɟɬɫɹ ɥɢ ɞɚɧɧɚɹ ɫɨɜɨɤɭɩɧɨɫɬɶ ɡɚɪɹɠɟɧɧɵɯ ɢ ɧɟɣɬɪɚɥɶɧɵɯ ɱɚɫɬɢɰ ɩɥɚɡɦɨɣ. Ɍɚɤɨɣ ɤɪɢɬɟɪɢɣ ɦɨɠɧɨ ɫɮɨɪɦɭɥɢɪɨɜɚɬɶ, ɨɩɢɪɚɹɫɶ ɧɚ ɩɨɧɹɬɢɹ ɥɟɧɝɦɸɪɨɜɫɤɨɣ ɱɚɫɬɨɬɵ ɢ ɞɟɛɚɟɜɫɤɨɝɨ ɪɚɞɢɭɫɚ (ɢɥɢ ɞɥɢɧɵ) ɷɤɪɚɧɢɪɨɜɚɧɢɹ. ɂɦɟɧɧɨ ɷɬɢ ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɟ ɜ ɮɢɡɢɤɟ ɩɥɚɡɦɵ ɩɚɪɚɦɟɬɪɵ ɡɚɞɚɸɬ ɦɢɧɢɦɚɥɶɧɵɟ ɯɚɪɚɤɬɟɪɧɵɟ ɜɪɟɦɟɧɧɨɣ ɢ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɣ ɦɚɫɲɬɚɛɵ ɩɨɞɞɟɪɠɚɧɢɹ (ɢɥɢ ɫɩɨɧɬɚɧɧɨɝɨ ɧɚɪɭɲɟɧɢɹ) ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɢ ɩɥɚɡɦɵ. Ɉɩɢɪɚɹɫɶ ɧɚ ɷɬɢ ɩɨɧɹɬɢɹ, ɦɨɠɧɨ ɭɫɬɚɧɨɜɢɬɶ, ɩɨɱɟɦɭ ɩɥɚɡɦɟɧɧɵɟ ɫɜɨɣɫɬɜɚ ɩɪɨɹɜɥɹɸɬ, ɧɚ ɩɟɪɜɵɣ ɜɡɝɥɹɞ ɪɚɡɥɢɱɧɵɟ ɫɪɟɞɵ ɷɥɟɤɬɪɨɧɧɵɣ ɝɚɡ ɜ ɦɟɬɚɥɥɚɯ, ɷɥɟɤɬɪɨɧɧɨ-ɞɵɪɨɱɧɚɹ “ɠɢɞɤɨɫɬɶ” ɩɨɥɭɩɪɨɜɨɞɧɢɤɨɜ ɢɥɢ, ɧɚɩɪɢɦɟɪ, ɪɚɡɪɟɠɟɧɧɵɣ ɝɚɡ ɤɨɫɦɨɫɚ. ɗɬɢ, ɚ ɬɚɤɠɟ ɞɪɭɝɢɟ ɫɪɟɞɵ, ɧɚɩɪɢɦɟɪ ɷɥɟɤɬɪɨɥɢɬɵ, ɤ ɤɨɬɨɪɵɦ ɨɬɧɨɫɹɬɫɹ ɢ «ɪɚɛɨɱɢɟ ɠɢɞɤɨɫɬɢ» ɠɢɜɵɯ ɫɢɫɬɟɦ, ɢɧɨɝɞɚ ɧɚɡɵɜɚɸɬ ɩɥɚɡɦɨɩɨɞɨɛɧɵɦɢ [3,4]. ɗɬɨ ɩɨɞɱɟɪɤɢɜɚɟɬ ɜɚɠɧɨɫɬɶ ɯɚɪɚɤɬɟɪɧɵɯ ɞɥɹ ɩɥɚɡɦɵ ɡɚɤɨɧɨɜ ɩɪɢ ɨɩɢɫɚɧɢɢ ɫɜɨɣɫɬɜ ɫɬɨɥɶ ɛɨɥɶɲɨɝɨ ɢ ɜɚɠɧɨɝɨ ɜ ɩɪɚɤɬɢɱɟɫɤɨɦ ɩɪɢɦɟɧɟɧɢɢ ɱɢɫɥɚ ɨɛɴɟɤɬɨɜ ɩɪɢɪɨɞɵ. ɗɥɟɤɬɪɨɧɧɚɹ ɩɥɚɡɦɚ ɦɟɬɚɥɥɨɜ ɧɚɡɵɜɚɟɬɫɹ ɜɵɪɨɠɞɟɧɧɨɣ. Ʉɪɢɬɟɪɢɟɦ ɜɵɪɨɠɞɟɧɢɹ, ɤɚɤ ɢɡɜɟɫɬɧɨ, ɹɜɥɹɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ ɷɧɟɪɝɢɟɣ Ɏɟɪɦɢ, ɜɨɡɪɚɫɬɚɸɳɟɣ ɫ ɪɨɫɬɨɦ ɤɨɧɰɟɧɬɪɚɰɢɢ ɱɚɫɬɢɰ, ɢ ɬɟɩɥɨɜɨɣ ɷɧɟɪɝɢɟɣ. ȿɫɥɢ ɬɟɩɥɨɜɚɹ ɷɧɟɪɝɢɹ ɦɟɧɶɲɟ ɷɧɟɪɝɢɢ Ɏɟɪɦɢ, ɬɨ ɩɥɚɡɦɚ ɜɵɪɨɠɞɟɧɚ ɢ ɫɭɳɟɫɬɜɟɧɧɵ ɤɜɚɧɬɨɜɵɟ ɷɮɮɟɤɬɵ. Ɇɵ ɛɭɞɟɦ ɢɦɟɬɶ ɞɟɥɨ ɫ ɧɟɜɵɪɨɠɞɟɧɧɨɣ ɩɥɚɡɦɨɣ, ɬ.ɟ. ɫ ɬɚɤɨɣ ɩɥɚɡɦɨɣ, ɜ ɤɨɬɨɪɨɣ ɤɨɧɰɟɧɬɪɚɰɢɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɞɨɫɬɚɬɨɱɧɨ ɦɚɥɚ (ɢɥɢ ɬɟɦɩɟɪɚɬɭɪɚ ɞɨɫɬɚɬɨɱɧɨ ɜɟɥɢɤɚ). ɋɬɪɨɝɨ ɝɨɜɨɪɹ, ɦɧɨɝɢɟ ɮɢɡɢɤɢ ɜɜɨɞɹɬ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɭɫɥɨɜɢɹ - ɫɱɢɬɚɸɬ, ɧɚɩɪɢɦɟɪ, ɨɛɹɡɚɬɟɥɶɧɨɣ ɤɨɦɩɨɧɟɧɬɨɣ ɩɥɚɡɦɵ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɟ ɢɡɥɭɱɟɧɢɟ. ɉɨɫɥɟɞɧɟɟ ɛɟɫɫɩɨɪɧɨ ɜɟɪɧɨ ɞɥɹ ɛɨɥɶɲɢɯ ɨɛɴɟɤɬɨɜ ɢɡ ɩɥɨɬɧɨɣ ɩɥɚɡɦɵ, ɧɚɩɪɢɦɟɪ, ɡɜɟɡɞ. ȼ ɧɢɯ ɢɡɥɭɱɟɧɢɟ "ɡɚɩɟɪɬɨ" ɢɡɥɭɱɟɧɢɟ ɦɨɠɟɬ ɜɵɯɨɞɢɬɶ ɥɢɲɶ ɢɡ ɫɪɚɜɧɢɬɟɥɶɧɨ ɬɨɧɤɢɯ ɧɚɪɭɠɧɵɯ ɫɥɨɟɜ. ȼ
3
ɛɨɥɶɲɢɧɫɬɜɟ ɥɚɛɨɪɚɬɨɪɧɵɯ ɭɫɬɪɨɣɫɬɜ ɩɥɚɡɦɚ ɨɩɬɢɱɟɫɤɢ ɬɨɧɤɚɹ, ɢɡɥɭɱɟɧɢɟ ɧɟ ɡɚɩɟɪɬɨ - ɨɧɨ ɫɜɨɛɨɞɧɨ ɩɪɨɯɨɞɢɬ ɱɟɪɟɡ ɜɫɸ ɩɥɚɡɦɭ. ɉɨɞɜɟɞɟɦ ɢɬɨɝɢ. ɉɨ ɫɨɜɪɟɦɟɧɧɵɦ ɩɪɟɞɫɬɚɜɥɟɧɢɹɦ ɩɥɚɡɦɚ - ɱɚɫɬɢɱɧɨ ɢɥɢ ɩɨɥɧɨɫɬɶɸ ɢɨɧɢɡɨɜɚɧɧɵɣ ɝɚɡ, ɜ ɤɨɬɨɪɨɦ ɨɛɴɟɦɧɵɟ ɩɥɨɬɧɨɫɬɢ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɡɚɪɹɞɨɜ ɩɪɚɤɬɢɱɟɫɤɢ ɨɞɢɧɚɤɨɜɵ. Ɍɚɤɨɟ ɫɜɨɣɫɬɜɨ ɩɥɚɡɦɵ ɧɚɡɵɜɚɸɬ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɶɸ. Ɂɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ ɩɥɚɡɦɵ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ ɫ ɫɢɥɨɣ, ɞɥɹ ɤɨɬɨɪɨɣ ɯɚɪɚɤɬɟɪɧɨ ɞɚɥɶɧɨɞɟɣɫɬɜɢɟ. ɗɬɨ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ ɨɩɪɟɞɟɥɹɟɬ ɢɫɤɥɸɱɢɬɟɥɶɧɭɸ ɪɨɥɶ ɜ ɩɥɚɡɦɟ, ɩɨɦɢɦɨ ɩɚɪɧɵɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɨɬɞɟɥɶɧɵɯ ɱɚɫɬɢɰ, ɤɨɥɥɟɤɬɢɜɧɵɯ ɷɮɮɟɤɬɨɜ, ɬ.ɟ. ɩɨɥɟɣ ɨɬ ɦɧɨɝɢɯ ɱɚɫɬɢɰ, ɩɪɨɹɜɥɹɸɳɢɯɫɹ ɜ ɧɚɪɚɫɬɚɧɢɢ ɩɥɚɡɦɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ, ɜɨɥɧ ɢ ɲɭɦɨɜ, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɜɨɡɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɞɜɢɠɟɧɢɟ ɱɚɫɬɢɰ ɩɥɚɡɦɵ. ȿɫɥɢ ɜɨɡɛɭɠɞɚɟɬɫɹ ɞɨɫɬɚɬɨɱɧɨ ɦɧɨɝɨ ɤɨɥɥɟɤɬɢɜɧɵɯ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ, ɬɨ ɤɨɥɟɛɚɧɢɹ ɩɥɚɡɦɵ ɫɬɚɧɨɜɹɬɫɹ ɧɟɪɟɝɭɥɹɪɧɵɦɢ, ɨɧɚ ɩɟɪɟɯɨɞɢɬ ɜ ɬɚɤ ɧɚɡɵɜɚɟɦɨɟ ɬɭɪɛɭɥɟɧɬɧɨɟ ɫɨɫɬɨɹɧɢɟ. ȼ ɷɬɢɯ ɭɫɥɨɜɢɹɯ ɫɬɚɧɨɜɹɬɫɹ ɫɭɳɟɫɬɜɟɧɧɵɦɢ ɧɟɥɢɧɟɣɧɵɟ ɷɮɮɟɤɬɵ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɤɨɥɥɟɤɬɢɜɧɵɯ ɜɨɡɛɭɠɞɟɧɢɣ (ɦɨɞ) ɩɥɚɡɦɵ. ɇɟɥɢɧɟɣɧɵɟ ɹɜɥɟɧɢɹ ɦɨɝɭɬ ɛɵɬɶ ɫɭɳɟɫɬɜɟɧɧɵ ɢ ɜ ɪɟɝɭɥɹɪɧɵɯ ɩɪɨɰɟɫɫɚɯ, ɧɚɩɪɢɦɟɪ, ɩɪɢ ɜɨɡɞɟɣɫɬɜɢɢ ɧɚ ɩɥɚɡɦɭ ɜɨɥɧ ɤɨɧɟɱɧɨɣ ɚɦɩɥɢɬɭɞɵ. ɉɨɧɹɬɧɨ ɩɨɷɬɨɦɭ, ɱɬɨ ɫɨɜɪɟɦɟɧɧɚɹ ɮɢɡɢɤɚ ɩɥɚɡɦɵ - ɷɬɨ ɮɢɡɢɤɚ ɧɟɥɢɧɟɣɧɵɯ ɹɜɥɟɧɢɣ. ȿɳɟ ɨɞɧɚ ɨɫɨɛɟɧɧɨɫɬɶ ɷɬɨɝɨ ɧɨɜɨɝɨ ɫɨɫɬɨɹɧɢɹ ɜɟɳɟɫɬɜɚ - ɩɥɚɡɦɵ - ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɫɢɥɶɧɨɦ ɜɨɡɞɟɣɫɬɜɢɢ ɧɚ ɧɟɝɨ ɜɧɟɲɧɢɯ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɢ ɦɚɝɧɢɬɧɵɯ ɩɨɥɟɣ, ɜɵɡɵɜɚɸɳɢɯ ɩɨɹɜɥɟɧɢɟ ɨɛɴɟɦɧɵɯ ɡɚɪɹɞɨɜ ɢ ɬɨɤɨɜ. ȼɦɟɫɬɟ ɫ ɬɟɦ, ɫɭɳɟɫɬɜɟɧɧɨɟ ɪɚɡɞɟɥɟɧɢɟ ɡɚɪɹɞɨɜ ɜ ɩɥɚɡɦɟ ɡɚɬɪɭɞɧɟɧɨ ɜ ɫɢɥɭ ɟɟ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɢ: ɢɡ-ɡɚ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɣ ɩɥɨɬɧɨɫɬɢ ɡɚɪɹɠɟɧɧɨɣ ɤɨɦɩɨɧɟɧɬɵ ɜ ɩɥɚɡɦɟ ɨɛɴɟɦɧɵɣ ɡɚɪɹɞ ɜɵɡɵɜɚɥ ɛɵ ɩɨɹɜɥɟɧɢɟ ɫɥɢɲɤɨɦ ɛɨɥɶɲɢɯ ɫɨɛɫɬɜɟɧɧɵɯ ɩɨɥɟɣ ɩɥɚɡɦɵ, ɱɟɝɨ ɜ ɞɟɣɫɬɜɢɬɟɥɶɧɨɫɬɢ ɧɟ ɩɪɨɢɫɯɨɞɢɬ. ȼ ɨɩɪɟɞɟɥɟɧɧɨɦ ɫɦɵɫɥɟ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɶ ɩɥɚɡɦɵ ɟɫɬɶ ɩɪɨɹɜɥɟɧɢɟ ɬɨɝɨ ɫɜɨɣɫɬɜɚ, ɱɬɨ ɝɥɚɜɧɭɸ ɪɨɥɶ ɜ ɩɥɚɡɦɟ ɢɝɪɚɟɬ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɱɚɫɬɢɰ ɱɟɪɟɡ ɫɚɦɨɫɨɝɥɚɫɨɜɚɧɧɵɟ ɩɨɥɹ. ȼ ɷɬɨɦ ɨɬɧɨɲɟɧɢɢ ɞɢɧɚɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ ɜ ɩɥɚɡɦɟ ɹɜɥɹɸɬɫɹ ɜɟɫɶɦɚ ɫɥɨɠɧɵɦɢ ɹɜɥɟɧɢɹɦɢ. Ɉɧɢ ɬɪɟɛɭɸɬ ɢɡɭɱɟɧɢɹ ɧɟ ɬɨɥɶɤɨ ɞɢɧɚɦɢɤɢ ɱɚɫɬɢɰ ɜ ɡɚɞɚɧɧɵɯ ɜɧɟɲɧɢɯ ɩɨɥɹɯ, ɧɨ ɢ ɨɞɧɨɜɪɟɦɟɧɧɨɝɨ ɭɱɟɬɚ ɜɥɢɹɧɢɹ ɫɨɛɫɬɜɟɧɧɵɯ, ɫɨɝɥɚɫɨɜɚɧɧɵɯ ɫ ɞɜɢɠɟɧɢɟɦ ɱɚɫɬɢɰ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɩɨɥɟɣ, ɫɚɦɵɦ ɫɭɳɟɫɬɜɟɧɧɵɦ ɨɛɪɚɡɨɦ ɫɤɚɡɵɜɚɸɳɢɯɫɹ ɧɚ ɞɜɢɠɟɧɢɢ ɫɚɦɢɯ ɱɚɫɬɢɰ ɩɥɚɡɦɵ. ȼ ɡɚɤɥɸɱɟɧɢɟ ɧɟɥɢɲɧɟ ɩɨɞɱɟɪɤɧɭɬɶ, ɱɬɨ ɩɥɚɡɦɚ ɜɨ ȼɫɟɥɟɧɧɨɣ ɢ ɜ ɪɚɡɧɨɨɛɪɚɡɧɵɯ ɩɪɢɪɨɞɧɵɯ ɩɪɨɰɟɫɫɚɯ ɢ ɹɜɥɟɧɢɹɯ ɩɪɟɞɫɬɚɜɥɟɧɚ ɜɟɫɶɦɚ ɲɢɪɨɤɨ. Ɇɟɠɝɚɥɚɤɬɢɱɟɫɤɚɹ, ɦɟɠɡɜɟɡɞɧɚɹ ɢ ɦɟɠɩɥɚɧɟɬɧɚɹ ɩɥɚɡɦɚ, ɩɥɚɡɦɚ ɡɜɟɡɞ ɢ ɡɜɟɡɞɧɵɯ ɚɬɦɨɫɮɟɪ, ɨɬ Ȼɟɥɵɯ Ʉɚɪɥɢɤɨɜ ɞɨ Ʉɪɚɫɧɵɯ Ƚɢɝɚɧɬɨɜ, ɧɟɣɬɪɨɧɧɵɯ ɡɜɟɡɞ, ɩɭɥɶɫɚɪɨɜ ɢ ɱɟɪɧɵɯ ɞɵɪ, ɩɥɚɡɦɚ ɜɟɪɯɧɢɯ ɫɥɨɟɜ ɚɬɦɨɫɮɟɪɵ ɩɥɚɧɟɬ ɢ ɩɥɚɡɦɚ ɪɚɞɢɚɰɢɨɧɧɵɯ ɩɨɹɫɨɜ, ɩɥɚɡɦɚ ɝɪɨɡɨɜɵɯ ɪɚɡɪɹɞɨɜ ɢ ɝɚɡɨɪɚɡɪɹɞɧɚɹ ɩɥɚɡɦɚ ɥɚɛɨɪɚɬɨɪɧɵɯ ɭɫɬɪɨɣɫɬɜ, “ɬɟɪɦɨɹɞɟɪɧɚɹ” ɩɥɚɡɦɚ ɫɨɜɪɟɦɟɧɧɵɯ ɬɟɪɦɨɹɞɟɪɧɵɯ ɭɫɬɚɧɨɜɨɤ - ɜɨɬ ɞɚɥɟɤɨ ɧɟ ɩɨɥɧɵɣ ɩɟɪɟɱɟɧɶ ɩɪɢɥɨɠɟɧɢɣ ɧɚɭɤɢ ɨ ɩɥɚɡɦɟ. ɇɚɤɨɧɟɰ, ɜ ɫɚɦɵɟ ɩɟɪɜɵɟ ɦɝɧɨɜɟɧɢɹ ɠɢɡɧɢ ȼɫɟɥɟɧɧɨɣ ɩɨɫɥɟ Ȼɨɥɶɲɨɝɨ ȼɡɪɵɜɚ, ɤɨɝɞɚ ɪɨɞɢɥɫɹ ɧɚɲ ɦɢɪ, ɤɚɤ ɩɨɥɚɝɚɸɬ, ɜɟɳɟɫɬɜɨ ɬɚɤɠɟ ɧɚɯɨɞɢɥɨɫɶ ɜ ɫɨɫɬɨɹɧɢɢ ɝɨɪɹɱɟɣ ɩɥɚɡɦɵ, ɨɬɝɨɥɨɫɤɨɦ ɤɨɬɨɪɨɝɨ ɹɜɥɹɟɬɫɹ ɪɟɥɢɤɬɨɜɨɟ ɢɡɥɭɱɟɧɢɟ, ɫɨɫɬɨɹɳɟɟ ɫɟɣɱɚɫ ɢɡ “ɯɨɥɨɞɧɵɯ” (ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ ɨɤɨɥɨ 2.7Ʉ), ɚ ɬɨɝɞɚ “ɝɨɪɹɱɢɯ” ɤɜɚɧɬɨɜ, ɧɚɯɨɞɢɜɲɢɯɫɹ ɜ ɪɚɜɧɨɜɟɫɢɢ ɫ ɩɥɚɡɦɨɣ ɱɭɞɨɜɢɳɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ - ɜ ɫɨɬɧɢ ɦɢɥɥɢɨɧɨɜ ɢ ɦɢɥɥɢɚɪɞɨɜ ɝɪɚɞɭɫɨɜ.
4
ȽɅȺȼȺ 1
ɈɋɇɈȼɇɕȿ ɉɈɇəɌɂə ɂ ɋȼɈɃɋɌȼȺ ɉɅȺɁɆɕ §1. Ɉɛɪɚɡɨɜɚɧɢɟ ɩɥɚɡɦɵ Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɨɛɵɱɧɵɣ ɝɚɡ ɩɟɪɟɜɟɫɬɢ ɜ ɩɥɚɡɦɟɧɧɨɟ ɫɨɫɬɨɹɧɢɟ, ɧɟɨɛɯɨɞɢɦɨ ɢɨɧɢɡɢɪɨɜɚɬɶ ɡɚɦɟɬɧɭɸ ɱɚɫɬɶ ɦɨɥɟɤɭɥ ɢɥɢ ɚɬɨɦɨɜ. ɉɪɨɰɟɫɫ ɢɨɧɢɡɚɰɢɢ ɹɜɥɹɟɬɫɹ ɩɨɪɨɝɨɜɵɦ. ɑɬɨɛɵ ɚɬɨɦ ɫɬɚɥ ɢɨɧɢɡɢɪɨɜɚɧɧɵɦ, ɷɥɟɤɬɪɨɧ ɜ ɚɬɨɦɟ ɞɨɥɠɟɧ ɩɪɢɨɛɪɟɫɬɢ ɷɧɟɪɝɢɸ ɛɨɥɶɲɭɸ, ɱɟɦ ɟɝɨ ɷɧɟɪɝɢɹ ɫɜɹɡɢ. ɉɟɪɟɞɚɱɚ ɷɧɟɪɝɢɢ, ɞɨɫɬɚɬɨɱɧɨɣ ɞɥɹ ɪɚɡɪɵɜɚ ɷɬɨɣ ɫɜɹɡɢ, ɜɨɡɦɨɠɧɚ ɩɪɢ ɫɨɭɞɚɪɟɧɢɢ ɚɬɨɦɚ ɢɥɢ ɦɨɥɟɤɭɥɵ ɫ ɞɪɭɝɨɣ ɛɵɫɬɪɨɣ ɱɚɫɬɢɰɟɣ - ɷɥɟɤɬɪɨɧɨɦ, ɢɨɧɨɦ, ɚɬɨɦɨɦ ɢɥɢ ɦɨɥɟɤɭɥɨɣ, ɩɪɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɢ ɫ ɮɨɬɨɧɨɦ, ɩɪɢ ɜɨɡɞɟɣɫɬɜɢɢ ɞɨɫɬɚɬɨɱɧɨ ɫɢɥɶɧɨɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. ɋɜɨɟɨɛɪɚɡɧɵɣ ɩɪɨɰɟɫɫ ɢɨɧɢɡɚɰɢɢ - ɬɚɤ ɧɚɡɵɜɚɟɦɚɹ ɥɨɪɟɧɰ-ɢɨɧɢɡɚɰɢɹ, ɜɨɡɦɨɠɟɧ ɩɪɢ ɞɜɢɠɟɧɢɢ ɛɵɫɬɪɨɝɨ ɚɬɨɦɚ ɜ ɫɢɥɶɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ. Ⱦɟɥɨ ɡɞɟɫɶ ɜ ɬɨɦ, ɱɬɨ ɜ ɫɨɛɫɬɜɟɧɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ, ɬ.ɟ. ɜ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ, ɨɬɧɨɫɢɬɟɥɶɧɨ ɤɨɬɨɪɨɣ ɚɬɨɦ ɧɟɩɨɞɜɢɠɟɧ, ɧɚ ɧɟɝɨ, ɫɨɝɥɚɫɧɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɦ Ʌɨɪɟɧɰɚ, ɞɟɣɫɬɜɭɟɬ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ E=(v/c)B. ȿɫɥɢ ɜɟɥɢɱɢɧɚ ɷɬɨɝɨ ɩɨɥɹ ɞɨɫɬɚɬɨɱɧɚ, ɚɬɨɦ ɦɨɠɟɬ ɛɵɬɶ ɢɨɧɢɡɢɪɨɜɚɧ. Ɋɚɫɫɦɨɬɪɢɦ ɩɪɨɰɟɫɫɵ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɩɪɨɢɡɨɣɬɢ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɢ ɞɜɭɯ ɛɵɫɬɪɵɯ (ɷɧɟɪɝɢɱɧɵɯ) ɦɨɥɟɤɭɥ Ⱥȼ ɢ CD: 1) Ⱥȼ + CD → Ⱥȼ + ɋD 2) Ⱥȼ + CD → Ⱥȼ* + ɋD
3) Ⱥȼ + ɋD → Ⱥ + ȼ + ɋD Ⱥȼ + CD → Ⱥȼ +ɋ+D Ⱥȼ + ɋD → Ⱥ + ȼ + ɋ + D 4) Ⱥȼ + ɋD → Ⱥȼ+ + ɋD + ɟ Ⱥȼ + ɋD → Ⱥȼ + CD+ + ɟ Ⱥȼ + ɋD → Aȼ+ + ȼɋ+ + 2ɟ
- ɭɩɪɭɝɨɟ ɪɚɫɫɟɹɧɢɟ; - ɧɟɭɩɪɭɝɨɟ ɪɚɫɫɟɹɧɢɟ. Ɇɨɥɟɤɭɥɚ Ⱥȼ* ɨɤɚɡɚɥɚɫɶ ɜ ɜɨɡɛɭɠɞɟɧɧɨɦ ɫɨɫɬɨɹɧɢɢ (ɡɧɚɱɨɤ * ). Ɇɨɠɟɬ ɨɤɚɡɚɬɶɫɹ ɜɨɡɛɭɠɞɟɧɧɨɣ CD* ɢɥɢ Ⱥȼ* ɢ ɋD* ɨɞɧɨɜɪɟɦɟɧɧɨ. ɉɨɥɧɚɹ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɭɦɟɧɶɲɢɥɚɫɶ ɧɚ ɷɧɟɪɝɢɸ ɜɨɡɛɭɠɞɟɧɢɹ. ȼɨɡɦɨɠɧɵ ɪɚɡɥɢɱɧɵɟ ɜɢɞɵ ɜɨɡɛɭɠɞɟɧɢɣ; -ɞɢɫɫɨɰɢɚɰɢɹ. Ɉɞɧɚ ɢɡ ɦɨɥɟɤɭɥ ɢɥɢ ɨɛɟ ɦɨɥɟɤɭɥɵ ɪɚɫɩɚɥɢɫɶ ɧɚ ɚɬɨɦɵ; -ɢɨɧɢɡɚɰɢɹ. Ɉɞɧɚ ɢɡ ɦɨɥɟɤɭɥ “ɩɨɬɟɪɹɥɚ” ɷɥɟɤɬɪɨɧ ɢ ɫɬɚɥɚ ɢɨɧɨɦ.
(ɢɥɢ
ɨɛɟ)
ȼ ɪɟɡɭɥɶɬɚɬɟ ɷɬɢɯ ɩɪɨɰɟɫɫɨɜ, ɤɚɤ ɦɵ ɜɢɞɢɦ, ɩɨɹɜɢɥɢɫɶ ɧɨɜɵɟ ɱɚɫɬɢɰɵ: ɜɨɡɛɭɠɞɟɧɧɵɟ ɦɨɥɟɤɭɥɵ, ɨɬɞɟɥɶɧɵɟ ɚɬɨɦɵ, ɢɨɧɵ ɢ ɷɥɟɤɬɪɨɧɵ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɥɸɛɚɹ ɢɡ ɦɨɥɟɤɭɥ ɦɨɠɟɬ ɫɬɨɥɤɧɭɬɶɫɹ ɫ ɥɸɛɨɣ ɢɡ ɷɬɢɯ ɧɨɜɵɯ ɱɚɫɬɢɰ, ɢ ɜɫɟ ɨɧɢ ɦɨɝɭɬ ɫɬɚɥɤɢɜɚɬɶɫɹ ɞɪɭɝ ɫ ɞɪɭɝɨɦ. ɉɪɢ ɷɬɨɦ ɜɨɡɦɨɠɧɵ ɧɟ ɬɨɥɶɤɨ “ɩɪɹɦɵɟ” ɩɪɨɰɟɫɫɵ, ɩɟɪɟɱɢɫɥɟɧɧɵɟ ɜɵɲɟ, ɧɨ ɢ ɨɛɪɚɬɧɵɟ. ɇɚɩɪɢɦɟɪ, ɩɪɨɰɟɫɫɨɦ ɨɛɪɚɬɧɵɦ ɞɢɫɫɨɰɢɚɰɢɢ ɹɜɥɹɟɬɫɹ ɚɫɫɨɰɢɚɰɢɹ - ɩɪɨɰɟɫɫ ɨɛɴɟɞɢɧɟɧɢɹ ɚɬɨɦɨɜ ɜ ɦɨɥɟɤɭɥɭ. ɉɪɨɰɟɫɫɨɦ, ɨɛɪɚɬɧɵɦ ɢɨɧɢɡɚɰɢɢ, ɹɜɥɹɟɬɫɹ ɪɟɤɨɦɛɢɧɚɰɢɹ. ɋɚɦɚ ɩɨ ɫɟɛɟ ɪɟɤɨɦɛɢɧɚɰɢɹ ɦɨɠɟɬ ɩɪɨɢɫɯɨɞɢɬɶ ɩɨ ɪɚɡɧɨɦɭ, ɧɚɩɪɢɦɟɪ ɜɨɡɦɨɠɧɵ: ɬɪɨɣɧɚɹ ɪɟɤɨɦɛɢɧɚɰɢɹ, ɢɡɥɭɱɚɬɟɥɶɧɚɹ ɪɟɤɨɦɛɢɧɚɰɢɹ ɢ ɞɢɫɫɨɰɢɚɬɢɜɧɚɹ ɪɟɤɨɦɛɢɧɚɰɢɹ. ȼ ɨɬɥɢɱɢɟ ɨɬ ɢɨɧɢɡɚɰɢɢ ɪɟɤɨɦɛɢɧɚɰɢɹ ɜɨɡɦɨɠɧɚ ɬɨɥɶɤɨ ɩɪɢ ɧɚɥɢɱɢɢ “ɬɪɟɬɶɟɝɨ ɬɟɥɚ”, ɭɧɨɫɹɳɟɝɨ ɢɡɛɵɬɨɤ ɷɧɟɪɝɢɢ, ɪɚɜɧɵɣ ɷɧɟɪɝɢɢ ɫɜɹɡɢ ɪɟɤɨɦɛɢɧɢɪɭɸɳɢɯ ɱɚɫɬɢɰ. 1
Ɍɚɤɢɦ ɬɪɟɬɶɢɦ ɬɟɥɨɦ ɦɨɠɟɬ ɛɵɬɶ ɟɳɟ ɨɞɢɧ ɷɥɟɤɬɪɨɧ, ɬɨɝɞɚ ɷɬɨ ɬɪɨɣɧɚɹ ɪɟɤɨɦɛɢɧɚɰɢɹ, ɮɨɬɨɧ - ɢɡɥɭɱɚɬɟɥɶɧɚɹ ɪɟɤɨɦɛɢɧɚɰɢɹ, ɢɥɢ ɷɧɟɪɝɢɹ ɫɜɹɡɢ ɚɬɨɦɨɜ ɜ ɦɨɥɟɤɭɥɹɪɧɨɦ ɢɨɧɟ - ɩɪɢ ɪɟɤɨɦɛɢɧɚɰɢɢ ɦɨɥɟɤɭɥɚ ɪɚɡɪɭɲɚɟɬɫɹ, ɩɨɷɬɨɦɭ ɷɬɨɬ ɩɪɨɰɟɫɫ ɧɚɡɵɜɚɟɬɫɹ ɞɢɫɫɨɰɢɚɬɢɜɧɨɣ ɪɟɤɨɦɛɢɧɚɰɢɟɣ. Ⱥɬɨɦɵ ɢ ɦɨɥɟɤɭɥɵ ɧɟ ɦɨɝɭɬ ɞɨɥɝɨ ɨɫɬɚɜɚɬɶɫɹ ɜ ɜɨɡɛɭɠɞɟɧɧɨɦ ɫɨɫɬɨɹɧɢɢ, ɩɨɫɤɨɥɶɤɭ ɜɨɡɛɭɠɞɟɧɧɵɟ ɫɨɫɬɨɹɧɢɹ ɢɦɟɸɬ ɜɩɨɥɧɟ ɨɩɪɟɞɟɥɟɧɧɨɟ ɤɨɧɟɱɧɨɟ ɜɪɟɦɹ ɠɢɡɧɢ, ɫɩɭɫɬɹ ɤɨɬɨɪɨɟ ɩɪɨɢɫɯɨɞɢɬ ɩɟɪɟɯɨɞ ɜ ɨɫɧɨɜɧɨɟ ɫɨɫɬɨɹɧɢɟ, ɫɨɩɪɨɜɨɠɞɚɸɳɢɣɫɹ ɢɡɥɭɱɟɧɢɟɦ ɤɜɚɧɬɚ. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜ ɚɬɨɦɚɯ ɜɨɡɦɨɠɧɵ ɜɨɡɛɭɠɞɟɧɧɵɟ ɫɨɫɬɨɹɧɢɹ ɬɨɥɶɤɨ ɷɥɟɤɬɪɨɧɧɵɯ ɭɪɨɜɧɟɣ, ɚ ɜ ɦɨɥɟɤɭɥɚɯ - ɬɚɤɠɟ ɟɳɟ ɜɨɡɛɭɠɞɟɧɢɹ ɤɨɥɟɛɚɬɟɥɶɧɵɯ ɢ ɜɪɚɳɚɬɟɥɶɧɵɯ ɭɪɨɜɧɟɣ. Ʉɨɥɟɛɚɬɟɥɶɧɵɟ ɜɨɡɛɭɠɞɟɧɢɹ ɨɬɦɟɱɚɸɬ ɢɧɞɟɤɫɨɦ ν, ɧɚɩɪɢɦɟɪ Ⱥȼν, ɜɪɚɳɚɬɟɥɶɧɵɟ, ɤɚɤ ɩɪɚɜɢɥɨ, ɢɧɞɟɤɫɨɦ j ɢɥɢ r (ɨɬ ɚɧɝɥɢɣɫɤɨɝɨ rotation), ɧɚɩɪɢɦɟɪ Dɋj (ɢɥɢ Dɋr). ȼɨɡɛɭɠɞɟɧɧɵɟ ɱɚɫɬɢɰɵ ɦɨɝɭɬ ɫɬɨɥɤɧɭɬɶɫɹ ɫ ɞɪɭɝɨɣ ɦɨɥɟɤɭɥɨɣ, ɚɬɨɦɨɦ, ɢɥɢ ɢɨɧɨɦ, ɩɟɪɟɞɚɬɶ ɢɦ ɜɫɸ ɷɧɟɪɝɢɸ ɜɨɡɛɭɠɞɟɧɢɹ (ɢɥɢ ɱɚɫɬɶ ɟɟ), ɢɥɢ ɜɵɞɟɥɢɬɶ ɷɧɟɪɝɢɸ ɜɨɡɛɭɠɞɟɧɢɹ ɜ ɜɢɞɟ ɤɜɚɧɬɚ (ɢɥɢ ɧɟɫɤɨɥɶɤɢɯ ɤɜɚɧɬɨɜ) ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɢɡɥɭɱɟɧɢɹ. Ɂɧɚɱɢɬ, ɩɨɹɜɥɟɧɢɟ ɜɨɡɛɭɠɞɟɧɧɵɯ ɱɚɫɬɢɰ ɨɛɹɡɚɬɟɥɶɧɨ ɫɨɩɪɨɜɨɠɞɚɟɬɫɹ ɩɨɹɜɥɟɧɢɟɦ ɤɜɚɧɬɨɜ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɢɡɥɭɱɟɧɢɹ - ɮɨɬɨɧɨɜ. Ɍɚɤ ɤɚɤ ɱɚɫɬɢɰ ɭɠɟ ɦɧɨɝɨ: ɦɨɥɟɤɭɥɵ, ɚɬɨɦɵ, ɦɨɥɟɤɭɥɹɪɧɵɟ ɢ ɚɬɨɦɚɪɧɵɟ ɢɨɧɵ (ɜ ɨɫɧɨɜɧɨɦ ɢ ɜ ɜɨɡɛɭɠɞɟɧɧɵɯ ɫɨɫɬɨɹɧɢɹɯ), ɷɥɟɤɬɪɨɧɵ, ɮɨɬɨɧɵ, ɬɨ ɱɢɫɥɨ ɜɨɡɦɨɠɧɵɯ ɜɡɚɢɦɨɞɟɣɫɬɜɢɣ ɫɬɚɧɨɜɢɬɫɹ ɨɱɟɧɶ ɛɨɥɶɲɢɦ ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɭɞɨɛɧɟɟ ɭɠɟ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɜɢɞɵ ɜɡɚɢɦɨɞɟɣɫɬɜɢɣ, ɢɯ ɜɨɡɦɨɠɧɨɫɬɶ (ɢɥɢ ɧɟɜɨɡɦɨɠɧɨɫɬɶ), ɚ ɩɪɢ ɜɨɡɦɨɠɧɨɫɬɢ - ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ ɢɥɢ ɢɧɨɝɨ ɩɪɨɰɟɫɫɚ. Ɍɚɤɭɸ ɫɨɜɨɤɭɩɧɨɫɬɶ ɫɜɨɛɨɞɧɵɯ ɡɚɪɹɠɟɧɧɵɯ ɢ ɧɟɣɬɪɚɥɶɧɵɯ ɱɚɫɬɢɰ ɢ ɤɜɚɧɬɨɜ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɢɡɥɭɱɟɧɢɹ ɚɦɟɪɢɤɚɧɫɤɢɣ ɮɢɡɢɤ Ʌɟɧɝɦɸɪ ɜ 1928 ɝ. ɧɚɡɜɚɥ ɩɥɚɡɦɨɣ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɥɚɡɦɚ - ɷɬɨ ɝɚɡ, ɧɨ ɝɚɡ ɫɩɟɰɢɮɢɱɟɫɤɢɣ: ɜ ɧɟɦ ɦɨɝɭɬ ɩɪɢɫɭɬɫɬɜɨɜɚɬɶ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ, ɨɱɟɧɶ ɫɢɥɶɧɨ ɪɚɡɥɢɱɚɸɳɢɟɫɹ ɩɨ ɦɚɫɫɟ (ɜ ɬɵɫɹɱɢ ɢ ɞɟɫɹɬɤɢ ɬɵɫɹɱ ɪɚɡ). ɇɚɩɪɢɦɟɪ, ɩɨɥɧɨɫɬɶɸ ɢɨɧɢɡɢɪɨɜɚɧɧɚɹ ɜɨɞɨɪɨɞɧɚɹ ɩɥɚɡɦɚ ɜ ɤɚɱɟɫɬɜɟ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɤɨɦɩɨɧɟɧɬɵ ɫɨɞɟɪɠɢɬ ɢɨɧɵ ɜɨɞɨɪɨɞɚ, ɬ.ɟ. “ɝɨɥɵɟ” ɩɪɨɬɨɧɵ, ɚ ɨɬɪɢɰɚɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɨɣ ɤɨɦɩɨɧɟɧɬɨɣ, ɧɟɣɬɪɚɥɢɡɭɸɳɟɣ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɡɚɪɹɞ ɩɪɨɬɨɧɨɜ, ɹɜɥɹɸɬɫɹ ɷɥɟɤɬɪɨɧɵ. Ʉɚɤ ɢɡɜɟɫɬɧɨ, ɦɚɫɫɵ ɷɬɢɯ ɱɚɫɬɢɰ mp = 1.67⋅10-24 ɝ , me = 0.91⋅10-27 ɝ, ɢ ɞɥɹ ɨɬɧɨɲɟɧɢɹ ɷɬɢɯ ɦɚɫɫ ɩɨɥɭɱɚɟɦ ɩɪɢɛɥɢɠɟɧɧɨ mp/me≅1836. Ɇɚɫɫɵ ɷɥɟɦɟɧɬɚɪɧɵɯ ɱɚɫɬɢɰ ɱɚɫɬɨ ɢɡɦɟɪɹɸɬ ɜ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɟɞɢɧɢɰɚɯ. Ⱦɥɹ ɷɥɟɤɬɪɨɧɚ ɢ ɩɪɨɬɨɧɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɜɟɥɢɱɢɧɵ ɪɚɜɧɵ meɫ2≅511ɤɷȼ, mɪɫ2≅938ɦɷȼ. ɋɬɨɥɤɧɨɜɟɧɢɹ ɱɚɫɬɢɰ ɞɪɭɝ ɫ ɞɪɭɝɨɦ ɩɪɢɧɹɬɨ ɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɫɟɱɟɧɢɹɦɢ ɫɬɨɥɤɧɨɜɟɧɢɣ σ . Ⱦɥɹ ɭɩɪɭɝɢɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɚɬɨɦɚɪɧɵɯ ɢɥɢ ɦɨɥɟɤɭɥɹɪɧɵɯ ɱɚɫɬɢɰ ɩɪɢ ɧɟɛɨɥɶɲɢɯ ɷɧɟɪɝɢɹɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɫɟɱɟɧɢɹ ɢɦɟɸɬ ɩɨɪɹɞɨɤ ɤɜɚɞɪɚɬɚ ɩɨɩɟɪɟɱɧɨɝɨ ɪɚɡɦɟɪɚ ɱɚɫɬɢɰ, ɚ ɞɥɹ ɫɬɨɥɤɧɨɜɟɧɢɣ ɦɟɞɥɟɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɫ ɚɬɨɦɨɦ − ɨɧɢ ɩɨɪɹɞɤɚ ɤɜɚɞɪɚɬɚ ɪɚɡɦɟɪɚ ɚɬɨɦɚ. ɇɚɩɪɢɦɟɪ, ɤɚɤ ɢɡɜɟɫɬɧɨ, ɪɚɡɦɟɪ ɚɬɨɦɚ ɜɨɞɨɪɨɞɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɞɢɭɫɨɦ Ȼɨɪɚ ɚB = 0.529⋅10-8ɫɦ, ɬɚɤ ɱɬɨ ɫɟɱɟɧɢɹ ɭɩɪɭɝɢɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɫɨɫɬɚɜɥɹɸɬ σ ɭɩɪ~10-16ɫɦ2. ɋɟɱɟɧɢɹ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ ɜ ɦɚɤɫɢɦɭɦɟ ɫɟɱɟɧɢɣ ɢɦɟɸɬ ɬɚɤɨɣ ɠɟ ɩɨɪɹɞɨɤ ɜɟɥɢɱɢɧɵ. ɉɪɢ ɷɬɨɦ ɧɚ ɩɨɪɨɝɟ ɢɨɧɢɡɚɰɢɢ, ɬɨ ɟɫɬɶ ɤɨɝɞɚ ɷɧɟɪɝɢɹ ɧɚɥɟɬɚɸɳɟɝɨ ɧɚ ɚɬɨɦ ɷɥɟɤɬɪɨɧɚ ɪɚɜɧɚ ɷɧɟɪɝɢɢ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚ, ɫɟɱɟɧɢɟ ɢɨɧɢɡɚɰɢɢ ɨɛɪɚɳɚɟɬɫɹ ɜ ɧɨɥɶ, ɡɚɬɟɦ ɩɨɫɥɟ ɩɪɨɯɨɠɞɟɧɢɹ ɦɚɤɫɢɦɭɦɚ ɭɛɵɜɚɟɬ ɫ ɪɨɫɬɨɦ ɷɧɟɪɝɢɢ ɫɬɨɥɤɧɨɜɟɧɢɹ. 2
ȼ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɩɪɢɜɟɞɟɦ ɮɨɪɦɭɥɭ, ɪɟɤɨɦɟɧɞɨɜɚɧɧɭɸ ɜ [5] ɞɥɹ ɨɰɟɧɤɢ ɜɟɥɢɱɢɧɵ ɫɟɱɟɧɢɹ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚɪɧɨɝɨ ɜɨɞɨɪɨɞɚ ɢɥɢ ɜɨɞɨɪɨɞɨɩɨɞɨɛɧɨɝɨ ɚɬɨɦɚ ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ: 2
nl § R· σi = π a ¨ ¸ Φ ( u ), © I ¹ 2l + 1 2 B
(1.1)
ɝɞɟ ɷɧɟɪɝɢɹ R=(Ɋɢɞɛɟɪɝ)≅13.6 ɷȼ – ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɚ ɧɚ ɩɟɪɜɨɦ ɛɨɪɨɜɫɤɨɦ ɪɚɞɢɭɫɟ ɚɬɨɦɚ ɜɨɞɨɪɨɞɚ, I- ɷɧɟɪɝɢɹ ɢɨɧɢɡɚɰɢɢ, nl ɱɢɫɥɨ ɷɤɜɢɜɚɥɟɧɬɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɜ ɨɛɨɥɨɱɤɟ ɚɬɨɦɚ, l ɨɪɛɢɬɚɥɶɧɨɟ ɤɜɚɧɬɨɜɨɟ ɱɢɫɥɨ, E -ɷɧɟɪɝɢɹ ɢɨɧɢɡɢɪɭɸɳɟɝɨ ɷɥɟɤɬɪɨɧɚ, ɚ u=(E-I)/I. Ɏɭɧɤɰɢɹ Ɏ(u) ɜ ɛɨɪɧɨɜɫɤɨɦ ɩɪɢɛɥɢɠɟɧɢɢ, ɫɩɪɚɜɟɞɥɢɜɨɦ, ɤɨɝɞɚ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɚ ɜɟɥɢɤɚ (u>1), ɪɚɜɧɚ
Φ ( u > 1) =
0.57 u + 1 . ln u + 1 0.012
(1.2)
ɋɟɱɟɧɢɹ ɢɨɧɢɡɚɰɢɢ ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ ɞɥɹ ɭɩɨɬɪɟɛɢɬɟɥɶɧɵɯ ɧɚ ɩɪɚɤɬɢɤɟ ɝɚɡɨɜ ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ. 1.1. Ɋɢɫ. 1.1. ɋɟɱɟɧɢɹ ɢɨɧɢɡɚɰɢɢ ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ ɢɡ ɨɫɧɨɜɧɨɝɨ ɫɨɫɬɨɹɧɢɹ
ɋɟɱɟɧɢɹ ɮɨɬɨɢɨɧɢɡɚɰɢɢ ɨɛɵɱɧɨ ɧɚ ɞɜɚ - ɬɪɢ ɩɨɪɹɞɤɚ ɧɢɠɟ ɫɟɱɟɧɢɣ ɢɨɧɢɡɚɰɢɢ ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ.
ȼ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɩɪɢɜɟɞɟɦ ɮɨɪɦɭɥɭ ɞɥɹ ɪɚɫɱɟɬɚ ɫɟɱɟɧɢɹ ɮɨɬɨɢɨɧɢɡɚɰɢɢ ɜɨɞɨɪɨɞɚ ɢɥɢ ɜɨɞɨɪɨɞɨɩɨɞɨɛɧɨɝɨ ɢɨɧɚ[5]: 4
σ ph ɝɞɟ
π 2 α a B2 § ωth · exp( −4κ arctgκ ) =2 , ¨ ¸ 3 Z 2 © ω ¹ 1 − exp( −2πκ )
α = 1137
9
- ɩɨɫɬɨɹɧɧɚɹ ɬɨɧɤɨɣ ɫɬɪɭɤɬɭɪɵ,
ω
κ=
ω ω − ωth
,
(1.3)
- ɤɪɭɝɨɜɚɹ ɱɚɫɬɨɬɚ ɮɨɬɨɧɚ, ɢɨɧɢɡɢɪɭɸɳɟɝɨ ɚɬɨɦ,
ωth - ɝɪɚɧɢɱɧɚɹ ɱɚɫɬɨɬɚ, ɧɢɠɟ ɤɨɬɨɪɨɣ ɢɨɧɢɡɚɰɢɹ ɧɟɜɨɡɦɨɠɧɚ. Ⱦɥɹ ɜɨɞɨɪɨɞɚ ɝɪɚɧɢɱɧɚɹ ɱɚɫɬɨɬɚ, ɢɡɦɟɪɟɧɧɚɹ ɜ ɨɛɪɚɬɧɵɯ ɫɚɧɬɢɦɟɬɪɚɯ, ɤɚɤ ɷɬɨ ɨɛɵɱɧɨ ɞɟɥɚɸɬ ɜ ɫɩɟɤɬɪɨɫɤɨɩɢɢ, ɪɚɜɧɚ 109678,758 ɫɦ-1. Ʌɸɛɨɩɵɬɧɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ, ɜ ɨɬɥɢɱɢɟ ɨɬ ɫɟɱɟɧɢɹ ɢɨɧɢɡɚɰɢɢ ɷɥɟɤɬɪɨɧɚɦɢ, ɫɟɱɟɧɢɟ ɮɨɬɨɧɧɨɣ ɢɨɧɢɡɚɰɢɢ ɧɟ ɨɛɪɚɳɚɟɬɫɹ ɜ ɧɨɥɶ ɧɚ ɩɨɪɨɝɟ, ɚ ɫɬɪɟɦɢɬɫɹ, ɤɚɤ ɥɟɝɤɨ ɩɪɨɜɟɪɢɬɶ, ɤ ɤɨɧɟɱɧɨɦɭ ɩɪɟɞɟɥɭ. Cɟɱɟɧɢɟ ɮɨɬɨɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚ ɜɨɞɨɪɨɞɚ ɮɨɬɨɧɚɦɢ, ɷɧɟɪɝɢɹ ɤɨɬɨɪɵɯ ɦɧɨɝɨ ɛɨɥɶɲɟ ɷɧɟɪɝɢɢ ɫɜɹɡɢ ɷɥɟɤɬɪɨɧɚ ɜ ɚɬɨɦɟ, ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɫ ɩɨɦɨɳɶɸ ɝɨɪɚɡɞɨ ɦɟɧɟɟ ɝɪɨɦɨɡɞɤɨɣ ɮɨɪɦɭɥɵ [6]: /2 σ ph [ ɫɦ 2 ] = 23.8 λ7[ ɫɦ ].
ɋɟɱɟɧɢɟ ɮɨɬɨɢɨɧɢɡɚɰɢɢ ɞɥɹ ɫɢɥɶɧɨɜɨɡɛɭɠɞɟɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɫ ɝɥɚɜɧɵɦ ɤɜɚɧɬɨɜɵɦ ɱɢɫɥɨɦ n ɭɦɟɧɶɲɚɟɬɫɹ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ n−5.
ɇɚɤɨɧɟɰ. ɨɬɦɟɬɢɦ, ɱɬɨ ɞɥɹ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ (ɩɨɥɟɜɚɹ ɢɨɧɢɡɚɰɢɹ) ɩɨɪɨɝɨɜɨɟ ɡɧɚɱɟɧɢɟ ɩɨɥɹ ɫɨɫɬɚɜɥɹɟɬ E ~ 108 ȼ/ɫɦ, ɚ ɢɨɧɢɡɚɰɢɹ ɢɡ ɜɨɡɛɭɠɞɟɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɜɨɡɦɨɠɧɚ ɩɪɢ ɦɟɧɶɲɢɯ ɩɨɥɹɯ E ~ 106 ȼ/ɫɦ.
3
§2. Ʉɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɶ, ɩɥɚɡɦɟɧɧɚɹ ɱɚɫɬɨɬɚ ɉɥɚɡɦɚ ɜ ɰɟɥɨɦ ɞɨɥɠɧɚ ɛɵɬɶ ɷɥɟɤɬɪɢɱɟɫɤɢ ɧɟɣɬɪɚɥɶɧɚ, ɤɨɥɢɱɟɫɬɜɚ ɪɚɡɧɨɢɦɟɧɧɵɯ ɡɚɪɹɞɨɜ ɜ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɣ ɟɞɢɧɢɰɟ ɟɟ ɨɛɴɟɦɚ ɪɚɜɧɵ. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɜɨɡɧɢɤɧɭɬ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɩɨɥɹ, ɬɟɦ ɛɨɥɶɲɢɟ, ɱɟɦ ɛɨɥɶɲɟ ɞɢɫɛɚɥɚɧɫ ɡɚɪɹɞɨɜ, ɚ ɫɨɡɞɚɧɢɟ ɬɚɤɢɯ ɩɨɥɟɣ ɬɪɟɛɭɟɬ ɫɨɜɟɪɲɟɧɢɹ ɪɚɛɨɬɵ ɩɨ ɪɚɡɞɟɥɟɧɢɸ ɡɚɪɹɞɨɜ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɜɧɟɲɧɢɯ ɜɨɡɞɟɣɫɬɜɢɣ ɷɬɚ ɪɚɛɨɬɚ ɦɨɠɟɬ ɩɪɨɢɡɜɨɞɢɬɶɫɹ ɬɨɥɶɤɨ ɡɚ ɫɱɟɬ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɫɚɦɢɯ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ. ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɜ ɧɟɤɨɬɨɪɨɦ ɨɛɴɟɦɟ ɮɥɭɤɬɭɚɬɢɜɧɨ ɪɚɡɨɲɥɢɫɶ ɡɚɪɹɞɵ (ɪɢɫ.1.2, ɫɱɢɬɚɟɦ, ɱɬɨ ɢɨɧɵ ɩɨɤɨɹɬɫɹ, ɚ ɷɥɟɤɬɪɨɧɵ ɭɯɨɞɹɬ), ɢ ɨɰɟɧɢɦ ɦɚɤɫɢɦɚɥɶɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɬɚɤɨɝɨ Ɋɢɫ. 1.2. ɋɯɟɦɚ ɪɚɡɞɟɥɟɧɢɹ ɡɚɪɹɞɨɜ ɪɚɫɯɨɠɞɟɧɢɹ. Ɋɚɫɯɨɞɹɳɢɟɫɹ ɧɚ ɪɚɫɫɬɨɹɧɢɟ x ɡɚɪɹɞɵ ɫɨɡɞɚɸɬ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ȿ=4πnex. Ɂɞɟɫɶ n - ɤɨɧɰɟɧɬɪɚɰɢɹ ɩɥɚɡɦɵ, ɚ ɟ - ɷɥɟɦɟɧɬɚɪɧɵɣ ɡɚɪɹɞ (ɪɚɜɧɵɣ ɩɨ ɜɟɥɢɱɢɧɟ ɡɚɪɹɞɭ ɷɥɟɤɬɪɨɧɚ). ɋɢɥɚ ɫɨ ɫɬɨɪɨɧɵ ɩɨɥɹ, ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɷɥɟɦɟɧɬɚɪɧɵɣ ɡɚɪɹɞ, ɪɚɜɧɚ ɟȿ; ɪɚɛɨɬɚ ɩɨ ɪɚɡɞɟɥɟɧɢɸ ɡɚɪɹɞɨɜ ɧɚ ɪɚɫɫɬɨɹɧɢɟ d ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɨɣ: d
A = ³ eEdx = 0
4π ⋅ e 2 n 2 d , 2
(1.4)
ɢ ɨɧɚ ɧɟ ɦɨɠɟɬ ɩɪɟɜɵɲɚɬɶ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɬɟɩɥɨɜɨɝɨ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰɵ, ɞɥɹ ɨɞɧɨɦɟɪɧɨɝɨ ɞɜɢɠɟɧɢɹ, ɤɚɤ ɢɡɜɟɫɬɧɨ, ɪɚɜɧɭɸ (1/2)Ɍ (ɡɞɟɫɶ, ɤɚɤ ɷɬɨ ɱɚɫɬɨ ɞɟɥɚɟɬɫɹ ɞɥɹ ɤɪɚɬɤɨɫɬɢ, ɦɵ ɢɫɩɨɥɶɡɭɟɦ ɨɛɨɡɧɚɱɟɧɢɟ Ɍ ɜɦɟɫɬɨ ɩɪɨɢɡɜɟɞɟɧɢɹ kȻT, ɢɡɦɟɪɹɹ, ɬɟɦ ɫɚɦɵɦ, ɬɟɦɩɟɪɚɬɭɪɭ ɜ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɟɞɢɧɢɰɚɯ). Ɉɬɫɸɞɚ
d=
T . 4πne 2
(1.5)
ɇɚ ɦɚɫɲɬɚɛɚɯ, ɦɟɧɶɲɢɯ d, ɜɫɟɝɞɚ ɛɭɞɭɬ ɜɨɡɧɢɤɚɬɶ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɩɨɥɹ; ɮɥɭɤɬɭɚɰɢɢ ɧɟɢɡɛɟɠɧɵ. Ⱥ ɜɨɬ ɪɚɡɨɣɬɢɫɶ ɧɚ ɪɚɫɫɬɨɹɧɢɹ, ɫɭɳɟɫɬɜɟɧɧɨ ɛɨɥɶɲɢɟ ɱɟɦ d, ɱɚɫɬɢɰɵ ɧɟ ɦɨɝɭɬ. ɉɨɷɬɨɦɭ ɩɥɚɡɦɚ ɢ ɹɜɥɹɟɬɫɹ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɣ - ɧɟɣɬɪɚɥɶɧɚɹ ɜ ɛɨɥɶɲɢɯ ɨɛɴɟɦɚɯ, ɧɨ ɜɫɟɝɞɚ ɫ ɷɥɟɤɬɪɢɱɟɫɤɢɦɢ ɩɨɥɹɦɢ ɧɚ ɪɚɫɫɬɨɹɧɢɹɯ ɦɚɫɲɬɚɛɚ d, ɡɚɜɢɫɹɳɟɝɨ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ. ȼɟɥɢɱɢɧɭ d ɨɛɵɱɧɨ ɧɚɡɵɜɚɸɬ ɞɟɛɚɟɜɫɤɢɦ ɪɚɞɢɭɫɨɦ (ɫɦ. ɫɥɟɞɭɸɳɢɣ ɩɚɪɚɝɪɚɮ). Ⱦɥɹ ɬɟɪɦɨɹɞɟɪɧɨɣ ɩɥɚɡɦɵ ɫ ɩɚɪɚɦɟɬɪɚɦɢ n≅1014ɫɦ-3, Ɍ≅104ɷȼ, ɩɨɥɭɱɚɟɦ d≅5⋅10-3ɫɦ. ɗɥɟɤɬɪɢɱɟɫɤɢɟ ɩɨɥɹ ɪɚɡɞɟɥɟɧɢɹ ɡɚɪɹɞɨɜ ɛɭɞɭɬ ɞɟɣɫɬɜɨɜɚɬɶ ɧɚ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ. ɉɨɥɚɝɚɹ, ɱɬɨ ɢɨɧɵ ɩɨɤɨɹɬɫɹ, ɪɚɫɫɦɨɬɪɢɦ ɞɜɢɠɟɧɢɟ ɧɟɤɨɬɨɪɨɝɨ ɜɵɞɟɥɟɧɧɨɝɨ ɷɥɟɤɬɪɨɧɚ ɜ ɬɚɤɨɦ ɨɞɧɨɦɟɪɧɨɦ ɩɨɥɟ ȿ (ɫɦ. ɪɢɫ. 1.2). ɍɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɧɚ ɨɤɚɡɵɜɚɟɬɫɹ ɫɥɟɞɭɸɳɢɦ
me x = − eE = −4πne 2 x ,
(1.6)
ɢ ɫɨɜɩɚɞɚɟɬ ɩɨ ɜɢɞɭ ɫ ɭɪɚɜɧɟɧɢɟɦ ɞɜɢɠɟɧɢɹ ɞɥɹ ɨɞɧɨɦɟɪɧɨɝɨ ɨɫɰɢɥɥɹɬɨɪɚ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɷɥɟɤɬɪɨɧ ɛɭɞɟɬ ɫɨɜɟɪɲɚɬɶ ɤɨɥɟɛɚɧɢɹ ɫ ɱɚɫɬɨɬɨɣ
ωp =
4πne 2 . me
(1.7)
ɗɬɭ ɱɚɫɬɨɬɭ, ɹɜɥɹɸɳɭɸɫɹ ɯɚɪɚɤɬɟɪɧɨɣ ɨɫɨɛɟɧɧɨɫɬɶɸ ɩɥɚɡɦɵ, ɧɚɡɵɜɚɸɬ ɩɥɚɡɦɟɧɧɨɣ (ɢ ɨɛɨɡɧɚɱɚɸɬ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɤɚɤ ωɪ ɢɥɢ ω0) ɢɥɢ ɷɥɟɤɬɪɨɧɧɨɣ ɥɟɧɝɦɸɪɨɜɫɤɨɣ ɱɚɫɬɨɬɨɣ (ɢ ɨɛɨɡɧɚɱɚɸɬ ɤɚɤ ωLe). ɋɥɟɞɭɟɬ ɩɨɞɱɟɪɤɧɭɬɶ, ɱɬɨ ɨɧɚ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ.
Ⱦɥɹ ɬɟɪɦɨɹɞɟɪɧɨɣ ɩɥɚɡɦɵ ɫ ɩɥɨɬɧɨɫɬɶɸ n≅1014ɫɦ-3 ɱɚɫɬɨɬɚ ɥɟɧɝɦɸɪɨɜɫɤɢɯ ɤɨɥɟɛɚɧɢɣ ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɨɣ ωp≅6⋅1011c-1.
§ 3. Ⱦɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ, ɞɟɛɚɟɜɫɤɢɣ ɫɥɨɣ Ʉɚɠɞɚɹ ɡɚɪɹɠɟɧɧɚɹ ɱɚɫɬɢɰɚ ɜ ɩɥɚɡɦɟ ɜɡɚɢɦɨɞɟɣɫɬɜɭɟɬ ɫ ɞɪɭɝɢɦɢ ɡɚɪɹɠɟɧɧɵɦɢ ɱɚɫɬɢɰɚɦɢ. ɉɨɷɬɨɦɭ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ϕ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜɵɞɟɥɟɧɧɨɣ ɱɚɫɬɢɰɵ ɢ ɨɤɪɭɠɚɸɳɢɯ ɟɺ ɱɚɫɬɢɰ ɡɚɜɢɫɢɬ ɨɬ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɝɨ ɪɚɫɩɨɥɨɠɟɧɢɹ ɷɬɢɯ ɱɚɫɬɢɰ. ȼ ɩɨɥɟ ɞɚɧɧɨɣ ɱɚɫɬɢɰɵ ɩɥɨɬɧɨɫɬɶ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɪɚɜɧɨɜɟɫɢɢ ɞɨɥɠɧɚ ɛɵɬɶ ɪɚɫɩɪɟɞɟɥɟɧɚ ɩɨ ɡɚɤɨɧɭ Ȼɨɥɶɰɦɚɧɚ § eϕ · (1.8) n = n0 exp¨ − ¸ , © T ¹ ɝɞɟ n0 – ɤɨɧɰɟɧɬɪɚɰɢɹ ɱɚɫɬɢɰ ɧɟɜɨɡɦɭɳɟɧɧɨɣ ɩɥɚɡɦɵ ɜɞɚɥɢ ɨɬ ɜɵɞɟɥɟɧɧɨɣ ɱɚɫɬɢɰɵ, ϕ ɩɨɬɟɧɰɢɚɥ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ. ɇɚɩɢɲɟɦ ɬɟɩɟɪɶ ɭɪɚɜɧɟɧɢɟ ɉɭɚɫɫɨɧɚ (ɜ ɫɮɟɪɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ) ɞɥɹ ɩɨɥɹ ɱɚɫɬɢɰ ɩɥɚɡɦɵ, ɨɤɪɭɠɚɸɳɢɯ ɜɵɞɟɥɟɧɧɭɸ ɱɚɫɬɢɰɭ: 1 ∂2 ( rϕ ) = −4πe( Zni − ne ) , r ∂r 2 ɝɞɟ ni,e – ɤɨɧɰɟɧɬɪɚɰɢɹ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɩɥɚɡɦɵ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, Z – ɤɪɚɬɧɨɫɬɶ ɢɨɧɢɡɚɰɢɢ ɢɨɧɚ ɩɥɚɡɦɵ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɧɨɫɬɢ ɫɱɢɬɚɟɦ, ɱɬɨ ɩɥɚɡɦɚ ɫɨɫɬɨɢɬ ɢɡ ɷɥɟɤɬɪɨɧɨɜ ɢ ɨɞɢɧɚɤɨɜɵɯ ɩɨɥɨɠɢɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɵɯ ɢɨɧɨɜ ɫ ɨɞɢɧɚɤɨɜɨɣ ɤɪɚɬɧɨɫɬɶɸ ɢɨɧɢɡɚɰɢɢ. Ⱦɥɹ ɦɧɨɝɨɤɨɦɩɨɧɟɧɬɧɨɣ ɩɥɚɡɦɵ ɫ ɢɨɧɚɦɢ ɪɚɡɧɵɯ ɫɨɪɬɨɜ ɢ ɫ ɪɚɡɧɨɣ ɤɪɚɬɧɨɫɬɶɸ ɢɨɧɢɡɚɰɢɢ ɧɟɨɛɯɨɞɢɦɨ ɛɵɥɨ ɛɵ ɜ ɩɪɚɜɨɣ ɱɚɫɬɢ ɩɪɨɢɡɜɨɞɢɬɶ ɫɭɦɦɢɪɨɜɚɧɢɟ ɩɨ ɜɫɟɦ ɫɨɪɬɚɦ ɢ ɜɫɟɦ ɤɪɚɬɧɨɫɬɹɦ ɢɨɧɢɡɚɰɢɢ ɱɚɫɬɢɰ. ɋɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɨɛɨɛɳɟɧɢɟ ɨɱɟɜɢɞɧɨ ɢ ɦɨɠɟɬ ɛɵɬɶ ɛɟɡ ɬɪɭɞɚ ɩɨɥɭɱɟɧɨ, ɩɨɷɬɨɦɭ, ɱɬɨɛɵ ɧɟ ɭɫɥɨɠɧɹɬɶ ɮɨɪɦɵ ɡɚɩɢɫɢ ɨɤɨɧɱɚɬɟɥɶɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ, ɡɞɟɫɶ ɨɝɪɚɧɢɱɢɦɫɹ ɭɤɚɡɚɧɧɨɣ ɩɪɨɫɬɨɣ ɦɨɞɟɥɶɸ ɞɜɭɯɤɨɦɩɨɧɟɧɬɧɨɣ ɢɨɧ-ɷɥɟɤɬɪɨɧɧɨɣ ɩɥɚɡɦɵ.
ɍɱɬɟɦ, ɱɬɨ ɩɥɨɬɧɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ ɜ ɩɨɥɟ ɜɵɞɟɥɟɧɧɨɣ ɱɚɫɬɢɰɵ ɩɨɞɱɢɧɹɸɬɫɹ ɡɚɤɨɧɭ Ȼɨɥɶɰɦɚɧɚ (1.8), ɢ ɩɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɬɟɦɩɟɪɚɬɭɪɵ Ɍe ɢ Ɍi ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ ɩɥɚɡɦɵ ɦɨɝɭɬ ɛɵɬɶ ɪɚɡɧɵɦɢ. Ɉɝɪɚɧɢɱɢɜɚɹɫɶ ɥɢɧɟɣɧɵɦ ɩɪɢɛɥɢɠɟɧɢɟɦ, ɬ.ɟ. ɫɱɢɬɚɹ |eϕ|<
q r
ϕ = e −r d ,
(1.11)
ɝɞɟ q - ɡɚɪɹɞ ɜɵɞɟɥɟɧɧɨɣ ɧɚɦɢ “ɩɪɨɛɧɨɣ” ɱɚɫɬɢɰɵ. ȿɫɥɢ ɷɬɨ ɩɨɥɨɠɢɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɵɣ ɢɨɧ ɫ ɤɪɚɬɧɨɫɬɶɸ ɢɨɧɢɡɚɰɢɢ Z, ɬɨ q=Z|e|. ȼɛɥɢɡɢ ɱɚɫɬɢɰɵ, ɧɚ ɪɚɫɫɬɨɹɧɢɹɯ r<>d ɩɨɥɟ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨ ɛɵɫɬɪɨ ɡɚɬɭɯɚɟɬ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɝɨɜɨɪɹɬ, ɱɬɨ ɧɚ ɬɚɤɢɯ ɪɚɫɫɬɨɹɧɢɹɯ ɨɬ ɱɚɫɬɢɰɵ ɩɥɚɡɦɚ ɷɤɪɚɧɢɪɭɟɬ ɫɨɡɞɚɜɚɟɦɨɟ ɱɚɫɬɢɰɟɣ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ. ɉɨɷɬɨɦɭ ɭɪɚɜɧɟɧɢɟ (1.9) ɢɧɨɝɞɚ ɧɚɡɵɜɚɸɬ ɭɪɚɜɧɟɧɢɟɦ ɷɤɪɚɧɢɪɨɜɤɢ.
ɉɨɦɟɫɬɢɦ ɜ ɩɥɚɡɦɭ ɩɥɨɫɤɢɣ ɷɥɟɤɬɪɨɞ, ɢɦɟɸɳɢɣ ɩɨɬɟɧɰɢɚɥ ϕ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɞɪɭɝɨɦɭ ɩɥɨɫɤɨɦɭ ɷɥɟɤɬɪɨɞɭ, ɭɞɚɥɟɧɧɨɦɭ ɨɬ ɩɟɪɜɨɝɨ ɧɚ ɪɚɫɫɬɨɹɧɢɟ x>>d (ɪɢɫ.1.3). ɉɪɢɦɟɦ ɞɥɹ ɩɪɨɫɬɨɬɵ, ɱɬɨ ɩɥɚɡɦɚ ɹɜɥɹɟɬɫɹ ɢɡɨɬɟɪɦɢɱɟɫɤɨɣ Ɍe=Ɍi, ɢ ɫɨɫɬɨɢɬ ɢɡ ɷɥɟɤɬɪɨɧɨɜ ɢ ɨɞɧɨɡɚɪɹɞɧɵɯ ɢɨɧɨɜ ɫ ɤɪɚɬɧɨɫɬɶɸ ɢɨɧɢɡɚɰɢɢ Z=1, ɬɚɤ ɱɬɨ ɭɫɥɨɜɢɟ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɢ ɡɚɩɢɫɵɜɚɟɬɫɹ ɬɟɩɟɪɶ ɜ ɜɢɞɟ noi=noe=no. Ɍɨɝɞɚ ɭɪɚɜɧɟɧɢɟ ɉɭɚɫɫɨɧɚ ɞɥɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨɬɟɧɰɢɚɥɚ ɜɛɥɢɡɢ ɷɥɟɤɬɪɨɞɚ ɫ ɭɱɟɬɨɦ (1.8) ɛɭɞɟɬ ɫɥɟɞɭɸɳɢɦ: dE d 2ϕ § eϕ · = − 2 = 4πe( ni − ne ) = −8πen0 sh¨ ¸ . (1.12) © T ¹ dx dx ɉɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɨɫɶ ɯ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɚ ɤ ɷɥɟɤɬɪɨɞɭ. Ɋɟɲɟɧɢɟ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ, ɱɬɨ eϕ/T<<1, ɢɦɟɟɬ ɫɥɟɞɭɸɳɢɣ ɜɢɞ: E = Eoe-x/d, ɝɞɟ Eo - ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɩɨɥɹ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɩɥɚɫɬɢɧɵ, ɪɚɫɩɨɥɨɠɟɧɧɨɣ ɩɪɢ ɯ=0 [7]. Ɇɵ ɜɢɞɢɦ, ɱɬɨ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɩɪɨɧɢɤɚɸɳɟɝɨ ɜ ɩɥɚɡɦɭ, ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨ ɛɵɫɬɪɨ ɡɚɬɭɯɚɟɬ. ɏɚɪɚɤɬɟɪɧɨɣ ɜɟɥɢɱɢɧɨɣ Ɋɢɫ.1.3. ɋɯɟɦɚ ɪɚɫɩɨɥɨɠɟɧɢɹ ɞɥɢɧɵ ɡɚɬɭɯɚɧɢɹ ɹɜɥɹɟɬɫɹ ɪɚɞɢɭɫ Ⱦɟɛɚɹ: ɷɥɟɤɬɪɨɞɨɜ
T . (1.13) 8πne 2 Ȼɨɥɟɟ ɫɥɨɠɧɚɹ ɤɚɪɬɢɧɚ ɜɨɡɧɢɤɚɟɬ, ɟɫɥɢ ɜ ɩɥɚɡɦɭ ɩɨɦɟɳɟɧɨ ɢɡɨɥɢɪɨɜɚɧɧɨɟ ɧɟɡɚɪɹɠɟɧɧɨɟ ɬɟɥɨ (ɧɚɩɪɢɦɟɪ, ɩɥɚɫɬɢɧɚ, ɫɦ. ɪɢɫ. 1.4). Ɍɚɤɨɟ ɬɟɥɨ ɜ ɩɥɚɡɦɟ ɞɨɥɠɧɨ ɡɚɪɹɠɚɬɶɫɹ, ɩɪɢɱɟɦ, ɜɜɢɞɭ ɝɨɪɚɡɞɨ ɛɨɥɶɲɟɣ ɩɨɞɜɢɠɧɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ, ɨɛɵɱɧɨ ɨɧɨ ɩɪɢɨɛɪɟɬɚɟɬ ɨɬɪɢɰɚɬɟɥɶɧɵɣ - ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ ɩɥɚɜɚɸɳɢɣ – ɩɨɬɟɧɰɢɚɥ. ȼɛɥɢɡɢ ɩɥɚɫɬɢɧɵ, ɤɚɤ ɩɨɤɚɡɵɜɚɸɬ ɱɢɫɥɟɧɧɵɟ ɪɚɫɱɟɬɵ [8], ɜɨɡɧɢɤɚɟɬ ɫɥɨɠɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ, ɤɚɱɟɫɬɜɟɧɧɨ ɩɨɤɚɡɚɧɧɨɟ ɧɚ ɪɢɫ. 1.4. ȼɛɥɢɡɢ ɩɥɚɫɬɢɧɵ, ɤɚɤ ɢ ɜ ɩɪɟɞɵɞɭɳɟɦ ɩɪɢɦɟɪɟ, ɜɨɡɧɢɤɚɟɬ ɞɟɛɚɟɜɫɤɢɣ ɫɥɨɣ ɫ ɫɭɳɟɫɬɜɟɧɧɵɦ ɪɚɡɞɟɥɟɧɢɟɦ ɡɚɪɹɞɚ. Ɋɚɡɦɟɪ ɷɬɨɝɨ ɫɥɨɹ ɩɪɢɦɟɪɧɨ ɪɚɜɟɧ ɞɟɛɚɟɜɫɤɨɦɭ ɪɚɞɢɭɫɭ (1.10). Ɋɢɫ. 1.4. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɜɛɥɢɡɢ Ɉɞɧɚɤɨ ɩɨɥɟ, ɫɨɝɥɚɫɧɨ ɪɟɡɭɥɶɬɚɬɚɦ ɪɚɫɱɟɬɨɜ, ɩɨɦɟɳɟɧɧɨɣ ɜ ɩɥɚɡɦɭ ɩɥɚɫɬɢɧɵ. ɩɪɨɧɢɤɚɟɬ ɜ ɩɥɚɡɦɭ ɝɨɪɚɡɞɨ ɞɚɥɶɲɟ, ɨɛɪɚɡɭɹ ɜɛɥɢɡɢ ɩɥɚɫɬɢɧɵ “ɩɪɟɞɫɥɨɣ” ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɣ ɩɥɚɡɦɵ. Ɍɟɨɪɢɹ ɷɬɨɣ ɫɬɪɭɤɬɭɪɵ ɫɥɨɠɧɚ ɢ ɡɞɟɫɶ ɟɟ ɨɛɫɭɠɞɚɬɶ ɧɟ ɛɭɞɟɦ. ɉɥɚɜɚɸɳɢɣ ɩɨɬɟɧɰɢɚɥ, ɤɨɬɨɪɵɣ ɩɪɢɨɛɪɟɬɚɟɬ ɬɟɥɨ, ɯɨɪɨɲɨ ɨɩɢɫɵɜɚɟɬɫɹ ɮɨɪɦɭɥɨɣ d=
§m T · 1 Te ln¨ i e ¸ . (1.14) 2 © me Ti ¹ Ɍɚɤɨɣ ɪɟɡɭɥɶɬɚɬ ɧɟɫɥɨɠɧɨ ɩɨɥɭɱɢɬɶ ɢɡ ɫɥɟɞɭɸɳɢɯ ɩɪɨɫɬɵɯ ɫɨɨɛɪɚɠɟɧɢɣ. ȿɫɥɢ ɫ ɬɟɱɟɧɢɟɦ ɜɪɟɦɟɧɢ ɩɨɬɟɧɰɢɚɥ ɢɡɨɥɢɪɨɜɚɧɧɨɣ ɩɥɚɫɬɢɧɵ ɩɟɪɟɫɬɚɟɬ ɦɟɧɹɬɶɫɹ, ɬɨ ɷɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɬɨɤɢ ɩɪɢɯɨɞɹɳɢɯ ɧɚ ɧɟɟ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɡɚɪɹɞɨɜ ɤɨɦɩɟɧɫɢɪɭɸɬɫɹ. Ɉɰɟɧɢɜɚɹ ɩɥɨɬɧɨɫɬɶ ɩɨɬɨɤɚ ɢɨɧɨɜ ɜɞɚɥɢ ɨɬ ɬɟɥɚ ɤɚɤ 1 ji = n0 vTi , 4 ɚ ɩɥɨɬɧɨɫɬɶ ɩɨɬɨɤɚ ɷɥɟɤɬɪɨɧɨɜ ɫ ɭɱɟɬɨɦ ɢɯ ɬɨɪɦɨɠɟɧɢɹ “ɧɚ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɝɨɪɤɟ” ɤɚɤ eϕ0 =
§ eϕ0 1 n0 v Te exp¨¨ − 4 © Te
· ¸, ¸ ¹ ɢ ɩɪɢɪɚɜɧɢɜɚɹ ɢɯ, ɩɪɢɯɨɞɢɦ ɤ ɮɨɪɦɭɥɟ (1.14). ȼɟɪɧɟɦɫɹ ɤ ɮɨɪɦɭɥɟ (1.10). ȿɫɥɢ ɜ ɧɟɣ ɩɨɥɨɠɢɬɶ, ɱɬɨ ne=ni ɢ Te=Ti, ɬɨ ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɟ (1.13). ȿɫɥɢ ɠɟ ɫɱɢɬɚɬɶ, ɱɬɨ ɩɥɚɡɦɚ ɹɜɥɹɟɬɫɹ ɫɢɥɶɧɨ ɧɟɢɡɨɬɟɪɦɢɱɟɫɤɨɣ, ɬɚɤ ɱɬɨ Ti>>Ɍe, ɬɨ ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɟ, ɫɨɜɩɚɞɚɸɳɟɟ ɫ ɮɨɪɦɭɥɨɣ (1.5) (ɬɟɩɟɪɶ c ɬɟɦɩɟɪɚɬɭɪɨɣ Ɍe ɜ ɤɚɱɟɫɬɜɟ Ɍ), ɢ ɨɬɥɢɱɚɸɳɟɟɫɹ ɨɬ ɜɵɪɚɠɟɧɢɹ, ɨɩɪɟɞɟɥɹɟɦɨɝɨ ɮɨɪɦɭɥɨɣ (1.13), ɜɫɟɝɨ ɜ 2 ɪɚɡ. ɉɨɷɬɨɦɭ ɜ ɥɸɛɨɣ ɩɥɚɡɦɟ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɟ ɦɚɫɲɬɚɛɵ ɷɤɪɚɧɢɪɨɜɚɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɨɥɟɣ ɢ ɮɥɭɤɬɭɚɬɢɜɧɨɝɨ ɪɚɡɞɟɥɟɧɢɹ ɡɚɪɹɞɨɜ ɩɪɢɦɟɪɧɨ ɨɞɢɧɚɤɨɜɵ. ɉɪɢ ɷɬɨɦ ɪɚɞɢɭɫ ɷɤɪɚɧɢɪɨɜɚɧɢɹ ɩɨɥɹ ɩɪɨɛɧɨɝɨ ɡɚɪɹɞɚ ɢɥɢ ɞɥɢɧɚ ɫɥɨɹ ɷɤɪɚɧɢɪɨɜɚɧɢɹ ɜɧɟɲɧɟɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɫɨɜɩɚɞɚɸɬ. Ɍɚɤ ɠɟ, ɤɚɤ ɢ ɧɚɥɢɱɢɟ ɥɟɧɝɦɸɪɨɜɫɤɢɯ ɤɨɥɟɛɚɧɢɣ ɫ ɩɥɚɡɦɟɧɧɨɣ ɱɚɫɬɨɬɨɣ, ɷɤɪɚɧɢɪɨɜɚɧɢɟ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɨɥɟɣ - ɜɚɠɧɚɹ ɯɚɪɚɤɬɟɪɧɚɹ ɨɫɨɛɟɧɧɨɫɬɶ ɩɥɚɡɦɵ.
je =
ɉɨɞɱɟɪɤɧɟɦ ɜ ɡɚɤɥɸɱɟɧɢɟ ɟɳɟ ɨɞɧɨ ɜɚɠɧɨɟ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ. ȼ ɩɪɟɞɵɞɭɳɟɦ ɩɚɪɚɝɪɚɮɟ ɩɪɢ ɜɵɜɨɞɟ ɮɨɪɦɭɥɵ ɞɥɹ ɥɟɧɝɦɸɪɨɜɫɤɨɣ ɱɚɫɬɨɬɵ ɩɪɟɧɟɛɪɟɝɚɥɨɫɶ ɜɨɡɦɨɠɧɨɫɬɶɸ ɜɨɜɥɟɱɟɧɢɹ ɜ ɞɜɢɠɟɧɢɟ ɢɨɧɨɜ, ɩɪɨɫɬɨ ɤɚɤ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɟɟ ɦɚɫɫɢɜɧɨɣ ɤɨɦɩɨɧɟɧɬɵ ɩɥɚɡɦɵ. ɇɟɬɪɭɞɧɨ ɨɬɤɚɡɚɬɶɫɹ ɨɬ ɷɬɨɝɨ ɩɪɟɞɩɨɥɨɠɟɧɢɹ ɢ ɮɚɤɬɢɱɟɫɤɢ ɩɨɜɬɨɪɹɹ ɷɬɨɬ ɜɵɜɨɞ, ɧɨ, ɭɱɢɬɵɜɚɹ ɬɟɩɟɪɶ ɤɨɧɟɱɧɨɫɬɶ ɨɬɧɨɲɟɧɢɹ ɦɚɫɫ ɱɚɫɬɢɰ, ɦɨɠɧɨ ɩɨɤɚɡɚɬɶ, ɱɬɨ ɩɨɥɧɚɹ ɮɨɪɦɭɥɚ, ɜɦɟɫɬɨ (1.7), ɞɥɹ ɱɚɫɬɨɬɵ ɩɥɚɡɦɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ ɨɤɚɡɵɜɚɟɬɫɹ ɫɥɟɞɭɸɳɟɣ:
ω p = ω Le2 + ω Li2 , ω Le =
4πe 2 ne , ω Li = me
4πZ 2 e 2 ni , mi
ɝɞɟ ωLe,Li ɦɨɠɧɨ ɧɚɡɜɚɬɶ «ɷɥɟɤɬɪɨɧɧɨɣ» ɢ «ɢɨɧɧɨɣ» ɥɟɧɝɦɸɪɨɜɫɤɢɦɢ ɱɚɫɬɨɬɚɦɢ. ɑɬɨɛɵ ɩɨɞɱɟɪɤɧɭɬɶ, ɤɚɤɢɦ ɨɛɪɚɡɨɦ ɜɯɨɞɹɬ ɩɚɪɚɦɟɬɪɵ ɤɨɦɩɨɧɟɧɬ ɩɥɚɡɦɵ ɜ ɮɨɪɦɭɥɭ (1.10) ɞɥɹ ɞɟɛɚɟɜɫɤɨɝɨ ɪɚɞɢɭɫɚ, ɩɟɪɟɩɢɲɟɦ ɟɟ ɜ ɜɢɞɟ:
1 = d
1 1 2 + 2 , rDe = rDe rDi
Te ,r = 4πe 2 ne Di
Ti , 4πZ 2 e 2 ni
ɝɞɟ rDe,i – «ɷɥɟɤɬɪɨɧɧɵɣ» ɢ «ɢɨɧɧɵɣ» ɞɟɛɚɟɜɫɤɢɟ ɪɚɞɢɭɫɵ. Ʉɚɤ ɦɵ ɜɢɞɢɦ, ɨɛɟ ɤɨɦɩɨɧɟɧɬɵ ɩɥɚɡɦɵ ɞɚɸɬ ɜɤɥɚɞ ɢ ɜ ɩɥɚɡɦɟɧɧɭɸ ɱɚɫɬɨɬɭ ɢ ɜ ɪɚɞɢɭɫ ɷɤɪɚɧɢɪɨɜɚɧɢɹ. ɇɨ ɷɬɨɬ ɜɤɥɚɞ ɨɤɚɡɵɜɚɟɬɫɹ ɧɟɨɞɢɧɚɤɨɜɵɦ: ɜ ɜɟɥɢɱɢɧɭ ɪɚɞɢɭɫɚ ɷɤɪɚɧɢɪɨɜɚɧɢɹ ɩɪɢ ɫɨɩɨɫɬɚɜɢɦɵɯ ɤɨɧɰɟɧɬɪɚɰɢɹɯ ɢ ɬɟɦɩɟɪɚɬɭɪɚɯ ɢɨɧɵ ɢ ɷɥɟɤɬɪɨɧɵ ɩɥɚɡɦɵ ɞɚɸɬ ɪɚɜɧɨɩɪɚɜɧɵɣ ɜɤɥɚɞ, ɬɨɝɞɚ ɤɚɤ ɜ ɜɟɥɢɱɢɧɭ ɩɥɚɡɦɟɧɧɨɣ ɱɚɫɬɨɬɵ ɜɜɢɞɭ ɝɨɪɚɡɞɨ ɦɟɧɶɲɟɣ ɦɚɫɫɵ ɨɩɪɟɞɟɥɹɸɳɢɣ ɜɤɥɚɞ ɞɚɟɬ ɷɥɟɤɬɪɨɧɧɚɹ ɤɨɦɩɨɧɟɧɬɚ. ɗɬɚ «ɧɟɪɚɜɧɨɩɪɚɜɧɨɫɬɶ» ɷɥɟɤɬɪɨɧɧɨɣ ɢ ɢɨɧɧɨɣ ɤɨɦɩɨɧɟɧɬ ɩɥɚɡɦɵ ɢɦɟɟɬ ɩɪɨɫɬɨɟ ɨɛɴɹɫɧɟɧɢɟ. Ⱦɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ ɹɜɥɹɟɬɫɹ ɩɨ ɫɭɳɟɫɬɜɭ ɫɬɚɬɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ, ɨɩɪɟɞɟɥɹɸɳɟɣ ɭɫɬɚɧɨɜɢɜɲɭɸɫɹ ɞɥɢɧɭ ɷɤɪɚɧɢɪɨɜɚɧɢɹ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɨɧ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɦɚɫɫɵ ɱɚɫɬɢɰ, ɬɚɤ ɤɚɤ ɡɚ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɟ ɜɪɟɦɹ ɭɫɩɟɜɚɸɬ ɩɟɪɟɫɬɪɨɢɬɫɹ ɨɛɟ ɤɨɦɩɨɧɟɧɬɵ ɩɥɚɡɦɵ, ɧɟɫɦɨɬɪɹ ɧɚ ɫɭɳɟɫɬɜɟɧɧɨɟ ɪɚɡɥɢɱɢɟ ɢɯ ɦɚɫɫ. ȼ ɬɨ ɜɪɟɦɹ ɤɚɤ ɥɟɧɝɦɸɪɨɜɫɤɚɹ ɱɚɫɬɨɬɚ – ɷɬɨ ɞɢɧɚɦɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ, ɨɩɪɟɞɟɥɹɸɳɚɹ ɨɬɤɥɢɤ ɩɥɚɡɦɵ ɧɚ ɞɢɧɚɦɢɱɟɫɤɨɟ ɢɡɦɟɧɟɧɢɟ ɩɨɥɹ. ɉɪɢ «ɛɵɫɬɪɨɦ ɜɤɥɸɱɟɧɢɢ» ɩɨɥɹ, ɨɱɟɜɢɞɧɨ, ɱɬɨ ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ɛɭɞɭɬ ɨɬɤɥɢɤɚɬɶɫɹ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɟɟ ɦɚɫɫɢɜɧɵɟ ɷɥɟɤɬɪɨɧɵ. ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ ɩɥɚɡɦɟɧɧɚɹ ɱɚɫɬɨɬɚ ɞɥɹ ɢɨɧ-ɷɥɟɤɬɪɨɧɧɨɣ ɩɥɚɡɦɵ ɦɚɥɨ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɷɥɟɤɬɪɨɧɧɨɣ ɥɟɧɝɦɸɪɨɜɫɤɨɣ ɱɚɫɬɨɬɵ. Ɉɬɦɟɬɢɦ, ɱɬɨ ɩɨ ɩɨɪɹɞɤɭ ɜɟɥɢɱɢɧɵ 1/ωp ɟɫɬɶ ɜɪɟɦɹ ɩɪɨɥɟɬɚ ɞɟɛɚɟɜɫɤɨɝɨ ɫɥɨɹ ɬɟɩɥɨɜɵɦ ɷɥɟɤɬɪɨɧɨɦ.
§ 4. ɂɞɟɚɥɶɧɨɫɬɶ ɩɥɚɡɦɵ ɉɨ ɚɧɚɥɨɝɢɢ ɫ ɝɚɡɨɦ ɩɥɚɡɦɭ ɫɱɢɬɚɸɬ ɢɞɟɚɥɶɧɨɣ, ɟɫɥɢ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɞɜɢɠɟɧɢɹ ɟɟ ɱɚɫɬɢɰ ɫɭɳɟɫɬɜɟɧɧɨ ɛɨɥɶɲɟ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɢɯ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ. ȼ ɝɚɡɟ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɱɚɫɬɢɰ ɨɛɭɫɥɨɜɥɟɧɚ ɫɢɥɚɦɢ ȼɚɧ-ɞɟɪ-ȼɚɚɥɶɫɚ, ɜ ɩɥɚɡɦɟ - ɤɭɥɨɧɨɜɫɤɢɦ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟɦ. ɗɧɟɪɝɢɹ ɤɭɥɨɧɨɜɫɤɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɞɜɭɯ ɱɚɫɬɢɰ ɫ ɡɚɪɹɞɨɦ ɟ, ɧɚɯɨɞɹɳɢɯɫɹ ɧɚ ɪɚɫɫɬɨɹɧɢɢ R ɞɪɭɝ ɨɬ ɞɪɭɝɚ, ɪɚɜɧɚ e2/R. ɋɪɟɞɧɟɟ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ ɩɪɢ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ n ɫɨɫɬɚɜɥɹɟɬ R∼n−1/3, ɚ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɱɚɫɬɢɰɵ ɩɨ ɩɨɪɹɞɤɭ ɜɟɥɢɱɢɧɵ ɪɚɜɧɚ ɬɟɦɩɟɪɚɬɭɪɟ T, ɢɡɦɟɪɹɟɦɨɣ ɜ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɟɞɢɧɢɰɚɯ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɭɫɥɨɜɢɟ ɢɞɟɚɥɶɧɨɫɬɢ ɩɥɚɡɦɵ ɦɨɠɧɨ ɫɮɨɪɦɭɥɢɪɨɜɚɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: e 2 n 1 / 3 << T , ɢɥɢ e6 n γ = 3 << 1 , (1.15) T ɝɞɟ γ - ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ ɩɚɪɚɦɟɬɪ ɧɟɢɞɟɚɥɶɧɨɫɬɢ. ɗɬɨɦɭ ɭɫɥɨɜɢɸ ɦɨɠɧɨ ɩɪɢɞɚɬɶ ɢ ɧɟɫɤɨɥɶɤɨ ɢɧɨɣ ɫɦɵɫɥ. ɋɟɱɟɧɢɟ ɤɭɥɨɧɨɜɫɤɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɱɚɫɬɢɰ ɨɩɪɟɞɟɥɹɟɬɫɹ ɚɦɩɥɢɬɭɞɨɣ ɪɚɫɫɟɹɧɢɹ, ɩɨ ɩɨɪɹɞɤɭ ɜɟɥɢɱɢɧɵ ɪɚɜɧɨɣ e2 f ~ . T Ɉɱɟɜɢɞɧɨ, ɩɥɚɡɦɚ ɹɜɥɹɟɬɫɹ ɢɞɟɚɥɶɧɨɣ, ɟɫɥɢ ɚɦɩɥɢɬɭɞɚ ɪɚɫɫɟɹɧɢɹ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɟ ɫɪɟɞɧɟɝɨ ɦɟɠɱɚɫɬɢɱɧɨɝɨ ɪɚɫɫɬɨɹɧɢɹ (ɜ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɫɭɳɟɫɬɜɟɧɧɵ ɤɨɪɪɟɥɹɰɢɢ ɜɡɚɢɦɧɨɝɨ ɪɚɫɩɨɥɨɠɟɧɢɹ ɱɚɫɬɢɰ) f << R ~ n −1/ 3 , ɢ ɜɧɨɜɶ ɩɪɢɯɨɞɢɦ ɤ ɤɪɢɬɟɪɢɸ (1.15). ɉɨɥɟɡɧɨ ɭɫɥɨɜɢɸ ɢɞɟɚɥɶɧɨɫɬɢ ɩɥɚɡɦɵ ɩɪɢɞɚɬɶ ɛɨɥɟɟ ɧɚɝɥɹɞɧɵɣ ɫɦɵɫɥ, ɞɥɹ ɷɬɨɝɨ ɩɨɫɬɭɩɢɦ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. ȼɵɞɟɥɢɦ ɜ ɨɛɴɟɦɟ ɩɥɚɡɦɵ ɲɚɪ ɫ ɪɚɞɢɭɫɨɦ, ɪɚɜɧɵɦ ɪɚɞɢɭɫɭ Ⱦɟɛɚɹ, ɢ ɩɨɞɫɱɢɬɚɟɦ ɱɢɫɥɨ ɱɚɫɬɢɰ ND, ɫɨɞɟɪɠɚɳɢɯɫɹ ɜ ɷɬɨɦ ɲɚɪɟ: 4 N D = πnrD3 ~ γ − 3 / 2 . (1.16) 3 ɋɪɚɜɧɢɜ ɫ ɤɪɢɬɟɪɢɟɦ (1.15), ɩɪɢɯɨɞɢɦ ɤ ɡɚɤɥɸɱɟɧɢɸ, ɱɬɨ ɩɥɚɡɦɚ ɹɜɥɹɟɬɫɹ ɢɞɟɚɥɶɧɨɣ, ɟɫɥɢ ɱɢɫɥɨ ɱɚɫɬɢɰ ɜ ɲɚɪɟ ɫ ɞɟɛɚɟɜɫɤɢɦ ɪɚɞɢɭɫɨɦ ɜɟɥɢɤɨ. ɑɚɫɬɨ ɢɦɟɧɧɨ ɱɢɫɥɨ ND ɢɫɩɨɥɶɡɭɟɬɫɹ ɜ ɤɚɱɟɫɬɜɟ ɦɟɪɵ ɢɞɟɚɥɶɧɨɫɬɢ ɢɥɢ ɧɟɢɞɟɚɥɶɧɨɫɬɢ ɩɥɚɡɦɵ. ɉɪɨɢɥɥɸɫɬɪɢɪɭɟɦ ɩɨɥɭɱɟɧɧɵɣ ɪɟɡɭɥɶɬɚɬ ɱɢɫɥɟɧɧɵɦ ɩɪɢɦɟɪɨɦ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɡɧɚɱɟɧɢɣ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɩɥɨɬɧɨɫɬɢ, ɬɢɩɢɱɧɵɯ ɞɥɹ ɬɟɪɦɨɹɞɟɪɧɨɣ ɩɥɚɡɦɵ (ɫɦ. §2), ɩɨɥɭɱɚɟɦ ND~108 >>1, ɢ ɬɚɤɚɹ ɩɥɚɡɦɚ ɹɜɥɹɟɬɫɹ ɜ ɜɵɫɨɤɨɣ ɫɬɟɩɟɧɢ ɢɞɟɚɥɶɧɨɣ. Ɍɨɝɞɚ ɤɚɤ ɞɥɹ ɩɥɚɡɦɵ ɥɢɧɟɣɧɨɣ ɦɨɥɧɢɢ, ɬɢɩɢɱɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɤɨɬɨɪɨɣ ɫɨɫɬɚɜɥɹɟɬ ~104Ʉ, ɚ ɤɨɧɰɟɧɬɪɚɰɢɹ ɩɪɢɦɟɪɧɨ ɪɚɜɧɚ ɤɨɧɰɟɧɬɪɚɰɢɢ ɜɨɡɞɭɯɚ, ~1019ɫɦ-3, Ɍɚɤɚɹ ɩɥɚɡɦɚ ɹɜɥɹɟɬɫɹ ɫɥɚɛɨɧɟɢɞɟɚɥɶɧɨɣ, ɫɩɨɫɨɛɧɨɣ ɤ ɪɨɠɞɟɧɢɸ ɩɨɥɭɱɚɟɦ ND~0.1. ɫɚɦɨɩɨɞɞɟɪɠɢɜɚɸɳɢɯɫɹ ɧɟɥɢɧɟɣɧɵɯ ɫɬɪɭɤɬɭɪ. ȼɨɡɦɨɠɧɨ, ɤɚɤ ɩɨɥɚɝɚɸɬ, ɢɦɟɧɧɨ ɬɚɤɨɜɚ ɩɪɢɪɨɞɚ ɲɚɪɨɜɨɣ ɦɨɥɧɢɢ, ɜɨɡɧɢɤɚɸɳɟɣ ɱɚɫɬɨ ɩɪɢ ɨɛɵɱɧɨɦ ɝɪɨɡɨɜɨɦ ɪɚɡɪɹɞɟ. ȼɩɪɨɱɟɦ, ɞɟɬɚɥɶɧɵɣ ɦɟɯɚɧɢɡɦ ɷɬɨɝɨ ɩɪɢɪɨɞɧɨɝɨ ɹɜɥɟɧɢɹ ɩɨɤɚ ɨɤɨɧɱɚɬɟɥɶɧɨ ɧɟ ɜɵɹɫɧɟɧ.
§ 5. ɉɪɹɦɵɟ ɢ ɨɛɪɚɬɧɵɟ ɩɪɨɰɟɫɫɵ ɜ ɩɥɚɡɦɟ Ɋɚɧɟɟ ɦɵ ɭɫɬɚɧɨɜɢɥɢ, ɱɬɨ ɜ ɝɚɡɟ-ɩɥɚɡɦɟ ɦɨɝɭɬ ɩɪɨɢɫɯɨɞɢɬɶ ɧɟɭɩɪɭɝɢɟ ɩɪɨɰɟɫɫɵ: ɜɨɡɛɭɠɞɟɧɢɟ ɱɚɫɬɢɰ, ɞɢɫɫɨɰɢɚɰɢɹ ɦɨɥɟɤɭɥ, ɢɨɧɢɡɚɰɢɹ ɱɚɫɬɢɰ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɞɨɥɠɧɵ ɛɵɬɶ ɢ ɨɛɪɚɬɧɵɟ ɩɪɨɰɟɫɫɵ - ɫɧɹɬɢɟ ɜɨɡɛɭɠɞɟɧɢɹ ɬɟɦ ɢɥɢ ɢɧɵɦ ɩɭɬɟɦ (ɬɚɤɢɟ ɩɪɨɰɟɫɫɵ ɱɚɫɬɨ ɧɚɡɵɜɚɸɬ ɬɭɲɟɧɢɟɦ), ɨɛɴɟɞɢɧɟɧɢɟ ɚɬɨɦɨɜ ɜ ɦɨɥɟɤɭɥɵ (ɨɛɵɱɧɨ ɬɚɤɨɣ ɩɪɨɰɟɫɫ ɧɚɡɵɜɚɸɬ ɚɫɫɨɰɢɚɰɢɟɣ), ɨɛɴɟɞɢɧɟɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ (ɪɟɤɨɦɛɢɧɚɰɢɹ). ɉɪɹɦɵɟ ɢ ɨɛɪɚɬɧɵɟ ɩɪɨɰɟɫɫɵ ɦɨɝɭɬ ɨɫɭɳɟɫɬɜɥɹɬɶɫɹ ɪɚɡɥɢɱɧɵɦɢ ɩɭɬɹɦɢ: ɞɥɹ ɩɪɹɦɵɯ ɩɪɨɰɟɫɫɨɜ ɧɟɨɛɯɨɞɢɦɨ ɫɨɨɛɳɢɬɶ ɱɚɫɬɢɰɚɦ ɞɨɫɬɚɬɨɱɧɭɸ ɷɧɟɪɝɢɸ, ɱɬɨɛɵ ɪɚɡɨɪɜɚɬɶ ɭɞɟɪɠɢɜɚɸɳɢɟ ɢɯ ɫɜɹɡɢ, ɩɪɢ ɨɛɪɚɬɧɵɯ ɩɪɨɰɟɫɫɚɯ ɞɨɥɠɟɧ ɜɵɞɟɥɢɬɶɫɹ ɢɡɛɵɬɨɤ ɷɧɟɪɝɢɢ ɩɨɪɹɞɤɚ ɷɧɟɪɝɢɢ ɫɜɹɡɢ. ɉɪɢ ɷɬɨɦ ɧɟɨɛɯɨɞɢɦɨ ɜɵɩɨɥɧɟɧɢɟ ɡɚɤɨɧɨɜ ɫɨɯɪɚɧɟɧɢɹ ɷɧɟɪɝɢɢ ɢ ɢɦɩɭɥɶɫɚ. Ɋɚɫɫɦɨɬɪɢɦ ɷɬɢ ɩɪɨɰɟɫɫɵ ɩɨɞɪɨɛɧɟɟ. ȼɨɡɛɭɠɞɟɧɢɟ ɢ ɬɭɲɟɧɢɟ ȼɨɡɛɭɠɞɟɧɧɵɟ ɫɨɫɬɨɹɧɢɹ ɜɨɡɦɨɠɧɵ ɞɥɹ ɜɫɟɯ ɫɥɨɠɧɵɯ ɱɚɫɬɢɰ - ɦɨɥɟɤɭɥ, ɚɬɨɦɨɜ, ɦɨɥɟɤɭɥɹɪɧɵɯ ɢ ɚɬɨɦɚɪɧɵɯ ɢɨɧɨɜ (ɤɪɨɦɟ ɢɨɧɚ ɚɬɨɦɚ ɜɨɞɨɪɨɞɚ). ȼ ɦɨɥɟɤɭɥɚɯ ɢ ɦɨɥɟɤɭɥɹɪɧɵɯ ɢɨɧɚɯ ɦɨɝɭɬ ɛɵɬɶ ɜɨɡɛɭɠɞɟɧɵ ɜɪɚɳɚɬɟɥɶɧɵɟ, ɤɨɥɟɛɚɬɟɥɶɧɵɟ ɢ ɷɥɟɤɬɪɨɧɧɵɟ ɫɨɫɬɨɹɧɢɹ, ɚ ɜ ɚɬɨɦɚɯ ɢ ɚɬɨɦɚɪɧɵɯ ɢɨɧɚɯ - ɬɨɥɶɤɨ ɷɥɟɤɬɪɨɧɧɵɟ. ɋ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ, ɧɚɢɛɨɥɟɟ ɥɟɝɤɨ ɜɨɡɛɭɠɞɚɸɬɫɹ ɜɪɚɳɚɬɟɥɶɧɵɟ ɭɪɨɜɧɢ, ɬɪɭɞɧɟɟ ɤɨɥɟɛɚɬɟɥɶɧɵɟ, ɟɳɟ ɬɪɭɞɧɟɟ ɷɥɟɤɬɪɨɧɧɵɟ. ȿɫɥɢ ɩɪɢɧɹɬɶ ɡɚ ɟɞɢɧɢɰɭ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɷɥɟɤɬɪɨɧɧɵɦɢ ɭɪɨɜɧɹɦɢ δȿɷ, ɬɨ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɤɨɥɟɛɚɬɟɥɶɧɵɦɢ ɭɪɨɜɧɹɦɢ δȿν m m ɛɭɞɟɬ ɦɟɧɶɲɟ ɜ ɪɚɡ, ɚ ɦɟɠɞɭ ɜɪɚɳɚɬɟɥɶɧɵɦɢ ɭɪɨɜɧɹɦɢ δȿj ɟɳɟ ɦɟɧɶɲɟ: ɜ ɪɚɡ, M M ɝɞɟ M - ɦɚɫɫɚ ɦɨɥɟɤɭɥɵ, ɚ m - ɦɚɫɫɚ ɷɥɟɤɬɪɨɧɚ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɦɨɥɟɤɭɥɵ ɇ2 ɪɚɫɱɟɬɧɵɟ ɡɧɚɱɟɧɢɹ ɷɧɟɪɝɢɣ ɜɨɡɛɭɠɞɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɫɨɫɬɨɹɧɢɣ ȿɷ= 4,7 ɷȼ, ȿν= 0,54 ɷȼ, ȿj= 7,6⋅10-3 ɷȼ. Ⱦɥɹ ɜɨɡɛɭɠɞɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɫɨɨɛɳɢɬɶ ɦɨɥɟɤɭɥɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɷɧɟɪɝɢɸ, ɧɚɩɪɢɦɟɪ ɩɪɢ ɫɨɭɞɚɪɟɧɢɢ ɫ ɞɪɭɝɨɣ ɱɚɫɬɢɰɟɣ. ɋɯɟɦɚɬɢɱɧɨ ɜɨɡɛɭɠɞɟɧɢɟ ɩɪɢ ɫɨɭɞɚɪɟɧɢɢ ɫ ɷɥɟɤɬɪɨɧɨɦ ɫɢɦɦɟɬɪɢɱɧɨɣ ɞɜɭɯɚɬɨɦɧɨɣ ɦɨɥɟɤɭɥɵ (ɇ2, N2, O2 ɢ ɬ.ɞ.) ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ.1.5. ȼ ɬɚɤɢɯ ɦɨɥɟɤɭɥɚɯ ɦɨɝɭɬ ɜɨɡɛɭɠɞɚɬɶɫɹ ɷɥɟɤɬɪɨɧɧɵɟ, ɨɞɧɚ ɜɪɚɳɚɬɟɥɶɧɚɹ ɢ ɨɞɧɚ ɤɨɥɟɛɚɬɟɥɶɧɚɹ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɜ ɛɨɥɟɟ ɫɥɨɠɧɵɯ ɦɨɥɟɤɭɥɚɯ ɛɨɥɶɲɟɟ ɱɢɫɥɨ ɜɨɡɦɨɠɧɵɯ ɤ ɜɨɡɛɭɠɞɟɧɢɸ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ. ɋɭɳɟɫɬɜɨɜɚɧɢɟ ɜɪɚɳɚɬɟɥɶɧɵɯ ɢ ɤɨɥɟɛɚɬɟɥɶɧɵɯ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɜ ɦɨɥɟɤɭɥɹɪɧɵɯ ɝɚɡɚɯ ɨɩɪɟɞɟɥɹɟɬ ɨɫɧɨɜɧɵɟ ɫɜɨɣɫɬɜɚ ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɵ ɷɬɢɯ ɝɚɡɨɜ ɢ ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɢɫɩɨɥɶɡɨɜɚɬɶ ɢɯ ɜ ɩɥɚɡɦɨɯɢɦɢɱɟɫɤɢɯ Ɋɢɫ.1.5. ɋɯɟɦɚ ɜɨɡɛɭɠɞɟɧɢɹ ɭɞɚɪɨɦ ɢ ɥɚɡɟɪɧɵɯ ɫɢɫɬɟɦɚɯ. Ⱦɟɥɨ ɜ ɬɨɦ, ɱɬɨ ɫɟɱɟɧɢɹ ɭɩɪɭɝɨɝɨ ɢ ɧɟɭɩɪɭɝɨɝɨ ɩɪɨɰɟɫɫɨɜ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɢ ɦɨɥɟɤɭɥ ɫ ɜɨɡɛɭɠɞɟɧɢɟɦ ɤɨɥɟɛɚɬɟɥɶɧɵɯ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɩɨɱɬɢ ɨɞɢɧɚɤɨɜɵ (ɨɬɥɢɱɚɸɬɫɹ ɥɢɲɶ ɜ ɧɟɫɤɨɥɶɤɨ ɪɚɡ), ɚ ɩɟɪɟɞɚɜɚɟɦɚɹ ɨɬ ɷɥɟɤɬɪɨɧɚ ɷɧɟɪɝɢɹ ɨɬɥɢɱɚɟɬɫɹ ɜ ɫɨɬɧɢ ɢ ɬɵɫɹɱɢ ɪɚɡ. ɉɪɢ ɭɩɪɭɝɨɦ ɫɨɭɞɚɪɟɧɢɢ ɦɨɥɟɤɭɥɟ ɩɟɪɟɞɚɟɬɫɹ ɦɚɥɚɹ (~m/Ɇ) ɞɨɥɹ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɚ, ɚ ɩɪɢ ɜɨɡɛɭɠɞɟɧɢɢ ɤɨɥɟɛɚɧɢɣ ɩɟɪɟɞɚɟɬɫɹ ɷɧɟɪɝɢɹ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɷɧɟɪɝɢɢ ɩɟɪɟɯɨɞɚ, ɬɨ ɟɫɬɶ ɦɚɫɲɬɚɛɚ ɞɟɫɹɬɵɯ ɞɨɥɟɣ ɷɥɟɤɬɪɨɧ-ɜɨɥɶɬɚ. Ʉɨɥɟɛɚɬɟɥɶɧɚɹ ɪɟɥɚɤɫɚɰɢɹ - ɩɟɪɟɯɨɞ ɤɨɥɟɛɚɬɟɥɶɧɨɣ ɷɧɟɪɝɢɢ ɜ ɬɟɩɥɨɜɭɸ - ɜɟɫɶɦɚ ɡɚɬɪɭɞɧɟɧɚ (ɩɪɢ ɤɨɦɧɚɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɜɟɪɨɹɬɧɨɫɬɶ ɦɚɫɲɬɚɛɚ 10-5-10-9). ɉɨɷɬɨɦɭ ɫɭɳɟɫɬɜɭɸɬ ɫɢɫɬɟɦɵ ɫ ɜɵɫɨɤɨɣ ɤɨɥɟɛɚɬɟɥɶɧɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ ɩɪɢ ɦɚɥɨɣ ɩɨɫɬɭɩɚɬɟɥɶɧɨɣ (ɬɟɩɥɨɜɨɣ). Ɍɚɤ ɦɨɠɧɨ ɨɛɟɫɩɟɱɢɬɶ ɜɵɫɨɤɭɸ ɢɧɜɟɪɫɧɭɸ ɡɚɫɟɥɟɧɧɨɫɬɶ ɤɨɥɟɛɚɬɟɥɶɧɨ-ɜɪɚɳɚɬɟɥɶɧɵɯ ɩɟɪɟɯɨɞɨɜ, ɬ.ɟ. ɫɨɡɞɚɬɶ ɚɤɬɢɜɧɭɸ ɫɪɟɞɭ ɞɥɹ ɥɚɡɟɪɨɜ.
Ⱦɥɹ ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɨɣ ɧɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɨɣ ɩɥɚɡɦɵ ɯɚɪɚɤɬɟɪɧɨ ɛɨɥɶɲɨɟ ɱɢɫɥɨ ɤɨɥɟɛɚɬɟɥɶɧɨ-ɜɪɚɳɚɬɟɥɶɧɨ ɜɨɡɛɭɠɞɟɧɧɵɯ ɦɨɥɟɤɭɥ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɱɢɫɥɨɦ ɷɥɟɤɬɪɨɧɧɨɜɨɡɛɭɠɞɟɧɧɵɯ. Ɂɚɫɟɥɟɧɢɟ ɤɨɥɟɛɚɬɟɥɶɧɨ-ɜɪɚɳɚɬɟɥɶɧɵɯ ɭɪɨɜɧɟɣ ɩɪɨɢɫɯɨɞɢɬ ɚɤɬɢɜɧɨ ɩɪɢ ɧɟɤɨɬɨɪɵɯ ɯɢɦɢɱɟɫɤɢɯ ɪɟɚɤɰɢɹɯ (ɧɚɩɪɢɦɟɪ, ɝɨɪɟɧɢɟ ɭɝɥɟɪɨɞɚ ɜ ɤɢɫɥɨɪɨɞɟ ɫ ɨɛɪɚɡɨɜɚɧɢɟɦ ɋɈ - ɞɨ 90% ɷɧɟɪɝɢɢ ɚɫɫɨɰɢɚɰɢɢ ɋɈ ɢɞɟɬ ɧɚ ɜɨɡɛɭɠɞɟɧɢɟ), ɜ ɬɥɟɸɳɟɦ ɪɚɡɪɹɞɟ. Ɍɭɲɢɬɶ ɜɨɡɛɭɠɞɟɧɢɟ ɦɨɠɧɨ ɪɚɡɥɢɱɧɵɦɢ ɩɭɬɹɦɢ — ɢɡɥɭɱɟɧɢɟɦ (ɢɫɩɨɥɶɡɭɟɬɫɹ ɜ ɥɚɡɟɪɚɯ), ɱɚɫɬɢɱɧɵɦ ɩɟɪɟɯɨɞɨɦ ɷɧɟɪɝɢɢ ɜɨɡɛɭɠɞɟɧɢɹ ɜ ɷɧɟɪɝɢɸ ɯɢɦɢɱɟɫɤɢɯ ɫɜɹɡɟɣ (ɢɫɩɨɥɶɡɭɟɬɫɹ ɜ ɩɥɚɡɦɨɯɢɦɢɢ). ɉɨ ɦɟɪɟ ɩɨɜɵɲɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɝɚɡɚ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɱɢɫɥɨ ɱɚɫɬɢɰ ɫ ɷɥɟɤɬɪɨɧɧɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ. ȼ ɨɛɵɱɧɵɯ ɭɫɥɨɜɢɹɯ ɷɥɟɤɬɪɨɧ ɧɚɯɨɞɢɬɫɹ ɜ ɚɬɨɦɟ, ɦɨɥɟɤɭɥɟ (ɢɥɢ ɢɨɧɟ) ɜ ɨɫɧɨɜɧɨɦ ɫɨɫɬɨɹɧɢɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦ ɦɢɧɢɦɭɦɭ ɟɝɨ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ. ɉɨɥɭɱɢɜ ɧɟɤɨɬɨɪɭɸ ɞɨɛɚɜɨɱɧɭɸ ɷɧɟɪɝɢɸ (ɨɬ ɮɨɬɨɧɚ ɢɥɢ ɞɪɭɝɨɣ ɱɚɫɬɢɰɵ), ɷɥɟɤɬɪɨɧ ɦɨɠɟɬ ɩɟɪɟɣɬɢ ɧɚ ɛɨɥɟɟ ɜɵɫɨɤɨ ɥɟɠɚɳɢɣ ɷɧɟɪɝɟɬɢɱɟɫɤɢɣ ɭɪɨɜɟɧɶ. ȼɟɪɨɹɬɧɨɫɬɶ ɬɚɤɨɝɨ ɩɪɨɰɟɫɫɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɫɟɱɟɧɢɹɦɢ ɜɨɡɛɭɠɞɟɧɢɹ ɢ ɫɢɥɶɧɨ ɡɚɜɢɫɢɬ ɨɬ ɫɩɨɫɨɛɚ ɜɨɡɛɭɠɞɟɧɢɹ. ȼɨɡɛɭɠɞɟɧɢɟ ɩɪɢ ɫɨɭɞɚɪɟɧɢɢ ɫ ɱɚɫɬɢɰɚɦɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɟɥɢɱɢɧɨɣ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɫɤɨɪɨɫɬɢ, ɡɚɪɹɞɨɜɵɦ ɫɨɫɬɨɹɧɢɟɦ ɫɨɭɞɚɪɹɸɳɢɯɫɹ ɱɚɫɬɢɰ ɢ ɢɦɟɟɬ ɪɟɡɨɧɚɧɫɧɵɣ ɯɚɪɚɤɬɟɪ. ȼɨɡɛɭɠɞɟɧɢɟ ɮɨɬɨɧɚɦɢ ɢɦɟɟɬ ɱɟɬɤɢɣ ɪɟɡɨɧɚɧɫɧɵɣ ɯɚɪɚɤɬɟɪ ɞɥɹ ɚɬɨɦɨɜ ɢ ɚɬɨɦɚɪɧɵɯ ɢɨɧɨɜ ɢ ɛɨɥɟɟ "ɪɚɡɦɵɬɨ" ɞɥɹ ɦɨɥɟɤɭɥ. ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɨɰɟɧɤɭ ɜɟɪɨɹɬɧɨɫɬɢ ɩɪɨɰɟɫɫɚ ɜɨɡɛɭɠɞɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɚɬɨɦɧɨɣ ɱɚɫɬɢɰɵ (ɚɬɨɦɚ, ɦɨɥɟɤɭɥɵ, ɢɨɧɚ) ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ, ɫɪɚɜɧɢɜɚɹ ɜɪɟɦɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɱɚɫɬɢɰ ɢ ɜɪɟɦɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɩɟɪɟɯɨɞɚ. Ⱥɬɨɦɧɵɟ ɱɚɫɬɢɰɵ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ ɫɜɨɢɦɢ ɷɥɟɤɬɪɨɧɧɵɦɢ ɨɛɨɥɨɱɤɚɦɢ, ɢ ɟɫɥɢ ɫɛɥɢɠɟɧɢɟ ɩɪɨɢɫɯɨɞɢɬ ɦɟɞɥɟɧɧɨ (ɬ.ɟ. ɨɬɧɨɫɢɬɟɥɶɧɵɟ ɫɤɨɪɨɫɬɢ ɚɬɨɦɧɵɯ ɱɚɫɬɢɰ ɦɚɥɵ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫɨ ɫɤɨɪɨɫɬɶɸ ɷɥɟɤɬɪɨɧɨɜ ɜ ɚɬɨɦɟ), ɬɨ ɢɯ ɷɥɟɤɬɪɨɧɧɵɟ ɨɛɨɥɨɱɤɢ ɭɫɩɟɜɚɸɬ ɩɨɫɬɟɩɟɧɧɨ ɩɟɪɟɫɬɪɨɢɬɶɫɹ, ɚ ɡɚɬɟɦ ɜɟɪɧɭɬɶɫɹ ɜ ɢɫɯɨɞɧɨɟ ɫɨɫɬɨɹɧɢɟ. ȿɫɥɢ ɠɟ ɜɪɟɦɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɚɥɨ, ɬɨ ɷɥɟɤɬɪɨɧɵ ɡɚ ɜɪɟɦɹ tɷ "ɩɟɪɟɛɪɚɫɵɜɚɸɬɫɹ" ɧɚ ɧɨɜɵɣ ɭɪɨɜɟɧɶ, ɩɪɨɢɫɯɨɞɢɬ ɜɨɡɛɭɠɞɟɧɢɟ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜɨɡɛɭɠɞɟɧɢɟ ɧɟ ɩɪɨɢɫɯɨɞɢɬ, ɟɫɥɢ tɚɬ>>tɷ. ɉɨ ɩɨɪɹɞɤɭ ɜɟɥɢɱɢɧɵ tɚɬ=a/v, ɝɞɟ a - ɪɚɡɦɟɪ ɚɬɨɦɚ, a v - ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɫɤɨɪɨɫɬɶ. ɉɨ ɩɨɪɹɞɤɭ ɜɟɥɢɱɢɧɵ tɷ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɢɡ ɩɪɢɧɰɢɩɚ ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɢ:
t ɷ = ! δE ,
ɝɞɟ δE - ɪɚɡɧɨɫɬɶ ɷɧɟɪɝɢɣ ɭɪɨɜɧɟɣ. ɉɨɷɬɨɦɭ ɩɨɥɭɱɚɟɦ ɭɫɥɨɜɢɟ
a / v >> ! δE
ɢɥɢ
aδE / v! >>1, ɱɬɨ ɢ ɹɜɥɹɟɬɫɹ ɤɪɢɬɟɪɢɟɦ ɦɚɥɨɜɟɪɨɹɬɧɨɫɬɢ ɩɟɪɟɯɨɞɚ ɢ ɧɚɡɵɜɚɟɬɫɹ ɚɞɢɚɛɚɬɢɱɟɫɤɢɦ ɤɪɢɬɟɪɢɟɦ Ɇɟɫɫɢ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɟɫɥɢ ɪɚɡɧɨɫɬɶ ɭɪɨɜɧɟɣ δȿ ɦɚɥɚ, ɬɨ ɩɪɨɰɟɫɫ ɛɨɥɟɟ ɜɟɪɨɹɬɟɧ. Ɍɚɤɢɟ ɩɪɨɰɟɫɫɵ ɧɚɡɵɜɚɸɬ ɪɟɡɨɧɚɧɫɧɵɦɢ (ɧɚɩɪɢɦɟɪ, ɪɟɡɨɧɚɧɫɧɚɹ ɩɟɪɟɡɚɪɹɞɤɚ, ɜɡɚɢɦɧɚɹ ɧɟɣɬɪɚɥɢɡɚɰɢɹ ɢɨɧɨɜ, ɩɟɪɟɞɚɱɚ ɜɨɡɛɭɠɞɟɧɢɹ). ɋɧɹɬɢɟ ɷɥɟɤɬɪɨɧɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɜɨɡɦɨɠɧɨ ɦɧɨɝɢɦɢ ɩɭɬɹɦɢ, ɧɚɩɪɢɦɟɪ:
ɚ) Ⱥ* → Ⱥ + γ
ɛ) Ⱥ* + ȼɋ → Ⱥ + ȼɋ Ⱥ+ȼ+ɋ ɜ) Ⱥ* + ȼ → Ⱥȼ+ + ɟ ɝ) Ⱥ* + ȼ → Ⱥ + ȼ+ + ɟ ɞ) Ⱥ* + ȼ → ȼ* + Ⱥ
- ɜɵɫɜɟɱɢɜɚɧɢɟ ɩɪɢ ɜɨɡɜɪɚɳɟɧɢɢ ɷɥɟɤɬɪɨɧɚ ɧɚ ɨɫɧɨɜɧɨɣ ɭɪɨɜɟɧɶ (ɜɨɡɦɨɠɧɨ ɫɬɭɩɟɧɱɚɬɨɟ ɩɭɬɟɦ ɢɫɩɭɫɤɚɧɢɹ ɪɹɞɚ ɮɨɬɨɧɨɜ); - ɬɭɲɟɧɢɟ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɢ ɫ ɦɨɥɟɤɭɥɨɣ, ɷɧɟɪɝɢɹ ɜɨɡɛɭɠɞɟɧɢɹ ɩɟɪɟɯɨɞɢɬ ɢɥɢ ɜ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɱɚɫɬɢɰ, ɢɥɢ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ ɞɢɫɫɨɰɢɚɰɢɸ ɦɨɥɟɤɭɥɵ. Ɍɭɲɟɧɢɟ ɩɪɢ ɫɨɭɞɚɪɟɧɢɢ ɫ ɚɬɨɦɨɦ ɦɚɥɨɜɟɪɨɹɬɧɨ; - ɚɫɫɨɰɢɚɬɢɜɧɚɹ ɢɨɧɢɡɚɰɢɹ. ɗɧɟɪɝɢɹ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ ɢɨɧɢɡɚɰɢɸ. ȼɟɫɶɦɚ ɜɟɪɨɹɬɧɵɣ ɩɪɨɰɟɫɫ ɞɥɹ ɧɟɤɨɬɨɪɵɯ ɫɨɫɬɨɹɧɢɣ; - ɷɮɮɟɤɬ ɉɟɧɧɢɝɚ; ɩɪɨɰɟɫɫ ɩɪɨɢɫɯɨɞɢɬ, ɟɫɥɢ ɷɧɟɪɝɢɹ ɜɨɡɛɭɠɞɟɧɢɹ ɚɬɨɦɚ Ⱥ* ɜ ɦɟɬɚɫɬɚɛɢɥɶɧɨɟ ɫɨɫɬɨɹɧɢɟ ɛɨɥɶɲɟ ɩɨɬɟɧɰɢɚɥɚ ɢɨɧɢɡɚɰɢɢ ɱɚɫɬɢɰɵ ȼ. - ɩɟɪɟɞɚɱɚ ɜɨɡɛɭɠɞɟɧɢɹ ɪɟɚɥɢɡɭɟɬɫɹ ɫ ɛɨɥɶɲɨɣ ɜɟɪɨɹɬɧɨɫɬɶɸ, ɟɫɥɢ ɦɚɥɨ ɢɡɦɟɧɟɧɢɟ ɷɧɟɪɝɢɢ ɩɟɪɟɯɨɞɚ (ɪɟɡɨɧɚɧɫɧɵɣ ɩɪɨɰɟɫɫ).
ȼɢɞɧɨ, ɱɬɨ ɧɟɤɨɬɨɪɵɟ ɩɭɬɢ ɬɭɲɟɧɢɹ ɩɪɢɜɨɞɹɬ ɤ ɨɛɪɚɡɨɜɚɧɢɸ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ, ɬ.ɟ. ɤ ɜɨɡɪɚɫɬɚɧɢɸ ɫɬɟɩɟɧɢ ɢɨɧɢɡɚɰɢɢ ɩɥɚɡɦɵ. ɂɨɧɢɡɚɰɢɹ ɢ ɪɟɤɨɦɛɢɧɚɰɢɹ ɉɪɨɰɟɫɫɵ ɨɛɪɚɡɨɜɚɧɢɹ ɢ ɪɚɡɪɭɲɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɨɩɪɟɞɟɥɹɸɬ ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɩɥɚɡɦɵ. Ⱦɥɹ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚɪɧɨɣ ɢɥɢ ɦɨɥɟɤɭɥɹɪɧɨɣ ɱɚɫɬɢɰɵ ɧɟɨɛɯɨɞɢɦɨ ɫɨɨɛɳɢɬɶ ɯɨɬɹ ɛɵ ɨɞɧɨɦɭ ɟɟ ɷɥɟɤɬɪɨɧɭ ɷɧɟɪɝɢɸ ɛɨɥɶɲɭɸ, ɱɟɦ ɷɧɟɪɝɢɹ ɟɝɨ ɫɜɹɡɢ ɫ ɷɬɨɣ ɱɚɫɬɢɰɟɣ. ɗɧɟɪɝɢɹ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɢɨɧɢɡɚɰɢɢ, ɜɵɪɚɠɟɧɧɚɹ ɜ ɷɥɟɤɬɪɨɧɜɨɥɶɬɚɯ, ɱɢɫɥɟɧɨ ɪɚɜɧɚ ɪɚɡɧɨɫɬɢ ɩɨɬɟɧɰɢɚɥɨɜ ɜ ɜɨɥɶɬɚɯ, ɤɨɬɨɪɭɸ ɞɨɥɠɟɧ ɩɪɨɣɬɢ ɷɥɟɤɬɪɨɧ ɞɥɹ ɟɟ ɩɪɢɨɛɪɟɬɟɧɢɹ. ɉɨɷɬɨɦɭ ɱɚɫɬɨ ɝɨɜɨɪɹɬ ɧɟ ɨɛ ɷɧɟɪɝɢɢ ɢɨɧɢɡɚɰɢɢ, ɚ ɨ ɩɨɬɟɧɰɢɚɥɟ ɢɨɧɢɡɚɰɢɢ. Ʌɟɝɱɟ ɜɫɟɝɨ ɨɬɨɪɜɚɬɶ ɩɟɪɜɵɣ, ɤɚɤ ɩɪɚɜɢɥɨ, ɜɧɟɲɧɢɣ, ɷɥɟɤɬɪɨɧ, ɜɬɨɪɨɣ ɢ ɩɨɫɥɟɞɭɸɳɢɟ - ɜɫɟ ɬɪɭɞɧɟɟ. ɇɚɢɛɨɥɶɲɢɣ ɩɟɪɜɵɣ ɩɨɬɟɧɰɢɚɥ ɢɨɧɢɡɚɰɢɢ ɭ ɇɟ (24,5 ȼ), ɧɚɢɦɟɧɶɲɢɣ ɭ Cs (3,9 ȼ). ȼɬɨɪɨɣ ɩɨɬɟɧɰɢɚɥ ɨɛɵɱɧɨ ɩɪɟɜɵɲɚɟɬ ɩɟɪɜɵɣ ɜ 2-3 ɪɚɡɚ, ɢɫɤɥɸɱɟɧɢɟɦ ɹɜɥɹɸɬɫɹ ɳɟɥɨɱɧɵɟ ɦɟɬɚɥɥɵ: ɧɚɢɛɨɥɶɲɚɹ ɪɚɡɧɢɰɚ ɭ Li (5,4 ɢ 75,6 ȼ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ). ɗɧɟɪɝɢɸ ɢɨɧɢɡɚɰɢɢ ɦɨɠɧɨ ɫɨɨɛɳɢɬɶ ɩɪɢ ɨɞɢɧɨɱɧɨɦ ɫɨɭɞɚɪɟɧɢɢ ɫ ɞɨɫɬɚɬɨɱɧɨ ɷɧɟɪɝɢɱɧɨɣ ɱɚɫɬɢɰɟɣ (ɫ ɷɥɟɤɬɪɨɧɨɦ, ɚɬɨɦɨɦ, ɢɨɧɨɦ, ɮɨɬɨɧɨɦ), ɧɨ ɟɟ ɦɨɠɧɨ ɩɟɪɟɞɚɬɶ ɢ ɜ ɩɪɨɰɟɫɫɟ ɧɟɫɤɨɥɶɤɢɯ ɫɨɭɞɚɪɟɧɢɣ, ɩɪɢɱɟɦ ɜ ɤɚɠɞɨɦ ɩɟɪɟɞɚɟɬɫɹ ɷɧɟɪɝɢɹ ɦɟɧɶɲɟ, ɱɟɦ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɨɬɪɵɜɚ ɷɥɟɤɬɪɨɧɚ. ɉɪɢ ɤɚɠɞɨɦ ɫɨɭɞɚɪɟɧɢɢ ɱɚɫɬɢɰɚ ɩɨɥɭɱɚɟɬ ɷɧɟɪɝɢɸ, ɩɟɪɟɯɨɞɢɬ ɜ ɛɨɥɟɟ ɜɨɡɛɭɠɞɟɧɧɨɟ ɫɨɫɬɨɹɧɢɟ, ɚ ɡɚɬɟɦ ɢɨɧɢɡɭɟɬɫɹ ɭɠɟ ɢɡ ɜɨɡɛɭɠɞɟɧɧɨɝɨ ɫɨɫɬɨɹɧɢɹ. Ɍɚɤɚɹ ɫɬɭɩɟɧɱɚɬɚɹ ɢɨɧɢɡɚɰɢɹ ɨɫɨɛɟɧɧɨ ɜɚɠɧɚ ɜ ɧɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɨɣ ɩɥɚɡɦɟ, ɤɨɝɞɚ ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɨɜ ɦɟɧɶɲɟ ɩɨɬɟɧɰɢɚɥɚ ɢɨɧɢɡɚɰɢɢ. ɉɪɨɰɟɫɫɨɦ, ɨɛɪɚɬɧɵɦ ɢɨɧɢɡɚɰɢɢ, ɹɜɥɹɟɬɫɹ ɨɛɴɟɞɢɧɟɧɢɟ ɢɨɧɚ ɢ ɷɥɟɤɬɪɨɧɚ ɨɛɪɚɡɨɜɚɧɢɟ ɧɟɣɬɪɚɥɶɧɨɣ ɱɚɫɬɢɰɵ ɢɥɢ ɩɨɧɢɠɟɧɢɟ ɡɚɪɹɞɧɨɫɬɢ ɢɨɧɚ, ɟɝɨ ɧɚɡɵɜɚɸɬ ɪɟɤɨɦɛɢɧɚɰɢɟɣ. ɉɪɢ ɪɟɤɨɦɛɢɧɚɰɢɢ ɜɵɞɟɥɹɟɬɫɹ ɷɧɟɪɝɢɹ, ɪɚɜɧɚɹ ɷɧɟɪɝɢɢ ɫɜɹɡɢ ɪɟɤɨɦɛɢɧɢɪɭɸɳɢɯ ɱɚɫɬɢɰ. ɗɬɚ ɷɧɟɪɝɢɹ ɦɨɠɟɬ ɜɵɞɟɥɢɬɶɫɹ ɜ ɜɢɞɟ ɢɡɥɭɱɟɧɢɹ, ɢɥɢ ɦɨɠɟɬ ɛɵɬɶ ɩɟɪɟɞɚɧɚ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɟ (ɨɛɵɱɧɨ ɨɞɧɨɦɭ ɢɡ ɷɥɟɤɬɪɨɧɨɜ ɩɥɚɡɦɵ). ȼ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɝɨɜɨɪɹɬ ɨ ɪɟɤɨɦɛɢɧɚɰɢɢ ɫ ɢɡɥɭɱɟɧɢɟɦ (ɢɥɢ ɢɡɥɭɱɚɬɟɥɶɧɨɣ ɪɟɤɨɦɛɢɧɚɰɢɢ), ɜɨ ɜɬɨɪɨɦ - ɨ ɪɟɤɨɦɛɢɧɚɰɢɢ ɩɪɢ ɬɪɨɣɧɵɯ ɫɨɭɞɚɪɟɧɢɹɯ (ɢɥɢ ɬɪɨɣɧɨɣ ɪɟɤɨɦɛɢɧɚɰɢɢ). Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɜɬɨɪɨɣ ɫɥɭɱɚɣ ɪɟɚɥɢɡɭɟɬɫɹ ɩɪɢ ɜɵɫɨɤɢɯ ɩɥɨɬɧɨɫɬɹɯ ɩɥɚɡɦɵ. Ⱦɥɹ ɧɟɤɨɬɨɪɵɯ ɚɬɨɦɨɜ (ɧɚɩɪɢɦɟɪ, ɇɟ) ɢ ɜɨɡɛɭɠɞɟɧɧɵɯ ɢɨɧɨɜ ɫɭɳɟɫɬɜɟɧɧɨ ɨɛɪɚɡɨɜɚɧɢɟ ɚɜɬɨɢɨɧɢɡɚɰɢɨɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɪɟɤɨɦɛɢɧɚɰɢɹ. Ⱥɜɬɨɢɨɧɢɡɚɰɢɨɧɧɵɦ ɫɨɫɬɨɹɧɢɟɦ ɧɚɡɵɜɚɸɬ ɫɜɹɡɚɧɧɨɟ ɫɨɫɬɨɹɧɢɟ ɜɨɡɛɭɠɞɟɧɧɨɝɨ ɢɨɧɚ ɢ ɷɥɟɤɬɪɨɧɚ, ɟɫɥɢ ɫɭɦɦɚɪɧɚɹ ɷɧɟɪɝɢɹ ɜɨɡɛɭɠɞɟɧɢɹ ɛɨɥɶɲɟ ɩɨɬɟɧɰɢɚɥɚ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚ. ȿɫɥɢ ɜɨɡɛɭɠɞɟɧɨ ɧɟɫɤɨɥɶɤɨ ɷɥɟɤɬɪɨɧɨɜ, ɢ ɟɫɥɢ ɷɧɟɪɝɢɹ ɜɨɡɛɭɠɞɟɧɢɹ ɛɭɞɟɬ ɩɟɪɟɞɚɧɚ ɨɞɧɨɦɭ ɷɥɟɤɬɪɨɧɭ, ɬɨ ɩɪɨɢɡɨɣɞɟɬ ɢɨɧɢɡɚɰɢɹ - ɷɥɟɤɬɪɨɧ ɩɟɪɟɣɞɟɬ ɜ ɫɜɨɛɨɞɧɨɟ ɫɨɫɬɨɹɧɢɟ, ɚ ɢɨɧ ɨɫɬɚɧɟɬɫɹ ɜ ɨɫɧɨɜɧɨɦ (ɧɟɜɨɡɛɭɠɞɟɧɧɨɦ) ɫɨɫɬɨɹɧɢɢ. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜɪɟɦɹ ɠɢɡɧɢ ɱɚɫɬɢɰɵ ɜ ɚɜɬɨɢɨɧɢɡɚɰɢɨɧɧɨɦ ɫɨɫɬɨɹɧɢɢ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ ɯɚɪɚɤɬɟɪɧɨɝɨ ɚɬɨɦɧɨɝɨ. ȼɨɡɦɨɠɟɧ ɢ ɩɪɨɰɟɫɫ, ɨɛɪɚɬɧɵɣ ɚɫɫɨɰɢɚɬɢɜɧɨɣ ɢɨɧɢɡɚɰɢɢ - ɬɚɤ ɧɚɡɵɜɚɟɦɚɹ ɞɢɫɫɨɰɢɚɬɢɜɧɚɹ ɪɟɤɨɦɛɢɧɚɰɢɹ: Ⱥȼ+ + ɟ → Ⱥ + ȼ+; ɨɧ ɩɪɨɯɨɞɢɬ ɱɟɪɟɡ ɚɜɬɨɢɨɧɢɡɚɰɢɨɧɧɨɟ ɫɨɫɬɨɹɧɢɟ ɦɨɥɟɤɭɥɵ Ⱥȼ*. ɂɧɨɝɞɚ ɪɟɤɨɦɛɢɧɚɰɢɟɣ ɧɚɡɵɜɚɸɬ ɢ ɚɫɫɨɰɢɚɰɢɸ ɦɨɥɟɤɭɥ ɢɡ ɚɬɨɦɨɜ, ɬ.ɟ. ɩɪɨɰɟɫɫɵ ɬɢɩɚ Ⱥ + 2ȼ → Ⱥȼ + ȼ, Ⱥ + ȼ + ɋ → Ⱥȼ + ɋ, ɢɥɢ Ⱥ + 2Ⱥ → Ⱥ2 + Ⱥ. Ⱦɢɫɫɨɰɢɚɰɢɹ ɢ ɚɫɫɨɰɢɚɰɢɹ Ⱦɢɫɫɨɰɢɚɰɢɟɣ ɧɚɡɵɜɚɸɬ ɩɪɨɰɟɫɫ ɪɚɡɞɟɥɟɧɢɹ ɫɥɨɠɧɵɯ ɦɨɥɟɤɭɥ (ɢɥɢ ɦɨɥɟɤɭɥɹɪɧɵɯ ɢɨɧɨɜ) ɧɚ ɛɨɥɟɟ ɩɪɨɫɬɵɟ ɦɨɥɟɤɭɥɵ, ɢɥɢ ɧɚ ɚɬɨɦɵ (ɢɥɢ ɢɨɧ ɢ ɚɬɨɦ, ɢɨɧ ɢ ɦɨɥɟɤɭɥɚ). ɗɧɟɪɝɢɹ ɪɚɡɪɵɜɚ ɦɨɥɟɤɭɥɹɪɧɵɯ ɫɜɹɡɟɣ ɩɨɱɬɢ ɜɫɟɝɞɚ ɦɟɧɶɲɟ ɷɧɟɪɝɢɢ ɢɨɧɢɡɚɰɢɢ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɩɨɠɚɥɭɣ, ɦɨɥɟɤɭɥ ɋɈ2 ɢ ɋ2ɇ2). ɑɚɫɬɨ ɞɢɫɫɨɰɢɚɰɢɸ ɨɛɥɟɝɱɚɟɬ ɧɚɤɨɩɥɟɧɢɟ ɷɧɟɪɝɢɢ ɧɚ ɤɨɥɟɛɚɬɟɥɶɧɨ-ɜɪɚɳɚɬɟɥɶɧɵɯ ɭɪɨɜɧɹɯ ɦɨɥɟɤɭɥɵ. Ⱥɫɫɨɰɢɚɰɢɟɣ ɧɚɡɵɜɚɸɬ ɨɛɪɚɬɧɵɣ ɩɪɨɰɟɫɫ: ɨɛɴɟɞɢɧɟɧɢɟ ɚɬɨɦɨɜ (ɢɥɢ ɢɨɧɚ ɢ ɚɬɨɦɚ) ɜ ɦɨɥɟɤɭɥɭ (ɢɥɢ ɩɪɨɫɬɵɯ ɦɨɥɟɤɭɥ ɜ ɛɨɥɟɟ ɫɥɨɠɧɵɟ).
ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɢ ɞɢɫɫɨɰɢɚɰɢɹ ɢ ɚɫɫɨɰɢɚɰɢɹ ɧɟɪɟɞɤɨ ɛɵɜɚɸɬ ɫɥɨɠɧɵɦɢ, ɪɟɚɥɶɧɨ ɦɧɨɝɨɫɬɚɞɢɣɧɵɦɢ, ɩɪɨɰɟɫɫɚɦɢ: ɜ ɧɢɯ ɭɱɚɫɬɜɭɟɬ ɧɟ ɦɟɧɟɟ ɬɪɟɯ ɱɚɫɬɢɰ, ɢ ɩɪɨɫɬɨɦɭ ɩɪɹɦɨɦɭ ɩɪɨɰɟɫɫɭ ɞɢɫɫɨɰɢɚɰɢɢ Ⱥȼ + ɋ →Ⱥ + ȼ + ɋ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɥɨɠɧɵɣ ɬɪɨɣɧɨɣ ɩɪɨɰɟɫɫ ɚɫɫɨɰɢɚɰɢɢ Ⱥ + ȼ + ɋ → Ⱥȼ + ɋ, ɤɨɝɞɚ ɱɚɫɬɢɰɚ Ⱥȼ ɨɛɪɚɡɭɟɬɫɹ ɜ ɜɨɡɛɭɠɞɟɧɧɨɦ ɫɨɫɬɨɹɧɢɢ ɢ ɩɟɪɟɯɨɞɢɬ ɜ ɨɫɧɨɜɧɨɟ ɫɨɫɬɨɹɧɢɟ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɹɞɚ ɩɨɫɥɟɞɭɸɳɢɯ ɩɚɪɧɵɯ ɫɬɨɥɤɧɨɜɟɧɢɣ.
§ 6. ɍɩɪɭɝɨɟ ɪɚɫɫɟɹɧɢɟ ȿɫɥɢ ɜ ɩɪɨɰɟɫɫɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɩɨɥɧɚɹ ɩɨɫɬɭɩɚɬɟɥɶɧɚɹ ɷɧɟɪɝɢɹ ɱɚɫɬɢɰ ɨɫɬɚɟɬɫɹ ɧɟɢɡɦɟɧɧɨɣ, ɬɨ ɩɪɨɰɟɫɫ ɹɜɥɹɟɬɫɹ ɭɩɪɭɝɢɦ ɪɚɫɫɟɹɧɢɟɦ. ȼ ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɟ ɜɚɠɧɵ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɫ ɧɟɣɬɪɚɥɶɧɵɦɢ ɱɚɫɬɢɰɚɦɢ. ȼ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ ɫ ɧɟɣɬɪɚɥɶɧɵɦɢ ɱɚɫɬɢɰɚɦɢ ɬɚɤ ɠɟ, ɤɚɤ ɢ ɧɟɣɬɪɚɥɶɧɵɟ ɱɚɫɬɢɰɵ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ ɦɟɠɞɭ ɫɨɛɨɣ. Ɉɞɧɚɤɨ ɩɪɢ ɛɨɥɟɟ ɫɬɪɨɝɨɦ ɩɨɞɯɨɞɟ ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ, ɱɬɨ ɡɚɪɹɠɟɧɧɚɹ ɱɚɫɬɢɰɚ ɫɜɨɢɦ ɩɨɥɟɦ ɩɨɥɹɪɢɡɭɟɬ ɧɟɣɬɪɚɥɶɧɭɸ ɱɚɫɬɢɰɭ, ɢ ɷɬɨ ɭɫɥɨɠɧɹɟɬ ɯɚɪɚɤɬɟɪ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ. ɋɟɱɟɧɢɟ ɪɚɫɫɟɹɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɧɟ ɬɨɥɶɤɨ ɝɟɨɦɟɬɪɢɱɟɫɤɢɦɢ ɪɚɡɦɟɪɚɦɢ ɧɟɣɬɪɚɥɶɧɨɣ ɱɚɫɬɢɰɵ, ɧɨ ɢ ɟɟ ɩɨɥɹɪɢɡɭɟɦɨɫɬɶɸ. Ɉɫɨɛɟɧɧɨ ɛɨɥɶɲɨɣ ɩɨɥɹɪɢɡɭɟɦɨɫɬɶɸ ɨɛɥɚɞɚɸɬ ɚɬɨɦɵ ɳɟɥɨɱɧɵɯ ɦɟɬɚɥɥɨɜ ɢ ɧɟɤɨɬɨɪɵɟ ɚɬɨɦɵ ɜ ɜɨɡɛɭɠɞɟɧɧɨɦ ɫɨɫɬɨɹɧɢɢ. ɉɨɥɹɪɢɡɭɟɦɨɫɬɶ ɦɨɥɟɤɭɥ ɫɭɳɟɫɬɜɟɧɧɨ ɧɢɠɟ, ɨɧɚ ɛɥɢɡɤɚ ɤ ɩɨɥɹɪɢɡɭɟɦɨɫɬɢ ɧɟ ɳɟɥɨɱɧɵɯ ɚɬɨɦɨɜ. ȼɟɪɨɹɬɧɨɫɬɶ ɭɩɪɭɝɨɝɨ ɪɚɫɫɟɹɧɢɹ ɧɟɣɬɪɚɥɶɧɵɯ ɱɚɫɬɢɰ ɫɥɚɛɨ ɡɚɜɢɫɢɬ ɨɬ ɢɯ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɫɤɨɪɨɫɬɟɣ. ɉɪɨɰɟɫɫɵ ɩɟɪɟɧɨɫɚ ɜ ɫɥɚɛɨ ɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɟ ɨɱɟɧɶ ɛɥɢɡɤɢ ɤ ɬɚɤɨɜɵɦ ɜ ɝɚɡɟ, ɤɪɨɦɟ, ɟɫɬɟɫɬɜɟɧɧɨ, ɩɨɞɜɢɠɧɨɫɬɢ ɧɚɩɪɚɜɥɟɧɧɨɣ ɫɤɨɪɨɫɬɢ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ, ɩɪɢɨɛɪɟɬɚɟɦɨɣ ɢɦɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. ɍɩɪɭɝɢɟ ɫɬɨɥɤɧɨɜɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɢɦɟɸɬ ɢɧɨɣ ɯɚɪɚɤɬɟɪ, ɢ ɜ ɫɢɥɶɧɨ ɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɟ ɢɦɟɧɧɨ ɨɧɢ ɨɩɪɟɞɟɥɹɸɬ ɮɨɪɦɭ ɮɭɧɤɰɢɣ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɢ ɩɪɨɰɟɫɫɵ ɩɟɪɟɧɨɫɚ. Ɋɚɫɫɦɨɬɪɢɦ ɩɨɜɟɞɟɧɢɟ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ (ɧɚɡɨɜɟɦ ɟɟ ɩɪɨɛɧɨɣ), ɩɪɨɥɟɬɚɸɳɟɣ ɱɟɪɟɡ ɨɛɥɚɤɨ ɩɨɤɨɹɳɢɯɫɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ (ɧɚɡɨɜɟɦ ɢɯ ɩɨɥɟɜɵɦɢ). ȼ ɢɞɟɚɥɶɧɨɣ ɩɥɚɡɦɟ ɤɚɠɞɨɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɞɜɭɯ ɱɚɫɬɢɰ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɧɚɥɢɱɢɹ ɨɫɬɚɥɶɧɵɯ, ɧɨ ɩɪɢ ɜɵɱɢɫɥɟɧɢɢ ɩɨɥɧɨɝɨ ɫɟɱɟɧɢɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɧɚɞɨ ɭɱɟɫɬɶ ɷɤɪɚɧɢɪɨɜɚɧɢɟ ɩɥɚɡɦɨɣ ɩɨɥɹ ɞɚɧɧɨɣ ɱɚɫɬɢɰɵ. ȿɫɥɢ ɩɪɨɛɧɚɹ ɱɚɫɬɢɰɚ ɞɜɢɠɟɬɫɹ ɬɚɤ, ɱɬɨ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɨɧɚ ɩɪɨɥɟɬɟɥɚ ɛɵ ɦɢɦɨ ɩɨɥɟɜɨɣ ɧɚ ɪɚɫɫɬɨɹɧɢɢ ρ (ɟɝɨ ɧɚɡɵɜɚɸɬ ɩɪɢɰɟɥɶɧɵɦ ɩɚɪɚɦɟɬɪɨɦ, ɪɢɫ. 1.6), ɬɨ ɨɧɚ ɨɬɤɥɨɧɢɬɫɹ ɧɚ ɭɝɨɥ θ, ɡɚɜɢɫɹɳɢɣ ɨɬ ɩɪɢɜɟɞɟɧɧɨɣ ɦɚɫɫɵ ɱɚɫɬɢɰ µ, ɢɯ ɡɚɪɹɞɨɜ Z ɢ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɫɤɨɪɨɫɬɢ v: Ɋɢɫ.1.6. ɋɯɟɦɚ ɭɩɪɭɝɨɝɨ ɫɨɭɞɚɪɟɧɢɹ Z1 Z 2 e 2 tg(θ/2) = ρ⊥/ρ, ρ⊥ = (1.17) µv 2 ɝɞɟ ρ⊥ - ɩɪɢɰɟɥɶɧɵɣ ɩɚɪɚɦɟɬɪ, ɩɪɢ ɤɨɬɨɪɨɦ ɩɪɨɛɧɚɹ ɱɚɫɬɢɰɚ ɨɬɤɥɨɧɹɟɬɫɹ ɧɚ ɭɝɨɥ π/2. ɉɨ ɫɭɳɟɫɬɜɭ ɬɚɤɨɟ ɪɚɫɫɦɨɬɪɟɧɢɟ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɨɩɢɫɚɧɢɸ ɞɜɢɠɟɧɢɹ ɨɞɧɨɣ ɱɚɫɬɢɰɵ ɫ ɩɪɢɜɟɞɟɧɧɨɣ ɦɚɫɫɨɣ µ ɜ ɩɨɥɟ ɰɟɧɬɪɚɥɶɧɵɯ ɫɢɥ. ɋ ɩɨɦɨɳɶɸ ɤɢɧɟɦɚɬɢɱɟɫɤɨɝɨ ɫɨɨɬɧɨɲɟɧɢɹ (1.17) ɜɵɜɨɞɢɬɫɹ ɮɨɪɦɭɥɚ Ɋɟɡɟɪɮɨɪɞɚ 2
· ρ⊥ dσ ρ dρ § ¸ . = = ¨¨ (1.18) dΩ sin θ dθ © 2 sin 2 (θ 2) ¸¹ ɋɤɨɪɨɫɬɶ ɩɪɨɛɧɨɣ ɱɚɫɬɢɰɵ ɩɪɢ ɭɩɪɭɝɨɦ ɪɚɫɫɟɹɧɢɢ ɦɟɧɹɟɬɫɹ ɬɨɥɶɤɨ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ, ɭɦɟɧɶɲɚɹɫɶ ɜ ɩɪɨɟɤɰɢɢ ɧɚ ɩɟɪɜɨɧɚɱɚɥɶɧɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɧɚ δv = v(1-cosθ) ɢ ɭɜɟɥɢɱɢɜɚɹɫɶ ɜ ɩɪɨɟɤɰɢɢ ɧɚ ɧɚɩɪɚɜɥɟɧɢɟ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɟ ɤ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɧɚ ɜɟɥɢɱɢɧɭ ∆v = v⋅sinθ. Ʉɚɠɞɚɹ ɢɡ ɧɢɯ ɨɩɪɟɞɟɥɹɟɬ ɡɧɚɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɩɟɪɟɧɨɫɚ: ∆v ɞɢɮɮɭɡɢɸ, δv - ɜɹɡɤɨɟ ɬɪɟɧɢɟ ɢ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ. Ɉɞɧɚɤɨ ɬɨɱɧɵɟ ɪɚɫɱɟɬɵ ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ ɢɧɬɟɝɪɚɥɶɧɵɟ ɫɟɱɟɧɢɹ ɷɬɢɯ ɩɪɨɰɟɫɫɨɜ ɨɬɥɢɱɚɸɬɫɹ ɧɟɡɧɚɱɢɬɟɥɶɧɨ ɢ ɩɨɷɬɨɦɭ ɨɛɵɱɧɨ ɪɚɫɫɦɚɬɪɢɜɚɸɬ ɜɟɥɢɱɢɧɭ δv, ɨɬɜɟɬɫɬɜɟɧɧɭɸ ɡɚ ɪɚɫɫɟɹɧɢɟ. ɉɪɨɜɟɞɹ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ δv ɩɨ ɜɫɟɦ ɭɝɥɚɦ ɪɚɫɫɟɹɧɢɹ θ (ɢɥɢ ɩɨ ɜɫɟɦ ɡɧɚɱɟɧɢɹɦ ɩɪɢɰɟɥɶɧɨɝɨ ɩɚɪɚɦɟɬɪɚ ρ), ɭɦɧɨɠɢɜ ɧɚ ɱɢɫɥɨ ɩɨɥɟɜɵɯ ɱɚɫɬɢɰ ɜ ɟɞɢɧɢɰɟ ɨɛɴɟɦɚ n ɢ ɧɚ ɩɭɬɶ ɩɪɨɛɧɨɣ ɱɚɫɬɢɰɵ dx, ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɜɟɥɢɱɢɧɭ ɢɡɦɟɧɟɧɢɹ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰɵ ɜ ɩɟɪɜɨɧɚɱɚɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ:
dv = −2πnvdx ³ ( 1 − cos θ ) ρdρ , ɩɨɞɫɬɚɜɥɹɹ (1.18) ɢ ɭɱɢɬɵɜɚɹ, ɱɬɨ sin (θ 2) = 2
ρ ⊥2
ρ 2 + ρ ⊥2
,
ɨɤɨɧɱɚɬɟɥɶɧɨ ɩɨɥɭɱɢɦ: ∞
dv = −4πnvdxρ⊥2 ³ 0
ρ dρ . ρ + ρ2 2 ⊥
(1.19)
Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɷɬɨɬ ɢɧɬɟɝɪɚɥ ɥɨɝɚɪɢɮɦɢɱɟɫɤɢ ɪɚɫɯɨɞɢɬɫɹ ɧɚ ɜɟɪɯɧɟɦ ɩɪɟɞɟɥɟ. Ɉɞɧɚɤɨ ɫɥɟɞɭɟɬ ɭɱɟɫɬɶ, ɱɬɨ ɪɟɚɥɶɧɨ ɜɵɞɟɥɟɧɧɚɹ ɧɚɦɢ ɩɨɥɟɜɚɹ ɱɚɫɬɢɰɚ ɷɤɪɚɧɢɪɭɟɬɫɹ ɨɤɪɭɠɚɸɳɟɣ ɩɥɚɡɦɨɣ ɢ ɟɟ ɩɨɥɟ ɛɵɫɬɪɨ ɭɦɟɧɶɲɚɟɬɫɹ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɪɚɫɫɬɨɹɧɢɹ. ɏɚɪɚɤɬɟɪɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɷɤɪɚɧɢɪɨɜɚɧɢɹ - ɞɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ d, ɢ ɢɧɬɟɝɪɢɪɨɜɚɬɶ ɫɥɟɞɭɟɬ ɜ ɩɪɟɞɟɥɚɯ 0 < ρ < d. Ɍɨɝɞɚ ɩɨɥɭɱɢɦ dv = −4πnvρ⊥2dxLc, (1.20) ɝɞɟ Lc = ln(d/ρ⊥) (1.21) - ɤɭɥɨɧɨɜɫɤɢɣ ɥɨɝɚɪɢɮɦ. ȼɟɥɢɱɢɧɚ Lc ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɫɫɟɹɧɢɟɦ ɧɚ ɦɚɥɵɟ ɭɝɥɵ, ɢ ɨɛɵɱɧɨ Lc ≈ 10÷20 ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɩɚɪɚɦɟɬɪɨɜ ɩɥɚɡɦɵ ɜ ɲɢɪɨɤɢɯ ɩɪɟɞɟɥɚɯ. Ɇɨɠɧɨ ɜɜɟɫɬɢ ɞɥɢɧɭ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ λ ɢ ɫɟɱɟɧɢɟ ɪɚɫɫɟɹɧɢɹ σc: dv dx =− , λ v 1 λ= , (1.22) nσ c σc = 4πρ⊥2Lc. Ɉɱɟɧɶ ɜɚɠɧɨ, ɱɬɨ ɫɟɱɟɧɢɟ ɪɚɫɫɟɹɧɢɹ σc ɫɢɥɶɧɨ ɡɚɜɢɫɢɬ ɨɬ ɷɧɟɪɝɢɢ ɱɚɫɬɢɰɵ, ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɤɜɚɞɪɚɬɭ ɟɟ ɷɧɟɪɝɢɢ (ɢɥɢ ɤɜɚɞɪɚɬɭ ɬɟɦɩɟɪɚɬɭɪɵ): 1 1 σc ~ 2 ∼ 2 . (1.23) T E ȼɜɨɞɹɬ ɢ ɩɨɧɹɬɢɟ ɜɪɟɦɟɧɢ ɪɚɫɫɟɹɧɢɹ ɢɥɢ ɤɭɥɨɧɨɜɫɤɨɝɨ ɜɪɟɦɟɧɢ, ɨɩɪɟɞɟɥɹɹ ɟɝɨ ɤɚɤ: λ 1 τc = = . (1.24) v nσ c v Ʌɟɝɤɨ ɜɢɞɟɬɶ, ɱɬɨ ɜɪɟɦɹ ɪɚɫɫɟɹɧɢɹ ɛɵɫɬɪɨ ɪɚɫɬɟɬ ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ τc ∼ T3/2. (1.25) Ⱦɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɩɨ ɦɟɪɟ ɪɨɫɬɚ ɬɟɦɩɟɪɚɬɭɪɵ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ ɪɚɫɫɟɢɜɚɸɬɫɹ ɦɟɞɥɟɧɧɟɟ. Ɍɪɚɟɤɬɨɪɢɹ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɜ ɩɥɚɡɦɟ ɫɭɳɟɫɬɜɟɧɧɨ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɬɪɚɟɤɬɨɪɢɢ ɧɟɣɬɪɚɥɶɧɨɣ ɱɚɫɬɢɰɵ ɜ ɝɚɡɟ (ɪɢɫ. 1.7): ɜ ɩɥɚɡɦɟ - ɷɬɨ ɦɟɞɥɟɧɧɨ ɦɟɧɹɸɳɚɹɫɹ ɩɥɚɜɧɚɹ ɤɪɢɜɚɹ. ɉɟɪɟɡɚɪɹɞɤɚ ȼɟɫɶɦɚ ɜɚɠɧɵɦ ɹɜɥɹɟɬɫɹ ɩɪɨɰɟɫɫ ɩɟɪɟɞɚɱɢ ɡɚɪɹɞɚ ɨɬ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɤ ɧɟɣɬɪɚɥɶɧɨɣ: Ⱥ+ + ȼ ↔ Ⱥ + ȼ+. ȼ ɫɥɭɱɚɟ ɬɨɠɞɟɫɬɜɟɧɧɵɯ ɱɚɫɬɢɰ Ⱥ ɢ ȼ (ɤɪɨɦɟ ɡɚɪɹɞɨɜɨɝɨ ɫɨɫɬɨɹɧɢɹ): A ≡ B - ɷɬɨ ɩɪɨɰɟɫɫ ɭɩɪɭɝɢɣ: ɩɨɥɧɚɹ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɨɛɟɢɯ ɱɚɫɬɢɰ ɫɨɯɪɚɧɹɟɬɫɹ ɧɟɢɡɦɟɧɧɨɣ. Ɋɢɫ.1.7. Ɍɪɚɟɤɬɨɪɢɢ ɱɚɫɬɢɰ
ȿɫɥɢ ɠɟ Ⱥ ≠ ȼ, ɬɨ ɩɪɨɰɟɫɫ ɩɟɪɟɡɚɪɹɞɤɢ ɧɟɭɩɪɭɝɢɣ, ɬɚɤ ɤɚɤ ɷɧɟɪɝɢɢ ɢɨɧɢɡɚɰɢɢ ɱɚɫɬɢɰ Ⱥ ɢ ȼ ɪɚɡɥɢɱɧɵ. ȿɫɥɢ ɩɨɬɟɧɰɢɚɥ ɢɨɧɢɡɚɰɢɢ ɧɟɣɬɪɚɥɶɧɨɣ ɱɚɫɬɢɰɵ ɛɨɥɶɲɟ ɩɨɬɟɧɰɢɚɥɚ ɢɨɧɢɡɚɰɢɢ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ, ɬɨ ɧɚ ɜɟɥɢɱɢɧɭ ɷɧɟɪɝɢɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɷɬɨɣ ɪɚɡɧɢɰɟ, ɭɦɟɧɶɲɢɬɫɹ ɩɨɥɧɚɹ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɱɚɫɬɢɰ. ȼ ɫɥɭɱɚɟ, ɟɫɥɢ ɷɧɟɪɝɢɹ ɢɨɧɢɡɚɰɢɢ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɛɨɥɶɲɟ ɷɧɟɪɝɢɢ ɢɨɧɢɡɚɰɢɢ ɧɟɣɬɪɚɥɶɧɨɣ ɱɚɫɬɢɰɵ, ɬɨ ɢɡɛɵɬɨɤ ɷɧɟɪɝɢɢ ɜɵɞɟɥɢɬɫɹ ɢɥɢ ɜ ɜɢɞɟ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɱɚɫɬɢɰ, ɢɥɢ ɩɨɣɞɟɬ ɧɚ ɜɨɡɛɭɠɞɟɧɢɟ (ɭ ɚɬɨɦɨɜ ɩɨɫɥɟɞɧɟɟ ɛɵɜɚɟɬ ɪɟɞɤɨ ).
§ 7. Ɋɚɜɧɨɜɟɫɢɹ ɜ ɩɥɚɡɦɟ ɉɪɢ ɩɨɥɧɨɦ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɦ ɪɚɜɧɨɜɟɫɢɢ ɞɨɥɠɧɨ ɭɫɬɚɧɨɜɢɬɶɫɹ ɪɚɜɟɧɫɬɜɨ ɫɤɨɪɨɫɬɟɣ ɜɫɟɯ ɩɪɹɦɵɯ ɢ ɨɛɪɚɬɧɵɯ ɩɪɨɰɟɫɫɨɜ, ɚ ɬɚɤɠɟ ɪɚɜɟɧɫɬɜɨ ɜɫɟɯ ɬɟɦɩɟɪɚɬɭɪ (ɜɪɚɳɚɬɟɥɶɧɵɯ, ɤɨɥɟɛɚɬɟɥɶɧɵɯ, ɷɥɟɤɬɪɨɧɧɨɣ, ɢɨɧɧɨɣ, ɚɬɨɦɧɨɣ). Ɍɚɤɭɸ ɫɥɨɠɧɭɸ ɫɯɟɦɭ ɪɚɫɫɦɨɬɪɟɬɶ ɤɪɚɣɧɟ ɬɪɭɞɧɨ, ɚ ɦɨɠɟɬ ɛɵɬɶ ɢ ɧɟɜɨɡɦɨɠɧɨ. ɑɚɫɬɨ ɝɨɜɨɪɹɬ ɨ ɱɚɫɬɢɱɧɵɯ ɪɚɜɧɨɜɟɫɢɹɯ — ɩɪɢ ɦɚɥɵɯ ɬɟɦɩɟɪɚɬɭɪɚɯ ɩɨ ɜɫɟɦ ɫɬɟɩɟɧɹɦ ɫɜɨɛɨɞɵ (ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ, ɤɨɥɟɛɚɬɟɥɶɧɵɦ, ɜɪɚɳɚɬɟɥɶɧɵɦ ɫɨɫɬɨɹɧɢɹɦ), ɩɪɢ ɛɨɥɶɲɢɯ, ɤɨɝɞɚ ɦɨɥɟɤɭɥ ɢ ɚɬɨɦɨɜ ɭɠɟ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɬ, - ɨɬɞɟɥɶɧɨ ɨ ɬɟɦɩɟɪɚɬɭɪɚɯ ɯɚɨɬɢɱɟɫɤɨɝɨ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ. Ɋɚɫɫɦɨɬɪɢɦ ɩɪɢɦɟɪɵ ɢɨɧɢɡɚɰɢɨɧɧɨɝɨ ɪɚɜɧɨɜɟɫɢɹ ɜ ɚɬɨɦɚɪɧɨɦ ɝɚɡɟ (ɪɚɫɫɦɨɬɪɟɧɢɟ ɦɨɥɟɤɭɥ ɪɟɡɤɨ ɭɫɥɨɠɧɹɟɬ ɡɚɞɚɱɭ: ɧɚɞɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɨɥɟɛɚɬɟɥɶɧɨ ɜɨɡɛɭɠɞɟɧɧɵɟ ɫɨɫɬɨɹɧɢɹ, ɚɫɫɨɰɢɚɬɢɜɧɭɸ ɢɨɧɢɡɚɰɢɸ ɢ ɬ.ɞ.; ɧɟ ɪɚɫɫɦɚɬɪɢɜɚɟɦ ɬɚɤɠɟ ɢ ɚɜɬɨɢɨɧɢɡɚɰɢɨɧɧɵɟ ɫɨɫɬɨɹɧɢɹ). ɉɪɨɫɬɟɣɲɢɦɢ, ɢ ɨɞɧɨɜɪɟɦɟɧɧɨ ɧɚɢɛɨɥɟɟ ɱɚɫɬɨ ɜɫɬɪɟɱɚɸɳɢɦɢɫɹ, ɹɜɥɹɸɬɫɹ ɫɥɟɞɭɸɳɢɟ ɬɪɢ ɫɥɭɱɚɹ. Ȼɚɥɚɧɫ ɦɟɠɞɭ ɢɨɧɢɡɚɰɢɟɣ ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ ɢ ɬɪɨɣɧɨɣ ɪɟɤɨɦɛɢɧɚɰɢɟɣ ɉɪɨɰɟɫɫ (ɩɪɹɦɨɣ/ɨɛɪɚɬɧɵɣ) a+e→i+2e (ɢɨɧɢɡɚɰɢɹ) i+2e→a+e (ɪɟɤɨɦɛɢɧɚɰɢɹ)
ɋɤɨɪɨɫɬɶ ɩɪɨɰɟɫɫɚ wi = kinane wr = krnine2
Ɂɞɟɫɶ na, ni, ne - ɩɥɨɬɧɨɫɬɢ ɚɬɨɦɨɜ, ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ; ki, kr ɤɨɷɮɮɢɰɢɟɧɬɵ ɫɤɨɪɨɫɬɢ ɢɨɧɢɡɚɰɢɢ ɢ ɪɟɤɨɦɛɢɧɚɰɢɢ. ɋɤɨɪɨɫɬɶ ɩɪɨɢɡɜɨɞɫɬɜɚ, ɧɚɩɪɢɦɟɪ, ɢɨɧɧɨɣ ɤɨɦɩɨɧɟɧɬɵ ɜ ɬɚɤɢɯ ɩɪɨɰɟɫɫɚɯ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ: dni = wi − wr . (1.26) dt ȼ ɪɚɜɧɨɜɟɫɢɢ ɫɤɨɪɨɫɬɢ ɩɪɹɦɨɝɨ ɢ ɨɛɪɚɬɧɨɝɨ ɩɪɨɰɟɫɫɨɜ ɫɨɜɩɚɞɚɸɬ, ɬɚɤ ɱɬɨ ɞɨɥɠɧɨ ɛɵɬɶ wi = wr. ɉɨɷɬɨɦɭ ɤɨɧɫɬɚɧɬɚ ɪɚɜɧɨɜɟɫɢɹ K, ɤɨɬɨɪɭɸ ɨɩɪɟɞɟɥɢɦ ɤɚɤ ɨɬɧɨɲɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɫɤɨɪɨɫɬɢ ɩɪɹɦɨɝɨ ɢ ɨɛɪɚɬɧɨɝɨ ɩɪɨɰɟɫɫɨɜ – ɡɞɟɫɶ ɢɨɧɢɡɚɰɢɢ ɢ ɪɟɤɨɦɛɢɧɚɰɢɢ, ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɨɣ: k nn K= i = e i. (1.27) kr na Ɂɚɦɟɬɢɦ, ɱɬɨ ɜɜɟɞɟɧɧɚɹ ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɤɨɧɫɬɚɧɬɚ ɪɚɜɧɨɜɟɫɢɹ ɢɦɟɟɬ ɪɚɡɦɟɪɧɨɫɬɶ ɤɭɛɚ ɨɛɪɚɬɧɨɣ ɞɥɢɧɵ. Ȼɚɥɚɧɫ ɦɟɠɞɭ ɮɨɬɨɢɨɧɢɡɚɰɢɟɣ ɢ ɢɡɥɭɱɚɬɟɥɶɧɨɣ ɪɟɤɨɦɛɢɧɚɰɢɟɣ ɉɪɨɰɟɫɫ (ɩɪɹɦɨɣ/ɨɛɪɚɬɧɵɣ) a+γ→i+e (ɢɨɧɢɡɚɰɢɹ) i+e→a+γ
(ɪɟɤɨɦɛɢɧɚɰɢɹ)
ɋɤɨɪɨɫɬɶ ɩɪɨɰɟɫɫɚ
wi′ = k i′na j w ′p = k p′ ni ne
Ɂɞɟɫɶ na, ni, ne - ɩɥɨɬɧɨɫɬɢ ɚɬɨɦɨɜ, ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, k i′ j , k p′ ɤɨɷɮɮɢɰɢɟɧɬɵ ɫɤɨɪɨɫɬɢ ɮɨɬɨɢɨɧɢɡɚɰɢɢ ɢ ɢɡɥɭɱɚɬɟɥɶɧɨɣ ɪɟɤɨɦɛɢɧɚɰɢɢ. ȼ ɪɚɜɧɨɜɟɫɢɢ wi′ = w ′p ,
(1.28)
ɢ ɤɨɧɫɬɚɧɬɚ ɪɚɜɧɨɜɟɫɢɹ, ɨɩɪɟɞɟɥɟɧɧɚɹ ɬɚɤ ɠɟ, ɤɚɤ ɢ ɜ ɩɪɟɞɵɞɭɳɟɦ ɫɥɭɱɚɟ, ɨɤɚɡɵɜɚɟɬɫɹ k′j n n (1.29) K= i = i e, k p′ na (ɩɨ ɩɪɢɧɰɢɩɭ ɞɟɬɚɥɶɧɨɝɨ ɪɚɜɧɨɜɟɫɢɹ), ɬɚɤ ɱɬɨ ɜ ɨɛɨɢɯ ɫɥɭɱɚɹɯ
K=
ni ne . na
(1.30)
Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɫɨɨɬɧɨɲɟɧɢɹ ɱɢɫɥɚ ɡɚɪɹɠɟɧɧɵɯ ɢ ɧɟɣɬɪɚɥɶɧɵɯ ɱɚɫɬɢɰ ɜ ɩɥɚɡɦɟ ɜɜɨɞɹɬ ɩɨɧɹɬɢɟ ɫɬɟɩɟɧɢ ɢɨɧɢɡɚɰɢɢ α (ɢɧɨɝɞɚ ɷɬɨɬ ɩɚɪɚɦɟɬɪ ɧɚɡɵɜɚɸɬ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɢɨɧɢɡɚɰɢɢ) - ɨɬɧɨɲɟɧɢɟ ɱɢɫɥɚ ɢɨɧɨɜ ɤ ɫɭɦɦɟ ɱɢɫɥɚ ɢɨɧɨɜ ɢ ɧɟɣɬɪɚɥɶɧɵɯ ɱɚɫɬɢɰ: ni n α= = i , n0 = ni + na , (1.31) ni + na no ɝɞɟ n0 - ɩɨɥɧɚɹ ɤɨɧɰɟɧɬɪɚɰɢɹ ɢɨɧɨɜ ɢ ɚɬɨɦɨɜ (ɧɚɱɚɥɶɧɚɹ ɤɨɧɰɟɧɬɪɚɰɢɹ).
Ʌɟɝɤɨ ɭɫɬɚɧɨɜɢɬɶ ɫɜɹɡɶ ɦɟɠɞɭ ɫɬɟɩɟɧɶɸ ɢɨɧɢɡɚɰɢɢ ɢ ɤɨɧɫɬɚɧɬɨɣ ɢɨɧɢɡɚɰɢɨɧɧɨɝɨ ɪɚɜɧɨɜɟɫɢɹ K [9]. ȼ ɩɪɟɞɩɨɥɨɠɟɧɢɢ, ɱɬɨ ni = nɟ., ɢɫɩɨɥɶɡɭɹ ɮɨɪɦɭɥɵ (1.27), (1.30) ɢ (1.31), ɩɨɥɭɱɚɟɦ ɫɨɨɬɧɨɲɟɧɢɟ
ni2 = Kna = K ( n0 − ni ) ,
ɩɪɟɞɫɬɚɜɥɹɸɳɟɟ ɫɨɛɨɣ ɤɜɚɞɪɚɬɧɨɟ ɭɪɚɜɧɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ni. Ɋɟɲɢɜ ɟɝɨ ɢ ɩɨɞɫɬɚɜɢɜ ɪɟɡɭɥɶɬɚɬ ɜ (1.31), ɜɵɪɚɡɢɦ ɫɬɟɩɟɧɶ ɢɨɧɢɡɚɰɢɢ ɱɟɪɟɡ ɤɨɧɫɬɚɧɬɭ ɪɚɜɧɨɜɟɫɢɹ ɢ ɧɚɱɚɥɶɧɭɸ ɤɨɧɰɟɧɬɪɚɰɢɸ ɝɚɡɚ: 2
§ K · K K . α=− + ¨ ¸ + n0 2 no © 2 no ¹
(1.32)
ɉɪɢ ɦɚɥɨɣ ɫɬɟɩɟɧɢ ɢɨɧɢɡɚɰɢɢ, ɤɨɝɞɚ ɤɨɧɰɟɧɬɪɚɰɢɹ ɢɨɧɨɜ ɦɚɥɚ, ni << no, ɧɚɯɨɞɢɦ
ni ≈ Kn0 , ɬɚɤ
ɱɬɨ
α=
ni ≈ n0
K , no
(1.33)
ɬ.ɟ. ɫɬɟɩɟɧɶ ɢɨɧɢɡɚɰɢɢ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɤɨɪɧɸ ɤɜɚɞɪɚɬɧɨɦɭ ɢɡ ɧɚɱɚɥɶɧɨɣ ɩɥɨɬɧɨɫɬɢ, ɬɚɤ ɤɚɤ ɤɨɧɫɬɚɧɬɚ ɪɚɜɧɨɜɟɫɢɹ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɬɨɥɶɤɨ ɬɟɦɩɟɪɚɬɭɪɵ ɝɚɡɚ. ɉɪɢ ɛɨɥɶɲɨɣ ɫɬɟɩɟɧɢ ɢɨɧɢɡɚɰɢɢ, ɤɨɝɞɚ ɤɨɧɰɟɧɬɪɚɰɢɹ ɧɟɣɬɪɚɥɶɧɵɯ ɚɬɨɦɨɜ ɦɚɥɚ, ni >> nɚ, ɩɨɥɭɱɚɟɦ α→1.
Ȼɚɥɚɧɫ ɦɟɠɞɭ ɢɨɧɢɡɚɰɢɟɣ ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ ɢ ɢɡɥɭɱɚɬɟɥɶɧɨɣ ɪɟɤɨɦɛɢɧɚɰɢɟɣ ȼ ɩɪɟɞɵɞɭɳɟɦ ɩɪɢɦɟɪɟ ɩɪɟɞɩɨɥɚɝɚɥɨɫɶ, ɱɬɨ ɢɡɥɭɱɟɧɢɟ ɡɚɩɟɪɬɨ ɢ ɧɟ ɜɵɯɨɞɢɬ ɢɡ ɪɟɚɤɰɢɨɧɧɨɝɨ ɨɛɴɟɦɚ. ȿɫɥɢ ɠɟ ɩɥɚɡɦɚ ɩɪɨɡɪɚɱɧɚ ɞɥɹ ɢɡɥɭɱɟɧɢɹ, ɬ.ɟ. ɟɺ ɩɥɨɬɧɨɫɬɶ ɞɨɫɬɚɬɨɱɧɨ ɦɚɥɚ, ɬɨ ɦɚɥɚ ɫɤɨɪɨɫɬɶ ɮɨɬɨɢɨɧɢɡɚɰɢɢ, ɢ ɢɨɧɢɡɚɰɢɹ ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɨɛɭɫɥɨɜɥɟɧɚ ɫɨɭɞɚɪɟɧɢɹɦɢ. ȼ ɩɥɚɡɦɟ ɦɚɥɨɣ ɩɥɨɬɧɨɫɬɢ ɦɚɥɨɜɟɪɨɹɬɧɵ ɢ ɬɪɨɣɧɵɟ ɫɨɭɞɚɪɟɧɢɹ, ɩɨɷɬɨɦɭ ɝɥɚɜɧɵɦ ɤɨɧɤɭɪɢɪɭɸɳɢɦ ɫ ɢɨɧɢɡɚɰɢɟɣ ɩɪɨɰɟɫɫɨɦ ɹɜɥɹɟɬɫɹ ɢɡɥɭɱɚɬɟɥɶɧɚɹ ɪɟɤɨɦɛɢɧɚɰɢɹ: ɉɪɨɰɟɫɫ (ɩɪɹɦɨɣ/ɨɛɪɚɬɧɵɣ) a+e→i+2e (ɢɨɧɢɡɚɰɢɹ) i+e→a+γ
(ɪɟɤɨɦɛɢɧɚɰɢɹ)
ɋɤɨɪɨɫɬɶ ɩɪɨɰɟɫɫɚ
wi = k i na ne w ′p = k p′ ni ne
ɉɪɢɪɚɜɧɢɜɚɹ ɫɤɨɪɨɫɬɢ ɩɪɹɦɨɝɨ ɢ ɨɛɪɚɬɧɨɝɨ ɩɪɨɰɟɫɫɨɜ, ɩɨɥɭɱɢɦ ɮɨɪɦɭɥɭ ɗɥɶɜɟɪɬɚ: n k (1.34) K′ = i = i , na k p′ ɢɡ ɤɨɬɨɪɨɣ ɜɢɞɧɨ, ɱɬɨ ɫɬɟɩɟɧɶ ɢɨɧɢɡɚɰɢɢ K′ α= (1.35) 1+ K′ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɬɨɥɶɤɨ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɩɥɨɬɧɨɫɬɢ. Ⱦɥɹ ɩɥɚɡɦɵ, ɧɚɯɨɞɹɳɟɣɫɹ ɜ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɦ ɪɚɜɧɨɜɟɫɢɢ, ɤɨɧɫɬɚɧɬɚ ɪɚɜɧɨɜɟɫɢɹ Ʉ ɦɨɠɟɬ ɛɵɬɶ ɩɨɥɭɱɟɧɚ ɤɚɤ ɩɨ ɚɧɚɥɨɝɢɢ ɫ ɤɨɧɫɬɚɧɬɨɣ ɯɢɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ, ɬɚɤ ɢ ɢɡ ɤɢɧɟɬɢɱɟɫɤɢɯ ɫɨɨɛɪɚɠɟɧɢɣ [9], ɢ ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɨɣ: 3/ 2 ne ni g i g e § me′T · K= = ¨ ¸ e−I /T , na g a © 2π! 2 ¹
ɝɞɟ gi, ge, ga — ɫɬɚɬɢɫɬɢɱɟɫɤɢɟ ɜɟɫɚ ɢɨɧɨɜ, ɷɥɟɤɬɪɨɧɨɜ ɢ ɚɬɨɦɨɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ; I - ɷɧɟɪɝɢɹ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚ, me′ = me mi / ( me + mi ) - ɩɪɢɜɟɞɟɧɧɚɹ ɦɚɫɫɚ. Ɉɬɜɟɱɚɸɳɚɹ ɷɬɨɦɭ ɪɚɜɧɨɜɟɫɢɸ ɫɬɟɩɟɧɶ ɢɨɧɢɡɚɰɢɢ α, ɤɚɤ ɥɟɝɤɨ ɜɵɜɟɫɬɢ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ 3/ 2 g i g e § me′T · T − I / T α2 , (1.36) = e ¨ ¸ g a © 2π! 2 ¹ p 1−α2 ɝɞɟ ɪ = (ne+ni+na)T - ɞɚɜɥɟɧɢɟ, ɨɩɪɟɞɟɥɹɟɦɨɟ ɱɢɫɥɨɦ ɱɚɫɬɢɰ ɜɫɟɯ ɫɨɪɬɨɜ ɜ ɟɞɢɧɢɰɟ ɨɛɴɟɦɚ. ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ, ɤɚɤ ɢ ɞɨɥɠɧɨ ɛɵɬɶ ɜ ɭɫɥɨɜɢɹɯ ɩɨɥɧɨɝɨ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ, ɪɚɜɧɨɜɟɫɧɚɹ ɫɬɟɩɟɧɶ ɢɨɧɢɡɚɰɢɢ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɞɚɜɥɟɧɢɹ ɩɥɚɡɦɵ. Ɏɨɪɦɭɥɚ (1.36) - ɮɨɪɦɭɥɚ ɋɚɯɚ - ɫɜɹɡɵɜɚɟɬ ɨɫɧɨɜɧɵɟ ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɱɚɫɬɢɰ: ɩɪɢɜɟɞɟɧɧɭɸ ɦɚɫɫɭ (ɞɥɹ ɩɪɨɰɟɫɫɚ ɢɨɧɢɡɚɰɢɢ ɨɧɚ ɩɪɢɦɟɪɧɨ ɪɚɜɧɚ ɦɚɫɫɟ ɷɥɟɤɬɪɨɧɚ me ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɦɚɥɨɝɨ ɨɬɧɨɲɟɧɢɹ me/mi, ɝɞɟ mi - ɦɚɫɫɚ ɢɨɧɚ), ɫɬɚɬɢɫɬɢɱɟɫɤɢɟ ɜɟɫɚ ɱɚɫɬɢɰ (ɢɨɧɚ, ɷɥɟɤɬɪɨɧɚ, ɚɬɨɦɚ), ɷɧɟɪɝɢɸ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚ ɢ ɬɟɦɩɟɪɚɬɭɪɭ ɩɥɚɡɦɵ ɫ ɤɨɧɫɬɚɧɬɨɣ ɪɚɜɧɨɜɟɫɢɹ Ʉ. Ɏɭɧɞɚɦɟɧɬɚɥɶɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɯɨɪɨɲɨ ɢɡɜɟɫɬɧɵ: ɫɬɚɬɢɫɬɢɱɟɫɤɢɣ ɜɟɫ ɷɥɟɤɬɪɨɧɚ ɪɚɜɟɧ ɞɜɭɦ, ɚ ɫɬɚɬɢɫɬɢɱɟɫɤɢɟ ɜɟɫɚ ɚɬɨɦɚ ɢ ɢɨɧɚ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɧɟɡɚɜɢɫɢɦɨ. Ɉɧɢ ɪɚɜɧɵ ɱɢɫɥɭ ɫɨɫɬɨɹɧɢɣ ɫ ɞɚɧɧɵɦ ɝɥɚɜɧɵɦ ɤɜɚɧɬɨɜɵɦ ɱɢɫɥɨɦ, ɧɚɩɪɢɦɟɪ, ɞɥɹ ɚɬɨɦɚ ɜɨɞɨɪɨɞɚ, ɜ ɫɨɫɬɨɹɧɢɢ ɫ ɝɥɚɜɧɵɦ ɤɜɚɧɬɨɜɵɦ ɱɢɫɥɨɦ, ɪɚɜɧɵɦ n, ɫɬɚɬɢɫɬɢɱɟɫɤɢɣ ɜɟɫ ɪɚɜɟɧ 2n2.
ɏɨɬɹ ɮɨɪɦɭɥɚ ɋɚɯɚ (ɢ ɟɟ ɚɧɚɥɨɝɢ) ɩɪɢɦɟɧɢɦɚ ɤ ɩɥɚɡɦɟ, ɧɚɯɨɞɹɳɟɣɫɹ ɜ ɩɨɥɧɨɦ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɦ ɪɚɜɧɨɜɟɫɢɢ, ɟɟ ɢɫɩɨɥɶɡɭɸɬ ɩɪɢ ɨɰɟɧɤɟ ɢ ɞɥɹ ɩɥɚɡɦɵ ɜ ɫɥɭɱɚɟ ɧɟɩɨɥɧɨɝɨ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ. ɋɥɟɞɭɟɬ ɢɦɟɬɶ ɜ ɜɢɞɭ, ɤɪɨɦɟ ɬɨɝɨ, ɱɬɨ ɨɧɚ ɜɟɪɧɚ ɥɢɲɶ ɩɪɢ ɧɟɤɨɬɨɪɵɯ ɭɩɪɨɳɚɸɳɢɯ ɩɪɟɞɩɨɥɨɠɟɧɢɹɯ ɨɬɧɨɫɢɬɟɥɶɧɨ ɷɬɨɝɨ ɪɚɜɧɨɜɟɫɢɹ: ɝɚɡ ɫɱɢɬɚɟɬɫɹ ɤɥɚɫɫɢɱɟɫɤɢɦ, ɩɨɞɱɢɧɹɸɳɢɦɫɹ ɪɚɫɩɪɟɞɟɥɟɧɢɸ ɆɚɤɫɜɟɥɥɚȻɨɥɶɰɦɚɧɚ. Ɍɟɦ ɫɚɦɵɦ, ɧɚɢɦɟɧɶɲɚɹ ɞɥɢɧɚ ɜɨɥɧɵ ɞɟ Ȼɪɨɣɥɹ, ɷɥɟɤɬɪɨɧɧɚɹ, ɞɨɥɠɧɚ ɛɵɬɶ ɦɟɧɶɲɟ ɫɪɟɞɧɟɝɨ ɦɟɠɱɚɫɬɢɱɧɨɝɨ ɪɚɫɫɬɨɹɧɢɹ. ɉɥɚɡɦɚ ɞɨɥɠɧɚ ɛɵɬɶ ɪɚɡɪɟɠɟɧɧɨɣ ɧɚ ɫɬɨɥɶɤɨ, ɱɬɨ ɫɪɟɞɧɟɟ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ ɜɟɥɢɤɨ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɚɦɩɥɢɬɭɞɨɣ ɪɚɫɫɟɹɧɢɹ. Ɍɨɝɞɚ ɷɥɟɤɬɪɨɧɵ, ɢɨɧɵ ɢ ɚɬɨɦɵ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɫɦɟɫɶ ɢɞɟɚɥɶɧɵɯ ɝɚɡɨɜ. ɇɚɤɨɧɟɰ, ɬɟɦɩɟɪɚɬɭɪɚ ɷɬɨɣ ɫɦɟɫɢ ɞɨɥɠɧɚ ɛɵɬɶ ɦɚɥɚ ɜ ɫɪɚɜɧɟɧɢɢ ɫ ɷɧɟɪɝɢɟɣ ɢɨɧɢɡɚɰɢɢ – ɬɨɥɶɤɨ ɩɪɢ ɷɬɨɦ ɭɫɥɨɜɢɢ ɤɨɥɢɱɟɫɬɜɨ ɜɨɡɛɭɠɞɟɧɧɵɯ ɚɬɨɦɨɜ ɦɚɥɨ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɱɢɫɥɨɦ ɚɬɨɦɨɜ ɜ ɨɫɧɨɜɧɨɦ ɫɨɫɬɨɹɧɢɢ. ȼ ɧɟɤɨɬɨɪɵɯ ɭɫɥɨɜɢɹɯ ɨɤɚɡɵɜɚɟɬɫɹ ɫɭɳɟɫɬɜɟɧɧɨɣ ɫɬɭɩɟɧɱɚɬɚɹ ɢɨɧɢɡɚɰɢɹ - ɨɛɪɚɡɨɜɚɧɢɟ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɢɡ ɜɨɡɛɭɠɞɟɧɧɵɯ ɚɬɨɦɨɜ, ɩɨɫɬɟɩɟɧɧɨ "ɞɨɜɨɡɛɭɠɞɚɟɦɵɯ" ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɹɯ ɱɟɪɟɡ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɜɨɡɛɭɠɞɟɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɞɨ ɢɨɧɢɡɚɰɢɢ. Ɋɟɚɥɢɡɚɰɢɹ ɷɬɨɣ ɜɨɡɦɨɠɧɨɫɬɢ ɡɚɜɢɫɢɬ ɨɬ ɜɪɟɦɟɧɢ ɠɢɡɧɢ ɜɨɡɛɭɠɞɟɧɧɵɯ ɚɬɨɦɨɜ, ɩɥɨɬɧɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ, ɩɨɬɟɧɰɢɚɥɨɜ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ ɜ ɨɫɧɨɜɧɨɦ ɢ ɜ ɜɨɡɛɭɠɞɟɧɧɵɯ ɫɨɫɬɨɹɧɢɹɯ. Ɋɟɚɥɶɧɨ ɫ ɩɨɥɧɨɫɬɶɸ ɬɟɪɦɨɥɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɨɣ ɫɬɚɥɤɢɜɚɸɬɫɹ, ɩɨɠɚɥɭɣ, ɬɨɥɶɤɨ ɚɫɬɪɨɮɢɡɢɤɢ, ɞɚ ɢ, ɜɨɡɦɨɠɧɨ, ɩɪɢ ɚɬɨɦɧɵɯ ɢ ɬɟɪɦɨɹɞɟɪɧɵɯ ɜɡɪɵɜɚɯ. ȼ ɬɟɪɦɨɹɞɟɪɧɵɯ ɭɫɬɚɧɨɜɤɚɯ ɫɬɪɟɦɹɬɫɹ ɩɨɥɭɱɢɬɶ ɬɚɤɭɸ ɬɟɪɦɨɥɢɡɨɜɚɧɧɭɸ ɩɥɚɡɦɭ; ɧɚɢɛɨɥɟɟ ɛɥɢɡɤɢ ɤ ɧɟɣ ɩɥɚɡɦɵ ɜ ɢɦɩɭɥɶɫɧɵɯ "ɜɡɪɵɜɧɵɯ" ɫɢɫɬɟɦɚɯ. ȼ ɫɢɫɬɟɦɚɯ ɫ ɦɚɝɧɢɬɧɨɣ ɬɟɪɦɨɢɡɨɥɹɰɢɟɣ (ɚɞɢɚɛɚɬɢɱɟɫɤɢɯ ɥɨɜɭɲɤɚɯ, ɬɨɤɚɦɚɤɚɯ ɢ ɬ.ɞ.) ɩɥɚɡɦɵ ɜɫɟɝɞɚ ɧɟɪɚɜɧɨɜɟɫɧɵɟ, ɯɨɬɹ ɢɧɨɝɞɚ ɢ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɱɚɫɬɢɱɧɨɟ ɪɚɜɧɨɜɟɫɢɟ - ɭɫɬɚɧɚɜɥɢɜɚɸɬɫɹ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ, ɛɥɢɡɤɢɟ ɤ ɦɚɤɫɜɟɥɥɨɜɫɤɢɦ, ɫɜɨɢ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɢ ɫɜɨɢ ɞɥɹ ɢɨɧɨɜ.
§ 8. ɇɟɪɚɜɧɨɜɟɫɧɨɫɬɶ ɩɥɚɡɦɟɧɧɵɯ ɫɢɫɬɟɦ Ɉɛɵɱɧɨ ɜ ɩɥɚɡɦɟ ɜɫɟɝɞɚ ɟɫɬɶ ɱɚɫɬɢɰɵ, ɨɱɟɧɶ ɫɢɥɶɧɨ ɪɚɡɥɢɱɚɸɳɢɟɫɹ ɩɨ ɦɚɫɫɟ: ɬɹɠɟɥɵɟ ɦɨɥɟɤɭɥɵ, ɚɬɨɦɵ ɢ ɢɯ ɢɨɧɵ, ɢ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɟɟ ɥɟɝɤɢɟ ɷɥɟɤɬɪɨɧɵ (ɨɬɧɨɲɟɧɢɟ ɦɚɫɫ ɩɪɨɬɨɧɚ ɢ ɷɥɟɤɬɪɨɧɚ ɪɚɜɧɨ mp/me≅1836). ȼɡɚɢɦɨɞɟɣɫɬɜɢɟ ɬɹɠɟɥɵɯ ɢ ɥɟɝɤɢɯ ɱɚɫɬɢɰ ɧɟ ɫɢɦɦɟɬɪɢɱɧɨ: ɥɟɝɤɢɟ ɱɚɫɬɢɰɵ ɫɢɥɶɧɨ ɪɚɫɫɟɢɜɚɸɬɫɹ ɧɚ ɬɹɠɟɥɵɯ ɢ ɨɱɟɧɶ ɦɟɞɥɟɧɧɨ ɩɟɪɟɞɚɸɬ ɢɦ ɫɜɨɸ ɷɧɟɪɝɢɸ, ɬɨɝɞɚ ɤɚɤ ɬɹɠɟɥɵɟ ɱɚɫɬɢɰɵ ɧɚ ɥɟɝɤɢɯ ɱɚɫɬɢɰɚɯ ɩɨɱɬɢ ɧɟ ɪɚɫɫɟɢɜɚɸɬɫɹ, ɧɨ ɞɨɜɨɥɶɧɨ ɢɧɬɟɧɫɢɜɧɨ ɬɨɪɦɨɡɹɬɫɹ. ȼ ɛɨɥɶɲɢɧɫɬɜɟ ɫɥɭɱɚɟɜ ɩɥɚɡɦɭ ɫɨɡɞɚɸɬ, ɩɪɢɦɟɧɹɹ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ: ɢɥɢ ɩɪɹɦɨ ɩɨɦɟɳɚɹ ɜ ɝɚɡ ɷɥɟɤɬɪɨɞɵ ɫ ɧɟɤɨɬɨɪɨɣ ɪɚɡɧɨɫɬɶɸ ɩɨɬɟɧɰɢɚɥɨɜ (ɧɚɩɪɢɦɟɪ, ɞɭɝɨɜɵɟ ɩɥɚɡɦɨɬɪɨɧɵ, ɩɪɢɛɨɪɵ ɫ ɬɥɟɸɳɢɦ ɪɚɡɪɹɞɨɦ, Z-ɩɢɧɱɢ ɢ ɬ.ɞ.), ɢɥɢ ɢɧɞɭɤɬɢɜɧɨ ɧɚɜɨɞɹ ɩɟɪɟɦɟɧɧɭɸ ɗȾɋ ɜ ɨɛɴɟɦɟ (ɧɚɩɪɢɦɟɪ, ɋȼɑɩɥɚɡɦɨɬɪɨɧɵ, θ-ɩɢɧɱɢ, ɬɨɤɚɦɚɤɢ ɢ ɬ.ɞ.). ɉɨɞɜɢɠɧɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ ɫɢɥɶɧɨ ɪɚɡɥɢɱɚɸɬɫɹ, ɫɟɱɟɧɢɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɢɯ ɫ ɚɬɨɦɚɪɧɵɦɢ ɱɚɫɬɢɰɚɦɢ ɪɚɡɧɵɟ, ɢ ɨɛɵɱɧɨ ɷɥɟɤɬɪɨɧɵ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ ɩɪɢɨɛɪɟɬɚɸɬ ɛɨɥɶɲɭɸ ɷɧɟɪɝɢɸ, ɱɟɦ ɢɨɧɵ. ȼ ɪɚɡɥɢɱɧɵɯ ɩɨ ɤɨɧɫɬɪɭɤɰɢɢ ɫɢɫɬɟɦɚɯ ɪɚɡɪɹɞɵ ɪɚɡɜɢɜɚɸɬɫɹ ɩɨɪɚɡɧɨɦɭ, ɧɨ, ɤɚɤ ɩɪɚɜɢɥɨ, ɧɟ ɬɨɥɶɤɨ ɧɚɩɪɚɜɥɟɧɧɵɟ ɫɤɨɪɨɫɬɢ, ɧɨ ɢ ɷɧɟɪɝɢɹ, ɩɪɢɨɛɪɟɬɚɟɦɚɹ ɷɥɟɤɬɪɨɧɨɦ ɜ ɪɚɡɪɹɞɟ, ɛɨɥɶɲɟ ɷɧɟɪɝɢɢ, ɩɪɢɨɛɪɟɬɚɟɦɨɣ ɢɨɧɨɦ. Ɉɫɨɛɟɧɧɨ ɱɟɬɤɨ ɷɬɨ ɩɪɨɹɜɥɹɟɬɫɹ ɜ ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɟ ɝɚɡɨɜɨɝɨ ɪɚɡɪɹɞɚ. Ɋɚɫɫɦɨɬɪɢɦ ɜ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɵ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ (§ 51), ɫɬɟɩɟɧɶ ɢɨɧɢɡɚɰɢɢ ɤɨɬɨɪɨɝɨ ɫɨɫɬɚɜɥɹɟɬ ~0.01. ɗɬɨ ɭɱɚɫɬɨɤ ɪɚɡɪɹɞɚ, ɝɞɟ ɩɨɬɟɧɰɢɚɥ ɦɟɧɹɟɬɫɹ ɧɚɢɛɨɥɟɟ ɩɥɚɜɧɨ ɢ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɩɪɢɦɟɪɧɨ ɩɨɫɬɨɹɧɧɚɹ. ȼ ɬɢɩɢɱɧɵɯ ɭɫɥɨɜɢɹɯ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɩɨɥɹ ɧɟ ɩɪɟɜɵɲɚɟɬ 1-10 ȼ/ɫɦ, ɚ ɞɚɜɥɟɧɢɟ ɝɚɡɚ ɫɨɫɬɚɜɥɹɟɬ 1-10 Ɍɨɪɪ. ɉɨɫɤɨɥɶɤɭ ɩɥɚɡɦɚ ɹɜɥɹɟɬɫɹ ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɨɣ, ɦɨɠɧɨ ɫɱɢɬɚɬɶ, ɱɬɨ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ ɫɬɚɥɤɢɜɚɸɬɫɹ ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɫ ɧɟɣɬɪɚɥɶɧɵɦɢ ɚɬɨɦɚɦɢ, ɚ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɦɟɠɞɭ ɫɨɛɨɣ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ. ɋɟɱɟɧɢɹ ɭɩɪɭɝɢɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɦɟɞɥɟɧɧɵɯ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɫ ɚɬɨɦɚɦɢ ɢ ɦɨɥɟɤɭɥɚɦɢ ɝɚɡɚ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɧɟɡɚɜɢɫɹɳɢɦɢ ɨɬ ɷɧɟɪɝɢɢ ɱɚɫɬɢɰ. Ʉɨɧɟɱɧɨ, ɜɟɥɢɱɢɧɵ ɫɟɱɟɧɢɣ ɡɚɜɢɫɹɬ ɨɬ ɪɨɞɚ ɝɚɡɚ, ɜ ɤɨɬɨɪɨɦ ɩɪɨɢɡɜɨɞɢɬɫɹ ɪɚɡɪɹɞ, ɧɨ ɜ ɬɢɩɢɱɧɵɯ ɭɫɥɨɜɢɹɯ ɫɟɱɟɧɢɟ ɭɩɪɭɝɨɝɨ ɪɚɫɫɟɹɧɢɹ ɞɥɹ ɢɨɧɨɜ ɦɨɠɟɬ ɞɨɫɬɢɝɚɬɶ ɜɟɥɢɱɢɧɵ σi~10-14ɫɦ2, ɬɨɝɞɚ ɤɚɤ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɨɧɨ ɩɪɢɦɟɪɧɨ ɧɚ ɩɨɪɹɞɨɤ ɦɟɧɶɲɟ σi~1015 ɫɦ2. ȼ ɷɬɢɯ ɭɫɥɨɜɢɹɯ ɫɪɟɞɧɹɹ ɞɥɢɧɚ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ λe ,i ~ 1 naσ e ,i , ɝɞɟ na ɩɥɨɬɧɨɫɬɶ ɝɚɡɚ, ɨɤɚɡɵɜɚɟɬɫɹ ɦɚɫɲɬɚɛɚ λi~10-4-10-3ɫɦ ɢ λɟ~10-3-10-2ɫɦ ɞɥɹ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. Ɍɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ ɨɛɵɱɧɨ ɩɪɢɦɟɪɧɨ ɪɚɜɧɚ ɢɨɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɢ ɞɥɹ ɪɚɡɪɹɞɚ ɦɚɥɨɣ ɦɨɳɧɨɫɬɢ ɩɨɪɹɞɤɚ ɤɨɦɧɚɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ, ɬ.ɟ. ɪɚɜɧɚ ɩɪɢɦɟɪɧɨ 0.03 ɷȼ, ɬɨɝɞɚ ɤɚɤ ɷɥɟɤɬɪɨɧɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ ɢ ɫɨɫɬɚɜɥɹɟɬ ~1ɷȼ. Ɉɛɫɭɞɢɦ ɩɪɢɱɢɧɭ ɬɚɤɨɝɨ ɧɟɪɚɜɧɨɜɟɫɢɹ. ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɫ ɧɚɩɪɹɠɟɧɧɨɫɬɶɸ ȿ, ɢɨɧ ɩɪɢɨɛɪɟɬɚɟɬ ɧɚ ɞɥɢɧɟ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ɦɟɠɞɭ ɫɨɭɞɚɪɟɧɢɹɦɢ ɷɧɟɪɝɢɸ ∆İi = eEλi, (1.37) ɚ ɷɥɟɤɬɪɨɧ ɷɧɟɪɝɢɸ ∆İe = eEλe. (1.38) ɋɱɢɬɚɟɦ, ɱɬɨ ɢɨɧɵ − ɨɞɧɨɡɚɪɹɞɧɵɟ, ɬɚɤ ɱɬɨ ɩɨ ɦɨɞɭɥɸ ɡɚɪɹɞ ɢɨɧɚ ɪɚɜɟɧ ɡɚɪɹɞɭ ɷɥɟɤɬɪɨɧɚ. Ⱦɥɹ ɩɪɢɜɟɞɟɧɧɵɯ ɜɵɲɟ ɩɚɪɚɦɟɬɪɨɜ ɨɰɟɧɤɚ ɞɚɟɬ ɞɥɹ ɷɬɢɯ ɜɟɥɢɱɢɧ ∆İi ≅10-4-10-3ɷȼ, ∆İɟ ≅10-3-10-2ɷȼ. ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɢ ɢɨɧɵ, ɢ ɷɥɟɤɬɪɨɧɵ ɩɪɢɨɛɪɟɬɚɸɬ ɧɚɩɪɚɜɥɟɧɧɭɸ ɫɤɨɪɨɫɬɶ, ɤɨɬɨɪɭɸ ɦɨɠɧɨ ɨɰɟɧɢɬɶ ɤɚɤ eE eE < ∆ui >≅ τi , < ∆ue >≅ − τ . (1.39) mi me e ȼ ɮɨɪɦɭɥɚɯ (1.39) ɜɪɟɦɹ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ ɫ ɧɟɣɬɪɚɥɶɧɵɦɢ ɱɚɫɬɢɰɚɦɢ
τ e ,i =
λe ,i < v e ,i >
, < v e ,i >=
2 < εe ,i > , me ,i
(1.40)
ɝɞɟ εe ,i - ɫɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ȼɜɢɞɭ ɝɨɪɚɡɞɨ ɛɨɥɶɲɟɣ ɩɨɞɜɢɠɧɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ (ɢɡ-ɡɚ ɦɚɥɨɣ ɦɚɫɫɵ), ɩɨ ɜɟɥɢɱɢɧɟ ɢɯ ɧɚɩɪɚɜɥɟɧɧɚɹ ɫɤɨɪɨɫɬɶ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ ɧɚɩɪɚɜɥɟɧɧɨɣ ɫɤɨɪɨɫɬɢ ɢɨɧɨɜ. ɋɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɢɨɧɚ ɛɭɞɟɬ ɩɪɚɤɬɢɱɟɫɤɢ ɪɚɜɧɚ ɫɪɟɞɧɟɣ ɷɧɟɪɝɢɢ ɧɟɣɬɪɚɥɶɧɵɯ ɱɚɫɬɢɰ, ɬɚɤ ɤɚɤ, ɩɪɢɨɛɪɟɬɚɹ ɦɟɠɞɭ ɫɨɭɞɚɪɟɧɢɹɦɢ ɦɚɥɭɸ ɞɨɩɨɥɧɢɬɟɥɶɧɭɸ ɷɧɟɪɝɢɸ ɩɨɪɹɞɤɚ ∆İi, ɢɨɧ ɩɪɢ ɫɨɭɞɚɪɟɧɢɢ ɫ ɚɬɨɦɚɦɢ ɟɟ ɨɬɞɚɟɬ, ɚ ɩɨɫɥɟɞɧɢɟ, ɩɨɥɭɱɢɜɲɢɟ ɷɧɟɪɝɢɸ ɩɪɢ ɫɨɭɞɚɪɟɧɢɢ, ɩɟɪɟɧɨɫɹɬ ɟɟ ɧɚ ɫɬɟɧɤɢ. ɗɥɟɤɬɪɨɧ ɠɟ, ɩɪɢɨɛɪɟɬɚɹ ɦɟɠɞɭ ɫɨɭɞɚɪɟɧɢɹɦɢ ɷɧɟɪɝɢɸ ɛɨɥɶɲɭɸ, ɱɟɦ ɢɨɧ, ɩɪɢ ɫɨɭɞɚɪɟɧɢɢ ɫ ɚɬɨɦɚɦɢ ɬɟɪɹɟɬ ɥɢɲɶ ɦɚɥɭɸ ɱɚɫɬɶ, ɩɨɪɹɞɤɚ ( me ma ) ε e , ɫɜɨɟɣ ɫɪɟɞɧɟɣ ɷɧɟɪɝɢɢ εe . ɇɨ ɜ ɫɬɚɰɢɨɧɚɪɧɵɯ ɭɫɥɨɜɢɹɯ ɢɦɟɧɧɨ ɷɬɚ ɦɚɥɚɹ ɩɨɬɟɪɹ ɷɧɟɪɝɢɢ ɢ ɨɝɪɚɧɢɱɢɜɚɟɬ ɧɚɛɨɪ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɚɦɢ ɜ ɩɨɥɟ. ɉɨɷɬɨɦɭ ɫɪɟɞɧɸɸ ɷɧɟɪɝɢɸ ɷɥɟɤɬɪɨɧɨɜ ɦɨɠɧɨ ɨɰɟɧɢɬɶ, ɩɨɬɪɟɛɨɜɚɜ ɛɚɥɚɧɫɚ ɷɧɟɪɝɢɢ, ɩɪɢɨɛɪɟɬɚɟɦɨɣ ɜ ɩɨɥɟ ɢ ɬɟɪɹɟɦɨɣ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɹɯ ɫ ɚɬɨɦɚɦɢ: 2
2
me ∆ue me m § eE · (1.41) εe ≅ = e ¨ τe ¸ . ma 2 2 © me ¹ ɉɨɫɤɨɥɶɤɭ ɜɯɨɞɹɳɟɟ ɜ ɷɬɭ ɮɨɪɦɭɥɭ ɯɚɪɚɤɬɟɪɧɨɟ ɜɪɟɦɹ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ ɷɥɟɤɬɪɨɧɚ ɫ ɧɟɣɬɪɚɥɶɧɵɦɢ ɱɚɫɬɢɰɚɦɢ τɟ ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɫɨɝɥɚɫɧɨ (1.40), ɡɚɜɢɫɢɬ ɨɬ ɫɪɟɞɧɟɣ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɨɜ, ɬɨ, ɜɵɪɚɡɢɜ ɢɡ (1.41) εe ɜ ɹɜɧɨɦ ɜɢɞɟ, ɩɨɥɭɱɢɦ
ma 1 eEλe . (1.42) me 2 ɉɨɥɭɱɟɧɧɵɣ ɪɟɡɭɥɶɬɚɬ ɥɢɲɶ ɱɢɫɥɟɧɧɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ (1/2 ɜɦɟɫɬɨ 0.43) ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɪɟɡɭɥɶɬɚɬɚ ɪɟɲɟɧɢɹ ɤɢɧɟɬɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ, ɩɪɢɜɟɞɟɧɧɨɝɨ ɜ [20]. ɋɪɚɜɧɢɜ (1.42) ɢ (1.38), ɦɵ ɜɢɞɢɦ, ɱɬɨ ɫɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɨɜ ɩɨɫɥɟ ɦɧɨɝɢɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɨɤɚɡɵɜɚɟɬɫɹ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ (ɩɪɢɦɟɪɧɨ ɜ ɤɨɪɟɧɶ ɢɡ ɨɬɧɨɲɟɧɢɹ ɦɚɫɫ ɧɟɣɬɪɚɥɶɧɨɣ ɱɚɫɬɢɰɵ ɢ ɷɥɟɤɬɪɨɧɚ) ɜɟɥɢɱɢɧɵ ɞɨɩɨɥɧɢɬɟɥɶɧɨɣ ɷɧɟɪɝɢɢ, ɩɪɢɨɛɪɟɬɚɟɦɨɣ ɷɥɟɤɬɪɨɧɨɦ ɧɚ ɞɥɢɧɟ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ. ɉɨɷɬɨɦɭ ɝɥɚɜɧɨɣ ɩɪɢɱɢɧɨɣ “ɩɟɪɟɝɪɟɜɚ” ɷɥɟɤɬɪɨɧɨɜ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɢɨɧɚɦɢ ɹɜɥɹɟɬɫɹ, ɩɨ ɫɭɳɟɫɬɜɭ, ɧɟ ɬɨɥɶɤɨ ɧɚɛɨɪ ɢɦɢ ɧɟɫɤɨɥɶɤɨ ɛɨɥɶɲɟɣ ɷɧɟɪɝɢɢ ɧɚ ɞɥɢɧɟ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ, ɚ ɝɨɪɚɡɞɨ ɛɨɥɟɟ ɫɥɚɛɵɣ ɬɟɦɩ ɩɨɬɟɪɶ ɩɨɥɭɱɟɧɧɨɣ ɜ ɩɨɥɟ ɷɧɟɪɝɢɢ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɹɯ ɫ ɚɬɨɦɚɦɢ. ɉɪɢ ɛɨɥɶɲɢɯ ɧɚɩɪɹɠɟɧɧɨɫɬɹɯ ɩɨɥɹ ɫɪɟɞɧɹɹ ɷɧɟɪɝɢɹ (1.42) ɫɭɳɟɫɬɜɟɧɧɨ ɜɵɲɟ ɬɟɦɩɟɪɚɬɭɪɵ ɝɚɡɚ. Ʉɚɤ ɭɩɨɦɢɧɚɥɨɫɶ ɪɚɧɟɟ, ɷɬɨ ɨɛɟɫɩɟɱɢɜɚɟɬ ɢɧɜɟɪɫɧɭɸ ɡɚɫɟɥɟɧɧɨɫɬɶ ɜ ɦɨɥɟɤɭɥɹɪɧɵɯ ɝɚɡɚɯ, ɩɪɚɜɞɚ, ɬɨɥɶɤɨ ɩɪɢ ɧɢɡɤɢɯ ɬɟɦɩɟɪɚɬɭɪɚɯ ɝɚɡɚ: ɜɟɪɨɹɬɧɨɫɬɶ ɤɨɥɟɛɚɬɟɥɶɧɨɣ ɪɟɥɚɤɫɚɰɢɢ ɨɱɟɧɶ ɛɵɫɬɪɨ ɜɨɡɪɚɫɬɟɬ ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ. ɉɨɷɬɨɦɭ ɢ ɩɪɢɯɨɞɢɬɫɹ ɨɯɥɚɠɞɚɬɶ ɥɚɡɟɪɵ, ɞɟɥɚɬɶ ɫɢɫɬɟɦɵ ɫ ɩɪɨɬɨɤɨɦ ɝɚɡɚ, ɬ.ɟ. ɨɛɟɫɩɟɱɢɜɚɬɶ ɭɫɥɨɜɢɹ, ɩɪɢ ɤɨɬɨɪɵɯ ɬɟɦɩɟɪɚɬɭɪɚ ɯɚɨɬɢɱɟɫɤɨɝɨ ɞɜɢɠɟɧɢɹ ɦɨɥɟɤɭɥ ɫɭɳɟɫɬɜɟɧɧɨ ɧɢɠɟ, ɱɟɦ «ɤɨɥɟɛɚɬɟɥɶɧɚɹ» ɬɟɦɩɟɪɚɬɭɪɚ ɜɨɡɛɭɠɞɟɧɧɵɯ ɚɬɨɦɨɜ. ɇɚɩɪɢɦɟɪ, ɜ ɥɚɡɟɪɚɯ ɧɚ ɨɤɢɫɢ ɭɝɥɟɪɨɞɚ ɩɪɢ ɤɨɦɧɚɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɝɚɡɚ ɞɨɫɬɢɠɢɦɵ ɤɨɥɟɛɚɬɟɥɶɧɵɟ ɬɟɦɩɟɪɚɬɭɪɵ, ɪɚɜɧɵɟ 7000 – 8000 Ʉ. ɇɟɪɚɜɧɨɜɟɫɧɨɫɬɶ, ɩɪɢ ɤɨɬɨɪɨɣ ɫɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɨɜ ɫɨɫɬɚɜɥɹɟɬ ɟɞɢɧɢɰɵ ɷɥɟɤɬɪɨɧ-ɜɨɥɶɬ, ɢ ɬɟɦɩɟɪɚɬɭɪɚ ɨɫɧɨɜɧɨɣ ɫɪɟɞɵ, ɤɨɬɨɪɚɹ ɧɟɦɧɨɝɨ ɛɨɥɶɲɟ ɤɨɦɧɚɬɧɨɣ, ɨɛɟɫɩɟɱɢɜɚɸɬ ɢ ɜɨɡɦɨɠɧɨɫɬɶ ɢɧɬɟɧɫɢɜɧɨɝɨ ɩɪɨɜɟɞɟɧɢɹ ɧɟɤɨɬɨɪɵɯ ɯɢɦɢɱɟɫɤɢɯ ɪɟɚɤɰɢɣ. ɗɥɟɤɬɪɨɧɵ ɩɟɪɟɞɚɸɬ ɷɧɟɪɝɢɸ ɧɚ ɜɨɡɛɭɠɞɟɧɢɟ ɤɨɥɟɛɚɬɟɥɶɧɵɯ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɦɨɥɟɤɭɥ, ɚ ɜɵɫɨɤɚɹ ɤɨɥɟɛɚɬɟɥɶɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɨɛɟɫɩɟɱɢɜɚɟɬ ɢ ɜɵɫɨɤɢɟ ɫɤɨɪɨɫɬɢ ɯɢɦɢɱɟɫɤɢɯ ɪɟɚɤɰɢɣ. ɇɟɨɛɯɨɞɢɦɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɩɪɢ ɷɬɨɦ ɫɭɳɟɫɬɜɟɧɧɨ ɜɨɡɪɚɫɬɚɟɬ ɢ ɄɉȾ ɩɨ ɜɵɯɨɞɭ ɤɨɧɟɱɧɨɝɨ ɩɪɨɞɭɤɬɚ ɭɫɬɚɧɨɜɨɤ, ɨɫɧɨɜɚɧɧɵɯ ɧɚ ɝɚɡɨɜɨɦ ɪɚɡɪɹɞɟ: ɷɥɟɤɬɪɨɧɧɨɟ ɜɨɡɛɭɠɞɟɧɢɟ ɨɛɟɫɩɟɱɢɜɚɟɬ ɩɟɪɟɞɚɱɭ ɷɧɟɪɝɢɢ ɢɦɟɧɧɨ ɧɚ “ɧɭɠɧɵɟ”
εe ≅
ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ, ɚ ɧɟ ɪɚɜɧɨɦɟɪɧɨ ɧɚ ɜɫɟ. Ɍɚɤ ɄɉȾ ɋɈ2-ɥɚɡɟɪɚ ɞɨɜɟɥɢ ɞɨ ∼25%, ɡɚɬɪɚɬɵ ɷɧɟɪɝɢɢ ɩɪɢ ɩɨɥɭɱɟɧɢɢ NO ɢɡ N2 ɢ O2 ɫɧɢɡɢɥɢ ɜ 6-7 ɪɚɡ. Ɇɵ ɪɚɫɫɦɨɬɪɟɥɢ ɧɟɪɚɜɧɨɜɟɫɧɨɫɬɶ ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɵ. ɇɨ ɢ ɩɪɚɤɬɢɱɟɫɤɢ ɩɨɥɧɨɫɬɶɸ ɢɨɧɢɡɨɜɚɧɧɚɹ ɝɨɪɹɱɚɹ ɩɥɚɡɦɚ ɬɨɠɟ, ɤɚɤ ɩɪɚɜɢɥɨ, ɧɟ ɪɚɜɧɨɜɟɫɧɚɹ. ɇɚɩɪɢɦɟɪ, ɜ ɢɡɜɟɫɬɧɵɯ ɬɨɤɚɦɚɤɚɯ ɭɫɬɚɧɚɜɥɢɜɚɸɬɫɹ ɪɚɡɧɵɟ ɬɟɦɩɟɪɚɬɭɪɵ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ, ɧɟ ɝɨɜɨɪɹ ɭɠɟ ɨɛ ɨɬɫɭɬɫɬɜɢɢ ɪɚɜɧɨɜɟɫɢɹ ɫ ɢɡɥɭɱɟɧɢɟɦ.
§ 9. ɉɪɨɰɟɫɫɵ ɪɟɥɚɤɫɚɰɢɢ ɜ ɩɥɚɡɦɟ ɉɪɨɰɟɫɫɵ ɪɟɥɚɤɫɚɰɢɢ ɩɪɢɜɨɞɹɬ ɤ ɭɫɬɚɧɨɜɥɟɧɢɸ ɦɚɤɫɜɟɥɥɨɜɫɤɨɣ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɱɚɫɬɢɰ ɩɨ ɷɧɟɪɝɢɹɦ, ɬ.ɟ. ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ, ɤɨɝɞɚ ɦɨɠɧɨ ɝɨɜɨɪɢɬɶ ɨ ɬɟɦɩɟɪɚɬɭɪɟ. ȼ ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɟ ɬɟɦɩɟɪɚɬɭɪɚ ɢɨɧɨɜ ɪɚɜɧɚ ɬɟɦɩɟɪɚɬɭɪɟ ɝɚɡɚ, ɦɚɫɫɵ ɢɨɧɨɜ ɢ ɚɬɨɦɨɜ ɩɪɚɤɬɢɱɟɫɤɢ ɨɞɢɧɚɤɨɜɵ. Ɍɟɦɩɟɪɚɬɭɪɚ ɷɥɟɤɬɪɨɧɨɜ ɦɨɠɟɬ ɛɵɬɶ ɞɪɭɝɨɣ, ɱɟɦ ɭ ɚɬɨɦɨɜ ɝɚɡɚ, ɞɚɠɟ ɬɨɝɞɚ, ɤɨɝɞɚ ɷɥɟɤɬɪɨɧɨɜ ɨɱɟɧɶ ɦɚɥɨ [8]. ȼ ɩɨɥɧɨɫɬɶɸ ɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɟ ɩɪɚɤɬɢɱɟɫɤɢ ɟɫɬɶ ɬɨɥɶɤɨ ɷɥɟɤɬɪɨɧɵ ɢ ɢɨɧɵ. Ɋɚɜɧɨɜɟɫɢɟ ɛɭɞɟɬ ɭɫɬɚɧɚɜɥɢɜɚɬɶɫɹ ɜɫɥɟɞɫɬɜɢɟ ɤɭɥɨɧɨɜɫɤɢɯ ɫɨɭɞɚɪɟɧɢɣ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ. Ɍɚɤ ɤɚɤ ɦɚɫɫɵ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɫɢɥɶɧɨ ɪɚɡɥɢɱɧɵ, ɬɨ ɪɚɫɫɦɨɬɪɢɦ ɨɬɞɟɥɶɧɨ ɷɥɟɤɬɪɨɧ-ɷɥɟɤɬɪɨɧɧɵɟ ɢ ɢɨɧ-ɢɨɧɧɵɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ. ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ Ʉ ɫɨɭɞɚɪɟɧɢɣ ɩɪɢɜɨɞɹɬ ɤ ɦɚɤɫɜɟɥɥɢɡɚɰɢɢ ɞɚɧɧɨɝɨ, ɧɚɩɪɢɦɟɪ, ɷɥɟɤɬɪɨɧɧɨɝɨ ɚɧɫɚɦɛɥɹ. Ɍɨɝɞɚ ɜɪɟɦɹ ɭɫɬɚɧɨɜɥɟɧɢɹ ɦɚɤɫɜɟɥɥɨɜɫɤɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫɪɟɞɢ ɷɥɟɤɬɪɨɧɨɜ 1 τ ee = K . (1.43) nvTeσ c ɝɞɟ σc ɤɭɥɨɧɨɜɫɤɨɟ ɫɟɱɟɧɢɟ, ɚ vTe – ɬɟɩɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ. ɉɨɞɫɬɚɜɥɹɹ ɡɧɚɱɟɧɢɟ ɤɭɥɨɧɨɜɫɤɨɝɨ ɫɟɱɟɧɢɹ σc ɢɡ (1.23) ɢ vTe = 3Te me , ɩɨɥɭɱɢɦ:
τ ee = K
3 3 4π e 4 Lc
me 3 / 2 T . n e
(1.44)
ɋɬɪɨɝɢɣ ɪɚɫɱɟɬ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ Ʉ<2. Ⱥɧɚɥɨɝɢɱɧɵɣ ɪɚɫɱɟɬ ɞɥɹ ɢɨɧɨɜ ɞɚɟɬ
mi 3 / 2 3 3 T , (1.45) 2 2 4 4π Z1 Z2 e Lc n i ɝɞɟ Z1,2 - ɤɪɚɬɧɨɫɬɢ ɢɨɧɢɡɚɰɢɢ. ɋɪɚɜɧɢɦ τee ɢ τii: ɞɥɹ ɪɚɜɧɵɯ ɬɟɦɩɟɪɚɬɭɪ Te=Ti , ɩɪɟɞɩɨɥɚɝɚɟɦ Z1=Z2=1: τ ee me . = τ ii mi
τ ii = K
Ɉɬɤɭɞɚ ɫɥɟɞɭɟɬ τee <<τii. ɉɪɢɜɟɞɟɧɧɵɟ ɮɨɪɦɭɥɵ ɞɥɹ ɯɚɪɚɤɬɟɪɧɵɯ ɜɪɟɦɟɧ ɫɬɨɥɤɧɨɜɟɧɢɣ, ɤɨɧɟɱɧɨ, ɢɦɟɸɬ ɥɢɲɶ ɯɚɪɚɤɬɟɪ ɨɰɟɧɤɢ. Ⱦɟɬɚɥɶɧɵɣ ɪɚɫɱɟɬ [11] ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɩɪɢ ɤɭɥɨɧɨɜɫɤɨɦ ɫɬɨɥɤɧɨɜɟɧɢɢ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɫɨɪɬɚ “α“ ɫ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɟɣ ɫɨɪɬɚ “β“ ɯɚɪɚɤɬɟɪɧɨɟ ɜɪɟɦɹ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ (ɜɪɟɦɹ ɬɨɪɦɨɠɟɧɢɹ) ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɵɦ ταβ = 3/4(2π)-1/2[Tα3/2/(eα2eβ2Lcnβ)]mαµαβ−1/2, µαβ = mβmα/( mβ+mα), (1.46) ɝɞɟ eα,eβ - ɡɚɪɹɞɵ ɷɬɢɯ ɱɚɫɬɢɰ, mα ,mβ - ɦɚɫɫɵ, ɚ µαβ - ɩɪɢɜɟɞɟɧɧɚɹ ɦɚɫɫɚ. Ɂɞɟɫɶ ɢɧɞɟɤɫɵ α ɢ β ɨɛɨɡɧɚɱɚɸɬ ɫɨɪɬ ɩɥɚɡɦɟɧɧɵɯ ɱɚɫɬɢɰ. ɂɫɩɨɥɶɡɭɹ ɷɬɭ ɨɛɳɭɸ ɮɨɪɦɭɥɭ, ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɯɚɪɚɤɬɟɪɧɵɟ ɜɪɟɦɟɧɚ ɷɥɟɤɬɪɨɧ-ɷɥɟɤɬɪɨɧɧɵɯ, ɷɥɟɤɬɪɨɧ-ɢɨɧɧɵɯ ɢ ɢɨɧ-ɢɨɧɧɵɯ ɫɬɨɥɤɧɨɜɟɧɢɣ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɩɥɚɡɦɵ ɢɡ ɷɥɟɤɬɪɨɧɨɜ ɢ ɨɞɧɨɡɚɪɹɞɧɵɯ ɢɨɧɨɜ ɩɨɥɭɱɚɟɦ ɫɥɟɞɭɸɳɢɣ ɧɚɛɨɪ ɯɚɪɚɤɬɟɪɧɵɯ ɜɪɟɦɟɧ: τei = 3/4(2π)−1/2[Te3/2/(e4Lcn)]me1/2, τee = 21/2 τei, τii = (2mi/me)1/2(Ti/Te)3/2τei. (1.47) Ɉɬɦɟɬɢɦ, ɱɬɨ ɩɪɢɜɟɞɟɧɧɵɟ ɯɚɪɚɤɬɟɪɧɵɟ ɜɪɟɦɟɧɚ ɨɬɜɟɱɚɸɬ ɪɚɡɧɵɦ ɩɪɨɰɟɫɫɚɦ, ɜɟɞɭɳɢɦ ɤ ɪɟɥɚɤɫɚɰɢɢ ɩɟɪɜɨɧɚɱɚɥɶɧɨ ɧɟɪɚɜɧɨɜɟɫɧɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɥɚɡɦɟɧɧɵɯ ɱɚɫɬɢɰ ɤ ɪɚɜɧɨɜɟɫɧɨɦɭ. ȼ ɱɚɫɬɧɨɫɬɢ, ɜɪɟɦɹ τei
ɷɥɟɤɬɪɨɧ-ɢɨɧɧɵɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɨɬɜɟɱɚɟɬ ɜɪɟɦɟɧɢ ɬɨɪɦɨɠɟɧɢɹ (ɬɨɱɧɟɟ, ɩɨɬɟɪɢ ɧɚɩɪɚɜɥɟɧɧɨɣ ɫɤɨɪɨɫɬɢ) ɷɥɟɤɬɪɨɧɨɜ ɜ ɫɪɟɞɟ ɢɨɧɨɜ, ɬɨɝɞɚ ɤɚɤ ɜɪɟɦɹ τie ɨɬɜɟɱɚɥɨ ɛɵ ɜɪɟɦɟɧɢ ɬɨɪɦɨɠɟɧɢɹ ɢɨɧɨɜ ɧɚ ɷɥɟɤɬɪɨɧɚɯ. Ɉɱɟɜɢɞɧɨ, ɷɬɢ ɜɪɟɦɟɧɚ ɫɭɳɟɫɬɜɟɧɧɨ ɪɚɡɥɢɱɚɸɬɫɹ. Ⱦɥɹ ɧɚɝɥɹɞɧɨɫɬɢ ɩɪɟɞɫɬɚɜɢɦ, ɱɬɨ ɦɹɱ ɞɥɹ ɧɚɫɬɨɥɶɧɨɝɨ ɬɟɧɧɢɫɚ ɜɥɟɬɚɟɬ ɜ ɨɛɥɚɤɨ ɚɪɛɭɡɨɜ ɫɪɟɞɧɟɝɨ ɪɚɡɦɟɪɚ; ɦɹɱ ɛɭɞɟɬ ɞɨɥɝɨ ɦɟɬɚɬɶɫɹ ɦɟɠɞɭ ɚɪɛɭɡɚɦɢ, ɩɨɱɬɢ ɧɟ ɫɞɜɢɝɚɹ ɢɯ ɫ ɦɟɫɬɚ. ɂ ɧɚɨɛɨɪɨɬ, ɚɪɛɭɡ, ɜɥɟɬɚɸɳɢɣ ɜ ɨɛɥɚɤɨ ɬɚɤɢɯ ɦɹɱɟɣ, ɛɭɞɟɬ ɞɜɢɝɚɬɶɫɹ, ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɦɟɧɹɹ ɧɚɩɪɚɜɥɟɧɢɹ, ɧɨ ɪɚɫɲɜɵɪɢɜɚɹ ɦɹɱɢ ɢ ɡɚɦɟɞɥɹɹ ɫɜɨɸ ɫɤɨɪɨɫɬɶ. ȼ ɩɥɚɡɦɟ ɱɚɫɬɢɰɵ - ɡɚɪɹɠɟɧɧɵɟ, ɯɚɪɚɤɬɟɪ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɢɧɨɣ, ɧɨ ɤɚɱɟɫɬɜɟɧɧɨ ɤɚɪɬɢɧɚ ɚɧɚɥɨɝɢɱɧɚɹ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɚɦɨɟ ɤɨɪɨɬɤɨɟ ɢɡ ɪɟɥɚɤɫɚɰɢɨɧɧɵɯ ɜɪɟɦɟɧ − ɷɬɨ ɜɪɟɦɹ, ɡɚ ɤɨɬɨɪɨɟ ɷɥɟɤɬɪɨɧɵ ɬɟɪɹɸɬ ɧɚɩɪɚɜɥɟɧɧɭɸ ɫɤɨɪɨɫɬɶ ɜ ɫɬɨɥɤɧɨɜɟɧɢɹɯ ɫ ɢɨɧɚɦɢ. ȼɪɟɦɹ ɦɚɤɫɜɟɥɥɢɡɚɰɢɢ ɷɥɟɤɬɪɨɧɧɨɣ ɩɨɞɫɢɫɬɟɦɵ, ɬɨ ɟɫɬɶ ɭɫɬɚɧɨɜɥɟɧɢɹ ɷɥɟɤɬɪɨɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ Te ɜ 2 ɪɚɡ ɛɨɥɶɲɟ. ɋɥɟɞɭɸɳɢɣ ɩɨ ɞɥɢɬɟɥɶɧɨɫɬɢ ɩɪɨɰɟɫɫ − ɦɚɤɫɜɟɥɥɢɡɚɰɢɹ ɢɨɧɧɨɣ ɩɨɞɫɢɫɬɟɦɵ ɩɥɚɡɦɵ. Ⱦɥɢɬɟɥɶɧɨɫɬɶ ɷɬɨɝɨ ɩɪɨɰɟɫɫɚ, ɜ ɬɟɱɟɧɢɟ ɤɨɬɨɪɨɝɨ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɢɨɧɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ Ti, ɩɪɢɦɟɪɧɨ ɜ mi me (~50 ɞɥɹ ɜɨɞɨɪɨɞɧɨɣ ɩɥɚɡɦɵ) ɪɚɡ ɛɨɥɶɲɟ. ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ Te ɢ Ti ɦɨɝɭɬ ɨɤɚɡɚɬɶɫɹ ɪɚɡɥɢɱɧɵɦɢ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɯɚɪɚɤɬɟɪɧɨɝɨ ɜɪɟɦɟɧɢ ɷɥɟɤɬɪɨɧ-ɢɨɧɧɨɣ ɢɥɢ ɢɨɧ-ɷɥɟɤɬɪɨɧɧɨɣ ɪɟɥɚɤɫɚɰɢɢ ɩɨ ɬɟɦɩɟɪɚɬɭɪɟ, ɬɨ ɟɫɬɶ ɭɫɬɚɧɨɜɥɟɧɢɹ ɟɞɢɧɨɣ, ɤɚɤ ɢ ɞɨɥɠɧɨ ɛɵɬɶ ɩɪɢ ɩɨɥɧɨɦ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɦ ɪɚɜɧɨɜɟɫɢɢ, ɬɟɦɩɟɪɚɬɭɪɵ ɜɫɟɯ ɤɨɦɩɨɧɟɧɬ ɩɥɚɡɦɵ, ɫɥɟɞɭɟɬ ɭɱɟɫɬɶ, ɱɬɨ ɢɡ-ɡɚ ɫɢɥɶɧɨɝɨ ɪɚɡɥɢɱɢɹ ɦɚɫɫ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɢ ɷɥɟɤɬɪɨɧɚ ɢ ɢɨɧɚ ɩɟɪɟɞɚɟɬɫɹ ɜɟɫɶɦɚ ɦɚɥɚɹ ɞɨɥɹ ɷɧɟɪɝɢɢ, ɩɨɪɹɞɤɚ ɨɬɧɨɲɟɧɢɹ ɦɚɫɫ, me/mi. ɉɨɷɬɨɦɭ ɷɬɨɬ ɩɪɨɰɟɫɫ ɟɳɟ ɛɨɥɟɟ ɞɥɢɬɟɥɶɧɵɣ. ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɞɥɢɬɟɥɶɧɨɫɬɶ ɷɬɨɝɨ ɩɪɨɰɟɫɫɚ ɫɨɫɬɚɜɥɹɟɬ[10]: 3 ( meTi + miTe )3 / 2 τε = . (1.48) 8 2 π me mi n( ei ee )2 Lc ɇɚɩɪɢɦɟɪ, ɜ ɩɥɚɡɦɟ, ɧɚɝɪɟɜɚɟɦɨɣ ɬɨɤɨɦ, ɤɨɝɞɚ ɜɵɞɟɥɟɧɢɟ ɞɠɨɭɥɟɜɚ ɬɟɩɥɚ ɩɪɨɢɫɯɨɞɢɬ ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɜ ɷɥɟɤɬɪɨɧɧɨɣ ɩɨɞɫɢɫɬɟɦɟ, ɛɵɫɬɪɟɟ ɜɫɟɝɨ ɭɫɬɚɧɨɜɢɬɫɹ ɬɟɦɩɟɪɚɬɭɪɚ ɷɥɟɤɬɪɨɧɨɜ, ɡɚɬɟɦ - ɬɟɦɩɟɪɚɬɭɪɚ ɢɨɧɨɜ (ɧɢɠɟ ɷɥɟɤɬɪɨɧɧɨɣ) ɢ ɨɱɟɧɶ ɞɨɥɝɨ ɛɭɞɟɬ ɭɫɬɚɧɚɜɥɢɜɚɬɶɫɹ (ɪɟɚɥɶɧɨ ɱɚɫɬɨ ɧɟ ɭɫɩɟɜɚɟɬ ɭɫɬɚɧɨɜɢɬɶɫɹ) ɟɞɢɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɱɚɫɬɨ ɝɨɜɨɪɹɬ ɨ ɧɚɥɢɱɢɢ “ɨɬɪɵɜɚ” ɷɥɟɤɬɪɨɧɧɨɣ ɢ ɢɨɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪ.
ȼ ɮɨɪɦɭɥɟ (1.48) Ɍɟ ɢ Ɍi ɢɦɟɸɬ ɫɦɵɫɥ ɧɚɱɚɥɶɧɵɯ ɬɟɦɩɟɪɚɬɭɪ ɧɚ ɫɬɚɞɢɢ ɩɪɟɞɲɟɫɬɜɭɸɳɟɣ ɩɪɨɰɟɫɫɭ ɪɟɥɚɤɫɚɰɢɢ. Ʌɸɛɨɩɵɬɧɨ, ɤɚɤɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɭɫɬɚɧɨɜɢɬɫɹ ɩɨɫɥɟ ɡɚɜɟɪɲɟɧɢɹ ɷɬɨɝɨ ɩɪɨɰɟɫɫɚ? ɑɬɨɛɵ ɨɬɜɟɬɢɬɶ ɧɚ ɷɬɨɬ ɜɨɩɪɨɫ, ɡɚɩɢɲɟɦ ɭɪɚɜɧɟɧɢɹ ɛɚɥɚɧɫɚ. ȼ ɩɪɨɫɬɟɣɲɟɦ ɫɥɭɱɚɟ ɨɧɢ ɡɚɩɢɫɵɜɚɸɬɫɹ ɜ ɜɢɞɟ:
dTe T − Ti dTi Te − Ti =− e , = . τε τε dt dt
ɗɬɢ ɭɪɚɜɧɟɧɢɹ ɨɩɢɫɵɜɚɸɬ ɩɟɪɟɞɚɱɭ ɷɧɟɪɝɢɢ ɦɟɠɞɭ ɷɥɟɤɬɪɨɧɧɨɣ ɢ ɢɨɧɧɨɣ ɩɨɞɫɢɫɬɟɦɚɦɢ. ɉɨɫɤɨɥɶɤɭ, ɤɚɤ ɡɞɟɫɶ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɜ ɰɟɥɨɦ ɧɟɬ ɩɨɬɟɪɶ ɷɧɟɪɝɢɢ ɫ ɩɟɪɟɞɚɱɟɣ ɟɟ ɨɤɪɭɠɚɸɳɢɦ ɬɟɥɚɦ, ɬɨ ɫɨɯɪɚɧɟɧɢɟ ɷɧɟɪɝɢɢ ɩɪɢɜɨɞɢɬ ɤ ɫɨɨɬɧɨɲɟɧɢɸ
Te + Ti = Te0 + Ti 0 = const .
ɉɨ ɡɚɜɟɪɲɟɧɢɢ ɩɪɨɰɟɫɫɚ ɪɟɥɚɤɫɚɰɢɢ ɜ ɫɢɫɬɟɦɟ ɞɨɥɠɧɚ ɭɫɬɚɧɨɜɢɬɶɫɹ ɬɟɦɩɟɪɚɬɭɪɚ Ɍ, ɨɛɳɚɹ ɞɥɹ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ, ɬɚɤ ɱɬɨ ɛɭɞɟɬ Ɍɟ=Ɍi=Ɍ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɥɭɱɚɟɦ Ɍ=(Ɍɟ0+Ɍi0)/2.
ɑɚɫɬɨ ɜɦɟɫɬɨ ɯɚɪɚɤɬɟɪɧɨɝɨ ɜɪɟɦɟɧɢ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ τ ɢɫɩɨɥɶɡɭɸɬ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɱɚɫɬɨɬɭ ɫɬɨɥɤɧɨɜɟɧɢɣ ν = τ−1. ȼ ɡɚɤɥɸɱɟɧɢɟ ɩɪɢɜɟɞɟɦ ɩɨɥɟɡɧɵɟ ɮɨɪɦɭɥɵ ɞɥɹ ɩɪɚɤɬɢɱɟɫɤɢɯ ɪɚɫɱɟɬɨɜ [12]:
2 Te2 L 4 Te λ ei = 4.5 ⋅ 10 , σ ei = 2 ⋅ 10 −6 c2 ≈ 3 ⋅ 10 −5 Te −2 , ≈ 3 ⋅ 10 nLc n Te 5
(1.49) 3/ 2 Te3 / 2 nLc n − 2 Te τ ei = 0.67 , ν ei = 1.5 3 / 2 ≈ 22 3 / 2 . ≈ 4.5 ⋅ 10 nLc n Te Te ɉɪɢ ɪɚɫɱɟɬɟ ɱɢɫɥɨɜɵɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɡɞɟɫɶ ɩɪɢɧɹɬɨ ɡɧɚɱɟɧɢɟ Lc=15, ɬɢɩɢɱɧɨɟ ɜ ɬɟɪɦɨɹɞɟɪɧɵɯ ɩɪɢɥɨɠɟɧɢɹɯ ɩɥɚɡɦɵ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɢɡɨɬɟɪɦɢɱɟɫɤɨɣ ɞɟɣɬɟɪɢɟɜɨɣ ɩɥɚɡɦɵ ɜ ɨɩɬɢɦɚɥɶɧɵɯ ɞɥɹ ɬɟɪɦɨɹɞɟɪɧɨɝɨ ɪɟɚɤɬɨɪɚ ɭɫɥɨɜɢɹɯ, ɤɨɝɞɚ ɬɟɦɩɟɪɚɬɭɪɚ ɢ ɤɨɧɰɟɧɬɪɚɰɢɹ ɩɥɚɡɦɵ ɪɚɜɧɵ T=108K, n=1014ɫɦ -3, ɫ ɩɨɦɨɳɶɸ ɷɬɢɯ ɮɨɪɦɭɥ ɩɨɥɭɱɚɟɦ ɫɥɟɞɭɸɳɢɟ ɡɧɚɱɟɧɢɹ λei ≈ 3⋅106ɫɦ, σei ≈ 3⋅10-22ɫɦ2, ɞɥɹ ɞɥɢɧɵ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ɢ ɫɟɱɟɧɢɹ ɤɭɥɨɧɨɜɫɤɢɯ ɫɬɨɥɤɧɨɜɟɧɢɣ, ɚ ɯɚɪɚɤɬɟɪɧɵɟ ɜɪɟɦɟɧɚ ɪɟɥɚɤɫɚɰɢɨɧɧɵɯ ɩɪɨɰɟɫɫɨɜ ɨɤɚɡɵɜɚɸɬɫɹ ɪɚɜɧɵɦɢ, c τei ≈ 4.5⋅10-4, τee ≈ 6.4⋅10-4, τii ≈ 0.04, τε ≈ 0.8.
§ 10. ɉɪɨɰɟɫɫɵ ɩɟɪɟɧɨɫɚ ɜ ɩɥɚɡɦɟ Ʉɚɤ ɢ ɜ ɨɛɵɱɧɨɦ ɝɚɡɟ, ɩɪɢ ɨɬɫɬɭɩɥɟɧɢɢ ɨɬ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ ɜ ɩɥɚɡɦɟ ɦɨɝɭɬ ɩɪɨɢɫɯɨɞɢɬɶ ɩɪɨɰɟɫɫɵ ɩɟɪɟɧɨɫɚ ɦɚɫɫɵ, ɢɦɩɭɥɶɫɚ ɢ ɷɧɟɪɝɢɢ, ɬ.ɟ. ɹɜɥɟɧɢɹ ɞɢɮɮɭɡɢɢ, ɜɹɡɤɨɝɨ ɬɪɟɧɢɹ ɢ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ. ɉɪɢ ɧɚɥɢɱɢɢ ɧɟɨɞɧɨɪɨɞɧɨɫɬɢ ɩɥɨɬɧɨɫɬɢ, ɢɦɩɭɥɶɫɚ ɢɥɢ ɬɟɦɩɟɪɚɬɭɪɵ, ɜɨɡɧɢɤɚɸɬ ɩɨɬɨɤɢ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵɟ ɝɪɚɞɢɟɧɬɭ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɜ ɩɥɚɡɦɟ, ɫɨɞɟɪɠɚɳɟɣ ɫɜɨɛɨɞɧɵɟ ɡɚɪɹɞɵ, ɦɨɠɟɬ ɩɨɹɜɢɬɶɫɹ ɢ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɚɹ ɧɟɨɞɧɨɪɨɞɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɡɚɪɹɞɚ, ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɟɪɟɧɨɫ ɡɚɪɹɞɚ - ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɬɨɤ. ɇɚɩɨɦɧɢɦ, ɱɬɨ ɫɨɝɥɚɫɧɨ ɝɚɡɨɤɢɧɟɬɢɱɟɫɤɨɣ ɬɟɨɪɢɢ ɤɨɷɮɮɢɰɢɟɧɬ ɞɢɮɮɭɡɢɢ ɦɨɠɧɨ ɨɰɟɧɢɬɶ ɤɚɤ 2 D ∼ ( ∆x ) / τ , (1.50) ɝɞɟ ∆x - ɫɪɟɞɧɟɟ ɫɦɟɳɟɧɢɟ ɱɚɫɬɢɰɵ ɩɪɢ ɯɚɨɬɢɱɟɫɤɢɯ ɛɥɭɠɞɚɧɢɹɯ, ɚ τ - ɜɪɟɦɹ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ. ȼɟɥɢɱɢɧɚ ∆x ɩɨɪɹɞɤɚ ɫɪɟɞɧɟɣ ɞɥɢɧɵ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ λ, ɢ ɦɨɠɧɨ ɩɨɤɚɡɚɬɶ, ɱɬɨ D = 1/3λvT , (1.51) T ɝɞɟ vT = 3 - ɬɟɩɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɱɚɫɬɢɰ ɝɚɡɚ. m ɂɡɜɟɫɬɧɵ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɜɹɡɤɨɫɬɢ η ɢ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ κ ɝɚɡɚ: η ~ mnD (1.52) κ ~ nD (1.53)
ɉɨɹɫɧɢɦ, ɤɚɤ ɜɨɡɧɢɤɚɸɬ ɫɨɨɬɧɨɲɟɧɢɹ (1.51)-(1.53). ȼ ɤɚɱɟɫɬɜɟ ɨɬɩɪɚɜɧɨɣ ɬɨɱɤɢ ɛɭɞɟɦ ɩɨɥɚɝɚɬɶ, ɱɬɨ ɫɟɱɟɧɢɟ ɭɩɪɭɝɢɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɦɨɥɟɤɭɥ ɹɜɥɹɟɬɫɹ ɩɪɢɛɥɢɠɟɧɧɨ ɩɨɫɬɨɹɧɧɨɣ ɜɟɥɢɱɢɧɨɣ, ɨɩɪɟɞɟɥɹɟɦɨɣ ɪɚɡɦɟɪɨɦ ɦɨɥɟɤɭɥɵ σ~πɚ2. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɫɪɟɞɧɹɹ ɞɥɢɧɚ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ɡɚɜɢɫɢɬ ɥɢɲɶ ɨɬ ɩɥɨɬɧɨɫɬɢ ɝɚɡɚ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ λ~1/(nσ)~1/(πɚ2n). ɇɚɩɪɢɦɟɪ, ɩɪɢ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ (0°ɋ, 1 ɚɬɦ.) $
ɩɥɨɬɧɨɫɬɶ ɝɚɡɚ ɪɚɜɧɚ ɱɢɫɥɭ Ʌɨɲɦɢɞɬɚ n≅2.7⋅1019ɫɦ-3, ɚ λ ɢɦɟɟɬ ɩɨɪɹɞɨɤ 10-6ɫɦ, ɟɫɥɢ ɚ=5 A . ȿɫɥɢ ɝɚɡ ɹɜɥɹɟɬɫɹ ɫɥɚɛɨ ɧɟɨɞɧɨɪɨɞɧɵɦ, ɬɨ ɫɪɟɞɧɸɸ ɞɥɢɧɭ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ɦɨɠɧɨ ɬɚɤɠɟ ɫɱɢɬɚɬɶ ɩɪɢɛɥɢɠɟɧɧɨ ɩɨɫɬɨɹɧɧɨɣ ɜɟɥɢɱɢɧɨɣ. ɉɭɫɬɶ ɝɚɡ ɫɥɚɛɨ ɧɟɨɞɧɨɪɨɞɟɧ ɩɨ ɨɞɧɨɣ ɤɨɨɪɞɢɧɚɬɟ, ɧɚɩɪɢɦɟɪ, ɩɨ ɤɨɨɪɞɢɧɚɬɟ ɯ ɢɡɦɟɧɹɟɬɫɹ ɩɥɨɬɧɨɫɬɶ ɝɚɡɚ. Ɋɚɫɫɦɨɬɪɢɦ ɩɥɨɫɤɨɫɬɶ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɭɸ ɨɫɢ ɯ. ɉɨ ɫɦɵɫɥɭ ɫɪɟɞɧɟɣ ɞɥɢɧɵ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ – ɞɥɢɧɵ, ɜ ɩɪɟɞɟɥɚɯ ɤɨɬɨɪɨɣ ɱɚɫɬɢɰɵ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɞɜɢɠɭɳɢɦɢɫɹ ɫɜɨɛɨɞɧɨ, - ɷɬɭ ɩɥɨɫɤɨɫɬɶ ɩɟɪɟɫɟɤɭɬ ɡɚ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ ɫɥɟɜɚ ɧɚ ɩɪɚɜɨ ɜɞɨɥɶ ɨɫɢ ɯ ɜɫɟ ɱɚɫɬɢɰɵ, ɢɦɟɸɳɢɟ ɩɨɥɨɠɢɬɟɥɶɧɭɸ ɩɪɨɟɤɰɢɸ ɫɤɨɪɨɫɬɢ vx>0 ɢ ɨɬɫɬɨɹɳɢɟ ɨɬ ɧɟɟ ɧɚ ɪɚɫɫɬɨɹɧɢɢ λvx/v vx>0. Ⱥɧɚɥɨɝɢɱɧɨ, ɫɩɪɚɜɚ ɧɚɥɟɜɨ ɜ ɨɛɪɚɬɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɩɥɨɫɤɨɫɬɶ ɩɟɪɟɫɟɤɚɸɬ ɜɫɟ ɱɚɫɬɢɰɵ ɫ ɨɬɪɢɰɚɬɟɥɶɧɨɣ ɤɨɦɩɨɧɟɧɬɨɣ ɫɤɨɪɨɫɬɢ ɢ ɨɬɫɬɨɹɳɢɟ ɨɬ ɧɟɟ ɧɚ ɪɚɫɫɬɨɹɧɢɢ /λvx/v/. ɑɬɨɛɵ ɧɚɣɬɢ ɪɟɡɭɥɶɬɢɪɭɸɳɢɣ ɩɨɬɨɤ, ɧɚɞɨ ɩɪɨɫɭɦɦɢɪɨɜɚɬɶ ɩɨ ɜɫɟɦ ɷɬɢɦ ɱɚɫɬɢɰɚɦ. ɍɱɬɟɦ, ɱɬɨ ɩɪɢ ɢɡɨɬɪɨɩɧɨɦ ɪɚɫɩɪɟɞɟɥɟɧɢɢ ɦɨɥɟɤɭɥ ɩɨ ɫɤɨɪɨɫɬɹɦ ɜ ɞɚɧɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɜ ɫɪɟɞɧɟɦ, ɨɱɟɜɢɞɧɨ, ɞɜɢɠɟɬɫɹ 1/6 ɱɚɫɬɶ ɦɨɥɟɤɭɥ ɩɪɢ ɫɪɟɞɧɟɣ ɫɤɨɪɨɫɬɢ ɯɚɨɬɢɱɟɫɤɨɝɨ ɞɜɢɠɟɧɢɹ vT. Ɍɨɝɞɚ ɪɟɡɭɥɶɬɢɪɭɸɳɚɹ ɩɥɨɬɧɨɫɬɶ ɩɨɬɨɤɚ ɱɚɫɬɢɰ, ɩɟɪɟɫɟɤɚɸɳɢɯ ɜɵɞɟɥɟɧɧɭɸ ɩɥɨɫɤɨɫɬɶ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɨɫɢ ɯ, ɩɪɢɛɥɢɠɟɧɧɨ ɪɚɜɧɚ
jx ≅
1 1 1 ∂n n( x − λ ) vT − n( x + λ ) vT ≅ − λvT . ∂x 6 6 3
Ɇɵ ɜɢɞɢɦ, ɱɬɨ ɩɥɨɬɧɨɫɬɶ ɩɨɬɨɤɚ ɨɤɚɡɵɜɚɟɬɫɹ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɣ ɝɪɚɞɢɟɧɬɭ ɤɨɧɰɟɧɬɪɚɰɢɢ. Ʉɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ ɡɞɟɫɶ ɢ ɟɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬ ɞɢɮɮɭɡɢɢ (1.51). Ⱥɧɚɥɨɝɢɱɧɨ, ɪɚɫɫɦɚɬɪɢɜɚɹ ɩɟɪɟɧɨɫ ɬɟɩɥɚ, ɢ ɭɱɢɬɵɜɚɹ, ɱɬɨ ɫɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɬɟɩɥɨɜɨɝɨ ɞɜɢɠɟɧɢɹ, ɧɚɩɪɢɦɟɪ, ɞɥɹ ɨɞɧɨɚɬɨɦɧɨɝɨ ɝɚɡɚ ɫɨɫɬɚɜɥɹɟɬ 3/2Ɍ, ɝɞɟ Ɍ – ɬɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ, ɤɨɬɨɪɚɹ ɬɟɩɟɪɶ ɫɱɢɬɚɟɬɫɹ ɩɟɪɟɦɟɧɧɨɣ ɜɟɥɢɱɢɧɨɣ, ɞɥɹ ɩɥɨɬɧɨɫɬɢ ɬɟɩɥɨɜɨɝɨ ɩɨɬɨɤɚ ɧɚɯɨɞɢɦ
qx =
∂T ∂T 1 3 1 1 · §3 nvT ¨ T ( x − λ ) − T ( x + λ )¸ ≅ − nλvT ≡ −κ , κ ≈ nλvT , ¹ ©2 6 2 2 2 ∂x ∂x
ɱɬɨ ɫɨɝɥɚɫɭɟɬɫɹ ɫ (1.53). ɇɚɩɨɦɧɢɦ, ɱɬɨ ɬɟɦɩɟɪɚɬɭɪɭ ɦɵ ɢɡɦɟɪɹɟɦ ɜ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɟɞɢɧɢɰɚɯ. ȼɹɡɤɨɫɬɶ ɜɨɡɧɢɤɚɟɬ ɩɪɢ ɧɚɥɢɱɢɢ ɝɪɚɞɢɟɧɬɚ ɫɪɟɞɧɟɣ ɩɨɬɨɤɨɜɨɣ ɫɤɨɪɨɫɬɢ. Ɍɚɤ, ɟɫɥɢ ɩɪɨɟɤɰɢɹ Vy ɫɪɟɞɧɟɣ ɫɤɨɪɨɫɬɢ ɦɟɧɹɟɬɫɹ ɩɨ ɯ, ɬɨ, ɢɡ-ɡɚ ɨɬɫɭɬɫɬɜɢɹ ɛɚɥɚɧɫɚ ɩɟɪɟɧɨɫɚ ɢɦɩɭɥɶɫɚ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɟ ɫɬɨɪɨɧɵ ɨɬ ɜɵɞɟɥɟɧɧɨɣ ɧɚɦɢ ɩɥɨɫɤɨɫɬɢ, ɜɨɡɧɢɤɚɟɬ ɩɨɬɨɤ ɭ-ɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɢɦɩɭɥɶɫɚ ɜɞɨɥɶ ɨɫɢ ɯ ɫ ɩɥɨɬɧɨɫɬɶɸ [5]
π yx = η
∂v y , η ~ pτ ∂x
,
ɝɞɟ ɪ – ɞɚɜɥɟɧɢɟ, ɚ τ - ɜɪɟɦɹ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ. ɉɨɫɤɨɥɶɤɭ ɞɥɹ ɨɞɧɨɤɨɦɩɨɧɟɧɬɧɨɝɨ ɝɚɡɚ p=nT, ɚ τ=λ/vT, ɬɨ ɩɨɥɭɱɚɟɦ
η ~ pτ ~ nT
λ
vT
= mn
λ T 1 = mnλvT , m 3T m 3
ɱɬɨ ɫɨɜɩɚɞɚɟɬ ɫ (1.52).
ɗɬɢ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɩɟɪɟɧɨɫɚ ɦɨɠɧɨ ɩɪɢɦɟɧɹɬɶ ɢ ɜ ɪɚɫɱɟɬɚɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɩɟɪɟɧɨɫɚ ɜ ɩɥɚɡɦɟ, ɢɦɟɹ, ɨɞɧɚɤɨ, ɜ ɜɢɞɭ, ɱɬɨ ɹɜɥɟɧɢɹ ɩɟɪɟɧɨɫɚ ɜ ɩɥɚɡɦɟ ɨɩɪɟɞɟɥɹɸɬɫɹ ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɭɩɪɭɝɢɦɢ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ. ɉɨɷɬɨɦɭ ɡɚɜɢɫɢɦɨɫɬɢ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɩɟɪɟɧɨɫɚ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɜ ɩɥɚɡɦɟ ɢ ɜ ɝɚɡɟ ɪɚɡɥɢɱɧɵ. ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɷɥɟɤɬɪɨɧɧɚɹ ɢ ɢɨɧɧɚɹ ɤɨɦɩɨɧɟɧɬɵ ɩɥɚɡɦɵ ɦɨɝɭɬ ɢɦɟɬɶ ɪɚɡɥɢɱɧɭɸ ɬɟɦɩɟɪɚɬɭɪɭ, ɢ ɬɨɝɞɚ ɪɚɫɫɦɨɬɪɟɧɢɟ ɩɪɨɰɟɫɫɨɜ ɩɟɪɟɧɨɫɚ ɭɫɥɨɠɧɹɟɬɫɹ, ɚ ɫɚɦɢ ɤɨɷɮɮɢɰɢɟɧɬɵ ɩɟɪɟɧɨɫɚ ɛɭɞɭɬ ɡɚɜɢɫɟɬɶ ɨɬ ɤɨɧɤɪɟɬɧɨɝɨ ɫɨɨɬɧɨɲɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪ. ȼ ɞɚɥɶɧɟɣɲɟɦ ɞɥɹ ɩɪɨɫɬɨɬɵ ɨɝɪɚɧɢɱɢɦ ɪɚɫɫɦɨɬɪɟɧɢɟ, ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ, ɫɥɭɱɚɟɦ ɢɡɨɬɟɪɦɢɱɟɫɤɨɣ ɞɜɭɯɤɨɦɩɨɧɟɧɬɧɨɣ ɩɥɚɡɦɵ. Ⱦɢɮɮɭɡɢɹ ȿɫɥɢ ɜ ɪɚɜɟɧɫɬɜɨ (1.51) ɩɨɞɫɬɚɜɢɬɶ ɡɧɚɱɟɧɢɟ λ ɢɡ ɜɵɪɚɠɟɧɢɹ (1.22) ɢ ɩɪɢɧɹɬɶ T vT = 3 , ɬɨ ɩɨɥɭɱɢɦ m 3 3 T 5/ 2 D= . (1.54) 4πe 4 Lc n m Ʉɨɷɮɮɢɰɢɟɧɬɵ ɞɢɮɮɭɡɢɢ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ, ɤɚɤ ɦɵ ɜɢɞɢɦ, ɡɧɚɱɢɬɟɥɶɧɨ ɪɚɡɥɢɱɚɸɬɫɹ (ɜ ɤɨɪɟɧɶ ɢɡ ɨɬɧɨɲɟɧɢɹ ɦɚɫɫ) ɢ ɨɱɟɧɶ ɫɢɥɶɧɨ ɡɚɜɢɫɹɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ (ɜ ɨɛɵɱɧɨɦ ɝɚɡɟ D ∼ T ). Ɉɞɧɚɤɨ ɜɫɟ ɨɫɨɛɟɧɧɨɫɬɢ ɞɢɮɮɭɡɢɢ ɜ ɩɥɚɡɦɟ ɷɬɢɦ ɧɟ ɨɝɪɚɧɢɱɢɜɚɸɬɫɹ. Ɍɚɤ ɤɚɤ ɤɨɷɮɮɢɰɢɟɧɬɵ ɞɢɮɮɭɡɢɢ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ ɫɢɥɶɧɨ ɪɚɡɥɢɱɚɸɬɫɹ, ɬɨ ɷɥɟɤɬɪɨɧɵ, ɢɦɟɸɳɢɟ ɛɨɥɶɲɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɞɢɮɮɭɡɢɢ, ɞɨɥɠɧɵ ɛɵ ɛɵɫɬɪɟɟ ɭɯɨɞɢɬɶ ɢɡ ɦɟɫɬ, ɝɞɟ ɩɥɨɬɧɨɫɬɶ ɩɥɚɡɦɵ ɛɨɥɶɲɟ. ɍɯɨɞ ɷɥɟɤɬɪɨɧɨɜ ɩɪɢɜɟɞɟɬ ɤ ɩɨɹɜɥɟɧɢɸ ɜ ɩɥɚɡɦɟ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɬɨɪɦɨɡɹɳɟɝɨ ɢɯ ɭɯɨɞ ɢ ɭɫɤɨɪɹɸɳɟɝɨ ɭɯɨɞ ɢɨɧɨɜ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɞɢɮɮɭɡɢɹ ɩɥɚɡɦɵ ɜ ɰɟɥɨɦ (ɦɚɫɫɚ ɩɥɚɡɦɵ ɮɚɤɬɢɱɟɫɤɢ ɨɛɭɫɥɨɜɥɟɧɚ ɢɨɧɚɦɢ) ɛɭɞɟɬ ɩɪɨɢɫɯɨɞɢɬɶ ɛɵɫɬɪɟɟ ɢɨɧɧɨɣ ɞɢɮɮɭɡɢɢ, ɜɨɡɧɢɤɚɟɬ ɬɚɤ ɧɚɡɵɜɚɟɦɚɹ ɚɦɛɢɩɨɥɹɪɧɚɹ ɞɢɮɮɭɡɢɹ. Ɉɩɪɟɞɟɥɢɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɚɦɛɢɩɨɥɹɪɧɨɣ ɞɢɮɮɭɡɢɢ, ɭɱɢɬɵɜɚɹ, ɱɬɨ ɜ ɭɫɬɚɧɨɜɢɜɲɟɦɫɹ ɞɜɢɠɟɧɢɢ ɩɨɬɨɤ ɢɨɧɨɜ ɛɭɞɟɬ ɨɩɪɟɞɟɥɹɬɶɫɹ ɤɚɤ ɨɛɵɱɧɨɣ ɞɢɮɮɭɡɢɟɣ, ɬɚɤ ɢ ɩɨɞɜɢɠɧɨɫɬɶɸ ɢɨɧɨɜ ɜ ɜɨɡɧɢɤɚɸɳɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ: dn dϕ ji = − Di i − bi , (1.55) dx dx ɝɞɟ bi - ɩɨɞɜɢɠɧɨɫɬɶ ɢɨɧɨɜ, ϕ - ɩɨɬɟɧɰɢɚɥ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. Ⱥɧɚɥɨɝɢɱɧɨ ɩɨɬɨɤ ɷɥɟɤɬɪɨɧɨɜ ɪɚɜɟɧ: dn dϕ je = − De e + be , (1.56) dx dx ɝɞɟ be - ɩɨɞɜɢɠɧɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ. Ɍɚɤ ɤɚɤ ɩɥɚɡɦɚ ɜ ɰɟɥɨɦ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɚ, ɬɨ, ɩɪɢɧɹɜ dϕ dni dne dn ne=ni=n ɢ = = , ɢ ɢɫɤɥɸɱɢɜ ɢɡ ɭɪɚɜɧɟɧɢɣ (1.55) ɢ (1.56), ɨɛɧɚɪɭɠɢɦ, ɱɬɨ dx dx dx dx ɩɥɨɬɧɨɫɬɶ ɩɨɬɨɤɚ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɝɪɚɞɢɟɧɬɭ ɟɟ ɤɨɧɰɟɧɬɪɚɰɢɢ: dn D b + De bi dn j=− i e = − Da . (1.57) bi + be dx dx
Ʉɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ ɦɟɠɞɭ ɩɥɨɬɧɨɫɬɶɸ ɩɨɬɨɤɚ ɱɚɫɬɢɰ ɢ ɝɪɚɞɢɟɧɬɨɦ ɤɨɧɰɟɧɬɪɚɰɢɢ ɢ ɟɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬ ɚɦɛɢɩɨɥɹɪɧɨɣ ɞɢɮɮɭɡɢɢ: D b + De bi Da = i e . (1.58) bi + be ɍɱɢɬɵɜɚɹ, ɱɬɨ, ɫɨɝɥɚɫɧɨ ɫɨɨɬɧɨɲɟɧɢɸ ɗɣɧɲɬɟɣɧɚ, ɩɨɞɜɢɠɧɨɫɬɶ ɱɚɫɬɢɰ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɞɢɮɮɭɡɢɢ ɫɜɹɡɚɧɵ ɦɟɠɞɭ ɫɨɛɨɣ ɫɨɨɬɧɨɲɟɧɢɹɦɢ be,i = (|e|D/T)e,i, (1.59) ɚ ɬɚɤɠɟ, ɭɱɢɬɵɜɚɹ, ɱɬɨ, ɫɨɝɥɚɫɧɨ ɜɵɪɚɠɟɧɢɸ (1.54), ɞɨɥɠɧɨ ɛɵɬɶ De>>Di ɢ, ɤɚɤ ɫɥɟɞɫɬɜɢɟ, ɷɥɟɤɬɪɨɧɵ ɡɧɚɱɢɬɟɥɶɧɨ ɩɨɞɜɢɠɧɟɟ ɢɨɧɨɜ, ɩɨɥɭɱɚɟɦ § T· Da = Di ¨ 1 + e ¸ . (1.60) Ti ¹ © Ɉɱɟɜɢɞɧɨ, ɢɦɟɸɬ ɦɟɫɬɨ ɧɟɪɚɜɟɧɫɬɜɚ Di
Da = 2Di. ɋɥɟɞɭɟɬ ɢɦɟɬɶ ɜ ɜɢɞɭ, ɱɬɨ ɤɨɝɞɚ ɝɨɜɨɪɹɬ ɨ ɞɢɮɮɭɡɢɢ, ɬɨ ɜɫɟɝɞɚ ɩɨɞɪɚɡɭɦɟɜɚɟɬɫɹ ɧɚɥɢɱɢɟ ɧɟɤɨɬɨɪɨɝɨ «ɮɨɧɚ» ɧɟɩɨɞɜɢɠɧɵɯ ɱɚɫɬɢɰ ɫɪɟɞɵ, ɫ ɤɨɬɨɪɵɦɢ ɫɬɚɥɤɢɜɚɸɬɫɹ ɞɢɮɮɭɧɞɢɪɭɸɳɢɟ ɱɚɫɬɢɰɵ. ɋɚɦɢ «ɮɨɧɨɜɵɟ» ɱɚɫɬɢɰɵ ɜ ɞɜɢɠɟɧɢɟ ɧɟ ɜɨɜɥɟɤɚɸɬɫɹ, ɨɫɬɚɜɚɹɫɶ ɧɟɩɨɞɜɢɠɧɵɦɢ. ɋɯɨɞɧɚɹ ɫɢɬɭɚɰɢɹ ɢɦɟɟɬ ɦɟɫɬɨ ɞɥɹ ɫɥɚɛɨ ɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɵ, ɤɨɝɞɚ ɡɚɪɹɠɟɧɧɚɹ ɤɨɦɩɨɧɟɧɬɚ ɫɬɨɥɶ ɦɚɥɨɱɢɫɥɟɧɧɚ, ɱɬɨ ɟɟ ɜɥɢɹɧɢɟɦ ɧɚ ɧɟɣɬɪɚɥɶɧɭɸ ɤɨɦɩɨɧɟɧɬɭ ɩɪɚɤɬɢɱɟɫɤɢ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ. ɉɨ ɷɬɨɣ ɠɟ ɩɪɢɱɢɧɟ ɧɟɫɭɳɟɫɬɜɟɧɧɵ ɫɬɨɥɤɧɨɜɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɞɪɭɝ ɫ ɞɪɭɝɨɦ, ɬɚɤ ɱɬɨ ɨɫɧɨɜɧɭɸ ɪɨɥɶ ɢɝɪɚɸɬ ɫɬɨɥɤɧɨɜɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɫ ɧɟɣɬɪɚɥɶɧɵɦɢ. ɂɦɟɧɧɨ ɨɧɢ ɨɩɪɟɞɟɥɹɸɬ ɜɟɥɢɱɢɧɵ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɩɨɞɜɢɠɧɨɫɬɢ ɢ, ɬɟɦ ɫɚɦɵɦ, ɤɨɷɮɮɢɰɢɟɧɬɵ ɞɢɮɮɭɡɢɢ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ. ɂɦɟɧɧɨ ɞɥɹ ɫɥɚɛɨ ɢɨɧɢɡɨɜɚɧɧɨɣ ɝɚɡɨɪɚɡɪɹɞɧɨɣ ɩɥɚɡɦɵ ɢ ɛɵɥ ɜɩɟɪɜɵɟ ɩɪɟɞɥɨɠɟɧ ɒɨɬɬɤɢ (1924) ɦɟɯɚɧɢɡɦ ɚɦɛɢɩɨɥɹɪɧɨɣ ɞɢɮɮɭɡɢɢ, ɤɨɬɨɪɵɣ ɨɛɫɭɠɞɚɥɫɹ ɜɵɲɟ. Ɍɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ ȼ ɝɚɡɨɤɢɧɟɬɢɱɟɫɤɨɣ ɬɟɨɪɢɢ ɤɨɷɮɮɢɰɢɟɧɬ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ ɩɥɚɡɦɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ
κ ~ nD ~ T5/2 / Lc m .
(1.61)
Ɉɧ ɫɢɥɶɧɨ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɫɥɚɛɨ (ɱɟɪɟɡ ɤɭɥɨɧɨɜɫɤɢɣ ɥɨɝɚɪɢɮɦ) ɡɚɜɢɫɢɬ ɨɬ ɩɥɨɬɧɨɫɬɢ ɱɚɫɬɢɰ. ɉɪɢ ɬɟɦɩɟɪɚɬɭɪɚɯ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɭɩɪɚɜɥɹɟɦɨɣ ɬɟɪɦɨɹɞɟɪɧɨɣ ɪɟɚɤɰɢɢ Ɍ~108 K, ɤɨɷɮɮɢɰɢɟɧɬ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ, ɚ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢ ɬɟɩɥɨɜɵɟ ɩɨɬɟɪɢ, ɨɛɭɫɥɨɜɥɟɧɧɵɟ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶɸ, ɫɬɚɧɨɜɹɬɫɹ ɧɟɞɨɩɭɫɬɢɦɨ ɛɨɥɶɲɢɦɢ, ɤɚɤ ɩɨɤɚɡɵɜɚɸɬ ɩɪɨɫɬɵɟ ɨɰɟɧɤɢ. ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ ɧɟɨɛɯɨɞɢɦɨ ɬɟɪɦɨɢɡɨɥɢɪɨɜɚɬɶ ɩɥɚɡɦɭ, ɬɨ ɟɫɬɶ ɢɫɤɥɸɱɢɬɶ ɟɟ ɩɪɹɦɨɣ ɤɨɧɬɚɤɬ ɫ ɨɯɥɚɠɞɚɟɦɵɦɢ ɫɬɟɧɤɚɦɢ. ɉɨɫɤɨɥɶɤɭ ɩɟɪɟɞɚɱɚ ɷɧɟɪɝɢɢ ɧɚɢɛɨɥɟɟ ɷɮɮɟɤɬɢɜɧɚ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɢ ɨɞɢɧɚɤɨɜɵɯ ɱɚɫɬɢɰ (ɫɦ. ɩɪɟɞɵɞɭɳɢɣ ɩɚɪɚɝɪɚɮ), ɬɨ ɦɨɠɧɨ ɜɵɞɟɥɢɬɶ ɨɬɞɟɥɶɧɨ ɷɥɟɤɬɪɨɧɧɭɸ ɢ ɢɨɧɧɭɸ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ. ɉɪɢ ɷɬɨɦ ɫɨɝɥɚɫɧɨ ɫɨɨɬɧɨɲɟɧɢɸ (1.61), ɢɡ-ɡɚ ɫɭɳɟɫɬɜɟɧɧɨɝɨ ɪɚɡɥɢɱɢɹ ɦɚɫɫ ɤɨɷɮɮɢɰɢɟɧɬ ɷɥɟɤɬɪɨɧɧɨɣ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɟɬ (ɩɪɢɦɟɪɧɨ ɜ ɤɨɪɟɧɶ ɢɡ ɨɬɧɨɲɟɧɢɹ ɦɚɫɫ) ɤɨɷɮɮɢɰɢɟɧɬ ɢɨɧɧɨɣ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ, ɬɚɤ ɱɬɨ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ ɩɨɥɧɨɫɬɶɸ ɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɷɥɟɤɬɪɨɧɚɦɢ. Ⱦɟɬɚɥɶɧɵɟ ɪɚɫɱɟɬɵ [13] ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɤɢɧɟɬɢɱɟɫɤɢɯ ɭɪɚɜɧɟɧɢɣ ɩɪɢɜɨɞɹɬ ɤ ɫɥɟɞɭɸɳɢɦ ɡɧɚɱɟɧɢɹɦ ɷɬɢɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɩɟɪɟɧɨɫɚ:
κi ≅ 3.9niTiτii/mi,
κe ≅ 3.16neTeτei/me.
(1.62)
ȼɹɡɤɨɫɬɶ ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɝɚɡɨɤɢɧɟɬɢɱɟɫɤɢɦɢ ɩɪɟɞɫɬɚɜɥɟɧɢɹɦɢ ɤɨɷɮɮɢɰɢɟɧɬ ɜɹɡɤɨɫɬɢ ɩɥɚɡɦɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ η = mnD ~ mT 5 / 2 /Lc. (1.63) Ʉɨɷɮɮɢɰɢɟɧɬ ɜɹɡɤɨɫɬɢ, ɬɚɤ ɠɟ ɤɚɤ ɢ ɤɨɷɮɮɢɰɢɟɧɬ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ, ɫɥɚɛɨ ɡɚɜɢɫɢɬ ɨɬ ɩɥɨɬɧɨɫɬɢ ɢ ɫɢɥɶɧɨ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ, ɩɪɢɱɟɦ ɤɨɷɮɮɢɰɢɟɧɬ ɢɨɧɧɨɣ ɜɹɡɤɨɫɬɢ ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɟɬ ɤɨɷɮɮɢɰɢɟɧɬ ɷɥɟɤɬɪɨɧɧɨɣ ɜɹɡɤɨɫɬɢ. ɋɨɝɥɚɫɧɨ [13] ɞɥɹ ɩɨɥɧɨɫɬɶɸ ɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɵ ɷɬɢ ɤɨɷɮɮɢɰɢɟɧɬɵ ɪɚɜɧɵ:
ηi≅0.96niTiτii,
ηe≅0.73neTeτei,
(1.64)
ɞɥɹ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ɉɪɨɜɨɞɢɦɨɫɬɶ (ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɶ) Ɍɚɤ ɤɚɤ ɩɥɚɡɦɚ ɫɨɞɟɪɠɢɬ ɫɜɨɛɨɞɧɵɟ ɡɚɪɹɞɵ, ɬɨ ɩɪɢ ɧɚɥɨɠɟɧɢɢ ɜɧɟɲɧɟɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜ ɩɥɚɡɦɟ ɜɨɡɦɨɠɟɧ ɩɟɪɟɧɨɫ ɡɚɪɹɞɚ. ɗɬɨ ɹɜɥɟɧɢɟ ɧɚɡɵɜɚɸɬ ɩɪɨɜɨɞɢɦɨɫɬɶɸ (ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɶɸ). ɉɨ ɨɩɪɟɞɟɥɟɧɢɸ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ j ɢ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ E ɫɜɹɡɚɧɵ ɫɨɨɬɧɨɲɟɧɢɟɦ dϕ j = σE = −σ , (1.65) dx ɝɞɟ σ - ɩɪɨɜɨɞɢɦɨɫɬɶ, ɚ ϕ - ɩɨɬɟɧɰɢɚɥ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. ȼɵɪɚɠɟɧɢɟ (1.65) ɫɨɨɬɜɟɬɫɬɜɭɟɬ, ɨɱɟɜɢɞɧɨ, ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɣ ɮɨɪɦɟ ɡɚɩɢɫɢ ɨɛɵɱɧɨɝɨ ɡɚɤɨɧɚ Ɉɦɚ, ɜɫɩɨɦɧɢɦ - U = IR. ȼ ɩɪɨɫɬɟɣɲɟɦ ɫɥɭɱɚɟ ɩɪɢ ɧɟ ɫɥɢɲɤɨɦ ɛɨɥɶɲɢɯ ɧɚɩɪɹɠɟɧɧɨɫɬɹɯ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɩɪɨɜɨɞɢɦɨɫɬɶ ɩɥɚɡɦɵ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɢ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɧɚɩɪɹɠɟɧɧɨɫɬɢ. ɋɥɟɞɭɟɬ ɢɦɟɬɶ ɜ ɜɢɞɭ, ɱɬɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɶ ɩɥɨɬɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ ɜɟɥɢɱɢɧɟ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɩɨɥɹ ɢɦɟɟɬ ɦɟɫɬɨ ɧɟ ɜɫɟɝɞɚ, ɱɚɫɬɨ ɷɬɚ ɡɚɜɢɫɢɦɨɫɬɶ ɫɥɨɠɧɟɟ, ɞɚɠɟ ɜ ɨɞɧɨɪɨɞɧɨɦ ɩɨɥɟ ɩɪɢ ȿ = const. Ⱦɥɹ ɧɟ ɫɥɢɲɤɨɦ ɛɨɥɶɲɢɯ (ɩɪɢ ɞɚɧɧɨɣ ɩɥɨɬɧɨɫɬɢ ɢ ɬɟɦɩɟɪɚɬɭɪɟ ɩɥɚɡɦɵ) ɧɚɩɪɹɠɟɧɧɨɫɬɹɯ ɩɨɥɹ ȿ = −dϕ/dx ɦɨɠɧɨ ɫɱɢɬɚɬɶ, ɱɬɨ ɜɟɫɶ ɡɚɪɹɞ ɩɟɪɟɧɨɫɢɬɫɹ ɷɥɟɤɬɪɨɧɚɦɢ, ɬɚɤ ɤɚɤ ɩɪɢɨɛɪɟɬɚɟɦɚɹ ɷɥɟɤɬɪɨɧɚɦɢ ɜ ɩɨɥɟ ɧɚɩɪɚɜɥɟɧɧɚɹ ɫɤɨɪɨɫɬɶ ɩɪɟɜɵɲɚɟɬ ɫɤɨɪɨɫɬɶ ɢɨɧɨɜ, ue>>ui. Ɋɚɫɫɦɨɬɪɢɦ ɭɩɪɨɳɟɧɧɭɸ ɤɚɪɬɢɧɭ. ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɡɚ ɜɪɟɦɹ ɦɟɠɞɭ ɞɜɭɦɹ ɤɭɥɨɧɨɜɫɤɢɦɢ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ ɫ ɢɨɧɚɦɢ τei ɷɥɟɤɬɪɨɧ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ȿ ɧɚɛɢɪɚɟɬ ɭɩɨɪɹɞɨɱɟɧɧɭɸ ɫɤɨɪɨɫɬɶ ue, ɬ.ɟ. ɢɦɩɭɥɶɫ meue = Fτei, ɤɨɬɨɪɵɣ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɟ ɢɦɩɭɥɶɫɚ, ɨɬɜɟɱɚɸɳɟɝɨ ɟɝɨ ɬɟɩɥɨɜɨɦɭ ɞɜɢɠɟɧɢɸ ~mevTe, ɢ ɩɭɫɬɶ ɩɪɢ ɤɚɠɞɨɦ ɫɬɨɥɤɧɨɜɟɧɢɢ ɷɥɟɤɬɪɨɧ ɬɟɪɹɟɬ ɩɨɥɭɱɟɧɧɵɣ ɢɦɩɭɥɶɫ ɧɚɩɪɚɜɥɟɧɧɨɝɨ ɞɜɢɠɟɧɢɹ. Ⱦɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɫɢɥɚ, ɭɫɤɨɪɹɸɳɚɹ ɷɥɟɤɬɪɨɧ F = eȿ, ɞɨɥɠɧɚ ɛɵɬɶ ɭɪɚɜɧɨɜɟɲɟɧɚ ɫɢɥɨɣ ɬɪɟɧɢɹ mue/τei, ɜɨɡɧɢɤɚɸɳɟɣ ɢɡ-ɡɚ ɫɬɨɥɤɧɨɜɟɧɢɣ ɫ ɧɟɩɨɞɜɢɠɧɵɦɢ ɢɨɧɚɦɢ: eE = mue/τei . (1.66) Ɉɩɪɟɞɟɥɢɜ ɢɡ ɪɚɜɟɧɫɬɜɚ (1.66) ue ɢ ɩɨɞɫɬɚɜɢɜ ɩɨɥɭɱɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɜ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ: j = neue, (1.67) ɩɨɥɭɱɢɦ j = ne2τeiE/m. (1.68) ɋɪɚɜɧɢɜ ɷɬɨɬ ɪɟɡɭɥɶɬɚɬ ɫ ɮɨɪɦɭɥɨɣ (1.65), ɧɚɯɨɞɢɦ ɜɟɥɢɱɢɧɭ ɩɪɨɜɨɞɢɦɨɫɬɢ ɩɥɚɡɦɵ: σ = ne2τei/me . (1.69) ɗɬɨɬ ɤɥɚɫɫɢɱɟɫɤɢɣ ɪɟɡɭɥɶɬɚɬ ɢɡɜɟɫɬɟɧ ɤɚɤ ɮɨɪɦɭɥɚ ɋɩɢɬɰɟɪɚ.
ɉɨɞɫɬɚɜɢɜ ɡɧɚɱɟɧɢɟ τei ɢɡ ɮɨɪɦɭɥɵ (1.47), ɩɨɥɭɱɢɦ ɫɥɟɞɭɸɳɭɸ ɡɚɜɢɫɢɦɨɫɬɶ ɩɪɨɜɨɞɢɦɨɫɬɢ ɨɬ ɩɚɪɚɦɟɬɪɨɜ ɩɥɚɡɦɵ: T 3/ 2 σ ∝ e ∼ Te 3 / 2 . (1.70) Lc Ɂɞɟɫɶ ɭɱɬɟɧɨ, ɱɬɨ ɩɨɫɤɨɥɶɤɭ ɤɭɥɨɧɨɜɫɤɢɣ ɥɨɝɚɪɢɮɦ, Lc, ɹɜɥɹɟɬɫɹ ɦɟɞɥɟɧɧɨɣ ɮɭɧɤɰɢɟɣ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ, ɬɨ ɦɨɠɧɨ ɩɪɢɛɥɢɠɟɧɧɨ ɫɱɢɬɚɬɶ ɟɝɨ ɩɨɫɬɨɹɧɧɨɣ ɜɟɥɢɱɢɧɨɣ. Ɍɨɝɞɚ, ɩɨ ɫɭɳɟɫɬɜɭ, ɩɪɨɜɨɞɢɦɨɫɬɶ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɬɨɥɶɤɨ ɷɥɟɤɬɪɨɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ. Ⱥɤɤɭɪɚɬɧɵɣ ɭɱɟɬ ɜɫɟɯ ɱɢɫɥɨɜɵɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɩɪɢɜɨɞɢɬ ɞɥɹ ɜɨɞɨɪɨɞɧɨɣ ɩɥɚɡɦɵ ɤ ɫɥɟɞɭɸɳɟɦɭ ɪɟɡɭɥɶɬɚɬɭ[13]: 0.9 ⋅ 10 13 3/ 2 , c −1 ɷȼ −3 / 2 . σ = 1.96σ1Te , σ1 ≅ (1.71) ( Lc / 10 ) ɉɨ ɜɟɥɢɱɢɧɟ ɩɪɨɜɨɞɢɦɨɫɬɢ ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɭɞɟɥɶɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɩɥɚɡɦɵ ρ=σ -1. ɉɨɫɤɨɥɶɤɭ ɩɥɚɡɦɚ ɢɦɟɟɬ ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ, ɬɨ ɜɨɡɦɨɠɟɧ ɟɟ ɧɚɝɪɟɜ ɞɠɨɭɥɟɜɵɦ ɬɟɩɥɨɦ. ɉɪɢ ɷɬɨɦ ɞɠɨɭɥɟɜɨ ɬɟɩɥɨ (ɫ ɩɥɨɬɧɨɫɬɶɸ ɬɟɩɥɨɜɵɞɟɥɟɧɢɹ, ɤɚɤ ɢɡɜɟɫɬɧɨ, ɪɚɜɧɨɣ j2/σ) ɜɵɞɟɥɹɟɬɫɹ ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɜ ɷɥɟɤɬɪɨɧɧɨɣ ɩɨɞɫɢɫɬɟɦɟ ɩɥɚɡɦɵ. ɗɥɟɤɬɪɨɧɵ ɧɚɛɢɪɚɸɬ ɷɧɟɪɝɢɸ ɨɬ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ȿ (ɚ ɨɧɨ ɦɨɠɟɬ ɛɵɬɶ ɜɧɟɲɧɢɦ, ɨɬ ɨɬɞɟɥɶɧɨɝɨ ɢɫɬɨɱɧɢɤɚ) ɢ ɥɢɲɶ ɡɚɬɟɦ ɜ ɩɪɨɰɟɫɫɟ ɬɟɩɥɨɨɛɦɟɧɚ ɩɟɪɟɞɚɸɬ ɷɬɭ ɷɧɟɪɝɢɸ ɢɨɧɚɦ. Ɍɚɤɨɣ ɧɚɝɪɟɜ ɧɚɡɵɜɚɟɬɫɹ ɨɦɢɱɟɫɤɢɦ ɧɚɝɪɟɜɨɦ. ɇɚ ɭɫɬɚɧɨɜɤɚɯ, ɢɫɩɨɥɶɡɭɸɳɢɯ ɨɦɢɱɟɫɤɢɣ ɧɚɝɪɟɜ, ɭɞɚɟɬɫɹ ɞɨɫɬɢɱɶ ɬɟɦɩɟɪɚɬɭɪɵ ~1ɤɷȼ. Ɉɞɧɚɤɨ ɞɥɹ ɞɚɥɶɧɟɣɲɟɝɨ ɟɟ ɩɨɜɵɲɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɢɫɤɚɬɶ ɢɧɵɟ ɩɭɬɢ. Ⱦɟɥɨ ɜ ɬɨɦ, ɱɬɨ ɫ ɪɨɫɬɨɦ ɬɟɦɩɟɪɚɬɭɪɵ, ɜɫɥɟɞɫɬɜɢɟ ɭɜɟɥɢɱɟɧɢɹ ɩɪɨɜɨɞɢɦɨɫɬɢ, ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɨɦɢɱɟɫɤɨɝɨ ɧɚɝɪɟɜɚ ɭɦɟɧɶɲɚɟɬɫɹ. Ʉɚɤ ɢɡɜɟɫɬɧɨ, ɭɞɟɥɶɧɚɹ ɦɨɳɧɨɫɬɶ ɩɨɬɟɪɶ ɷɧɟɪɝɢɢ ɩɥɚɡɦɨɣ ɡɚ ɫɱɟɬ ɢɡɥɭɱɟɧɢɹ ɹɜɥɹɟɬɫɹ, ɧɚɩɪɨɬɢɜ, ɪɚɫɬɭɳɟɣ ɮɭɧɤɰɢɟɣ ɬɟɦɩɟɪɚɬɭɪɵ (ɧɚɩɪɢɦɟɪ, ɞɥɹ ɬɨɪɦɨɡɧɨɝɨ ɦɟɯɚɧɢɡɦɚ ɢɡɥɭɱɟɧɢɹ ɨɧɚ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɩɪɨɢɡɜɟɞɟɧɢɸ n 2 T ). ȼ ɪɟɡɭɥɶɬɚɬɟ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɜ [12], ɧɚɱɢɧɚɹ ɫ ɧɟɤɨɬɨɪɨɣ ɬɟɦɩɟɪɚɬɭɪɵ, ɞɠɨɭɥɟɜɨ ɬɟɩɥɨɜɵɞɟɥɟɧɢɟ ɭɠɟ ɧɟ ɦɨɠɟɬ ɤɨɦɩɟɧɫɢɪɨɜɚɬɶ ɩɨɬɟɪɢ ɩɥɚɡɦɵ ɧɚ ɢɡɥɭɱɟɧɢɟ. ɋɥɟɞɭɟɬ ɭɱɟɫɬɶ ɢ ɟɳɟ ɨɞɧɨ ɱɪɟɡɜɵɱɚɣɧɨ ɜɚɠɧɨɟ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ. Ɏɨɪɦɭɥɚ ɞɥɹ ɩɪɨɜɨɞɢɦɨɫɬɢ ɩɥɚɡɦɵ (1.69) ɜɟɪɧɚ ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ, ɱɬɨ ɧɚɛɢɪɚɟɦɚɹ ɷɥɟɤɬɪɨɧɨɦ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ ɧɚ ɞɥɢɧɟ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ɷɧɟɪɝɢɹ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɟ ɫɪɟɞɧɟɣ ɬɟɩɥɨɜɨɣ ɷɧɟɪɝɢɢ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɨɛɥɚɫɬɶ ɟɟ ɩɪɢɦɟɧɢɦɨɫɬɢ ɨɝɪɚɧɢɱɟɧɚ ɫɥɚɛɵɦɢ ɷɥɟɤɬɪɢɱɟɫɤɢɦɢ ɩɨɥɹɦɢ. ȼ ɩɨɥɟ ɫ ɛɨɥɶɲɟɣ ɧɚɩɪɹɠɟɧɧɨɫɬɶɸ ɷɥɟɤɬɪɨɧ ɞɨɥɠɟɧ ɧɚɛɢɪɚɬɶ ɛɨɥɶɲɭɸ ɷɧɟɪɝɢɸ. Ɇɟɠɞɭ ɬɟɦ, ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɚ ɫɟɱɟɧɢɟ ɟɝɨ ɤɭɥɨɧɨɜɫɤɨɝɨ ɪɚɫɫɟɹɧɢɹ ɧɚ ɢɨɧɟ, ɤɨɬɨɪɨɟ ɞɨɥɠɧɨ ɨɝɪɚɧɢɱɢɜɚɬɶ ɧɚɛɨɪ ɷɧɟɪɝɢɢ, ɛɵɫɬɪɨ, ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɤɜɚɞɪɚɬɭ ɷɧɟɪɝɢɢ, ɭɛɵɜɚɟɬ. Ɍɚɤ ɱɬɨ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɚ ɛɵɫɬɪɨ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɜɪɟɦɹ ɟɝɨ ɞɜɢɠɟɧɢɹ ɦɟɠɞɭ ɫɨɭɞɚɪɟɧɢɹɦɢ (~v3), ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɷɥɟɤɬɪɨɧ ɦɟɠɞɭ ɫɨɭɞɚɪɟɧɢɹɦɢ ɦɨɠɟɬ ɭɫɩɟɬɶ ɧɚɛɪɚɬɶ ɜɨ ɜɧɟɲɧɟɦ ɩɨɥɟ ɢɦɩɭɥɶɫ, ɩɪɟɜɵɲɚɸɳɢɣ ɢɦɩɭɥɶɫ, ɨɬɜɟɱɚɸɳɢɣ ɟɝɨ ɬɟɩɥɨɜɨɦɭ ɞɜɢɠɟɧɢɸ. Ʉɪɢɬɟɪɢɣ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɬɚɤɨɣ ɫɢɬɭɚɰɢɢ ɦɨɠɧɨ ɫɮɨɪɦɭɥɢɪɨɜɚɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: |e|Eτ > mevTe. (1.72) ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɷɬɨɝɨ ɭɫɥɨɜɢɹ ɱɚɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ɩɥɚɡɦɵ ɩɨɩɚɞɚɟɬ, ɤɚɤ ɝɨɜɨɪɹɬ, ɜ ɪɟɠɢɦ «ɩɚɞɚɸɳɟɝɨ ɬɪɟɧɢɹ», ɤɨɝɞɚ ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɧɢɯ ɷɮɮɟɤɬɢɜɧɚɹ ɫɢɥɚ ɬɪɟɧɢɹ ɭɦɟɧɶɲɚɟɬɫɹ ɫ ɪɨɫɬɨɦ ɢɯ ɷɧɟɪɝɢɢ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɬɟɪɹ ɢɦɩɭɥɶɫɚ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɹɯ ɫ ɢɨɧɚɦɢ ɧɟ ɦɨɠɟɬ ɨɝɪɚɧɢɱɢɬɶ ɧɚɛɨɪ ɢɦɩɭɥɶɫɚ ɷɥɟɤɬɪɨɧɚɦɢ ɜɨ ɜɧɟɲɧɟɦ ɩɨɥɟ, ɬɚɤ ɱɬɨ ɱɚɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ɦɨɠɟɬ ɩɟɪɟɣɬɢ ɜ ɪɟɠɢɦ ɧɟɩɪɟɪɵɜɧɨɝɨ ɭɫɤɨɪɟɧɢɹ. Ɍɚɤɢɟ ɷɥɟɤɬɪɨɧɵ ɩɨɥɭɱɢɥɢ ɧɚɡɜɚɧɢɟ "ɩɪɨɫɜɢɫɬɧɵɯ" ɢɥɢ "ɭɛɟɝɚɸɳɢɯ" ɷɥɟɤɬɪɨɧɨɜ. ȿɫɥɢ ɩɪɟɞɩɨɥɨɠɢɬɶ, ɱɬɨ τ≈τei, ɬɨ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɧɟɤɨɬɨɪɨɟ ɩɪɟɞɟɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɩɨɥɹ ȿɤɪ, ɬɚɤ ɧɚɡɵɜɚɟɦɨɟ ɩɨɥɟ Ⱦɪɚɣɫɟɪɚ, ɜɵɲɟ ɤɨɬɨɪɨɝɨ ɷɥɟɤɬɪɨɧɵ ɧɚɱɧɭɬ "ɭɯɨɞɢɬɶ ɜ ɩɪɨɫɜɢɫɬ", ɬ.ɟ. ɛɭɞɭɬ ɧɟɩɪɟɪɵɜɧɨ ɭɫɤɨɪɹɬɶɫɹ [11]: E > Eɤɪ ≈ 0.214Lce/rDe2. (1.73)
ɉɪɚɤɬɢɱɟɫɤɢ, ɡɚɦɟɬɧɚɹ ɱɚɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ɩɥɚɡɦɵ ɧɚɱɢɧɚɟɬ «ɭɯɨɞɢɬɶ ɜ ɩɪɨɫɜɢɫɬ» ɭɠɟ ɩɪɢ ȿ > 0.1Eɤɪ.
§ 11. Ⱦɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɥɚɡɦɵ ɉɨɦɟɫɬɢɦ ɩɥɚɡɦɭ ɜɨ ɜɧɟɲɧɟɟ ɩɟɪɟɦɟɧɧɨɟ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɢ ɩɨɩɵɬɚɟɦɫɹ ɩɪɨɫɥɟɞɢɬɶ ɢɡɦɟɧɟɧɢɟ ɟɟ ɫɜɨɣɫɬɜ, ɩɨɫɬɟɩɟɧɧɨ ɭɜɟɥɢɱɢɜɚɹ ɟɝɨ ɱɚɫɬɨɬɭ. ɋɬɚɬɢɱɟɫɤɨɟ ɜɧɟɲɧɟɟ ɩɨɥɟ, ɤɚɤ ɦɵ ɭɠɟ ɡɧɚɟɦ, ɩɪɨɧɢɤɚɟɬ ɜ ɩɥɚɡɦɭ ɧɚ ɬɨɥɳɢɧɭ ɦɚɫɲɬɚɛɚ ɞɟɛɚɟɜɫɤɨɝɨ ɫɥɨɹ. ɗɬɨ ɜɵɬɟɤɚɟɬ ɢɡ ɭɪɚɜɧɟɧɢɹ ɷɤɪɚɧɢɪɨɜɤɢ (ɫɦ. §3), ɤɨɬɨɪɨɟ, ɧɚɩɪɢɦɟɪ, ɞɥɹ ɨɞɧɨɦɟɪɧɨɝɨ ɫɥɭɱɚɹ ɡɚɩɢɫɵɜɚɟɬɫɹ ɜ ɜɢɞɟ: d 2ϕ ϕ = 2 . (1.74) dx 2 rDe Ɂɞɟɫɶ rDe – ɷɥɟɤɬɪɨɧɧɵɣ ɞɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ. ɍɞɨɛɧɨ ɩɟɪɟɩɢɫɚɬɶ ɷɬɨ ɭɪɚɜɧɟɧɢɟ, ɢɫɩɨɥɶɡɭɹ ɩɪɟɞɫɬɚɜɥɟɧɢɟ Ɏɭɪɶɟ ϕ ~ ϕ k exp( ikx − iωt ) . Ɋɟɡɭɥɶɬɚɬ ɞɥɹ ɚɦɩɥɢɬɭɞɵ Ɏɭɪɶɟ-ɝɚɪɦɨɧɢɤɢ ɩɨɬɟɧɰɢɚɥɚ ϕɤ, ɤɚɤ ɥɟɝɤɨ ɩɪɨɜɟɪɢɬɶ, ɛɭɞɟɬ ɫɥɟɞɭɸɳɢɦ: 1 k 2 ( 1 + 2 2 )ϕ k = 0. (1.75) k rDe ɋɪɚɜɧɢɦ ɷɬɨ ɭɪɚɜɧɟɧɢɟ ɫ ɭɪɚɜɧɟɧɢɟɦ ɞɥɹ ɢɧɞɭɤɰɢɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ dD =0 . (1.76) dx Ⱦɥɹ Ɏɭɪɶɟ-ɝɚɪɦɨɧɢɤɢ ɟɝɨ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ: k 2 εk ϕ k = 0 , (1.77) ɝɞɟ εk - ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɥɚɡɦɵ, ɨɩɢɫɵɜɚɸɳɚɹ ɨɬɤɥɢɤ ɩɥɚɡɦɵ ɧɚ ɫɬɚɬɢɱɟɫɤɨɟ ɜɨɡɞɟɣɫɬɜɢɟ. Ʉɚɤ ɜɢɞɢɦ ɢɡ ɫɪɚɜɧɟɧɢɹ (1.75) ɢ (1.77), ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ 1 εk = 1 + 2 2 . (1.78) k rDe Ɉɬɤɥɢɤ ɩɥɚɡɦɵ ɧɚ ɫɬɚɬɢɱɟɫɤɨɟ ɜɨɡɞɟɣɫɬɜɢɟ ɨɤɚɡɵɜɚɟɬɫɹ ɜɩɨɥɧɟ ɷɤɜɢɜɚɥɟɧɬɟɧ ɷɮɮɟɤɬɭ ɩɨɥɹɪɢɡɚɰɢɢ ɨɛɵɱɧɨɝɨ ɞɢɷɥɟɤɬɪɢɤɚ, ɩɨɦɟɳɟɧɧɨɝɨ ɜɨ ɜɧɟɲɧɟɟ ɩɨɥɟ, ɯɨɬɹ, ɤɨɧɟɱɧɨ, ɦɟɯɚɧɢɡɦ ɩɨɥɹɪɢɡɚɰɢɢ ɢɧɨɣ: ɟɫɥɢ ɞɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ ɦɚɥ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɯɚɪɚɤɬɟɪɧɨɣ ɞɥɢɧɨɣ ɜɨɥɧɵ, ɬɨ ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɨɤɚɡɵɜɚɟɬɫɹ ɨɱɟɧɶ ɛɨɥɶɲɨɣ ɢ ɩɨɥɟ ɜ ɩɥɚɡɦɭ, ɮɚɤɬɢɱɟɫɤɢ, ɧɟ ɩɪɨɧɢɤɚɟɬ. ɉɪɢ ɧɢɡɤɢɯ, ɧɨ ɧɟɧɭɥɟɜɵɯ, ɱɚɫɬɨɬɚɯ ω ɤɚɱɟɫɬɜɟɧɧɨ ɤɚɪɬɢɧɚ ɧɟ ɢɡɦɟɧɢɬɫɹ − ɡɚɪɹɞɵ ɛɭɞɭɬ ɷɤɪɚɧɢɪɨɜɚɬɶ ɜɧɟɲɧɟɟ ɩɨɥɟ ɜ ɫɥɨɹɯ ɦɚɫɲɬɚɛɚ ɞɟɛɚɟɜɫɤɢɯ. ɉɥɚɡɦɚ ɛɭɞɟɬ ɜɟɫɬɢ ɫɟɛɹ ɤɚɤ ɩɪɨɜɨɞɧɢɤ − ɜɧɟɲɧɟɟ ɩɨɥɟ ɜ ɧɟɟ ɧɟ ɛɭɞɟɬ ɩɪɨɧɢɤɚɬɶ. ɇɨ ɟɫɥɢ ɱɚɫɬɨɬɚ ɩɨɥɹ ɛɭɞɟɬ ɜɟɥɢɤɚ, ɢ ɛɭɞɟɬ ɩɪɟɜɵɲɚɬɶ ɩɥɚɡɦɟɧɧɭɸ ɱɚɫɬɨɬɭ, ɬɨ ɤɚɪɬɢɧɚ ɤɚɱɟɫɬɜɟɧɧɨ ɢɡɦɟɧɢɬɫɹ: ɷɥɟɤɬɪɨɧɵ ɢɡ-ɡɚ ɢɧɟɪɰɢɢ ɧɟ ɛɭɞɭɬ ɭɫɩɟɜɚɬɶ ɩɨɞɫɬɪɚɢɜɚɬɶɫɹ ɩɨɞ ɤɨɥɟɛɚɧɢɹ ɩɨɥɹ, ɨɧɢ ɛɭɞɭɬ ɨɫɰɢɥɥɢɪɨɜɚɬɶ ɨɤɨɥɨ ɧɟɤɨɬɨɪɨɝɨ ɫɪɟɞɧɟɝɨ ɩɨɥɨɠɟɧɢɹ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɥɟ ɫɦɨɠɟɬ ɩɪɨɧɢɤɧɭɬɶ ɜ ɩɥɚɡɦɭ. ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ, ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɫɬɶ ɫɥɭɱɚɸ ɧɢɡɤɢɯ ɱɚɫɬɨɬ, ɩɪɨɧɢɤɚɸɳɟɟ ɜ ɩɥɚɡɦɭ ɩɨɥɟ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɨɞɧɨɪɨɞɧɵɦ. ɑɬɨɛɵ ɧɚɣɬɢ ɞɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɥɚɡɦɵ ɜ ɷɬɨɦ ɩɪɟɞɟɥɟ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬ, ɛɭɞɟɦ ɫɱɢɬɚɬɶ ɩɟɪɟɦɟɧɧɨɟ ɩɨɥɟ ɝɚɪɦɨɧɢɱɟɫɤɢɦ: ~ = E e iω t . E (1.79) 0 ɋɦɟɳɟɧɢɟ ∆ɯ ɷɥɟɤɬɪɨɧɚ ɢɡ ɩɨɥɨɠɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɬɚɤɨɝɨ ɩɨɥɹ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɫ ɩɨɦɨɳɶɸ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ~ = eE e iωt , me x = eE 0 (1.80) e ~ ∆x = − E . mω 2 ɉɨɞɫɱɢɬɚɟɦ ɬɟɩɟɪɶ ɢɧɞɭɤɰɢɸ ɩɨɥɹ ɜ ɩɥɚɡɦɟ ~=ε E ~=E ~ + 4π P , D (1.81) ω
ɝɞɟ Ɋ = ɩɟ∆x - ɞɢɩɨɥɶɧɵɣ ɦɨɦɟɧɬ ɟɞɢɧɢɰɵ ɨɛɴɟɦɚ ɩɥɚɡɦɵ, ɨɛɭɫɥɨɜɥɟɧɧɵɣ ɫɦɟɳɟɧɢɟɦ ɷɥɟɤɬɪɨɧɨɜ. ɉɪɨɢɡɜɟɞɹ ɩɨɞɫɬɚɧɨɜɤɭ, ɩɨɥɭɱɢɦ ɜɟɥɢɱɢɧɭ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ: 2
§ ωp · 4πne 2 2 εω = 1 − ¨ ¸ , ω p = , me ©ω¹
(1.82)
ɨɩɢɫɵɜɚɸɳɟɣ ɨɬɤɥɢɤ ɩɥɚɡɦɵ ɧɚ ɜɵɫɨɤɨɱɚɫɬɨɬɧɨɟ ɢ ɨɞɧɨɪɨɞɧɨɟ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ. ɉɨɥɭɱɟɧɧɭɸ ɮɨɪɦɭɥɭ ɞɥɹ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɢ ɩɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɜɨɡɞɟɣɫɬɜɢɹ ɧɚ ɩɥɚɡɦɭ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɜɨɥɧɵ, ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɤɨɬɨɪɨɣ ɨɩɪɟɞɟɥɹɟɬ ɭɪɚɜɧɟɧɢɟ (ɩɨɞɪɨɛɧɟɟ ɫɦ. Ƚɥɚɜɭ 3):
N2 = ε ,
(1.83)
ɝɞɟ N=ɤɫ/ω – ɩɨɤɚɡɚɬɟɥɶ ɩɪɟɥɨɦɥɟɧɢɹ. ɂɡ ɮɨɪɦɭɥɵ (1.82) ɨɱɟɜɢɞɧɨ, ɱɬɨ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɟ ɜɨɥɧɵ ɫ ɱɚɫɬɨɬɨɣ ω > ωp ɦɨɝɭɬ ɩɪɨɧɢɤɚɬɶ ɜ ɩɥɚɡɦɭ ɢ ɪɚɫɩɪɨɫɬɪɚɧɹɬɶɫɹ ɜ ɧɟɣ, ɬɚɤ ɤɚɤ ɞɥɹ ɧɢɯ ɛɭɞɟɬ N2>0. ɇɚɩɪɨɬɢɜ, ɜ ɨɛɥɚɫɬɢ ɱɚɫɬɨɬ ω<ωp ɫɨɝɥɚɫɧɨ (1.82) ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɨɬɪɢɰɚɬɟɥɶɧɚɹ, ɬɚɤ ɱɬɨ ɞɥɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɜɨɥɧɵ ɫ ɬɚɤɨɣ ɱɚɫɬɨɬɨɣ ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɟɥɨɦɥɟɧɢɹ ɨɤɚɡɵɜɚɟɬɫɹ ɱɢɫɬɨ ɦɧɢɦɵɦ, ɢ ɩɨɩɟɪɟɱɧɚɹ ɜɨɥɧɚ ɧɟ ɦɨɠɟɬ ɪɚɫɩɪɨɫɬɪɚɧɹɬɶɫɹ ɜ ɩɥɚɡɦɟ. Ɉɞɧɚɤɨ ɜ ɷɬɢɯ ɭɫɥɨɜɢɹɯ ɜɨɡɦɨɠɧɨ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɜ ɩɥɚɡɦɟ ɩɪɨɞɨɥɶɧɵɯ - ɬɚɤ ɧɚɡɵɜɚɟɦɵɯ, ɥɟɧɝɦɸɪɨɜɫɤɢɯ ɜɨɥɧ. Ʉɚɤ ɦɵ ɜɢɞɢɦ, ɜ ɫɬɚɬɢɱɟɫɤɨɦ ɩɪɟɞɟɥɟ ɢ ɜ ɜɵɫɨɤɨɱɚɫɬɨɬɧɨɦ ɩɪɟɞɟɥɟ ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɥɚɡɦɵ ɨɩɢɫɵɜɚɟɬɫɹ ɪɚɡɥɢɱɧɵɦɢ ɮɨɪɦɭɥɚɦɢ. ȼ ɞɟɣɫɬɜɢɬɟɥɶɧɨɫɬɢ, ɨɛɟ ɨɧɢ ɹɜɥɹɸɬɫɹ ɩɪɟɞɟɥɶɧɵɦɢ ɫɥɭɱɚɹɦɢ ɨɞɧɨɣ ɛɨɥɟɟ ɨɛɳɟɣ ɮɨɪɦɭɥɵ:
εk ,ω = 1 −
ω p2 ω 2 − k 2 rDe2
,
ɨɛɴɟɞɢɧɹɸɳɟɣ, ɤɚɤ ɥɟɝɤɨ ɜɢɞɟɬɶ, ɨɛɚ ɩɪɟɞɟɥɶɧɵɯ ɫɥɭɱɚɹ.
(1.84)
ȽɅȺȼȺ 2 ɉɅȺɁɆȺ ȼ ɆȺȽɇɂɌɇɈɆ ɉɈɅȿ § 12. Ɉɞɧɨɱɚɫɬɢɱɧɨɟ ɪɚɫɫɦɨɬɪɟɧɢɟ ɋɭɬɶ ɨɞɧɨɱɚɫɬɢɱɧɨɝɨ ɪɚɫɫɦɨɬɪɟɧɢɹ, ɢɥɢ ɩɪɢɛɥɢɠɟɧɢɹ, ɜ ɨɩɢɫɚɧɢɢ ɩɥɚɡɦɟɧɧɵɯ ɩɪɨɰɟɫɫɨɜ ɫɜɨɞɢɬɫɹ ɤ ɢɡɭɱɟɧɢɸ ɞɜɢɠɟɧɢɹ ɨɬɞɟɥɶɧɵɯ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɜ ɩɨɥɹɯ, ɤɨɬɨɪɵɟ ɫɱɢɬɚɸɬɫɹ ɡɚɞɚɧɧɵɦɢ ɢɡɧɚɱɚɥɶɧɨ. Ɍɟɦ ɫɚɦɵɦ ɩɪɟɧɟɛɪɟɝɚɟɬɫɹ ɜɥɢɹɧɢɟɦ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɧɚ ɩɨɥɹ «ɭɩɪɚɜɥɹɸɳɢɟ» ɢɯ ɞɜɢɠɟɧɢɟɦ, ɬ.ɟ. ɩɪɟɧɟɛɪɟɝɚɟɬɫɹ ɷɮɮɟɤɬɚɦɢ ɫɚɦɨɫɨɝɥɚɫɨɜɚɧɢɹ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɢ ɜɵɡɵɜɚɟɦɨɝɨ ɢɦ ɢɡɦɟɧɟɧɢɹ ɩɨɥɹ. ȼ ɤɚɱɟɫɬɜɟ ɩɟɪɜɨɝɨ ɲɚɝɚ ɬɚɤɨɟ ɩɪɢɛɥɢɠɟɧɢɟ ɜɩɨɥɧɟ ɨɩɪɚɜɞɚɧɨ ɢ ɩɨɜɫɟɦɟɫɬɧɨ ɢɫɩɨɥɶɡɭɟɬɫɹ, ɨɫɨɛɟɧɧɨ, ɟɫɥɢ ɟɫɬɶ ɜɨɡɦɨɠɧɨɫɬɶ, ɩɨ ɤɪɚɣɧɟɣ ɦɟɪɟ, ɷɮɮɟɤɬɢɜɧɨ ɭɱɟɫɬɶ ɜɥɢɹɧɢɟ ɩɨɥɟɣ ɨɫɬɚɥɶɧɵɯ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɧɚ ɞɜɢɠɟɧɢɟ ɤɚɤɨɣ-ɥɢɛɨ ɨɞɧɨɣ ɜɵɞɟɥɟɧɧɨɣ ɱɚɫɬɢɰɵ. ɉɨɞɱɟɪɤɧɟɦ, ɜɦɟɫɬɟ ɫ ɬɟɦ, ɱɬɨ ɧɟɞɨɭɱɟɬ ɷɮɮɟɤɬɨɜ ɫɚɦɨɫɨɝɥɚɫɨɜɚɧɢɹ ɫɨɞɟɪɠɢɬ ɜ ɫɟɛɟ ɦɧɨɠɟɫɬɜɨ ɧɟɩɪɢɹɬɧɵɯ «ɫɸɪɩɪɢɡɨɜ», ɢ ɜ ɢɫɬɨɪɢɢ ɪɚɡɜɢɬɢɹ ɢɫɫɥɟɞɨɜɚɧɢɣ ɜ ɨɛɥɚɫɬɢ ɭɩɪɚɜɥɹɟɦɨɝɨ ɬɟɪɦɨɹɞɟɪɧɨɝɨ ɫɢɧɬɟɡɚ ɬɚɤɢɯ ɩɪɢɦɟɪɨɜ ɩɪɟɞɨɫɬɚɬɨɱɧɨ. ɇɚɩɪɢɦɟɪ, ɜ ɤɥɚɫɫɢɱɟɫɤɢɯ ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɵɯ ɚɞɢɚɛɚɬɢɱɟɫɤɢɯ ɥɨɜɭɲɤɚɯ (ɫɦ. §18), ɩɪɟɤɪɚɫɧɨ ɭɞɟɪɠɢɜɚɸɳɢɯ ɨɬɞɟɥɶɧɵɟ ɱɚɫɬɢɰɵ ɩɥɚɡɦɵ ɨɱɟɧɶ ɧɢɡɤɨɣ ɩɥɨɬɧɨɫɬɢ, ɤɨɝɞɚ ɨɞɧɨɱɚɫɬɢɱɧɨɟ ɩɪɢɛɥɢɠɟɧɢɟ ɜɩɨɥɧɟ ɨɩɪɚɜɞɚɧɨ, ɫ ɩɨɜɵɲɟɧɢɟɦ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ, ɤɨɝɞɚ ɜɫɟ ɛɨɥɶɲɭɸ ɪɨɥɶ ɧɚɱɢɧɚɸɬ ɢɝɪɚɬɶ ɫɨɛɫɬɜɟɧɧɵɟ ɩɨɥɹ ɩɥɚɡɦɵ, ɩɨɹɜɥɹɟɬɫɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ ɢ ɭɞɟɪɠɚɧɢɟ ɩɥɨɬɧɨɣ ɩɥɚɡɦɵ ɛɟɡ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɭɫɢɥɢɣ ɩɪɨɫɬɨ ɧɟɜɨɡɦɨɠɧɨ. ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɜ ɡɚɞɚɧɧɵɯ ɜɧɟɲɧɢɯ ɩɨɥɹɯ ɢɦɟɟɬ ɜɢɞ: & q& & & & mr = qE + v × B + F , (2.1) c ɝɞɟ ɩɟɪɜɨɟ ɫɥɚɝɚɟɦɨɟ ɫɩɪɚɜɚ ɨɬɜɟɱɚɟɬ ɫɢɥɟ ɫɨ ɫɬɨɪɨɧɵ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɜɬɨɪɨɟ ɨɩɢɫɵɜɚɟɬ ɫɢɥɭ ɫɨ ɫɬɨɪɨɧɵ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ (ɫɢɥɚ Ʌɨɪɟɧɰɚ), ɚ ɩɨɫɥɟɞɧɟɟ ɨɛɨɡɧɚɱɚɟɬ ɪɚɜɧɨɞɟɣɫɬɜɭɸɳɭɸ ɩɪɨɱɢɯ ɜɧɟɲɧɢɯ ɫɢɥ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɞɟɣɫɬɜɨɜɚɬɶ ɧɚ ɱɚɫɬɢɰɭ. ɍɪɚɜɧɟɧɢɟ (2.1) ɦɨɠɟɬ ɛɵɬɶ ɩɪɨɢɧɬɟɝɪɢɪɨɜɚɧɨ ɬɨɥɶɤɨ ɜ ɨɬɞɟɥɶɧɵɯ, ɧɚɢɛɨɥɟɟ ɩɪɨɫɬɵɯ ɫɥɭɱɚɹɯ. ɗɬɨ ɩɨɧɹɬɧɨ, ɟɫɥɢ ɭɱɟɫɬɶ, ɱɬɨ ɞɟɣɫɬɜɭɸɳɢɟ ɧɚ ɱɚɫɬɢɰɭ ɩɨɥɹ ɹɜɥɹɸɬɫɹ ɮɭɧɤɰɢɹɦɢ ɤɨɨɪɞɢɧɚɬ ɢ ɜɪɟɦɟɧɢ ɢ, ɤɪɨɦɟ ɬɨɝɨ, ɱɬɨ ɨɧɢ ɫɚɦɢ ɫɜɹɡɚɧɵ ɭɪɚɜɧɟɧɢɹɦɢ Ɇɚɤɫɜɟɥɥɚ. ɉɨɷɬɨɦɭ ɪɚɫɫɦɨɬɪɢɦ ɧɚɢɛɨɥɟɟ ɩɪɨɫɬɵɟ, ɱɚɫɬɨ ɜɫɬɪɟɱɚɸɳɢɟɫɹ ɫɥɭɱɚɢ. Ɍɚɤ, ɞɟɣɫɬɜɢɟɦ ɜɧɟɲɧɢɯ, ɧɟɷɥɟɤɬɪɢɱɟɫɤɢɯ ɫɢɥ, ɨɛɵɱɧɨ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ, ɚ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɱɚɫɬɨ ɨɬɫɭɬɫɬɜɭɟɬ. ɗɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɞɜɢɠɟɧɢɸ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɜ ɩɨɫɬɨɹɧɧɨɦ ɜɨ ɜɪɟɦɟɧɢ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ. Ɋɚɫɫɦɨɬɪɢɦ ɫɧɚɱɚɥɚ ɞɜɢɠɟɧɢɟ ɜ ɨɞɧɨɪɨɞɧɨɦ ɩɨɥɟ, ɬ.ɟ. ɧɟ ɦɟɧɹɸɳɟɦɫɹ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ.
§ 13. Ⱦɜɢɠɟɧɢɟ ɜ ɩɨɫɬɨɹɧɧɨɦ ɢ ɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ȼ ɫɥɭɱɚɟ ɟɫɥɢ ɞɪɭɝɢɯ ɫɢɥ, ɤɪɨɦɟ ɫɢɥɵ Ʌɨɪɟɧɰɚ ɧɟɬ, ɬɨ ɭɪɚɜɧɟɧɢɟ (2.1) ɢɦɟɟɬ ɜɢɞ & q& & mv = v × B . (2.2) c ɍɦɧɨɠɚɹ ɫɤɚɥɹɪɧɨ ɩɪɚɜɭɸ ɢ ɥɟɜɭɸ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ (2.2) ɧɚ ɫɤɨɪɨɫɬɶ, ɭɱɢɬɵɜɚɹ, ɱɬɨ ɫɢɥɚ Ʌɨɪɟɧɰɚ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɚ ɤ ɨɛɨɢɦ ɜɟɤɬɨɪɚɦ, ɜɯɨɞɹɳɢɦ ɜ ɜɟɤɬɨɪɧɨɟ ɩɪɨɢɡɜɟɞɟɧɢɟ (2.2), ɩɨɥɭɱɢɦ ɫɨɨɬɧɨɲɟɧɢɟ 2 && d mv mvv ≡ = 0. dt 2 ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɱɚɫɬɢɰɵ ɫɨɯɪɚɧɹɟɬɫɹ: mv 2 (2.3) = const . 2 ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɩɨɫɬɨɹɧɧɨɟ ɜɨ ɜɪɟɦɟɧɢ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɧɟ ɩɪɨɢɡɜɨɞɢɬ ɪɚɛɨɬɵ ɧɚɞ ɱɚɫɬɢɰɟɣ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɦɨɞɭɥɶ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰɵ, ɡɚɞɚɧɧɵɣ ɧɚɱɚɥɶɧɵɦɢ ɭɫɥɨɜɢɹɦɢ, ɫɨɯɪɚɧɹɟɬ ɩɨɫɬɨɹɧɧɨɟ ɡɧɚɱɟɧɢɟ. && Ɋɚɡɥɨɠɢɜ ɜɟɤɬɨɪ ɫɤɨɪɨɫɬɢ ɧɚ ɤɨɦɩɨɧɟɧɬɵ: ɩɚɪɚɥɥɟɥɶɧɭɸ v|| = ( vB ) / B ɦɚɝɧɢɬɧɨɦɭ & & & ɩɨɥɸ ɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɭɸ v ⊥ = v − v|| B / B ɤ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ, ɩɨɥɭɱɢɦ ɞɥɹ ɩɪɨɞɨɥɶɧɨɝɨ ɭɫɤɨɪɟɧɢɹ:
& eB & & mv|| = (v × B) ≡ 0 , cB - ɩɨɫɬɨɹɧɧɨɟ ɢ ɨɞɧɨɪɨɞɧɨɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɧɟ ɦɟɧɹɟɬ ɩɪɨɞɨɥɶɧɭɸ ɤɨɦɩɨɧɟɧɬɭ ɫɤɨɪɨɫɬɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, && v|| = ( vB ) / B = const . (2.4)
Ⱦɥɹ ɩɨɩɟɪɟɱɧɨɝɨ ɭɫɤɨɪɟɧɢɹ ɩɨɥɭɱɚɟɦ & q& & mv ⊥ = v ⊥ × B , (2.5) c ɢ, ɤɚɤ ɦɵ ɜɢɞɢɦ, ɩɨɩɟɪɟɱɧɚɹ ɤɨɦɩɨɧɟɧɬɚ ɦɟɧɹɟɬɫɹ ɬɨɥɶɤɨ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɱɚɫɬɢɰɚ ɪɚɜɧɨɦɟɪɧɨ ɞɜɢɠɟɬɫɹ ɜɞɨɥɶ ɫɢɥɨɜɨɣ ɥɢɧɢɢ ɩɨɥɹ, ɜɪɚɳɚɹɫɶ ɩɪɢ ɷɬɨɦ ɜɨɤɪɭɝ ɫɢɥɨɜɨɣ ɥɢɧɢɢ ɩɨ ɨɤɪɭɠɧɨɫɬɢ ɫ ɩɨɫɬɨɹɧɧɨɣ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ. Ɉɩɪɟɞɟɥɢɦ ɪɚɞɢɭɫ ɷɬɨɣ ɨɤɪɭɠɧɨɫɬɢ ρ ɢ ɭɝɥɨɜɭɸ ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ω. & Ɍɚɤ ɤɚɤ v ⊥ ɹɜɥɹɟɬɫɹ ɰɟɧɬɪɨɫɬɪɟɦɢɬɟɥɶɧɵɦ ɭɫɤɨɪɟɧɢɟɦ, ɬɨ, ɜɫɩɨɦɧɢɜ ɨɩɪɟɞɟɥɟɧɢɟ ɜɟɥɢɱɢɧɵ ɦɨɞɭɥɹ ɰɟɧɬɪɨɫɬɪɟɦɢɬɟɥɶɧɨɝɨ ɭɫɤɨɪɟɧɢɹ − ɨɬɧɨɲɟɧɢɟ ɤɜɚɞɪɚɬɚ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɤ ɪɚɞɢɭɫɭ ɨɤɪɭɠɧɨɫɬɢ, ɢɥɢ ɩɪɨɢɡɜɟɞɟɧɢɟ ɤɜɚɞɪɚɬɚ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɧɚ ɪɚɞɢɭɫ ɨɤɪɭɠɧɨɫɬɢ, − ɦɨɠɟɦ ɡɚɩɢɫɚɬɶ mv ⊥2 q m| v ⊥ | = = vB = mρω 2 . ρ c Ɉɬɤɭɞɚ ɢ ɩɨɥɭɱɚɟɦ ɬɪɟɛɭɟɦɵɟ ɧɚɦ ɜɟɥɢɱɢɧɵ qB ω = ω ɥɚ ɪ ɦ ≡ ; (2.6) mc v mcv ⊥ ρ = ρɥɚ ɪ ɦ ≡ ⊥ = (2.7) qB ω ɥɚ ɪ ɦ Ɋɚɞɢɭɫ ρɥɚɪɦ ɧɚɡɵɜɚɸɬ ɥɚɪɦɨɪɨɜɫɤɢɦ ɪɚɞɢɭɫɨɦ ɱɚɫɬɢɰɵ, ɚ ɭɝɥɨɜɭɸ ɫɤɨɪɨɫɬɶ ωɥɚɪɦ ɥɚɪɦɨɪɨɜɫɤɨɣ ɢɥɢ ɰɢɤɥɨɬɪɨɧɧɨɣ ɱɚɫɬɨɬɨɣ ɜɪɚɳɟɧɢɹ ɱɚɫɬɢɰɵ (ɞɥɹ ɷɬɢɯ ɜɟɥɢɱɢɧ ɭɩɨɬɪɟɛɢɬɟɥɶɧɵ ɢ ɞɪɭɝɢɟ ɨɛɨɡɧɚɱɟɧɢɹ, ɧɚɩɪɢɦɟɪ, ɫ ɢɧɞɟɤɫɨɦ “B”: ρȼ ɢ ωȼ, ɩɨɞɱɟɪɤɢɜɚɸɳɢɟ ɜ ɹɜɧɨɦ ɜɢɞɟ, ɱɬɨ ɨɧɢ ɨɬɧɨɫɹɬɫɹ ɤ ɫɥɭɱɚɸ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰɵ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ). ɂɡ ɫɨɨɬɧɨɲɟɧɢɣ (2.6) ɢ (2.7) ɜɢɞɧɨ, ɱɬɨ ɰɢɤɥɨɬɪɨɧɧɚɹ ɱɚɫɬɨɬɚ ɡɚɜɢɫɢɬ ɨɬ ɦɚɫɫɵ ɢ ɡɚɪɹɞɚ ɱɚɫɬɢɰɵ, ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɧɨ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɜɟɥɢɱɢɧɵ
ɫɤɨɪɨɫɬɢ ɜɪɚɳɚɸɳɟɣɫɹ ɜ ɩɨɥɟ ɱɚɫɬɢɰɵ, ɚ ɥɚɪɦɨɪɨɜɫɤɢɣ ɪɚɞɢɭɫ ɡɚɜɢɫɢɬ ɨɬ ɫɨɫɬɚɜɥɹɸɳɟɣ ɫɤɨɪɨɫɬɢ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ ɤ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ, ɩɪɢɱɟɦ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɟɟ ɨɧ ɜɨɡɪɚɫɬɚɟɬ ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜɟɤɬɨɪ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɩɨɥɨɠɢɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɚɧɬɢɩɚɪɚɥɥɟɥɟɧ, ɚ ɨɬɪɢɰɚɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ (ɧɚɩɪɢɦɟɪ, ɷɥɟɤɬɪɨɧɚ) - ɩɚɪɚɥɥɟɥɟɧ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ. Ɍɚɤ ɤɚɤ ɞɜɢɠɟɧɢɟ ɱɚɫɬɢɰɵ ɩɨ ɨɤɪɭɠɧɨɫɬɢ ɦɨɠɧɨ ɭɩɨɞɨɛɢɬɶ ɤɪɭɝɨɜɨɦɭ ɬɨɤɭ j = qω/2π, ɬɨ ɜɪɚɳɟɧɢɸ ɱɚɫɬɢɰɵ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɦɨɠɧɨ ɫɨɩɨɫɬɚɜɢɬɶ ɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ, ɪɚɜɧɵɣ ɦɚɝɧɢɬɧɨɦɭ ɦɨɦɟɧɬɭ ɷɬɨɝɨ ɤɪɭɝɨɜɨɝɨ ɬɨɤɚ: & j & µ= S. (2.8) c & Ɂɞɟɫɶ S - ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɨɪɢɟɧɬɢɪɨɜɚɧɧɚɹ ɩɥɨɳɚɞɶ ɤɪɭɝɚ, ɨɯɜɚɬɵɜɚɟɦɚɹ ɥɚɪɦɨɪɨɜɫɤɨɣ ɨɤɪɭɠɧɨɫɬɶɸ, ɪɚɜɧɚɹ S = πρ2. ɉɨɞɫɬɚɜɥɹɹ ɡɧɚɱɟɧɢɹ j ɢ S ɜ ɭɪɚɜɧɟɧɢɟ (2.8), ɩɨɥɭɱɚɟɦ & mv ⊥2 / 2 B & µ = −µ , µ= . (2.9) B B Ɇɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɜɪɚɳɚɸɳɟɣɫɹ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɱɚɫɬɢɰɵ ɜɫɟɝɞɚ ɧɚɩɪɚɜɥɟɧ ɩɪɨɬɢɜ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɨɥɨɠɢɬɟɥɶɧɨ ɢ ɨɬɪɢɰɚɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ ɜɪɚɳɚɸɬɫɹ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɯ ɧɚɩɪɚɜɥɟɧɢɹɯ (ɪɢɫ. 2.1). ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɬɪɚɟɤɬɨɪɢɹ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰɵ ɜ ɩɨɫɬɨɹɧɧɨɦ ɢ ɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɩɢɪɚɥɶ. Ʉɨɧɤɪɟɬɧɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɜɪɚɳɟɧɢɹ ɱɚɫɬɢɰɵ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɢɡɜɟɫɬɧɨɦɭ «ɩɪɚɜɢɥɭ Ʌɟɧɰɚ», ɫɨɝɥɚɫɧɨ ɤɨɬɨɪɨɦɭ, ɥɸɛɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɫɢɫɬɟɦɚ ɫɬɪɟɦɢɬɫɹ ɞɜɢɝɚɬɶɫɹ ɬɚɤ, ɱɬɨɛɵ ɩɪɨɬɢɜɨɞɟɣɫɬɜɨɜɚɬɶ ɩɪɢɱɢɧɟ, ɜɵɡɵɜɚɸɳɟɣ ɟɟ ɞɜɢɠɟɧɢɟ. ȼɪɚɳɚɸɳɚɹɫɹ ɩɨ ɥɚɪɦɨɪɨɜɫɤɨɣ ɨɤɪɭɠɧɨɫɬɢ ɱɚɫɬɢɰɚ Ɋɢɫ.2.1. Ⱦɜɢɠɟɧɢɟ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɩɨɫɬɨɹɧɧɨɦ ɜɟɞɟɬ ɫɟɛɹ ɤɚɤ ɞɢɚɦɚɝɧɟɬɢɤ − ɨɧɚ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ (ɩɪɨɞɨɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɧɚɩɪɚɜɥɟɧɚ ɫɬɪɟɦɢɬɫɹ ɨɫɥɚɛɢɬɶ ɨɯɜɚɬɵɜɚɟɦɵɣ ɟɺ ɜɞɨɥɶ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɨɛɨɢɯ ɫɥɭɱɚɹɯ) ɥɚɪɦɨɪɨɜɫɤɨɣ ɨɤɪɭɠɧɨɫɬɶɸ ɩɨɬɨɤ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ɗɬɨ ɜɵɪɚɠɚɟɬ ɫɭɬɶ ɬɚɤ ɧɚɡɵɜɚɟɦɨɝɨ ɩɪɢɧɰɢɩɚ ɞɢɚɦɚɝɧɟɬɢɡɦɚ ɫɜɨɛɨɞɧɵɯ ɱɚɫɬɢɰ.
ȼɨɡɧɢɤɚɟɬ «ɡɚɤɨɧɧɵɣ» ɜɨɩɪɨɫ: ɟɫɥɢ ɛɵ ɜɪɚɳɟɧɢɟ ɱɚɫɬɢɰɵ ɩɨ ɥɚɪɦɨɪɨɜɫɤɨɣ ɨɤɪɭɠɧɨɫɬɢ ɜɵɡɵɜɚɥɨ ɢɡɦɟɧɟɧɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɜ ɤɨɬɨɪɨɦ ɨɧɚ ɜɪɚɳɚɟɬɫɹ, ɬɨ ɷɬɨ ɞɨɥɠɧɨ ɛɵɥɨ ɛɵ ɫɤɚɡɵɜɚɬɶɫɹ ɧɚ ɬɪɚɟɤɬɨɪɢɢ ɟɺ ɞɜɢɠɟɧɢɹ, ɚ ɢɡɦɟɧɟɧɢɟ ɬɪɚɟɤɬɨɪɢɢ ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɩɪɢɜɟɥɨ ɛɵ ɤ ɞɨɩɨɥɧɢɬɟɥɶɧɨɦɭ ɢɫɤɚɠɟɧɢɸ ɩɨɥɹ ɢ ɬ.ɞ. ȼ ɞɟɣɫɬɜɢɬɟɥɶɧɨɫɬɢ ɷɬɨ ɥɨɠɧɵɣ ɩɭɬɶ. ȼ ɷɥɟɤɬɪɨɞɢɧɚɦɢɤɟ ɩɨɫɬɭɥɢɪɭɟɬɫɹ, ɱɬɨ ɬɨɱɟɱɧɵɟ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ ɞɪɭɝ ɫ ɞɪɭɝɨɦ ɱɟɪɟɡ ɩɨɫɪɟɞɫɬɜɨ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɫɨɡɞɚɜɚɟɦɨɝɨ ɢɦɢ ɜ ɨɤɪɭɠɚɸɳɟɦ ɩɪɨɫɬɪɚɧɫɬɜɟ, ɬɟɦ ɫɚɦɵɦ «ɫɚɦɨɞɟɣɫɬɜɢɟ» ɱɚɫɬɢɰ ɢɫɤɥɸɱɚɟɬɫɹ. ɇɚɩɪɢɦɟɪ, ɜ ɪɚɫɫɦɨɬɪɟɧɧɨɦ ɫɥɭɱɚɟ ɞɜɢɠɟɧɢɹ ɜɵɞɟɥɟɧɧɨɣ ɱɚɫɬɢɰɵ ɜ ɡɚɞɚɧɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɷɬɨ ɩɨɥɟ ɫɨɡɞɚɟɬɫɹ ɞɪɭɝɢɦɢ, ɞɜɢɠɭɳɢɦɢɫɹ ɡɚɞɚɧɧɵɦ ɨɛɪɚɡɨɦ ɡɚɪɹɠɟɧɧɵɦɢ ɱɚɫɬɢɰɚɦɢ, ɡɞɟɫɶ ɭɧɟɫɟɧɧɵɦɢ ɧɚ ɛɟɫɤɨɧɟɱɧɨɫɬɶ. ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ ɜɥɢɹɧɢɟɦ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɱɚɫɬɢɰɵ ɧɚ ɞɜɢɠɟɧɢɟ ɢɫɬɨɱɧɢɤɨɜ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ, − ɚ ɬɨɥɶɤɨ ɬɚɤ, ɜɥɢɹɹ ɧɚ ɬɪɚɟɤɬɨɪɢɢ ɷɬɢɯ ɢɫɬɨɱɧɢɤɨɜ, ɢ ɡɚɬɪɚɱɢɜɚɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɷɧɟɪɝɢɸ, ɱɚɫɬɢɰɚ ɦɨɝɥɚ ɛɵ «ɭɩɪɚɜɥɹɬɶ» ɫɜɨɟɣ ɬɪɚɟɤɬɨɪɢɟɣ.
§ 14. Ⱦɜɢɠɟɧɢɟ ɜ ɫɢɥɶɧɨɦ ɦɟɞɥɟɧɧɨ ɦɟɧɹɸɳɟɦɫɹ ɩɨɥɟ. Ⱦɪɟɣɮɨɜɨɟ ɩɪɢɛɥɢɠɟɧɢɟ ȿɫɥɢ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɦɟɞɥɟɧɧɨ ɦɟɧɹɟɬɫɹ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɢ ɜɨ ɜɪɟɦɟɧɢ, ɬɨ, ɞɜɢɠɭɳɚɹɫɹ ɜ ɧɟɦ ɱɚɫɬɢɰɚ, ɩɪɟɠɞɟ ɱɟɦ ɩɨɱɭɜɫɬɫɬɜɭɟɬ ɜɥɢɹɧɢɟ ɢɡɦɟɧɟɧɢɹ ɩɨɥɹ, ɫɨɜɟɪɲɢɬ ɜ ɧɟɦ ɦɧɨɠɟɫɬɜɨ ɥɚɪɦɨɪɨɜɫɤɢɯ ɨɛɨɪɨɬɨɜ, ɧɚɜɢɜɚɹɫɶ ɧɚ ɫɢɥɨɜɭɸ ɥɢɧɢɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ɗɬɨ ɞɜɢɠɟɧɢɟ, ɮɚɤɬɢɱɟɫɤɢ ɜ ɩɨɫɬɨɹɧɧɨɦ ɩɨɥɟ, ɦɵ ɭɠɟ ɢɡɭɱɢɥɢ. ɉɨɷɬɨɦɭ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɞɜɢɠɟɧɢɟ ɧɟ ɫɨɛɫɬɜɟɧɧɨ ɱɚɫɬɢɰɵ, ɚ ɟɺ ɦɝɧɨɜɟɧɧɨɝɨ ɰɟɧɬɪɚ ɜɪɚɳɟɧɢɹ, ɬɚɤ ɧɚɡɵɜɚɟɦɨɝɨ ɜɟɞɭɳɟɝɨ ɰɟɧɬɪɚ (ɜ ɡɚɪɭɛɟɠɧɨɣ ɥɢɬɟɪɚɬɭɪɟ ɬɚɤɨɣ ɩɨɞɯɨɞ ɢɡɜɟɫɬɟɧ ɤɚɤ ɩɪɢɛɥɢɠɟɧɢɟ ɜɟɞɭɳɟɝɨ ɰɟɧɬɪɚ - guiding center approximation). ɋɥɟɞɭɟɬ, ɨɞɧɚɤɨ, ɢɦɟɬɶ ɜ ɜɢɞɭ, ɱɬɨ ɜ ɫɥɭɱɚɟ, ɟɫɥɢ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɦɟɧɹɟɬɫɹ ɜɨ ɜɪɟɦɟɧɢ, ɬɨ ɧɭɠɧɨ ɭɱɢɬɵɜɚɬɶ ɢ ɫɥɚɛɵɟ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɩɨɥɹ. ɋɨɝɥɚɫɧɨ ɭɪɚɜɧɟɧɢɹɦ Ɇɚɤɫɜɟɥɥɚ, ɜ ɫɢɥɭ & 1∂B rotE = − , c ∂t ɩɟɪɟɦɟɧɧɨɟ ɜɨ ɜɪɟɦɟɧɢ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɜɵɡɵɜɚɟɬ ɩɨɹɜɥɟɧɢɟ ɜɢɯɪɟɜɨɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. ɇɚ ɦɟɞɥɟɧɧɨɟ ɞɜɢɠɟɧɢɟ ɜɟɞɭɳɟɝɨ ɰɟɧɬɪɚ, ɨɩɪɟɞɟɥɹɟɦɨɝɨ ɤɚɤ ɩɪɨɞɨɥɶɧɨɣ ɫɤɨɪɨɫɬɶɸ ɱɚɫɬɢɰɵ, ɬɚɤ ɢ ɜɥɢɹɧɢɟɦ ɫɥɚɛɨɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɢ ɫɥɚɛɵɯ ɧɟɨɞɧɨɪɨɞɧɨɫɬɟɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɧɚɥɨɠɢɬɫɹ ɛɵɫɬɪɨɟ ɜɪɚɳɟɧɢɟ ɱɚɫɬɢɰɵ ɜɨɤɪɭɝ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. Ɍɚɤɨɟ ɪɚɡɞɟɥɶɧɨɟ ɪɚɫɫɦɨɬɪɟɧɢɟ ɛɵɫɬɪɨɝɨ ɜɪɚɳɟɧɢɹ ɱɚɫɬɢɰɵ ɩɨ ɥɚɪɦɨɪɨɜɫɤɨɣ ɨɤɪɭɠɧɨɫɬɢ ɢ ɦɟɞɥɟɧɧɨɝɨ «ɞɪɟɣɮɚ» ɰɟɧɬɪɚ ɷɬɨɣ ɨɤɪɭɠɧɨɫɬɢ ɛɭɞɟɬ ɫɩɪɚɜɟɞɥɢɜɨ, ɟɫɥɢ ɢɡɦɟɧɟɧɢɟ ɥɚɪɦɨɪɨɜɫɤɨɝɨ ɪɚɞɢɭɫɚ ɧɚ ɨɞɧɨɦ ɨɛɨɪɨɬɟ ɛɭɞɟɬ ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɶɲɟ ɫɚɦɨɝɨ ɥɚɪɦɨɪɨɜɫɤɨɝɨ ɪɚɞɢɭɫɚ. ɗɬɨ ɭɫɥɨɜɢɟ, ɨɱɟɜɢɞɧɨ, ɛɭɞɟɬ ɜɵɩɨɥɧɟɧɨ, ɟɫɥɢ ɯɚɪɚɤɬɟɪɧɨɟ ɜɪɟɦɹ ɢɡɦɟɧɟɧɢɹ ɩɨɥɟɣ ɛɭɞɟɬ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ ɜɪɟɦɟɧɢ ɥɚɪɦɨɪɨɜɫɤɨɝɨ ɨɛɨɪɨɬɚ, ɢ ɟɫɥɢ ɯɚɪɚɤɬɟɪɧɵɣ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɣ ɦɚɫɲɬɚɛ ɢɡɦɟɧɟɧɢɹ ɩɨɥɟɣ ɛɭɞɟɬ ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɬɶ ɥɚɪɦɨɪɨɜɫɤɢɣ ɪɚɞɢɭɫ: ɯɚ ɪ ɯɚ ɪ ∆t ɩɨɥɹ >> Tɥɚ ɪ ɦ , ∆lɩɨɥɹ >> ρɥɚ ɪ ɦ . Ʉɨɥɢɱɟɫɬɜɟɧɧɨ ɷɬɢ ɤɪɢɬɟɪɢɢ ɦɨɠɧɨ ɫɮɨɪɦɭɥɢɪɨɜɚɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
∂B∂t << 1 , ω ɥɚ ɪ ɦ B
∂E ∂t << 1 , ω ɥɚ ɪ ɦ E
∇B ∇E ρɥɚ ɪ ɦ (2.10) << 1 , << 1 . B E Ɉɱɟɜɢɞɧɨ, ɷɬɢ ɭɫɥɨɜɢɹ ɜɵɩɨɥɧɟɧɵ ɬɟɦ ɥɭɱɲɟ, ɱɟɦ ɛɨɥɶɲɟ ɜɟɥɢɱɢɧɚ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɬɚɤ ɤɚɤ ɥɚɪɦɨɪɨɜɫɤɚɹ ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɱɚɫɬɢɰɵ ɜɨɡɪɚɫɬɚɟɬ ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɜɟɥɢɱɢɧɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɚ ɥɚɪɦɨɪɨɜɫɤɢɣ ɪɚɞɢɭɫ ɭɛɵɜɚɟɬ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɜɟɥɢɱɢɧɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ȼɦɟɫɬɟ ɫ ɬɟɦ, ɜɟɥɢɱɢɧɚ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ E ɧɟ ɞɨɥɠɧɚ ɛɵɬɶ ɫɥɢɲɤɨɦ ɛɨɥɶɲɨɣ. ɇɚ ɨɞɧɨɦ ɨɛɨɪɨɬɟ ɱɚɫɬɢɰɵ ɟɟ ɫɤɨɪɨɫɬɶ ɞɨɥɠɧɚ ɦɟɧɹɬɶɫɹ ɧɟɡɧɚɱɢɬɟɥɶɧɨ, ɧɚɫɬɨɥɶɤɨ ɧɟɡɧɚɱɢɬɟɥɶɧɨ, ɱɬɨɛɵ ɜɵɩɨɥɧɹɥɨɫɶ ɭɫɥɨɜɢɟ qE qE E δv ~ ≡ c << v . Tɥɚ ɪ ɦ ~ m mω ɥɚ ɪ ɦ B Ɉɬɤɭɞɚ ɢ ɩɨɥɭɱɚɟɦ ɬɪɟɛɭɟɦɨɟ ɨɝɪɚɧɢɱɟɧɢɟ ɧɚ ɜɟɥɢɱɢɧɭ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ v E << B . (2.11) c ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɭɫɥɨɜɢɣ (2.10) ɢ (2.11) ɢɫɬɢɧɧɚɹ ɬɪɚɟɤɬɨɪɢɹ ɱɚɫɬɢɰɵ ɨɛɵɱɧɨ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɦɟɞɥɟɧɧɨ ɢɡɝɢɛɚɸɳɭɸɫɹ ɫɩɢɪɚɥɶ ɫ ɦɟɞɥɟɧɧɨ ɦɟɧɹɸɳɢɦɫɹ ɪɚɞɢɭɫɨɦ ɢ ɲɚɝɨɦ. ɉɪɨɟɤɰɢɹ ɬɪɚɟɤɬɨɪɢɢ ɱɚɫɬɢɰɵ ɧɚ ɩɥɨɫɤɨɫɬɶ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɭɸ ɤ ɫɢɥɨɜɵɦ ɥɢɧɢɹɦ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɬɪɨɯɨɢɞɭ.
ρɥɚ ɪ ɦ
Ⱦɜɢɠɟɧɢɟ ɜɟɞɭɳɟɝɨ ɰɟɧɬɪɚ ɨɛɵɱɧɨ ɧɚɡɵɜɚɸɬ ɞɪɟɣɮɨɜɵɦ ɞɜɢɠɟɧɢɟɦ, ɚ ɩɪɢɛɥɢɠɟɧɧɨɟ ɨɩɢɫɚɧɢɟ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰɵ ɤɚɤ ɞɜɢɠɟɧɢɟ ɜɟɞɭɳɟɝɨ ɰɟɧɬɪɚ - ɞɪɟɣɮɨɜɵɦ ɩɪɢɛɥɢɠɟɧɢɟɦ. Ɋɚɫɫɦɨɬɪɢɦ ɧɟɤɨɬɨɪɵɟ ɫɥɭɱɚɢ, ɩɪɟɞɫɬɚɜɥɹɸɳɢɟ ɨɛɳɢɣ ɢɧɬɟɪɟɫ, ɬɚɤ ɤɚɤ ɤ ɧɢɦ ɦɨɠɧɨ ɫɜɟɫɬɢ ɦɧɨɝɢɟ ɜɢɞɵ ɞɜɢɠɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɧɟɨɞɧɨɪɨɞɧɵɯ ɦɚɝɧɢɬɧɵɯ ɩɨɥɹɯ ɢ ɜ ɩɨɥɹɯ ɞɪɭɝɢɯ ɜɧɟɲɧɢɯ ɫɢɥ.
§ 15. Ⱦɜɢɠɟɧɢɟ ɱɚɫɬɢɰɵ ɜ ɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɩɨɫɬɨɹɧɧɨɣ ɫɢɥɵ & ȿɫɥɢ ɧɚ ɱɚɫɬɢɰɭ, ɩɨɦɢɦɨ ɫɢɥɵ Ʌɨɪɟɧɰɚ, ɞɟɣɫɬɜɭɟɬ ɩɨɫɬɨɹɧɧɚɹ ɫɢɥɚ F , ɬɨ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰɵ ɢɦɟɟɬ ɜɢɞ:
& q& & & mv = v × B + F . c
(2.12)
& & Ɋɚɡɥɨɠɢɜ ɜɟɤɬɨɪɵ v ɢ F ɧɚ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɭɸ ɢ ɩɚɪɚɥɥɟɥɶɧɭɸ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ ɤɨɦɩɨɧɟɧɬɵ, ɤɚɤ ɷɬɨ ɭɠɟ ɞɟɥɚɥɨɫɶ ɜ ɩɪɟɞɵɞɭɳɟɦ ɩɚɪɚɝɪɚɮɟ, ɨɩɪɟɞɟɥɢɦ, ɱɬɨ & & q& & mv ⊥ = F⊥ + v ⊥ × B . (2.13) mv|| = F|| c Ɇɵ ɜɢɞɢɦ, ɱɬɨ ɩɪɨɞɨɥɶɧɨɟ ɢ ɩɨɩɟɪɟɱɧɨɟ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰɵ ɨɤɚɡɵɜɚɸɬɫɹ ɧɟɡɚɜɢɫɢɦɵɦɢ, ɢ ɢɯ ɦɨɠɧɨ ɪɚɫɫɦɨɬɪɟɬɶ ɪɚɡɞɟɥɶɧɨ. ɉɪɢ ɷɬɨɦ ɫɨɫɬɚɜɥɹɸɳɚɹ ɫɢɥɵ, ɩɚɪɚɥɥɟɥɶɧɚɹ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ, ɨɛɭɫɥɚɜɥɢɜɚɟɬ ɧɟɧɭɥɟɜɨɟ ɩɪɨɞɨɥɶɧɨɟ ɭɫɤɨɪɟɧɢɟ ɱɚɫɬɢɰɵ, ɤɨɬɨɪɨɟ ɢɡɦɟɧɹɟɬ ɩɪɨɞɨɥɶɧɭɸ ɤɨɦɩɨɧɟɧɬɭ ɫɤɨɪɨɫɬɢ. ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɫɨɫɬɚɜɥɹɸɳɟɣ ɫɢɥɵ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ ɤ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ, ɱɚɫɬɢɰɚ ɫɨɜɟɪɲɚɟɬ ɫɥɨɠɧɨɟ ɞɜɢɠɟɧɢɟ, ɹɜɥɹɸɳɟɟɫɹ ɫɭɩɟɪɩɨɡɢɰɢɟɣ ɜɪɚɳɟɧɢɹ ɱɚɫɬɢɰɵ ɢ ɫɢɫɬɟɦɚɬɢɱɟɫɤɨɝɨ ɫɧɨɫɚ (ɞɪɟɣɮɚ) ɫ ɧɟɤɨɬɨɪɨɣ ɩɨɫɬɨɹɧɧɨɣ ɫɤɨɪɨɫɬɶɸ. ɑɬɨɛɵ ɭɛɟɞɢɬɶɫɹ ɜ ɷɬɨɦ, ɩɪɟɞɫɬɚɜɢɦ ɫɤɨɪɨɫɬɶ ɩɨɩɟɪɟɱɧɨɝɨ ɞɜɢɠɟɧɢɹ ɜ ɜɢɞɟ ɫɭɦɦɵ & & & v⊥ = v d + vr , (2.14) & & ɝɞɟ v d — ɩɨɫɬɨɹɧɧɚɹ ɫɤɨɪɨɫɬɶ, ɚ v r — ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ɜɨɤɪɭɝ ɜɟɞɭɳɟɝɨ ɰɟɧɬɪɚ. Ɍɚɤɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɦɨɠɧɨ ɢɧɬɟɪɩɪɟɬɢɪɨɜɚɬɶ ɢ ɤɚɤ ɩɟɪɟɯɨɞ ɜ ɞɜɢɠɭɳɭɸɫɹ ɫ ɩɨɫɬɨɹɧɧɨɣ, ɧɨ ɡɚɪɚɧɟɟ ɧɟ ɢɡɜɟɫɬɧɨɣ (!), ɫɤɨɪɨɫɬɶɸ ɫɢɫɬɟɦɭ ɤɨɨɪɞɢɧɚɬ. ɉɨɞɫɬɚɧɨɜɤɚ ɜɵɪɚɠɟɧɢɹ (2.14) ɜɨ ɜɬɨɪɭɸ ɢɡ ɮɨɪɦɭɥ (2.13) ɞɚɟɬ & & q& & q& & & mv ⊥ ≡ mv r = F⊥ + v d × B + v r × B . (2.15) c c Ɍɚɤ ɤɚɤ ɩɟɪɜɵɟ ɞɜɚ ɫɥɚɝɚɟɦɵɯ ɫɩɪɚɜɚ − ɩɨɫɬɨɹɧɧɵɟ ɜɟɤɬɨɪɵ, ɬɨ ɨɧɢ ɦɨɝɭɬ ɤɨɦɩɟɧɫɢɪɨɜɚɬɶ ɞɪɭɝ ɞɪɭɝɚ. ɗɬɨ ɩɨɡɜɨɥɹɟɬ ɩɨɬɪɟɛɨɜɚɬɶ ɜɵɩɨɥɧɟɧɢɟ ɪɚɜɟɧɫɬɜɚ & & q& F⊥ + v d × B = 0 . c ɗɬɨ ɬɪɟɛɨɜɚɧɢɟ ɢ ɨɩɪɟɞɟɥɹɟɬ ɜɟɥɢɱɢɧɭ ɫɤɨɪɨɫɬɢ ɞɪɟɣɮɚ ɱɚɫɬɢɰɵ: & & c F×B & vd = . (2.16) q B2
Ɉɫɬɚɜɲɚɹɫɹ ɱɚɫɬɶ ɭɪɚɜɧɟɧɢɹ (2.15) & e& & mv r = v r × B , c
(2.17)
ɨɩɢɫɵɜɚɟɬ ɜɪɚɳɟɧɢɟ ɜɨɤɪɭɝ ɜɟɞɭɳɟɝɨ ɰɟɧɬɪɚ, ɤɚɤ ɷɬɨ ɨɱɟɜɢɞɧɨ ɢɡ ɫɪɚɜɧɟɧɢɹ ɫ ɭɪɚɜɧɟɧɢɟɦ (2.5). ɋɤɨɪɨɫɬɶ ɱɚɫɬɢɰɵ ɜ ɬɚɤɨɦ ɞɜɢɠɟɧɢɢ, ɤɚɤ ɦɵ ɭɠɟ ɨɛɫɭɠɞɚɥɢ ɜ ɩɪɟɞɵɞɭɳɟɦ ɩɚɪɚɝɪɚɮɟ, ɦɨɠɟɬ ɬɨɥɶɤɨ ɩɨɜɨɪɚɱɢɜɚɬɶɫɹ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ, ɧɟ ɦɟɧɹɹɫɶ ɩɨ ɚɛɫɨɥɸɬɧɨɣ ɜɟɥɢɱɢɧɟ. ȼɟɥɢɱɢɧɚ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɦɨɠɟɬ ɛɵɬɶ ɧɚɣɞɟɧɚ ɩɨ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰɵ, ɤɨɬɨɪɚɹ, ɤɨɧɟɱɧɨ, ɞɨɥɠɧɚ ɛɵɬɶ ɢɡɧɚɱɚɥɶɧɨ ɡɚɞɚɧɚ: & & v r =| v ⊥ 0 − v d | , (2.18)
& ɝɞɟ v ⊥ 0 - ɩɨɩɟɪɟɱɧɚɹ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ ɤɨɦɩɨɧɟɧɬɚ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ. & ɇɚɩɪɢɦɟɪ, ɜ ɱɚɫɬɧɨɦ ɫɥɭɱɚɟ v ⊥ 0 = 0 ɩɨɥɭɱɚɟɦ
vr = vd =
cF⊥ . qB
(2.19)
Ɇɨɞɭɥɶ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɨɩɪɟɞɟɥɹɟɬ ɪɚɞɢɭɫ ɨɤɪɭɠɧɨɫɬɢ:
ρ =
mcv r . qB
(2.20)
ɩɨ ɤɨɬɨɪɨɣ ɜɪɚɳɚɟɬɫɹ ɱɚɫɬɢɰɚ ɜ ɩɨɞɜɢɠɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ, ɞɜɢɠɭɳɟɣɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ (2.16). ɇɟ ɫɨɫɬɚɜɥɹɟɬ ɛɨɥɶɲɨɝɨ ɬɪɭɞɚ ɧɚɣɬɢ ɢ ɬɨɱɧɵɣ ɡɚɤɨɧ ɩɨɩɟɪɟɱɧɨɝɨ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰɵ: & & & & & v − vd ( v⊥0 − vd ) × B & & & r⊥ = r⊥ 0 + v d t + ( 1 − cos ω t ) + ⊥ 0 sin ω t . (2.21) ωB ω ɂɧɞɟɤɫɨɦ ɧɨɥɶ ɡɞɟɫɶ ɩɨɦɟɱɟɧɵ ɧɚɱɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɜɟɥɢɱɢɧ. ɋɨɫɬɚɜɢɬɶ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɨ ɪɚɡɧɨɨɛɪɚɡɢɢ ɜɨɡɦɨɠɧɵɯ ɬɪɚɟɤɬɨɪɢɣ ɩɨɩɟɪɟɱɧɨɝɨ ɞɜɢɠɟɧɢɹ ɦɨɠɧɨ ɩɨ ɧɢɠɟɫɥɟɞɭɸɳɟɦɭ ɪɢɫ. 2.2: Ʉɪɨɦɟ ɬɨɝɨ, ɫɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɟɫɥɢ ɩɨɩɟɪɟɱɧɚɹ ɤɨɦɩɨɧɟɧɬɚ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɜ ɬɨɱɧɨɫɬɢ ɫɨɜɩɚɞɚɟɬ ɫɨ ɫɤɨɪɨɫɬɶɸ ɞɪɟɣɮɚ: & & v⊥ 0 = vd , (2.22) ɬɨ, ɤɚɤ ɷɬɨ ɫɥɟɞɭɟɬ ɢɡ ɡɚɤɨɧɚ ɞɜɢɠɟɧɢɹ, ɱɚɫɬɢɰɚ ɞɜɢɠɟɬɫɹ ɪɚɜɧɨɦɟɪɧɨ ɩɨɩɟɪɟɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. Ɍɚɤɚɹ ɜɨɡɦɨɠɧɨɫɬɶ ɩɪɟɞɫɬɚɜɥɹɟɬ ɛɨɥɶɲɨɣ ɢɧɬɟɪɟɫ ɜ ɩɪɨɛɥɟɦɟ ɬɪɚɧɫɩɨɪɬɚ ɱɚɫɬɢɰ ɩɨɩɟɪɟɤ ɫɢɥɶɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. Ɋɢɫ.2.2. Ɍɢɩɵ ɜɨɡɦɨɠɧɵɯ ɬɪɚɟɤɬɨɪɢɣ ɞɥɹ ɇɚɦɢ ɧɟ ɜɵɫɤɚɡɵɜɚɥɨɫɶ & ɧɢɤɚɤɢɯ ɧɟɤɨɬɨɪɵɯ ɱɚɫɬɧɵɯ ɫɥɭɱɚɟɜ ɧɚɩɪɚɜɥɟɧɢɹ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɩɨɩɟɪɟɱɧɨɝɨ ɞɜɢɠɟɧɢɹ ɩɪɟɞɩɨɥɨɠɟɧɢɣ ɨ ɩɪɢɪɨɞɟ ɫɢɥɵ F , ɩɨɷɬɨɦɭ ɱɚɫɬɢɰɵ ɜ ɫɤɪɟɳɟɧɧɵɯ ɩɨɥɹɯ (ɲɬɪɢɯɨɜɚɹ ɜɵɜɨɞ ɨ ɯɚɪɚɤɬɟɪɟ ɞɜɢɠɟɧɢɹ & ɫɩɪɚɜɟɞɥɢɜ ɞɥɹ ɥɢɧɢɹ − ɩɨɥɨɠɟɧɢɟ ɰɟɧɬɪɚ ɥɚɪɦɨɪɨɜɫɤɨɣ ɥɸɛɨɣ ɩɨɫɬɨɹɧɧɨɣ ɫɢɥɵ F : ɩɪɨɞɨɥɶɧɨɟ (ɜ ) ɨɛɳɟɦ ɫɥɭɱɚɟ) ɭɫɤɨɪɟɧɢɟ ɢ ɫɢɫɬɟɦɚɬɢɱɟɫɤɢɣ ɫɧɨɫ ɫ ɩɨɫɬɨɹɧɧɨɣ ɫɤɨɪɨɫɬɶɸ ɜ ɫɨɜɨɤɭɩɧɨɫɬɢ ɫ ɪɚɜɧɨɦɟɪɧɵɦ ɜɪɚɳɟɧɢɟɦ ɜ ɩɨɩɟɪɟɱɧɨɣ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ ɩɥɨɫɤɨɫɬɢ. ɂɡ ɮɨɪɦɭɥɵ (2.16) ɫɥɟɞɭɟɬ, ɱɬɨ ɫɤɨɪɨɫɬɶ ɞɪɟɣɮɚ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɦɚɫɫɵ ɱɚɫɬɢɰɵ, ɧɨ ɡɚɜɢɫɢɬ ɨɬ ɡɧɚɤɚ ɟɟ ɡɚɪɹɞɚ, ɟɫɥɢ ɫɢɥɚ ɨɬ ɡɧɚɤɚ ɡɚɪɹɞɚ ɧɟ ɡɚɜɢɫɢɬ. ɉɨɥɟɡɧɨ ɨɬɦɟɬɢɬɶ ɬɚɤɠɟ, ɱɬɨ ɞɟɣɫɬɜɢɟ ɩɨɫɬɨɹɧɧɨɣ ɫɢɥɵ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ ɤ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ, ɩɪɢɜɨɞɢɬ (ɜ ɫɪɟɞɧɟɦ ɩɨ ɨɫɰɢɥɥɹɰɢɹɦ!) ɧɟ ɤ ɭɜɟɥɢɱɟɧɢɸ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰɵ, ɚ ɤ ɞɜɢɠɟɧɢɸ ɟɟ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɤ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ ɫ ɩɨɫɬɨɹɧɧɨɣ ɫɤɨɪɨɫɬɶɸ. ɋ ɩɨɯɨɠɢɦ ɹɜɥɟɧɢɟɦ ɦɵ ɜɫɬɪɟɱɚɟɦɫɹ ɜ ɦɟɯɚɧɢɤɟ ɩɪɢ ɢɡɭɱɟɧɢɢ ɩɪɟɰɟɫɫɢɢ ɨɫɢ ɝɢɪɨɫɤɨɩɚ, ɤɨɝɞɚ ɩɪɢɥɨɠɟɧɧɵɣ ɤ ɝɢɪɨɫɤɨɩɭ ɦɨɦɟɧɬ ɜɵɡɵɜɚɟɬ ɜɪɚɳɟɧɢɟ ɟɝɨ ɨɫɢ ɜ ɧɚɩɪɚɜɥɟɧɢɢ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɦ ɤɚɤ ɤ ɦɨɦɟɧɬɭ ɤɨɥɢɱɟɫɬɜɚ ɞɜɢɠɟɧɢɹ ɝɢɪɨɫɤɨɩɚ, ɬɚɤ ɢ ɤ ɦɨɦɟɧɬɭ ɫɢɥɵ.
§ 16. Ⱦɪɟɣɮ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜɞɨɥɶ ɩɥɨɫɤɨɫɬɢ ɫɤɚɱɤɚ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ȼ ɤɚɱɟɫɬɜɟ ɟɳɟ ɨɞɧɨɝɨ ɬɨɱɧɨ ɪɚɡɪɟɲɢɦɨɝɨ ɩɪɢɦɟɪɚ ɫ ɞɪɟɣɮɨɜɵɦ ɞɜɢɠɟɧɢɟɦ ɪɚɫɫɦɨɬɪɢɦ ɡɚɞɚɱɭ ɨ ɞɜɢɠɟɧɢɢ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɫɨ ɫɤɚɱɤɨɦ, ɫɥɟɜɚ ɢ ɫɩɪɚɜɚ ɨɬ ɩɥɨɫɤɨɫɬɢ ɤɨɬɨɪɨɝɨ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɨɞɧɨɪɨɞɧɨ ɢ ɨɞɢɧɚɤɨɜɨ ɧɚɩɪɚɜɥɟɧɨ, ɧɨ ɢɦɟɟɬ ɪɚɡɧɭɸ ɜɟɥɢɱɢɧɭ (ɫɦ. ɪɢɫ. 2.3), ɩɭɫɬɶ ɫɩɪɚɜɚ ɛɭɞɟɬ ȼ2>ȼ1. ȼɧɟ ɫɤɚɱɤɚ, ɝɞɟ ɩɨɥɟ ɨɞɧɨɪɨɞɧɨ, ɧɚ ɪɚɫɫɬɨɹɧɢɢ, ɩɪɟɜɵɲɚɸɳɟɦ ɥɚɪɦɨɪɨɜɫɤɢɣ ɪɚɞɢɭɫ, ɱɚɫɬɢɰɵ ɨɩɢɫɵɜɚɸɬ ɨɤɪɭɠɧɨɫɬɢ, ɪɚɡɦɟɪ ɤɨɬɨɪɵɯ ɛɨɥɶɲɟ ɜ ɨɛɥɚɫɬɢ ɫɥɚɛɨɝɨ ɩɨɥɹ (ɫɥɟɜɚ ɧɚ ɪɢɫ.2.3). ɇɚ ɦɟɧɶɲɟɦ ɪɚɫɫɬɨɹɧɢɢ ɩɪɢ ɞɜɢɠɟɧɢɢ ɱɚɫɬɢɰɵ ɟɺ ɥɚɪɦɨɪɨɜɫɤɚɹ ɨɤɪɭɠɧɨɫɬɶ ɩɟɪɟɫɟɤɚɟɬ ɩɥɨɫɤɨɫɬɶ ɫɤɚɱɤɚ, ɯɚɪɚɤɬɟɪ ɟɺ ɞɜɢɠɟɧɢɹ ɪɟɡɤɨ ɦɟɧɹɟɬɫɹ, ɬɚɤ ɤɚɤ ɤɚɠɞɵɣ ɪɚɡ ɩɨɫɥɟ ɩɟɪɟɫɟɱɟɧɢɹ ɷɬɨɣ ɩɥɨɫɤɨɫɬɢ ɫɤɚɱɤɨɦ ɢɡɦɟɧɹɟɬɫɹ ɪɚɞɢɭɫ ɨɤɪɭɠɧɨɫɬɢ. Ɍɪɚɟɤɬɨɪɢɹ ɩɪɢɨɛɪɟɬɚɟɬ ɫɥɨɠɧɵɣ ɯɚɪɚɤɬɟɪ ɫ ɧɚɥɢɱɢɟɦ ɫɢɫɬɟɦɚɬɢɱɟɫɤɨɝɨ «ɫɧɨɫɚ» ɱɚɫɬɢɰɵ ɜɞɨɥɶ ɩɥɨɫɤɨɫɬɢ ɫɤɚɱɤɚ. Ʉɚɤ ɜɢɞɧɨ ɢɡ ɪɢɫɭɧɤɚ, ɞɪɟɣɮ ɩɟɪɩɟɧɞɢɤɭɥɹɪɟɧ ɧɚɩɪɚɜɥɟɧɢɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɟɝɨ ɝɪɚɞɢɟɧɬɚ, ɩɪɢɱɟɦ, ɨɱɟɜɢɞɧɨ, ɢɦɟɟɬ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɣ ɡɧɚɤ ɞɥɹ ɪɚɡɧɨɢɦɟɧɧɨ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ: ɞɥɹ ɝɟɨɦɟɬɪɢɢ ɪɢɫ.2.3 ɨɧ ɧɚɩɪɚɜɥɟɧ ɜɜɟɪɯ ɞɥɹ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɡɚɪɹɞɚ, ɢɥɢ ɛɵɥ ɛɵ ɧɚɩɪɚɜɥɟɧ ɜɧɢɡ, ɟɫɥɢ ɛɵ ɡɚɪɹɞ ɛɵɥ ɨɬɪɢɰɚɬɟɥɶɧɵɦ. ɇɟɬɪɭɞɧɨ ɩɨɞɫɱɢɬɚɬɶ ɫɤɨɪɨɫɬɶ ɷɬɨɝɨ ɞɪɟɣɮɚ. ɉɭɫɬɶ ɞɥɹ ɩɪɨɫɬɨɬɵ ɱɚɫɬɢɰɚ ɩɟɪɟɫɟɤɚɟɬ ɩɥɨɫɤɨɫɬɶ ɫɤɚɱɤɚ ɩɨ ɧɨɪɦɚɥɢ. Ɍɨɝɞɚ ɡɚ ɜɪɟɦɹ, ɪɚɜɧɨɟ ɫɭɦɦɟ ɥɚɪɦɨɪɨɜɫɤɢɯ ɩɨɥɭɩɟɪɢɨɞɨɜ ɞɥɹ ɨɛɥɚɫɬɢ ɫɥɟɜɚ ɢ ɫɩɪɚɜɚ Ɋɢɫ.2.3. ɋɯɟɦɚ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɞɪɟɣɮɚ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɡɚɪɹɞɚ ɧɚ ɝɪɚɧɢɰɟ ɫɨ ɫɤɚɱɤɨɦ ɜɟɥɢɱɢɧɵ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ
∆ t = T1 + T2 =
π π + , ω1 ω2
(2.23)
ɝɞɟ qB1 ,2 , mc ɰɢɤɥɨɬɪɨɧɧɵɟ ɱɚɫɬɨɬɵ, ɜɵɱɢɫɥɟɧɧɵɟ ɩɨ ɡɧɚɱɟɧɢɸ ɩɨɥɹ ɫɥɟɜɚ ɢ ɫɩɪɚɜɚ ɨɬ ɩɥɨɫɤɨɫɬɢ ɫɤɚɱɤɚ. ɑɚɫɬɢɰɚ ɫɦɟɳɚɟɬɫɹ ɜɞɨɥɶ ɷɬɨɣ ɩɥɨɫɤɨɫɬɢ ɧɚ ɞɥɢɧɭ v v ∆x = 2( ρ 1 − ρ 2 ) = 2( − ). (2.24)
ω 1 ,2 =
ω1
ω2
Ɂɞɟɫɶ v − ɫɤɨɪɨɫɬɶ ɱɚɫɬɢɰɵ, ɤɨɬɨɪɚɹ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ ɢɡɧɚɱɚɥɶɧɨ ɧɚɩɪɚɜɥɟɧɧɨɣ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɩɥɨɫɤɨɫɬɢ ɫɤɚɱɤɚ. Ɉɱɟɜɢɞɧɨ, ɫɤɨɪɨɫɬɶ ɞɪɟɣɮɚ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɤɚɤ ∆x 2 v B2 − B1 v ∆B vd = = ≡ , (2.25) ∆ t π B2 + B1 π < B > ɝɞɟ ∆ȼ=ȼ2−ȼ1 − ɜɟɥɢɱɢɧɚ ɫɤɚɱɤɚ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɚ <ȼ>=(ȼ2+ȼ1)/2 − ɟɝɨ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ. ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɩɨɥɭɱɟɧɧɨɟ ɪɟɲɟɧɢɟ − ɬɨɱɧɨɟ, ɩɪɢɱɟɦ ɜ ɭɫɥɨɜɢɹɯ, ɤɨɝɞɚ ɞɪɟɣɮɨɜɨɟ ɩɪɢɛɥɢɠɟɧɢɟ ɡɚɜɟɞɨɦɨ ɧɟɩɪɢɦɟɧɢɦɨ: ɪɚɡɦɟɪ
ɧɟɨɞɧɨɪɨɞɧɨɫɬɢ, ɤɚɤ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɞɨɥɠɟɧ ɛɵɬɶ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɟ, ɱɟɦ ɥɚɪɦɨɪɨɜɫɤɢɟ ɪɚɞɢɭɫɵ ɱɚɫɬɢɰ! ȼɟɥɢɱɢɧɚ ɫɤɨɪɨɫɬɢ ɞɪɟɣɮɚ ɡɚɜɢɫɢɬ, ɨɱɟɜɢɞɧɨ, ɢ ɨɬ ɭɝɥɚ, ɩɨɞ ɤɨɬɨɪɵɦ ɱɚɫɬɢɰɚ ɩɟɪɟɫɟɤɚɟɬ ɨɛɥɚɫɬɶ ɫɤɚɱɤɚ. Ɇɵ ɧɟ ɛɭɞɟɦ ɨɫɬɚɧɚɜɥɢɜɚɬɶɫɹ ɧɚ ɷɬɨɦ ɢɧɬɟɪɟɫɧɨɦ ɜɨɩɪɨɫɟ − ɷɬɭ ɡɚɜɢɫɢɦɨɫɬɶ ɧɟɫɥɨɠɧɨ ɩɨɥɭɱɢɬɶ, ɩɨ ɫɭɬɢ ɞɟɥɚ, ɬɟɦ ɠɟ ɫɚɦɵɦ ɩɭɬɟɦ, ɤɚɤ ɢ ɪɚɫɫɦɨɬɪɟɧɧɵɣ ɜɵɲɟ ɛɨɥɟɟ ɩɪɨɫɬɨɣ ɫɥɭɱɚɣ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɝɨ ɩɟɪɟɫɟɱɟɧɢɹ. Ⱦɪɟɣɮ ɜɨɡɧɢɤɚɟɬ ɢ ɬɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɫɥɟɜɚ ɢ ɫɩɪɚɜɚ ɨɬ ɧɟɤɨɬɨɪɨɣ ɩɥɨɫɤɨɫɬɢ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɩɨ ɜɟɥɢɱɢɧɟ ɧɟ ɦɟɧɹɟɬɫɹ, ɧɨ ɢɡɦɟɧɹɟɬ ɧɚɩɪɚɜɥɟɧɢɟ (ɫɦ. ɪɢɫ.2.4). Ɇɚɝɧɢɬɧɚɹ ɤɨɧɮɢɝɭɪɚɰɢɹ ɬɚɤɨɝɨ ɬɢɩɚ ɜɨɡɧɢɤɚɟɬ ɜ ɬɚɤ ɧɚɡɵɜɚɟɦɵɯ ɬɨɤɨɜɵɯ ɫɥɨɹɯ. ȼ ɰɟɧɬɪɟ ɫɢɦɦɟɬɪɢɱɧɨɝɨ, ɧɚɩɪɢɦɟɪ, ɩɥɨɫɤɨɝɨ ɬɨɤɨɜɨɝɨ ɫɥɨɹ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɪɚɜɧɨ ɧɭɥɸ, ɚ ɜɧɟ ɷɬɨɣ ɰɟɧɬɪɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ, ɤɚɤ ɷɬɨ ɫɥɟɞɭɟɬ ɢɡ ɡɚɤɨɧɚ Ⱥɦɩɟɪɚ
& 4π & rot B = j , ɦɟɧɹɟɬ ɡɧɚɤ. ȿɫɥɢ ɬɨɥɳɢɧɨɣ ɫɥɨɹ c
ɩɪɟɧɟɛɪɟɱɶ, ɩɨɥɭɱɢɦ ɫɤɚɱɨɤ ɧɚɩɪɚɜɥɟɧɢɹ ɩɨɥɹ. ȼɧɟ ɫɥɨɹ ɱɚɫɬɢɰɵ ɜɪɚɳɚɸɬɫɹ ɩɨ ɥɚɪɦɨɪɨɜɫɤɢɦ ɨɤɪɭɠɧɨɫɬɹɦ, ɡɞɟɫɶ − ɨɞɢɧɚɤɨɜɨɝɨ ɪɚɞɢɭɫɚ, ɧɨ ɫ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɦ ɧɚɩɪɚɜɥɟɧɢɟɦ ɜɪɚɳɟɧɢɹ, ɢ ɞɪɟɣɮɚ ɧɟɬ, ɟɫɥɢ ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɩɥɨɫɤɨɫɬɢ ɫɥɨɹ ɩɪɟɜɵɲɚɟɬ ɥɚɪɦɨɪɨɜɫɤɢɣ ɪɚɞɢɭɫ. Ⱦɪɟɣɮ ɜɨɡɧɢɤɚɟɬ, ɤɨɝɞɚ ɥɚɪɦɨɪɨɜɫɤɚɹ ɨɤɪɭɠɧɨɫɬɶ ɩɟɪɟɫɟɤɚɟɬ ɷɬɭ ɩɥɨɫɤɨɫɬɶ. Ɍɪɚɟɤɬɨɪɢɸ ɱɚɫɬɢɰɵ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. ɉɭɫɬɶ ɩɟɪɟɫɟɱɟɧɢɟ ɩɥɨɫɤɨɫɬɢ ɫɥɨɹ ɱɚɫɬɢɰɟɣ – ɩɨ ɧɨɪɦɚɥɢ, ɬɨɝɞɚ ɥɚɪɦɨɪɨɜɫɤɭɸ ɨɤɪɭɠɧɨɫɬɶ ɫɥɟɞɭɟɬ «ɪɚɡɪɟɡɚɬɶ» ɜɞɨɥɶ ɜɟɪɬɢɤɚɥɶɧɨɝɨ ɞɢɚɦɟɬɪɚ ɢ ɡɚɬɟɦ, ɞɥɹ Ɋɢɫ.2.4. Ⱦɪɟɣɮ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɡɚɪɹɞɚ, ɩɪɚɜɭɸ ɩɨɥɨɜɢɧɭ ɫɥɟɞɭɟɬ ɡɚɪɹɞɚ ɩɪɢ ɫɦɟɧɟ ɧɚɩɪɚɜɥɟɧɢɹ ɨɬɪɚɡɢɬɶ ɡɟɪɤɚɥɶɧɨ ɜɜɟɪɯ, ɤɚɤ ɷɬɨ ɢɡɨɛɪɚɠɟɧɨ ɧɚ ɪɢɫ.2.4. ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɉɪɢ ɷɬɨɦ ɡɚ ɥɚɪɦɨɪɨɜɫɤɢɣ ɩɟɪɢɨɞ ɫɦɟɳɟɧɢɟ ɜɞɨɥɶ ɫɥɨɹ, ɨɱɟɜɢɞɧɨ, ɫɨɫɬɚɜɥɹɟɬ ɞɜɚ ɥɚɪɦɨɪɨɜɫɤɢɯ ɞɢɚɦɟɬɪɚ, ɬɚɤ ɱɬɨ ɫɤɨɪɨɫɬɶ ɞɪɟɣɮɚ ɞɥɹ ɷɬɨɝɨ ɫɥɭɱɚɹ:
vd =
∆x 4 ρ 4 v / ω 2 = = = v. ∆t T 2π / ω π
(2.26)
ɉɪɢ ɩɟɪɟɫɟɱɟɧɢɢ «ɨɛɳɟɝɨ ɩɨɥɨɠɟɧɢɹ», ɩɪɢ ɩɪɨɢɡɜɨɥɶɧɨɦ ɭɝɥɟ, ɫɤɨɪɨɫɬɶ ɞɪɟɣɮɚ, ɨɱɟɜɢɞɧɨ, ɦɟɧɹɟɬɫɹ ɫ ɢɡɦɟɧɟɧɢɟɦ ɭɝɥɚ, ɧɨ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɜɟɥɢɱɢɧɵ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ! ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɢ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɞɪɟɣɮɨɜɨɟ ɩɪɢɛɥɢɠɟɧɢɟ ɧɟɩɪɢɦɟɧɢɦɨ.
§17. ȼɚɠɧɟɣɲɢɟ ɬɢɩɵ ɞɪɟɣɮɨɜɵɯ ɞɜɢɠɟɧɢɣ ɱɚɫɬɢɰ ɜ ɩɥɚɡɦɟ Ɋɚɫɫɦɨɬɪɟɧɧɵɣ ɜ §15 ɩɪɢɦɟɪ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɞɨɩɨɥɧɢɬɟɥɶɧɨɣ ɩɨɫɬɨɹɧɧɨɣ ɫɢɥɵ ɹɜɥɹɟɬɫɹ ɬɨɱɧɵɦ ɪɟɲɟɧɢɟɦ ɧɟɪɟɥɹɬɢɜɢɫɬɫɤɢɯ ɭɪɚɜɧɟɧɢɣ ɞɜɢɠɟɧɢɹ. ȼɟɫɶɦɚ ɜɚɠɧɵɦ ɹɜɥɹɟɬɫɹ ɬɨ, ɱɬɨ ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɫɭɳɢɟ ɷɬɨɦɭ ɞɜɢɠɟɧɢɸ, ɫɨɯɪɚɧɹɸɬɫɹ ɢ ɜ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɩɨɥɹ, ɞɟɣɫɬɜɭɸɳɢɟ ɧɚ ɱɚɫɬɢɰɭ, ɹɜɥɹɸɬɫɹ ɩɟɪɟɦɟɧɧɵɦɢ. Ɉɞɧɚɤɨ ɯɚɪɚɤɬɟɪɧɵɟ ɦɚɫɲɬɚɛɵ ɢɯ ɢɡɦɟɧɟɧɢɹ ɜɨ ɜɪɟɦɟɧɢ ɢ ɩɨ ɩɪɨɫɬɪɚɧɫɬɜɭ ɞɨɥɠɧɵ ɛɵɬɶ, ɤɚɤ ɭɠɟ ɨɛɫɭɠɞɚɥɨɫɶ, ɞɨɫɬɚɬɨɱɧɨ ɦɟɞɥɟɧɧɵɦɢ ɜ ɫɪɚɜɧɟɧɢɢ ɫ ɥɚɪɦɨɪɨɜɫɤɢɦ ɩɟɪɢɨɞɨɦ ɨɫɰɢɥɥɹɰɢɣ ɱɚɫɬɢɰɵ ɢ ɥɚɪɦɨɪɨɜɫɤɢɦ ɪɚɞɢɭɫɨɦ ɨɩɢɫɵɜɚɟɦɨɣ ɟɸ ɨɤɪɭɠɧɨɫɬɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɞɥɹ ɫɤɨɪɨɫɬɢ ɞɪɟɣɮɚ ɜɧɨɜɶ ɫɩɪɚɜɟɞɥɢɜɚ ɮɨɪɦɭɥɚ (2.16). ɋ ɬɟɦ ɥɢɲɶ ɫɭɳɟɫɬɜɟɧɧɵɦ ɨɬɥɢɱɢɟɦ, ɱɬɨ ɫɤɨɪɨɫɬɶ ɞɪɟɣɮɚ ɞɨɥɠɧɚ ɛɵɬɶ ɞɨɫɬɚɬɨɱɧɚ ɦɚɥɚ, ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɟ ɫɪɟɞɧɟɣ ɫɤɨɪɨɫɬɢ ɯɚɨɬɢɱɟɫɤɨɝɨ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɩɥɚɡɦɵ. ɉɨɫɥɟɞɧɹɹ, ɤɚɤ ɢɡɜɟɫɬɧɨ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɟɩɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ ɱɚɫɬɢɰ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɢɯɨɞɢɦ ɤ ɭɫɥɨɜɢɸ v d << vT , (2.27) ɨɝɪɚɧɢɱɢɜɚɸɳɟɦɭ, ɩɪɢɱɟɦ ɡɚɱɚɫɬɭɸ ɜɟɫɶɦɚ ɫɭɳɟɫɬɜɟɧɧɨ, ɨɛɥɚɫɬɶ ɩɪɢɦɟɧɢɦɨɫɬɢ ɞɪɟɣɮɨɜɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ ɜ ɨɩɢɫɚɧɢɢ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɩɥɚɡɦɵ. ɉɪɟɞɩɨɥɚɝɚɹ ɭɤɚɡɚɧɧɵɟ ɨɝɪɚɧɢɱɟɧɢɹ ɜɵɩɨɥɧɟɧɧɵɦɢ, ɪɚɫɫɦɨɬɪɢɦ ɤɪɚɬɤɨ ɧɟɤɨɬɨɪɵɟ ɩɪɢɦɟɪɵ ɞɪɟɣɮɨɜɵɯ ɞɜɢɠɟɧɢɣ ɩɥɚɡɦɵ. Ⱦɪɟɣɮ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ & ɉɪɢɪɨɞɚ ɫɢɥɵ F ɦɨɠɟɬ ɛɵɬɶ ɥɸɛɨɣ, ɧɚɩɪɢɦɟɪ ɝɪɚɜɢɬɚɰɢɨɧɧɨɣ ɢɥɢ & & ɷɥɟɤɬɪɢɱɟɫɤɨɣ. ȼ ɱɚɫɬɧɨɦ ɫɥɭɱɚɟ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɢɪɨɞɵ ɫɢɥɵ, ɤɨɝɞɚ F = eE , ɩɨɥɭɱɢɦ ɞɪɟɣɮ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ & & E⊥ × B & vE = c . (2.28) B2 Ⱦɪɟɣɮ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɡɧɚɤɚ ɡɚɪɹɞɚ - ɩɥɚɡɦɚ ɞɪɟɣɮɭɟɬ ɤɚɤ ɰɟɥɨɟ. Ɍɟɩɟɪɶ ɫɬɚɧɨɜɢɬɫɹ ɩɨɧɹɬɧɵɦ ɫɦɵɫɥ ɨɝɪɚɧɢɱɟɧɢɹ (2.11), ɧɚɥɨɠɟɧɧɨɝɨ ɧɚ ɡɧɚɱɟɧɢɟ ɜɟɥɢɱɢɧɵ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. ɇɟɨɛɯɨɞɢɦɨ, ɱɬɨɛɵ ɫɤɨɪɨɫɬɶ ɞɪɟɣɮɚ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɛɵɥɚ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɟ ɬɟɩɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰɵ, ɜ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɧɟɥɶɡɹ ɝɨɜɨɪɢɬɶ ɨ ɦɟɞɥɟɧɧɨɦ ɞɜɢɠɟɧɢɢ ɜɟɞɭɳɟɝɨ ɰɟɧɬɪɚ. ɋɭɳɟɫɬɜɟɧɧɨ, ɱɬɨ ɯɚɪɚɤɬɟɪ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɦɟɧɧɨ ɫɨɨɬɧɨɲɟɧɢɟɦ ɜɟɥɢɱɢɧ ɩɨɥɟɣ ȿ ɢ ȼ: ɩɪɢ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɹɯ ɩɨɥɹ ȿ ɜɥɢɹɧɢɟɦ ɩɨɥɹ ȼ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ, ɢ, ɨɱɟɜɢɞɧɨ, ɧɟ ɦɨɠɟɬ ɢɞɬɢ ɪɟɱɢ ɨ ɞɪɟɣɮɟ. ɉɪɢ ɦɚɥɵɯ ɡɧɚɱɟɧɢɹɯ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɦɚɝɧɢɬɧɵɦ ɱɚɫɬɢɰɚ "ɡɚɦɚɝɧɢɱɟɧɚ" ɢ ɦɟɞɥɟɧɧɨ ɞɪɟɣɮɭɟɬ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. Ⱦɪɟɣɮ ɜ ɧɟɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ( ∇B ≠0) Ⱦɪɟɣɮ ɜ ɧɟɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɫɜɹɡɚɧ ɫ ɤɪɢɜɢɡɧɨɣ ɦɚɝɧɢɬɧɵɯ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɢ ɫ ɫɢɥɨɣ, ɜɨɡɧɢɤɚɸɳɟɣ ɩɪɢ ɞɜɢɠɟɧɢɢ ɱɚɫɬɢɰɵ ɜɞɨɥɶ ɤɪɢɜɨɥɢɧɟɣɧɵɯ ɫɢɥɨɜɵɯ ɥɢɧɢɣ. Ɋɚɫɫɦɨɬɪɢɦ ɞɜɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɷɬɨɣ ɫɢɥɵ ɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɨɥɭɱɢɦ ɞɜɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɞɪɟɣɮɚ. • ɐɟɧɬɪɨɛɟɠɧɵɣ ɞɪɟɣɮ. ɉɪɢ ɞɜɢɠɟɧɢɢ ɱɚɫɬɢɰɵ, ɧɚɜɢɜɚɸɳɟɣɫɹ ɧɚ ɫɢɥɨɜɭɸ ɥɢɧɢɸ ɫ ɪɚɞɢɭɫɨɦ ɤɪɢɜɢɡɧɵ R, ɧɚ ɧɟɟ ɞɟɣɫɬɜɭɟɬ ɰɟɧɬɪɨɛɟɠɧɚɹ ɫɢɥɚ ɢɧɟɪɰɢɢ mv||2 & & n, (2.29) Fɰɛ = − R ɢ ɜɨɡɧɢɤɚɟɬ ɞɪɟɣɮɨɜɚɹ ɫɤɨɪɨɫɬɶ, ɪɚɜɧɚɹ ɩɨ ɜɟɥɢɱɢɧɟ 2 v||2 1 v||2 | ∇B| c mv|| v ɰɛ = = = , (2.30) e RB ω R ω B
ɢ ɧɚɩɪɚɜɥɟɧɧɚɹ ɩɨ ɛɢɧɨɪɦɚɥɢ (ɡɚ ɩɥɨɫɤɨɫɬɶ ɪɢɫɭɧɤɚ, ɫɦ. ɪɢɫ. 2.5): & v||2 [ B∇B ] & v ɰɛ = , ω B2 ɝɞɟ vɰɛ - ɫɤɨɪɨɫɬɶ ɰɟɧɬɪɨɛɟɠɧɨɝɨ ɞɪɟɣɮɚ, ɚ ω − ɰɢɤɥɨɬɪɨɧɧɚɹ ɱɚɫɬɨɬɚ.
Ɋɢɫ. 2.5. Ⱦɪɟɣɮ ɜ ɧɟɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ
(2.31)
• Ƚɪɚɞɢɟɧɬɧɵɣ ɞɪɟɣɮ. ɋɤɨɪɨɫɬɶ ɞɪɟɣɮɚ ɜ ɧɟɨɞɧɨɪɨɞɧɨɦ ɩɨɥɟ ɡɚɜɢɫɢɬ ɬɚɤɠɟ ɨɬ ɫɨɫɬɚɜɥɹɸɳɟɣ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰɵ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ ɤ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ. ɍɩɨɞɨɛɢɦ ɜɪɚɳɚɸɳɭɸɫɹ ɜɨɤɪɭɝ ɫɢɥɨɜɨɣ ɥɢɧɢɢ ɱɚɫɬɢɰɭ ɦɚɝɧɢɬɧɨɦɭ ɞɢɩɨɥɸ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɤɪɭɝɨɜɨɝɨ ɬɨɤɚ. Ɍɨɝɞɚ ɬɨɱɧɨɟ ɜɵɪɚɠɟɧɢɟ ɫɤɨɪɨɫɬɢ ɝɪɚɞɢɟɧɬɧɨɝɨ ɞɪɟɣɮɚ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɢɡ ɢɡɜɟɫɬɧɨɝɨ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɫɢɥɵ, ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɦɚɝɧɢɬɧɵɣ ɞɢɩɨɥɶ ɜ ɧɟɨɞɧɨɪɨɞɧɨɦ ɩɨɥɟ: & F = − µ ∇B . (2.32) Ⱦɥɹ ɜɚɤɭɭɦɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɤɚɤ ɦɨɠɧɨ ɩɨɤɚɡɚɬɶ, ɫɩɪɚɜɟɞɥɢɜɨ ɫɨɨɬɧɨɲɟɧɢɟ:
& ∇⊥ B n = , (2.33) B R ɝɞɟ R, ɧɚɩɨɦɧɢɦ, - ɪɚɞɢɭɫ ɤɪɢɜɢɡɧɵ ɫɢɥɨɜɨɣ ɥɢɧɢɢ. ɉɨɷɬɨɦɭ ɩɨɩɟɪɟɱɧɚɹ ɤɨɦɩɨɧɟɧɬɚ ɫɢɥɵ, ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɞɢɩɨɥɶ, ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɨɣ & B& (2.34) F⊥ = − µ n , R & ɝɞɟ n - ɟɞɢɧɢɱɧɵɣ ɜɟɤɬɨɪ ɧɨɪɦɚɥɢ. & ɉɨɞɫɬɚɜɥɹɹ ɷɬɨ ɡɧɚɱɟɧɢɟ F⊥ ɜ ɜɵɪɚɠɟɧɢɟ (2.16), ɩɨɥɭɱɚɟɦ & v ⊥2 [ B∇B ] & vɝ ɪ = . (2.35) 2ω B 2 Ɋɟɚɥɶɧɨ ɦɟɯɚɧɢɡɦ ɝɪɚɞɢɟɧɬɧɨɝɨ ɞɪɟɣɮɚ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ ɱɚɫɬɢɰɚ ɢɦɟɟɬ ɪɚɡɥɢɱɧɵɟ ɪɚɞɢɭɫɵ ɜɪɚɳɟɧɢɹ ɜ ɪɚɡɧɵɯ ɬɨɱɤɚɯ ɬɪɚɟɤɬɨɪɢɢ: ɱɚɫɬɶ ɜɪɟɦɟɧɢ ɨɧɚ ɩɪɨɜɨɞɢɬ ɜ ɛɨɥɟɟ ɫɢɥɶɧɨɦ ɩɨɥɟ, ɱɚɫɬɶ ɜ ɛɨɥɟɟ ɫɥɚɛɨɦ ɩɨɥɟ. ɂɡɦɟɧɟɧɢɟ ɪɚɞɢɭɫɚ ɢ ɫɨɡɞɚɟɬ ɞɪɟɣɮ, ɤɚɤ ɷɬɨ ɨɛɫɭɠɞɚɥɢ ɜ ɩɪɟɞɵɞɭɳɟɦ ɩɚɪɚɝɪɚɮɟ. ɋɤɨɪɨɫɬɶ ɞɪɟɣɮɚ ɜ ɧɟɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɭɦɦɭ ɫɤɨɪɨɫɬɟɣ ɰɟɧɬɪɨɛɟɠɧɨɝɨ ɢ ɝɪɚɞɢɟɧɬɧɨɝɨ ɞɪɟɣɮɨɜ (ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ ɞɪɟɣɮ ɩɨ ɛɢɧɨɪɦɚɥɢ): & 2 v||2 + v ⊥2 [ B∇B ] & 1 & vb = = (2.36) ( v ⊥2 + 2 v||2 )b , 2 2ω 2ω R B & ɝɞɟ b — ɨɪɬ ɛɢɧɨɪɦɚɥɢ (ɫɦ.ɪɢɫ.2.5). ɋɤɨɪɨɫɬɶ ɞɪɟɣɮɚ ɡɚɜɢɫɢɬ ɨɬ ɡɚɪɹɞɚ ɱɚɫɬɢɰɵ (ɷɥɟɤɬɪɨɧɵ ɢ ɢɨɧɵ ɞɪɟɣɮɭɸɬ ɜ ɪɚɡɧɵɟ ɫɬɨɪɨɧɵ), ɨɬ ɟɺ ɦɚɫɫɵ, ɨɬ ɧɚɩɪɚɜɥɟɧɢɹ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰɵ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ ɢ ɨɬ ɜɟɥɢɱɢɧ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɢ ɝɪɚɞɢɟɧɬɚ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ȼɚɠɧɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɬɪɚɟɤɬɨɪɢɹ ɜɟɞɭɳɟɝɨ ɰɟɧɬɪɚ ɩɪɨɯɨɞɢɬ ɜ ɨɛɥɚɫɬɢ ɩɨɫɬɨɹɧɧɨɝɨ ɡɧɚɱɟɧɢɹ ȼ, & & & ɬɚɤ ɤɚɤ v b ⊥B ɢ v b ⊥∇B . ȼ ɧɟɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ( ∇B ≠ 0 ) ɷɥɟɤɬɪɨɧɵ ɢ ɢɨɧɵ ɞɪɟɣɮɭɸɬ ɜ ɪɚɡɧɵɟ ɫɬɨɪɨɧɵ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɜ ɩɥɚɡɦɟ ɜɨɡɧɢɤɚɟɬ ɬɨɤ ɫ ɩɥɨɬɧɨɫɬɶɸ: & j = ¦ nev b , (2.37) e ,i
ɝɞɟ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ ɫɭɦɦɢɪɨɜɚɧɢɟ ɩɨ ɫɨɪɬɚɦ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ. ɗɬɨɬ ɬɨɤ ɧɚɡɵɜɚɸɬ ɞɪɟɣɮɨɜɵɦ.
Ⱦɚɥɟɟ ɭɜɢɞɢɦ, ɱɬɨ ɝɪɚɞɢɟɧɬ ɞɚɜɥɟɧɢɹ ( ∇p ≠ 0 ) ɬɚɤɠɟ ɩɪɢɜɨɞɢɬ ɤ ɩɨɹɜɥɟɧɢɸ ɞɪɟɣɮɨɜɵɯ ɬɨɤɨɜ. ɉɨɥɹɪɢɡɚɰɢɨɧɧɵɣ ɞɪɟɣɮ Ʉɨɝɞɚ ɱɚɫɬɢɰɚ ɢɫɩɵɬɵɜɚɟɬ ɬɨ ɜ ɞɜɢɠɭɳɟɣɫɹ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ ɧɚ ɧɟɟ & ɭɫɤɨɪɟɧɢɟ, & ɞɟɣɫɬɜɭɟɬ ɢɧɟɪɰɢɨɧɧɚɹ ɫɢɥɚ F = − mv , ɢ ɜɨɡɧɢɤɚɟɬ ɞɪɟɣɮ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɭɫɥɨɜɢɟɦ (2.17). ȼ ɩɥɚɡɦɟ ɱɚɫɬɨ ɩɨɹɜɥɹɸɬɫɹ ɩɟɪɟɦɟɧɧɵɟ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɩɨɥɹ, ɨɩɪɟɞɟɥɹɟɦɵɟ ɦɟɫɬɧɵɦ ɪɚɡɞɟɥɟɧɢɟɦ ɡɚɪɹɞɨɜ, ɬɚɤ ɧɚɡɵɜɚɟɦɵɟ ɩɨɥɹɪɢɡɚɰɢɨɧɧɵɟ ɩɨɥɹ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɧɚ ɱɚɫɬɢɰɭ ɞɟɣɫɬɜɭɟɬ ɩɟɪɟɦɟɧɧɚɹ ɫɢɥɚ, ɢ ɜɨɡɧɢɤɚɟɬ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɞɪɟɣɮ ɫ ɩɟɪɟɦɟɧɧɨɣ ɫɤɨɪɨɫɬɶɸ ~& × B& E &~ vn = c ⊥ 2 , B & ~& - ɫɨɫɬɚɜɥɹɸɳɚɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ~ ɝɞɟ v n - ɞɪɟɣɮɨɜɚɹ ɩɨɥɹɪɢɡɚɰɢɨɧɧɚɹ ɫɤɨɪɨɫɬɶ; E ⊥ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɚɹ ɤ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ. ɂɦɟɧɧɨ ɨɧɚ ɢ ɜɵɡɵɜɚɟɬ ɞɪɟɣɮ. ɉɪɢ ɩɟɪɟɦɟɧɧɨɦ & & & ~& ɦɟɧɹɟɬɫɹ ɢ ~ E v n , ɬ.ɟ. ɩɨɹɜɥɹɟɬɫɹ ɭɫɤɨɪɟɧɢɟ, ɚ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢ ɫɢɥɚ ɢɧɟɪɰɢɢ Fu = − mv n . ⊥ ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɷɬɨɣ ɫɢɥɵ ɜɨɡɧɢɤɚɟɬ ɩɨɥɹɪɢɡɚɰɢɨɧɧɵɣ ɞɪɟɣɮ ~& 2 c mE & ⊥ vn = . (2.38) e B2 & ȼɟɥɢɱɢɧɚ v n ɡɚɜɢɫɢɬ ɨɬ ɦɚɫɫɵ (ɛɨɥɶɲɚɹ ɜɟɥɢɱɢɧɚ ɭ ɢɨɧɨɜ), ɡɚɪɹɞɚ ɱɚɫɬɢɰɵ, ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɫɤɨɪɨɫɬɢ ɢɡɦɟɧɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. ~& - ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɉɨɥɹɪɢɡɚɰɢɨɧɧɵɣ ɞɪɟɣɮ ɧɚɩɪɚɜɥɟɧ ɜɞɨɥɶ ɜɟɤɬɨɪɚ E ⊥ ɩɪɨɢɡɜɨɞɧɨɣ ɩɨ ɜɪɟɦɟɧɢ ɨɬ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ - ɩɚɪɚɥɥɟɥɶɧɨ ɢɥɢ ɚɧɬɢɩɚɪɚɥɥɟɥɶɧɨ ɟɦɭ. ɗɬɨɬ ɞɪɟɣɮ ɫɨɡɞɚɟɬ ɩɨɥɹɪɢɡɚɰɢɨɧɧɵɣ ɬɨɤ - ɚɧɚɥɨɝ ɬɨɤɚ ɫɦɟɳɟɧɢɹ: c2 & & & jn = nev n = ρm 2 E ⊥ , (2.39) B ɝɞɟ ρm - ɦɚɫɫɨɜɚɹ ɩɥɨɬɧɨɫɬɶ ɩɥɚɡɦɵ. Ɇɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɢ ɫɨɫɬɚɜɥɹɸɳɭɸ ε⊥ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɨɫɬɨɹɧɧɨɣ ɩɥɚɡɦɵ, & ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɭɸ ɤ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ. Ⱦɨɛɚɜɥɹɹ ɤ ɩɨɥɹɪɢɡɚɰɢɨɧɧɨɦɭ ɬɨɤɭ jn 1 & & ɩɨɩɟɪɟɱɧɭɸ ɤɨɦɩɨɧɟɧɬɭ ɬɨɤɚ ɫɦɟɳɟɧɢɹ jɫɦ = E (ɡɞɟɫɶ ɬɨɱɤɨɣ ɨɬɦɟɱɟɧɚ ɱɚɫɬɧɚɹ 4π ⊥ ɩɪɨɢɡɜɨɞɧɚɹ ɨɬ ɩɨɥɹ ɩɨ ɜɪɟɦɟɧɢ), ɩɨɥɭɱɢɦ c2 & 1 & & & ( 1 + 4π ρm 2 )E ⊥ . (2.40) j = jɩ + jɫɦ = B 4π ɍɱɢɬɵɜɚɹ ɞɚɥɟɟ, ɱɬɨ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ ɫɜɹɡɚɧɚ ɫ ɩɪɨɢɡɜɨɞɧɨɣ ɩɨɥɹ ɩɨ ɜɪɟɦɟɧɢ ɯɨɪɨɲɨ ɢɡɜɟɫɬɧɵɦ ɫɨɨɬɧɨɲɟɧɢɟɦ & ε & (2.41) j= E, 4π ɧɚɯɨɞɢɦ c2 ε⊥ = 1 + 4πρm 2 . (2.42) B Ɍɨɪɨɢɞɚɥɶɧɵɣ ɞɪɟɣɮ ɢ ɜɪɚɳɚɬɟɥɶɧɨɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ Ɋɚɫɫɦɨɬɪɢɦ ɩɨɜɟɞɟɧɢɟ ɩɥɚɡɦɵ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɬɨɪɨɢɞɚɥɶɧɨɝɨ ɫɨɥɟɧɨɢɞɚ. Ɇɚɝɧɢɬɧɨɟ ɩɨɥɟ ɬɨɪɨɢɞɚɥɶɧɨɝɨ ɫɨɥɟɧɨɢɞɚ ɚɧɚɥɨɝɢɱɧɨ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ ɩɪɹɦɨɝɨ ɩɪɨɜɨɞɧɢɤɚ ɢ ɭɛɵɜɚɟɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɛɨɥɶɲɨɝɨ ɪɚɞɢɭɫɚ ɩɨ ɡɚɤɨɧɭ 1/R (ɪɢɫ.2.6). ɗɬɨ ɫɬɚɧɨɜɢɬɫɹ ɨɱɟɜɢɞɧɵɦ, ɟɫɥɢ ɭɱɟɫɬɶ, ɱɬɨ ɜɟɥɢɱɢɧɚ ɬɨɤɚ ɧɚ ɟɞɢɧɢɰɭ ɞɥɢɧɵ ɨɤɪɭɠɧɨɫɬɢ
2π(R-r) ɛɨɥɶɲɟ, ɱɟɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɜɟɥɢɱɢɧɚ ɧɚ ɨɤɪɭɠɧɨɫɬɢ 2π(R+r), ɝɞɟ r - ɪɚɞɢɭɫ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɬɨɪɚ (ɫɦ. ɪɢɫ.2.6). ɇɟɨɞɧɨɪɨɞɧɨɫɬɶ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜɵɡɵɜɚɟɬ ɜɨɡɧɢɤɧɨɜɟɧɢɟ ɞɪɟɣɮɚ, ɩɪɢɜɨɞɹɳɟɝɨ ɤ ɫɦɟɳɟɧɢɸ ɢɨɧɨɜ ɧɚ ɨɞɧɭ (ɧɚ ɪɢɫ.2.6 - ɜɧɢɡ), ɚ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɞɪɭɝɭɸ (ɧɚ ɪɢɫ.2.6 - ɜɜɟɪɯ) ɫɬɨɪɨɧɭ ɫɨɥɟɧɨɢɞɚ, ɚ, ɡɧɚɱɢɬ, ɤ ɩɨɹɜɥɟɧɢɸ ɞɪɟɣɮɨɜɨɝɨ ɬɨɤɚ. Ɍɚɤ ɤɚɤ ɞɪɟɣɮɨɜɵɣ ɬɨɤ ɡɚɦɤɧɭɬɶɫɹ ɧɟ ɦɨɠɟɬ, ɬɨ ɜɨɡɧɢɤɚɟɬ ɪɚɡɞɟɥɟɧɢɟ ɡɚɪɹɞɨɜ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɟɦɭ ɩɨɥɹɪɢɡɚɰɢɨɧɧɨɟ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ȿ. ɇɨ ɬɟɩɟɪɶ ɩɨɹɜɥɟɧɢɟ ɷɬɨɝɨ ɩɨɥɹ ɩɪɢɜɨɞɢɬ ɤ ɜɨɡɧɢɤɧɨɜɟɧɢɸ ɞɪɟɣɮɚ ɩɥɚɡɦɵ ɜ ɰɟɥɨɦ ɜ ɫɤɪɟɳɟɧɧɵɯ ɜɡɚɢɦɧɨ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɵɯ ȿ⊥ȼ ɩɨɥɹɯ, ɜɵɛɪɚɫɵɜɚɸɳɟɝɨ ɩɥɚɡɦɭ ɧɚ ɧɚɪɭɠɧɭɸ ɫɬɟɧɤɭ ɬɨɪɨɢɞɚɥɶɧɨɝɨ ɫɨɥɟɧɨɢɞɚ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɫɜɨɛɨɞɧɨɦ ɨɬ ɜɧɭɬɪɟɧɧɢɯ ɬɨɤɨɜ ɬɨɪɨɢɞɚɥɶɧɨɦ ɫɨɥɟɧɨɢɞɟ ɩɥɚɡɦɚ ɧɟ ɛɭɞɟɬ ɭɫɬɨɣɱɢɜɨ ɭɞɟɪɠɢɜɚɬɶɫɹ. Ʉɚɪɬɢɧɚ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɢɡɦɟɧɢɬɫɹ, ɟɫɥɢ ɜɧɭɬɪɢ, ɜ ɰɟɧɬɪɟ ɫɟɱɟɧɢɹ ɫɨɥɟɧɨɢɞɚ, ɩɨɦɟɫɬɢɬɶ ɩɪɨɜɨɞɧɢɤ ɫ ɬɨɤɨɦ, ɢɥɢ ɩɪɨɩɭɫɬɢɬɶ ɬɨɤ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɩɨ ɩɥɚɡɦɟ. ɗɬɨɬ ɬɨɤ ɫɨɡɞɚɫɬ ɫɨɛɫɬɜɟɧɧɨɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ȼϕ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɟ ɤ ɩɨɥɸ ɫɨɥɟɧɨɢɞɚ ȼz, ɬɚɤ ɱɬɨ Ɋɢɫ. 2.6. Ɍɨɪɨɢɞɚɥɶɧɵɣ ɞɪɟɣɮ. ɫɭɦɦɚɪɧɚɹ ɫɢɥɨɜɚɹ ɥɢɧɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɩɨɣɞɟɬ ɩɨ ɜɢɧɬɨɜɨɣ ɬɪɚɟɤɬɨɪɢɢ, ɨɯɜɚɬɵɜɚɸɳɟɣ ɨɫɶ ɫɨɥɟɧɨɢɞɚ. Ɉɛɪɚɡɨɜɚɧɢɟ ɜɢɧɬɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɩɨɥɭɱɢɥɨ ɧɚɡɜɚɧɢɟ ɜɪɚɳɚɬɟɥɶɧɨɝɨ (ɢɥɢ ɪɨɬɚɰɢɨɧɧɨɝɨ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ. ɗɬɢ ɥɢɧɢɢ ɛɭɞɭɬ ɡɚɦɵɤɚɬɶɫɹ ɫɚɦɢ ɧɚ ɫɟɛɹ, ɟɫɥɢ ɤɨɷɮɮɢɰɢɟɧɬ ɡɚɩɚɫɚ ɭɫɬɨɣɱɢɜɨɫɬɢ, ɩɪɟɞɫɬɚɜɥɹɸɳɢɣ ɫɨɛɨɣ ɨɬɧɨɲɟɧɢɟ ɲɚɝɚ ɜɢɧɬɨɜɨɣ ɫɢɥɨɜɨɣ ɥɢɧɢɢ ɤ ɞɥɢɧɟ ɨɫɢ ɬɨɪɚ B a q= z , (2.43) Bϕ R ɛɭɞɟɬ ɪɚɜɟɧ ɨɬɧɨɲɟɧɢɸ ɞɜɭɯ ɰɟɥɵɯ ɱɢɫɟɥ, ɬ.ɟ. ɪɚɜɟɧ ɪɚɰɢɨɧɚɥɶɧɨɦɭ ɱɢɫɥɭ - ɨɬɧɨɲɟɧɢɸ ɱɢɫɥɚ ɨɛɨɪɨɬɨɜ ɫɢɥɨɜɨɣ ɥɢɧɢɢ ɜɨɤɪɭɝ ɬɨɪɚ ɢ ɱɢɫɥɚ ɨɛɨɪɨɬɨɜ ɜɨɤɪɭɝ ɨɫɢ ɬɨɪɚ. ɉɪɢ ɡɧɚɱɟɧɢɹɯ ɷɬɨɣ ɜɟɥɢɱɢɧɵ, ɧɟ ɪɚɜɧɵɯ ɪɚɰɢɨɧɚɥɶɧɨɦɭ ɱɢɫɥɭ, ɫɢɥɨɜɵɟ ɥɢɧɢɣ, ɧɢɤɨɝɞɚ ɧɟ ɡɚɦɵɤɚɹɫɶ, ɡɚ ɛɟɫɤɨɧɟɱɧɨɟ ɱɢɫɥɨ ɨɛɨɪɨɬɨɜ ɨɛɪɚɡɭɸɬ ɡɚɦɤɧɭɬɵɟ ɬɨɪɨɢɞɚɥɶɧɵɟ ɦɚɝɧɢɬɧɵɟ ɩɨɜɟɪɯɧɨɫɬɢ, ɜɥɨɠɟɧɧɵɟ ɞɪɭɝ ɜ ɞɪɭɝɚ ɢ ɨɛɪɚɡɨɜɚɧɧɵɟ ɤɚɠɞɚɹ ɟɞɢɧɫɬɜɟɧɧɨɣ ɫɢɥɨɜɨɣ ɥɢɧɢɟɣ. ȼɢɧɬɨɜɵɟ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɫɞɟɥɚɸɬ ɧɟɜɨɡɦɨɠɧɨɣ ɩɨɥɹɪɢɡɚɰɢɸ ɩɥɚɡɦɵ: ɩɟɪɟɦɟɳɚɹɫɶ ɜɞɨɥɶ ɧɢɯ, ɷɥɟɤɬɪɨɧɵ ɢ ɢɨɧɵ ɫɨɡɞɚɞɭɬ ɞɪɟɣɮɨɜɵɟ ɬɨɤɢ, ɤɨɬɨɪɵɟ ɛɭɞɭɬ ɜɡɚɢɦɧɨ ɧɟɣɬɪɚɥɢɡɨɜɚɧɵ, ɧɟ ɛɭɞɟɬ ɪɚɡɞɟɥɟɧɢɹ ɡɚɪɹɞɨɜ, ɧɟ ɩɨɹɜɢɬɫɹ ɢ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɧɟ ɜɨɡɧɢɤɧɟɬ ɢ ɬɨɪɨɢɞɚɥɶɧɵɣ ɞɪɟɣɮ, ɜɵɛɪɚɫɵɜɚɸɳɢɣ ɩɥɚɡɦɭ ɧɚ ɧɚɪɭɠɧɭɸ ɫɬɟɧɤɭ, ɢɦɟɸɳɢɣ ɦɟɫɬɨ ɜ ɛɟɫɬɨɤɨɜɨɦ ɬɨɪɨɢɞɚɥɶɧɨɦ ɫɨɥɟɧɨɢɞɟ. ɋɭɳɟɫɬɜɟɧɧɨ, ɱɬɨ ɜ ɤɚɠɞɨɣ ɬɨɱɤɟ ɫɜɨɟ ɫɨɨɬɧɨɲɟɧɢɟ ɜɟɥɢɱɢɧ ɦɚɝɧɢɬɧɵɯ ɩɨɥɟɣ ɬɨɤɚ ɢ ɫɨɥɟɧɨɢɞɚ (ɜɟɞɶ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɬɨɤɚ ɛɭɞɟɬ ɭɛɵɜɚɬɶ ɩɨ ɡɚɤɨɧɭ 1/r (r ɦɚɥɨɟ!) ɜɨ ɜɫɟ ɫɬɨɪɨɧɵ ɨɬ ɬɨɤɚ). ɉɨɷɬɨɦɭ ɫɢɥɨɜɵɟ ɥɢɧɢɢ ɪɚɫɩɨɥɨɠɟɧɧɵɯ ɪɹɞɨɦ ɦɚɝɧɢɬɧɵɯ ɩɨɜɟɪɯɧɨɫɬɟɣ ɫɤɪɟɳɢɜɚɸɬɫɹ, ɩɪɢɱɟɦ ɭɝɨɥ ɧɚɤɥɨɧɚ ɧɟɩɪɟɪɵɜɧɨ ɦɟɧɹɟɬɫɹ ɫ ɢɡɦɟɧɟɧɢɟɦ R. Ɉɛɪɚɡɭɟɬɫɹ ɫɥɨɠɧɚɹ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɚɹ ɫɟɬɤɚ ɦɚɝɧɢɬɧɵɯ ɫɢɥɨɜɵɯ ɥɢɧɢɣ, ɩɨɥɭɱɢɜɲɚɹ ɧɚɡɜɚɧɢɟ ɲɢɪ. Ɍɚɤɚɹ ɫɟɬɤɚ ɫɭɳɟɫɬɜɟɧɧɨ ɡɚɬɪɭɞɧɹɟɬ ɩɟɪɟɦɟɳɟɧɢɟ ɩɥɚɡɦɵ Ɋɢɫ.2.7. ɋɯɟɦɚ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɩɨɩɟɪɟɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ.
ȼ ɫɢɫɬɟɦɚɯ ɬɢɩɚ ɬɨɤɚɦɚɤ (ɫɨɤɪɚɳɟɧɧɨɟ ɨɬ «ɬɨɤɨɜɚɹ ɤɚɦɟɪɚ ɫ ɦɚɝɧɢɬɧɵɦɢ ɤɚɬɭɲɤɚɦɢ») ɜɧɭɬɪɢ ɬɨɪɨɢɞɚɥɶɧɨɝɨ ɫɨɥɟɧɨɢɞɚ ɩɨ ɩɥɚɡɦɟ ɬɟɱɟɬ ɬɨɤ, ɢɦɟɟɬɫɹ ɜɪɚɳɚɬɟɥɶɧɨɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ɢ ɲɢɪ. Ʉɨɧɟɱɧɨ, ɬɨɤ ɪɚɫɩɪɟɞɟɥɟɧ ɩɨ ɫɟɱɟɧɢɸ ɩɥɚɡɦɟɧɧɨɝɨ ɲɧɭɪɚ (ɚ ɬɟɱɟɬ ɧɟ ɬɨɥɶɤɨ ɜ ɰɟɧɬɪɟ), ɡɧɚɱɢɬ, ɪɟɚɥɶɧɚɹ ɤɚɪɬɢɧɚ ɫɥɨɠɧɟɟ ɪɚɫɫɦɨɬɪɟɧɧɨɣ ɜɵɲɟ, ɧɨ ɜɨɡɦɨɠɧɨɫɬɶ ɤɨɦɩɟɧɫɚɰɢɢ ɷɮɮɟɤɬɚ ɬɨɪɨɢɞɚɥɶɧɨɝɨ ɞɪɟɣɮɚ ɨɫɬɚɟɬɫɹ ɜ ɫɢɥɟ. Ⱥɦɟɪɢɤɚɧɫɤɢɣ ɮɢɡɢɤ ɋɩɢɬɰɟɪ ɞɨɤɚɡɚɥ, ɱɬɨ ɜɪɚɳɚɬɟɥɶɧɨɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɢ ɛɟɡ ɬɨɤɚ ɜ ɩɥɚɡɦɟ. Ɍɚɤɨɝɨ ɬɢɩɚ ɫɢɫɬɟɦɵ ɞɥɹ ɭɞɟɪɠɚɧɢɹ ɩɥɚɡɦɵ ɩɨɥɭɱɢɥɢ ɧɚɡɜɚɧɢɟ ɫɬɟɥɥɚɪɚɬɨɪɵ. ȼɨɡɦɨɠɧɨɫɬɶ ɪɟɚɥɢɡɚɰɢɢ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɛɟɡ ɬɨɤɚ ɜ ɩɥɚɡɦɟ ɦɨɠɧɨ ɩɨɹɫɧɢɬɶ ɫ ɩɨɦɨɳɶɸ ɫɯɟɦɵ, ɢɡɨɛɪɚɠɟɧɧɨɣ ɧɚ ɪɢɫ. 2.7. Ɋɚɡɪɟɠɟɦ (ɦɵɫɥɟɧɧɨ) ɬɨɪɨɢɞɚɥɶɧɵɣ ɫɨɥɟɧɨɢɞ ɩɨɩɨɥɚɦ ɢ ɫɨɟɞɢɧɢɦ ɟɝɨ ɤɨɧɰɵ: ɚ) ɩɪɹɦɨɥɢɧɟɣɧɵɦɢ ɭɱɚɫɬɤɚɦɢ – ɩɨɥɭɱɢɦ ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ ɪɟɣɫɬɪɟɤ (ɜ ɩɪɹɦɵɯ ɭɱɚɫɬɤɚɯ ɬɨɠɟ ɫɨɡɞɚɟɬɫɹ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ). ɋɢɥɨɜɵɟ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɡɚɦɵɤɚɸɬɫɹ, ɞɪɟɣɮ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɩɪɚɜɨɣ ɢ ɥɟɜɨɣ ɬɨɪɨɢɞɚɥɶɧɵɯ ɱɚɫɬɹɯ ɢɦɟɟɬ ɨɞɢɧɚɤɨɜɨɟ ɧɚɩɪɚɜɥɟɧɢɟ. ɉɨɷɬɨɦɭ ɩɨ-ɩɪɟɠɧɟɦɭ ɨɫɬɚɟɬɫɹ ɜɨɡɦɨɠɧɨɫɬɶ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɩɨɥɹɪɢɡɚɰɢɨɧɧɨɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ȿ ɢ ɞɪɟɣɮɚ ɜ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɵɯ ȿ⊥ȼ ɩɨɥɹɯ, ɧɚɩɪɚɜɥɟɧɧɨɝɨ ɤ ɧɚɪɭɠɧɨɣ ɫɬɟɧɤɟ ɤɚɦɟɪɵ; ɛ) ɧɚɤɪɟɫɬ - ɩɨɥɭɱɢɦ ɫɬɟɥɥɚɪɚɬɨɪ ɬɢɩɚ ɜɨɫɶɦɟɪɤɢ (ɜ ɩɪɹɦɵɯ ɭɱɚɫɬɤɚɯ ɬɨɠɟ ɫɨɡɞɚɟɬɫɹ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ). ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɦɚɝɧɢɬɧɵɟ ɫɢɥɨɜɵɟ ɥɢɧɢɢ ɢɦɟɸɬ ɜɨɡɦɨɠɧɨɫɬɶ «ɩɪɨɤɪɭɱɢɜɚɬɶɫɹ» ɜɨɤɪɭɝ ɨɫɢ ɫɢɫɬɟɦɵ ɢ, ɜɨɨɛɳɟ ɝɨɜɨɪɹ, ɧɟ ɛɭɞɭɬ ɡɚɦɵɤɚɬɶɫɹ: ɦɨɠɧɨ ɩɨɤɚɡɚɬɶ, ɱɬɨ ɧɚ ɤɚɠɞɨɦ “ɨɛɯɨɞɟ” ɫɢɥɨɜɚɹ ɥɢɧɢɹ ɩɨɜɨɪɚɱɢɜɚɟɬɫɹ ɧɚ ɭɱɟɬɜɟɪɟɧɧɵɣ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɣ ɭɝɨɥ ɦɟɠɞɭ ɬɨɪɨɢɞɚɥɶɧɵɦɢ ɭɱɚɫɬɤɚɦɢ, ɬɟɦ ɫɚɦɵɦ ɫɬɚɧɨɜɢɬɫɹ ɜɢɧɬɨɜɨɣ ɥɢɧɢɟɣ ɢ ɪɟɚɥɢɡɭɟɬɫɹ ɷɮɮɟɤɬ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɤɨɦɩɟɧɫɚɰɢɟɣ ɬɨɪɨɢɞɚɥɶɧɨɝɨ ɞɪɟɣɮɚ. ɗɬɨ ɠɟ ɦɨɠɧɨ ɨɛɴɹɫɧɢɬɶ ɧɟɫɤɨɥɶɤɨ ɩɪɨɳɟ: ɜ ɪɟɣɫɬɪɟɤɟ ɩɪɢ ɩɟɪɟɯɨɞɟ ɨɬ ɥɟɜɨɣ ɩɨɥɨɜɢɧɵ ɬɨɪɚ ɤ ɩɪɚɜɨɣ (ɪɢɫ.2.7,ɚ)& ɦɟɧɹɟɬɫɹ ɧɚɩɪɚɜɥɟɧɢɟ ɭ ɜɟɤɬɨɪɨɜ ȼ ɢ ∇ȼ, ɬɚɤ ɱɬɨ & ɧɚɩɪɚɜɥɟɧɢɟ ɫɤɨɪɨɫɬɢ ɞɪɟɣɮɚ v d ∼ B × ∇B ɫɨɯɪɚɧɹɟɬɫɹ, ɜɨɡɦɨɠɧɚ ɩɨɥɹɪɢɡɚɰɢɹ ɩɥɚɡɦɵ, ɜɨɡɧɢɤɧɨɜɟɧɢɟ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɢ ɬ.ɞ. ȼ ɫɬɟɥɥɚɪɚɬɨɪɟ ɬɢɩɚ «ɜɨɫɶɦɟɪɤɢ» ɋɩɢɬɰɟɪɚ ɩɪɢ ɩɟɪɟɯɨɞɟ ɨɬ ɥɟɜɨɣ ɩɨɥɨɜɢɧɵ ɬɨɪɚ ɤ ɩɪɚɜɨɣ (ɪɢɫ.2.7,ɛ), ɩɪɢ ɩɪɟɠɧɟɣ ɨɪɢɟɧɬɚɰɢɢ ɜɟɤɬɨɪɨɜ ∇ȼ, ɡɚ ɫɱɟɬ ɷɮɮɟɤɬɚ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɜɨɫɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɧɚɩɪɚɜɥɟɧɢɟ & ɜɟɤɬɨɪɚ ȼ, ɬɚɤ ɱɬɨ ɧɚɩɪɚɜɥɟɧɢɟ ɫɤɨɪɨɫɬɢ ɞɪɟɣɮɚ v d ɦɟɧɹɟɬɫɹ ɧɚ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɟ. ɉɨɥɹɪɢɡɚɰɢɹ ɧɟɜɨɡɦɨɠɧɚ − ɤɚɤ ɛɵ ɫɨɡɞɚɸɬɫɹ ɞɜɚ ɨɞɢɧɚɤɨɜɵɯ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɨɥɹ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɚɧɬɢɩɚɪɚɥɥɟɥɶɧɨ, ɬ.ɟ. ɤɨɦɩɟɧɫɢɪɭɸɳɢɯ ɞɪɭɝ ɞɪɭɝɚ. Ɋɚɫɱɟɬɵ ɩɨɤɚɡɚɥɢ (ɢ ɨɩɵɬ ɩɨɞɬɜɟɪɞɢɥ), ɱɬɨ ɜɦɟɫɬɨ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɝɨ ɩɟɪɟɤɪɟɳɢɜɚɧɢɹ ɤɨɧɰɨɜ, ɬɨ ɟɫɬɶ ɜɦɟɫɬɨ ɫɨɡɞɚɧɢɹ ɦɚɝɧɢɬɧɨɣ ɫɢɫɬɟɦɵ ɫ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɨɫɶɸ, ɱɬɨ ɹɜɥɹɟɬɫɹ ɞɨɫɬɚɬɨɱɧɨ ɫɥɨɠɧɨɣ ɬɟɯɧɢɱɟɫɤɢ ɡɚɞɚɱɟɣ, ɦɨɠɧɨ ɧɚ ɬɨɪɨɢɞɚɥɶɧɵɟ ɱɚɫɬɢ ɪɟɣɫɬɪɟɤɚ ɧɚɤɥɚɞɵɜɚɬɶ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɫɩɟɰɢɚɥɶɧɵɟ ɦɧɨɝɨɡɚɯɨɞɧɵɟ (ɨɛɵɱɧɨ ɞɜɭɯɢɥɢ ɬɪɟɯɡɚɯɨɞɧɵɟ) ɨɛɦɨɬɤɢ. ɉɪɢ ɷɬɨɦ ɬɨɤɢ ɜ ɫɨɫɟɞɧɢɯ ɜɢɬɤɚɯ ɜɵɛɢɪɚɸɬɫɹ ɬɟɤɭɳɢɦɢ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɯ ɧɚɩɪɚɜɥɟɧɢɹɯ (ɪɢɫ.2.7,ɜ). ȼ ɬɚɤɨɣ ɫɢɫɬɟɦɟ ɬɚɤɠɟ ɜɨɡɧɢɤɚɟɬ ɜɪɚɳɚɬɟɥɶɧɨɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɫɬɚɧɨɜɢɬɫɹ ɜɨɡɦɨɠɧɵɦ ɨɛɪɚɡɨɜɚɧɢɟ ɜɥɨɠɟɧɧɵɯ ɞɪɭɝ ɜ ɞɪɭɝɚ ɡɚɦɤɧɭɬɵɯ ɦɚɝɧɢɬɧɵɯ ɩɨɜɟɪɯɧɨɫɬɟɣ. ɉɪɚɜɞɚ, ɷɬɢ ɩɨɜɟɪɯɧɨɫɬɢ ɧɚɯɨɞɹɬɫɹ ɜɧɭɬɪɢ ɧɟɤɨɬɨɪɨɣ ɝɪɚɧɢɱɧɨɣ, ɧɚɡɵɜɚɟɦɨɣ ɫɟɩɚɪɚɬɪɢɫɨɣ, ɡɚɩɨɥɧɹɸɬ ɧɟ ɜɫɟ ɫɟɱɟɧɢɟ ɤɚɦɟɪɵ ɢ ɢɦɟɸɬ ɞɨɜɨɥɶɧɨ ɫɥɨɠɧɭɸ ɮɨɪɦɭ. ɇɨ ɫɭɳɟɫɬɜɨ ɞɟɥɚ ɫɨɯɪɚɧɹɟɬɫɹ: ɥɸɛɨɣ ɫɬɟɥɥɚɪɚɬɨɪ ɹɜɥɹɟɬɫɹ ɢɞɟɚɥɶɧɨɣ ɦɚɝɧɢɬɧɨɣ ɥɨɜɭɲɤɨɣ ɞɥɹ ɨɬɞɟɥɶɧɵɯ ɱɚɫɬɢɰ ɢ ɫɩɨɫɨɛɟɧ ɯɨɪɨɲɨ ɭɞɟɪɠɢɜɚɬɶ ɩɥɚɡɦɭ ɛɟɡ ɩɪɨɩɭɫɤɚɧɢɹ ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɬɨɤɚ ɜ ɧɟɣ. Ɍɚɤ ɤɚɤ ɜ ɬɚɤɢɯ ɫɢɫɬɟɦɚɯ ɢɦɟɸɬɫɹ ɦɚɝɧɢɬɧɵɟ ɫɢɥɨɜɵɟ ɥɢɧɢɢ, ɧɟ ɜɵɯɨɞɹɳɢɟ ɡɚ ɩɪɟɞɟɥɵ ɫɢɫɬɟɦɵ (ɡɚɦɤɧɭɬɵɟ ɢɥɢ ɭɯɨɞɹɳɢɟ ɜ ɛɟɫɤɨɧɟɱɧɨɫɬɶ ɧɚ ɡɚɦɤɧɭɬɨɣ ɩɨɜɟɪɯɧɨɫɬɢ), ɬɨ ɩɨɞɨɛɧɵɟ ɫɢɫɬɟɦɵ ɧɚɡɵɜɚɸɬ ɡɚɤɪɵɬɵɦɢ (ɢɧɨɝɞɚ ɡɚɦɤɧɭɬɵɦɢ).
§ 18. Ⱥɞɢɚɛɚɬɢɱɟɫɤɢɟ ɢɧɜɚɪɢɚɧɬɵ Ʉɚɤ ɢɡɜɟɫɬɧɨ ɢɡ ɦɟɯɚɧɢɤɢ, ɥɸɛɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɫɢɫɬɟɦɚ, ɫɨɜɟɪɲɚɸɳɚɹ ɮɢɧɢɬɧɨɟ ɞɜɢɠɟɧɢɟ, ɧɚɩɪɢɦɟɪ, ɦɚɬɟɦɚɬɢɱɟɫɤɢɣ ɦɚɹɬɧɢɤ ɢɥɢ ɝɪɭɡ, ɩɨɞɜɟɲɟɧɧɵɣ ɧɚ ɩɪɭɠɢɧɤɟ, ɢɦɟɟɬ ɬɪɚɟɤɬɨɪɢɸ, ɡɚɧɢɦɚɸɳɭɸ ɜ ɮɚɡɨɜɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ ɨɝɪɚɧɢɱɟɧɧɭɸ ɨɛɥɚɫɬɶ (ɜ ɩɪɨɫɬɟɣɲɟɦ ɫɥɭɱɚɟ ɨɞɧɨɦɟɪɧɨɝɨ ɞɜɢɠɟɧɢɹ ɷɬɨ ɩɥɨɫɤɨɫɬɶ ɨɛɨɛɳɟɧɧɨɝɨ ɢɦɩɭɥɶɫɚ ɢ ɨɛɨɛɳɟɧɧɨɣ ɤɨɨɪɞɢɧɚɬɵ, ɪɢɫ.2.8). ȿɫɥɢ ɷɧɟɪɝɢɹ ɷɬɨɣ ɫɢɫɬɟɦɵ ɫɨɯɪɚɧɹɟɬɫɹ, ɬɨ ɬɪɚɟɤɬɨɪɢɹ, ɨɬɜɟɱɚɸɳɚɹ ɡɚɞɚɧɧɨɣ ɷɧɟɪɝɢɢ W, ɹɜɥɹɟɬɫɹ ɡɚɦɤɧɭɬɨɣ. Ɉɯɜɚɬɵɜɚɟɦɚɹ ɷɬɨɣ ɬɪɚɟɤɬɨɪɢɟɣ ɩɥɨɳɚɞɶ, ɨɱɟɜɢɞɧɨ, ɹɜɥɹɟɬɫɹ ɬɨɱɧɵɦ ɢɧɬɟɝɪɚɥɨɦ ɞɜɢɠɟɧɢɹ. ɋɭɳɟɫɬɜɟɧɧɨ, ɱɬɨ ɩɪɢɛɥɢɠɟɧɧɨɟ ɫɨɯɪɚɧɟɧɢɟ ɷɬɨɣ ɩɥɨɳɚɞɢ ɢɦɟɟɬ ɦɟɫɬɨ ɢ ɬɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɷɧɟɪɝɢɹ ɫɢɫɬɟɦɵ ɦɟɧɹɟɬɫɹ ɫɨ ɜɪɟɦɟɧɟɦ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɤɚɤɨɝɨ-ɥɢɛɨ ɜɨɡɦɭɳɟɧɢɹ (ɧɚɩɪɢɦɟɪ, ɫɥɚɛɨɝɨ ɬɪɟɧɢɹ, ɢɥɢ ɢɡɦɟɧɟɧɢɹ ɞɥɢɧɵ ɦɚɹɬɧɢɤɚ ɢ ɬɨɦɭ ɩɨɞɨɛɧɨɟ), ɧɨ ɷɬɨ ɢɡɦɟɧɟɧɢɟ Ɋɢɫ.2.8. «Ɏɚɡɨɜɵɣ ɩɨɪɬɪɟɬ» ɨɞɧɨɦɟɪɧɨɝɨ ɨɫɰɢɥɥɹɬɨɪɚ ɦɟɞɥɟɧɧɨɟ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɩɟɪɢɨɞɨɦ ɧɟɜɨɡɦɭɳɟɧɧɨɝɨ ɞɜɢɠɟɧɢɹ. Ɍɟɩɟɪɶ ɷɬɚ ɩɥɨɳɚɞɶ ɭɠɟ ɧɟ ɹɜɥɹɟɬɫɹ ɬɨɱɧɵɦ ɢɧɬɟɝɪɚɥɨɦ ɞɜɢɠɟɧɢɹ, ɢ ɫɨɯɪɚɧɟɧɢɟ ɢɦɟɟɬ ɦɟɫɬɨ ɥɢɲɶ ɜ ɫɪɟɞɧɟɦ ɩɨ ɩɟɪɢɨɞɭ ɧɟɜɨɡɦɭɳɟɧɧɨɝɨ ɞɜɢɠɟɧɢɹ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɝɨɜɨɪɹɬ ɨ ɫɨɯɪɚɧɟɧɢɢ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɢɧɜɚɪɢɚɧɬɚ. ɉɨ ɪɚɡɦɟɪɧɨɫɬɢ ɷɬɚ ɩɥɨɳɚɞɶ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɩɪɨɢɡɜɟɞɟɧɢɸ ɫɪɟɞɧɟɣ ɡɚ ɩɟɪɢɨɞ ɷɧɟɪɝɢɢ ɱɚɫɬɢɰɵ ɧɚ ɜɟɥɢɱɢɧɭ ɷɬɨɝɨ ɩɟɪɢɨɞɚ: J ~<W > T . (2.44) ɉɨɷɬɨɦɭ, ɟɫɥɢ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɤɚɤɨɝɨ-ɥɢɛɨ ɩɚɪɚɦɟɬɪɚ ɫɢɫɬɟɦɵ ɩɟɪɢɨɞ ɞɜɢɠɟɧɢɹ ɭɦɟɧɶɲɚɟɬɫɹ (ɧɚɩɪɢɦɟɪ, ɞɥɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɚɹɬɧɢɤɚ ɩɟɪɢɨɞ, ɤɚɤ ɢɡɜɟɫɬɧɨ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ T = 2π l / g , ɢ ɩɟɪɢɨɞ ɭɦɟɧɶɲɚɟɬɫɹ ɫ ɭɦɟɧɶɲɟɧɢɟɦ ɞɥɢɧɵ ɦɚɹɬɧɢɤɚ), ɬɨ ɟɺ ɷɧɟɪɝɢɹ ɜ ɫɪɟɞɧɟɦ ɜɨɡɪɚɫɬɚɟɬ. ɉɪɢɧɰɢɩ ɚɞɢɚɛɚɬɢɱɟɫɤɨɣ ɢɧɜɚɪɢɚɧɬɧɨɫɬɢ ɧɚɯɨɞɢɬ ɜɚɠɧɵɟ ɩɪɢɥɨɠɟɧɢɹ ɤ ɩɪɨɛɥɟɦɟ ɭɞɟɪɠɚɧɢɹ ɩɥɚɡɦɵ − ɩɨ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɬɪɚɟɤɬɨɪɢɢ ɱɚɫɬɢɰ ɞɨɥɠɧɵ ɛɵɬɶ ɮɢɧɢɬɧɵɦɢ. Ɋɚɫɫɦɨɬɪɢɦ ɤɪɚɬɤɨ ɧɟɤɨɬɨɪɵɟ ɩɪɢɥɨɠɟɧɢɹ ɷɬɨɝɨ ɩɪɢɧɰɢɩɚ ɞɥɹ ɫɥɭɱɚɹ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ. ɂɧɜɚɪɢɚɧɬɧɨɫɬɶ ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ µ ɱɚɫɬɢɰɵ ɜɨ ɜɪɟɦɟɧɢ ȿɫɥɢ ɡɚɪɹɠɟɧɧɚɹ ɱɚɫɬɢɰɚ ɞɜɢɠɟɬɫɹ ɜ ɨɞɧɨɪɨɞɧɨɦ, ɧɨ ɦɟɧɹɸɳɟɦɫɹ ɜɨ ɜɪɟɦɟɧɢ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ, ɬɨ ɟɟ ɥɚɪɦɨɪɨɜɫɤɢɣ ɪɚɞɢɭɫ ɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɚɹ ɫɤɨɪɨɫɬɶ ɛɭɞɭɬ ɦɟɧɹɬɶɫɹ. ɗɬɨ ɩɪɨɢɫɯɨɞɢɬ ɩɨɬɨɦɭ, ɱɬɨ ɢɧɞɭɰɢɪɨɜɚɧɧɨɟ ɦɟɧɹɸɳɢɦɫɹ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɛɭɞɟɬ ɭɫɤɨɪɹɬɶ (ɢɥɢ ɡɚɦɟɞɥɹɬɶ) ɱɚɫɬɢɰɭ. ȼɵɛɟɪɟɦ ɰɢɥɢɧɞɪɢɱɟɫɤɭɸ ɫɢɫɬɟɦɭ ɤɨɨɪɞɢɧɚɬ ɬɚɤ, ɱɬɨɛɵ ɜɟɤɬɨɪ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɛɵɥ ɩɚɪɚɥɥɟɥɟɧ ɨɫɢ z ɷɬɨɣ ɫɢɫɬɟɦɵ (ɫɦ. & & & ɪɢɫ.2.9), ɬɨɝɞɚ B( t ) = B( t )e z , ɝɞɟ ez - ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɟɞɢɧɢɱɧɵɣ ɜɟɤɬɨɪ. ɂɡ ɡɚɤɨɧɚ ɢɧɞɭɤɰɢɢ
−
Ɋɢɫ.2.9. Ƚɟɨɦɟɬɪɢɹ ɩɨɥɟɣ (ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ - ɭɛɵɜɚɟɬ)
1ρ Eϕ = − B ( t ) . 2c
& 1 ∂ 1 ∂ Bz = rot z E ≡ ρE , c∂t ρ ∂ρ ϕ
(2.45)
ɧɚɯɨɞɢɦ
ɉɨɞɫɬɚɜɥɹɹ ɬɟɩɟɪɶ ɷɬɢ ɩɨɥɹ ɜ ɨɫɬɚɜɲɢɟɫɹ ɭɪɚɜɧɟɧɢɹ Ɇɚɤɫɜɟɥɥɚ, ɨɛɧɚɪɭɠɢɜɚɟɦ, ɱɬɨ
(2.46)
1 ∂ E = rotϕ Bz ≡ 0 , c∂t ϕ & div B ≡ 0 , & 1 ∂ div E = Eϕ ≡ 0.
(2.47)
ρ ∂ϕ
ɉɨɷɬɨɦɭ ɭɪɚɜɧɟɧɢɹ Ɇɚɤɫɜɟɥɥɚ ɭɞɨɜɥɟɬɜɨɪɹɸɬɫɹ ɬɨɠɞɟɫɬɜɟɧɧɨ ɩɪɢ ɜɵɛɨɪɟ ɥɢɧɟɣɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɨɬ ɜɪɟɦɟɧɢ, ɬɚɤ ɱɬɨ:
B( t ) = B0 + B 0 t ,
Eϕ = −
1ρ B 2c 0
(2.48)
0 - ɩɨɫɬɨɹɧɧɚɹ ɜɟɥɢɱɢɧɚ (ɫɤɨɪɨɫɬɶ ɢɡɦɟɧɟɧɢɹ ɩɨɥɹ), ɤɨɬɨɪɚɹ ɦɨɠɟɬ ɛɵɬɶ ɤɚɤ ɩɨɥɨɠɢɬɟɥɶɧɨɣ (ɩɨɥɟ ɝɞɟ B ɪɚɫɬɟɬ), ɬɚɤ ɢ ɨɬɪɢɰɚɬɟɥɶɧɨɣ (ɩɨɥɟ ɭɛɵɜɚɟɬ); B0 - ɧɚɱɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɩɨɥɹ. ɉɨɥɭɱɟɧɧɨɟ ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɣ Ɇɚɤɫɜɟɥɥɚ − ɬɨɱɧɨɟ, ɧɨ ɧɟɫɤɨɥɶɤɨ ɢɫɤɭɫɫɬɜɟɧɧɨɟ: ɬɪɭɞɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɫɟɛɟ ɫɢɬɭɚɰɢɸ, ɤɨɝɞɚ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɧɚɪɚɫɬɚɟɬ ɫɪɚɡɭ ɜɨ ɜɫɟɦ ɩɪɨɫɬɪɚɧɫɬɜɟ. ɇɚ ɩɪɚɤɬɢɤɟ ɱɚɫɬɨ ɢɫɩɨɥɶɡɭɸɬ ɩɪɢɛɥɢɠɟɧɧɨɟ ɪɟɲɟɧɢɟ, ɫɱɢɬɚɹ, ɱɬɨ ɩɨɪɨɠɞɚɸɳɢɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɬɨɤɢ ɦɟɧɹɸɬɫɹ ɧɚɫɬɨɥɶɤɨ ɦɟɞɥɟɧɧɨ, ɱɬɨ ɬɨɤɚɦɢ ɫɦɟɳɟɧɢɹ (ɢ, ɬɟɦ ɫɚɦɵɦ, ɜɨɥɧɨɜɵɦ ɩɪɨɰɟɫɫɨɦ ɭɫɬɚɧɨɜɥɟɧɢɹ ɩɨɥɹ) ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ. Ɍɨɝɞɚ ɮɨɪɦɭɥɵ
& & B( t ) = B( t )e z ,
& 1ρ & E=− B ( t )eϕ 2c
(2.49)
ɩɪɢɛɥɢɠɟɧɧɨ ɨɩɢɫɵɜɚɸɬ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɥɟɣ ɩɪɢ ɩɪɨɢɡɜɨɥɶɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ȼ(t), ɦɟɞɥɟɧɧɨɣ ɧɚ ɦɚɫɲɬɚɛɚɯ ɜɪɟɦɟɧɢ ∆t~L/c, ɝɞɟ L - ɪɚɡɦɟɪ ɨɛɥɚɫɬɢ, ɡɚɧɢɦɚɟɦɨɣ ɩɨɥɟɦ.
Ɋɢɫ.2.10. ɂɥɥɸɫɬɪɚɰɢɹ ɫɨɯɪɚɧɟɧɢɹ ɩɨɩɟɪɟɱɧɨɝɨ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɢɧɜɚɪɢɚɧɬɚ ɜ ɫɥɚɛɨ ɩɟɪɟɦɟɧɧɨɦ, ɦɟɞɥɟɧɧɨ ɨɫɰɢɥɥɢɪɭɸɳɟɦ ɩɨɥɟ ȼ=ȼ0(1+εcosΩt); ω - ɥɚɪɦɨɪɨɜɫɤɚɹ ɱɚɫɬɨɬɚ, µ0 ɧɚɱɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ
Ⱦɥɹ ɢɥɥɸɫɬɪɚɰɢɢ ɫɨɯɪɚɧɟɧɢɹ µ − ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ ɢɥɢ ɩɨɩɟɪɟɱɧɨɝɨ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɢɧɜɚɪɢɚɧɬɚ − ɩɪɢ ɞɜɢɠɟɧɢɢ ɱɚɫɬɢɰɵ ɜ ɩɟɪɟɦɟɧɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɨɝɪɚɧɢɱɢɦɫɹ ɝɪɭɛɵɦ ɩɪɢɛɥɢɠɟɧɢɟɦ, ɫɱɢɬɚɹ, ɱɬɨ ɪɚɞɢɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɬɨɠɞɟɫɬɜɟɧɧɨ ɪɚɜɧɚ ɧɭɥɸ ɢ ɪɚɞɢɭɫ ɨɪɛɢɬɵ − ɩɨɫɬɨɹɧɧɵɣ. ȼ ɷɬɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɫɜɨɞɹɬɫɹ ɤ ɜɢɞɭ
e mvϕ = − ρB (2.50) c ɢ, ɤɚɤ ɧɟ ɬɪɭɞɧɨ ɩɪɨɜɟɪɢɬɶ, ɞɚɸɬ ɫɨɨɬɧɨɲɟɧɢɟ 2 2 d § vϕ · vϕ dB ¨ ¸= . (2.51) dt ¨© 2 ¸¹ 2 B dt ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɨɬɧɨɲɟɧɢɟ vϕ2 = const (2.52) B ɫɨɯɪɚɧɹɟɬɫɹ. ɉɟɪɟɨɛɨɡɧɚɱɢɜ vϕ→v⊥, ɩɨɥɭɱɢɦ ɨɤɨɧɱɚɬɟɥɶɧɨ mv ⊥2 = µ = const . (2.53) 2B Ƚɪɭɛɨɟ ɩɪɢɛɥɢɠɟɧɢɟ, ɢɫɩɨɥɶɡɨɜɚɧɧɨɟ ɜɵɲɟ, ɜɨɜɫɟ ɧɟ ɨɛɹɡɚɬɟɥɶɧɨ. Ⱦɟɬɚɥɶɧɵɟ ɪɚɫɱɟɬɵ (ɫɦ., ɧɚɩɪɢɦɟɪ [11]) ɩɨɤɚɡɵɜɚɸɬ ɫɨɯɪɚɧɟɧɢɟ µ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɜ ɭɫɥɨɜɢɹɯ ɩɪɢɦɟɧɢɦɨɫɬɢ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ. Ⱦɥɹ ɢɥɥɸɫɬɪɚɰɢɢ «ɤɚɱɟɫɬɜɚ» ɫɨɯɪɚɧɟɧɢɹ µ ɧɚ ɪɢɫ.2.10 ɩɪɢɜɟɞɟɧɵ ɪɟɡɭɥɶɬɚɬɵ ɬɨɱɧɵɯ ɱɢɫɥɟɧɧɵɯ ɪɚɫɱɟɬɨɜ ɷɬɨɝɨ ɩɚɪɚɦɟɬɪɚ ɞɥɹ ɱɚɫɬɧɨɝɨ ɜɢɞɚ ɨɫɰɢɥɥɢɪɭɸɳɟɝɨ ɩɨɥɹ. mvϕ = eEϕ ,
ɂɧɜɚɪɢɚɧɬɧɨɫɬɶ µ ɱɚɫɬɢɰɵ ɜ ɩɨɫɬɨɹɧɧɨɦ ɜɨ ɜɪɟɦɟɧɢ ɢ ɧɟɨɞɧɨɪɨɞɧɨɦ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ Ʉɨɝɞɚ ɩɨɥɟ ȼ ɩɨɫɬɨɹɧɧɨɟ ɜɨ ɜɪɟɦɟɧɢ, ɧɨ ɦɟɞɥɟɧɧɨ ɦɟɧɹɟɬɫɹ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ, ɬɨ ɩɪɢ ɩɟɪɟɯɨɞɟ ɱɚɫɬɢɰɵ ɢɡ ɫɥɚɛɨɝɨ ɩɨɥɹ ɜ ɛɨɥɟɟ ɫɢɥɶɧɨɟ ɧɚ ɧɟɟ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ (ɪɢɫ.2.11): dv|| ∂B Fz = − µ =m ; (2.54) ∂z dt Ɂɞɟɫɶ dz v|| = . (2.55) dt ɉɨɫɥɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɜɞɨɥɶ ɬɪɚɟɤɬɨɪɢɢ ɩɨɥɭɱɢɦ Ɋɢɫ.2.11. ȼɵɬɚɥɤɢɜɚɧɢɟ ɡɚɪɹɠɟɧɧɨɣ 2 ɱɚɫɬɢɰɵ ɧɟɨɞɧɨɪɨɞɧɵɦ ɦɚɝɧɢɬɧɵɦ dB d § mv|| · ¸. −µ = ¨ (2.56) ɩɨɥɟɦ. dt dt ¨© 2 ¸¹ Ɍɚɤ ɤɚɤ ɩɨɥɧɚɹ ɷɧɟɪɝɢɹ ɩɪɢ ɞɜɢɠɟɧɢɢ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɫɨɯɪɚɧɹɟɬɫɹ mv ||2 mv ⊥2 + = const , 2 2 ɬɨ ɩɨɥɭɱɚɟɦ dB d § mv ⊥2 · d −µ =− ¨ (2.57) ¸ − ( µB ) ; dt dt © 2 ¹ dt ɱɬɨ ɜɨɡɦɨɠɧɨ, ɬɨɥɶɤɨ ɟɫɥɢ µ=const. (2.58) ɇɟɬɨɱɧɨɫɬɶ, ɞɨɩɭɳɟɧɧɚɹ ɩɪɢ ɜɵɜɨɞɟ, ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɫɜɹɡɚɧɚ ɫ ɬɟɦ, ɱɬɨ ɢɡɦɟɧɟɧɢɹ ȼ ɜ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɧɟ ɭɱɬɟɧɵ. ɗɬɨ ɞɨɩɭɫɬɢɦɨ ɥɢɲɶ ɩɪɢ ɦɟɞɥɟɧɧɨɦ ɢɡɦɟɧɟɧɢɢ. ȼ, ɬ.ɟ. ɟɫɥɢ ɜɵɩɨɥɧɹɟɬɫɹ ɭɫɥɨɜɢɟ (2.10). Ɉɛɨɛɳɚɹ ɭɪɚɜɧɟɧɢɹ (2.53) ɢ (2.58), ɦɨɠɧɨ ɫɤɚɡɚɬɶ, ɱɬɨ ɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɚɞɢɚɛɚɬɢɱɟɫɤɢɣ ɢɧɜɚɪɢɚɧɬ ɞɜɢɠɟɧɢɹ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɜ ɦɟɞɥɟɧɧɨ ɢɡɦɟɧɹɸɳɟɦɫɹ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ. Ɉɬɫɸɞɚ ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɧɟɫɤɨɥɶɤɨ ɢɧɬɟɪɟɫɧɵɯ ɜɵɜɨɞɨɜ. ɂɡ ɜɩɨɥɧɟ ɨɱɟɜɢɞɧɵɯ ɚɥɝɟɛɪɚɢɱɟɫɤɢɯ ɜɵɤɥɚɞɨɤ
mv ⊥2 m2 v ⊥2 c 2 e 2 2 = 2 2 2 B = const ⋅ ρ B = const ⋅ Φ = const 2B e B 2 mc
(2.59)
ɫɥɟɞɭɟɬ, ɱɬɨ ɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤ, ɩɪɨɧɢɡɵɜɚɸɳɢɣ ɥɚɪɦɨɪɨɜɫɤɢɣ ɤɪɭɠɨɤ, ɚɞɢɚɛɚɬɢɱɟɫɤɢ ɩɨɫɬɨɹɧɟɧ. ɗɬɨ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ ɩɪɢɜɨɞɢɬ ɤ ɜɵɜɨɞɭ, ɱɬɨ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɥɚɪɦɨɪɨɜɫɤɢɣ ɪɚɞɢɭɫ ɢɡɦɟɧɹɟɬɫɹ ɩɨ ɡɚɤɨɧɭ:
ρ~
1 , B
(2.60)
ɬɨ ɟɫɬɶ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɞɥɟɧɧɟɟ, ɱɟɦ ɜ ɫɥɭɱɚɟ ɩɨɫɬɨɹɧɧɨɣ ɩɨɩɟɪɟɱɧɨɣ ɫɤɨɪɨɫɬɢ. Ⱥɧɚɥɨɝɢɱɧɨ ɩɨɥɭɱɢɦ: mv ⊥ ρ = const , ɬɨ ɟɫɬɶ ɦɨɦɟɧɬ ɤɨɥɢɱɟɫɬɜɚ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰɵ ɬɚɤɠɟ ɨɫɬɚɟɬɫɹ ɚɞɢɚɛɚɬɢɱɟɫɤɢ ɩɨɫɬɨɹɧɧɵɦ.
(2.61)
ɂɧɜɚɪɢɚɧɬɧɨɫɬɶ ɜɟɥɢɱɢɧɵ v||⋅l Ɋɚɫɫɦɨɬɪɢɦ ɞɜɢɠɟɧɢɟ ɱɚɫɬɢɰɵ ɜ ɹɳɢɤɟ ɫ ɭɩɪɭɝɢɦɢ ɫɬɟɧɤɚɦɢ (ɪɢɫ.2.12). ɉɭɫɬɶ ɫɤɨɪɨɫɬɶ ɱɚɫɬɢɰɵ, ɧɚɩɪɚɜɥɟɧɧɚɹ ɜɞɨɥɶ ɞɧɚ ɹɳɢɤɚ, ɪɚɜɧɚ v||, ɚ ɨɞɧɚ ɢɡ ɫɬɟɧɨɤ ɹɳɢɤɚ ɞɜɢɠɟɬɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ U<
Ɋɢɫ.2.12. ɑɚɫɬɢɰɚ ɜ ɹɳɢɤɟ ɫ ɞɜɢɠɭɳɟɣɫɹ ɫɬɟɧɤɨɣ.
ɢɥɢ
ɛɭɞɟɬ ɪɚɜɧɨ dv|| δv 2U = = v. dt δt 2l || dl Ɍɚɤ ɤɚɤ U = − , ɬɨ ɩɨɥɭɱɚɟɦ dt dv|| dl + =0 v|| l
v||l = const .
ɋɛɥɢɠɚɸɳɢɟɫɹ ɫɬɟɧɤɢ ɭɜɟɥɢɱɢɜɚɸɬ ɫɤɨɪɨɫɬɶ ɱɚɫɬɢɰɵ.
(2.63)
(2.64) (2.65)
§ 19. ɉɪɢɦɟɧɟɧɢɟ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɢ ɞɪɟɣɮɨɜɨɝɨ ɩɪɢɛɥɢɠɟɧɢɣ Ɂɟɪɤɚɥɶɧɵɟ ɥɨɜɭɲɤɢ (ɩɪɨɛɤɨɬɪɨɧɵ) ɇɚ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɚɞɢɚɛɚɬɢɱɟɫɤɨɣ ɢɧɜɚɪɢɚɧɬɧɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɨɫɧɨɜɚɧɵ ɨɬɤɪɵɬɵɟ ɦɚɝɧɢɬɧɵɟ ɥɨɜɭɲɤɢ. Ɋɚɫɫɦɨɬɪɢɦ ɞɜɢɠɟɧɢɟ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɜ ɩɨɫɬɨɹɧɧɨɦ ɜɨ ɜɪɟɦɟɧɢ ɚɤɫɢɚɥɶɧɨɫɢɦɦɟɬɪɢɱɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɫɨɥɟɧɨɢɞɚ, ɭɫɢɥɟɧɧɨɦ ɧɚ ɨɛɨɢɯ ɤɨɧɰɚɯ. Ɏɨɪɦɚ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɞɥɹ ɷɬɨɝɨ ɫɥɭɱɚɹ ɢɡɨɛɪɚɠɟɧɚ ɧɚ ɪɢɫ.2.13,ɚ. ɉɭɫɬɶ ɜ ɧɟɤɨɬɨɪɨɣ ɬɨɱɤɟ Ⱥ ɪɨɞɢɥɚɫɶ ɡɚɪɹɠɟɧɧɚɹ ɱɚɫɬɢɰɚ, & ɞɜɢɠɭɳɚɹɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ v, ɧɚɩɪɚɜɥɟɧɧɨɣ ɩɨɞ ɭɝɥɨɦ α ɤ ɫɢɥɨɜɨɣ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ (0≤α≤π). ɂɫɩɨɥɶɡɭɹ ɨɩɪɟɞɟɥɟɧɢɟ ɩɨɩɟɪɟɱɧɨɝɨ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɢɧɜɚɪɢɚɧɬɚ (2.53), ɢ ɭɱɢɬɵɜɚɹ, ɱɬɨ v ⊥ = v sin α , ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɫɨɨɬɧɨɲɟɧɢɟ: sin 2 α µ = , (2.66) B mv 2 2 ɝɞɟ ȼ - ɜɟɥɢɱɢɧɚ ɢɧɞɭɤɰɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɬɨɱɤɟ «ɪɨɠɞɟɧɢɹ» ɱɚɫɬɢɰɵ. Ɂɚɦɟɬɢɦ, ɱɬɨ ɩɨɫɤɨɥɶɤɭ ɩɪɚɜɚɹ Ɋɢɫ.2.13. Ɂɚɪɹɠɟɧɧɚɹ ɱɚɫɬɢɰɚ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɱɚɫɬɶ (2.66) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɪɨɛɤɨɬɪɨɧɚ. ɨɬɧɨɲɟɧɢɟ ɞɜɭɯ ɫɨɯɪɚɧɹɸɳɢɯɫɹ ɜɟɥɢɱɢɧ – ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɢɧɜɚɪɢɚɧɬɚ µ ɢ ɩɨɥɧɨɣ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ mv2/2, ɬɨ ɷɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɫɩɪɚɜɟɞɥɢɜɨ ɧɟ ɬɨɥɶɤɨ ɜ ɧɚɱɚɥɶɧɨɣ ɬɨɱɤɟ, ɧɨ ɢ ɜ ɥɸɛɨɣ ɞɪɭɝɨɣ ɬɨɱɤɟ ɜɞɨɥɶ ɬɪɚɟɤɬɨɪɢɢ ɱɚɫɬɢɰɵ, ɟɫɥɢ ɩɨɞ ɜɟɥɢɱɢɧɚɦɢ α ɢ ȼ ɩɨɧɢɦɚɬɶ ɬɟɤɭɳɢɟ ɡɧɚɱɟɧɢɹ ɭɝɥɚ ɧɚɤɥɨɧɚ ɢ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ. ɂɧɵɦɢ ɫɥɨɜɚɦɢ, ɫɨɝɥɚɫɧɨ (2.66) ɩɪɢ ɫɦɟɳɟɧɢɢ ɱɚɫɬɢɰɵ ɜɞɨɥɶ ɬɪɚɟɤɬɨɪɢɢ ɢɡɦɟɧɟɧɢɟ ɨɞɧɨɣ ɢɡ ɜɟɥɢɱɢɧ sin2α ɢɥɢ ȼ ɜɵɡɵɜɚɟɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɟ ɢɡɦɟɧɟɧɢɟ ɞɪɭɝɨɣ ɢɡ ɧɢɯ. ɇɨ ɬɨɝɞɚ ɦɵ ɜɢɞɢɦ, ɱɬɨ ɩɪɢ ɞɜɢɠɟɧɢɢ ɜ ɨɛɥɚɫɬɶ ɫ ɭɜɟɥɢɱɢɜɚɸɳɢɦɫɹ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ ɩɨ ɦɟɪɟ ɪɨɫɬɚ ɜɟɥɢɱɢɧɵ ɢɧɞɭɤɰɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɭɝɨɥ ɧɚɤɥɨɧɚ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰɵ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɫɢɥɨɜɨɣ ɥɢɧɢɢ, ɚ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢ ɩɨɩɟɪɟɱɧɚɹ ɤɨɦɩɨɧɟɧɬɚ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰɵ v⊥ ɞɨɥɠɧɵ ɭɜɟɥɢɱɢɜɚɬɶɫɹ. ȿɫɥɢ ɫɢɧɭɫ ɷɬɨɝɨ ɭɝɥɚ ɞɨɫɬɢɝɧɟɬ ɩɪɟɞɟɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ, ɪɚɜɧɨɝɨ ɟɞɢɧɢɰɟ, ɬɨ ɛɭɞɟɬ v⊥=v, ɚ ɩɪɨɞɨɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɱɚɫɬɢɰɵ ɨɛɪɚɬɢɬɫɹ ɜ ɧɨɥɶ, v||=0. ɑɚɫɬɢɰɚ ɩɟɪɟɫɬɚɧɟɬ ɫɦɟɳɚɬɶɫɹ ɜɞɨɥɶ ɫɢɥɨɜɨɣ ɥɢɧɢɢ - ɨɧɚ ɨɬɪɚɡɢɬɫɹ ɢ ɫɬɚɧɟɬ ɞɜɢɝɚɬɶɫɹ ɧɚɡɚɞ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɤ ɰɟɧɬɪɭ ɫɢɫɬɟɦɵ (ɪɢɫ.2.13,a), ɡɚɬɟɦ, ɩɪɨɣɞɹ ɨɛɥɚɫɬɶ ɫ ɦɢɧɢɦɚɥɶɧɵɦ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ, ɞɨɫɬɢɝɧɟɬ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɝɨ ɤɨɧɰɚ, ɝɞɟ ɩɨɥɟ ɜɧɨɜɶ ɭɜɟɥɢɱɢɜɚɟɬɫɹ, ɜɧɨɜɶ ɨɬɪɚɡɢɬɫɹ ɬɟɩɟɪɶ ɡɞɟɫɶ, ɢ ɬɚɤ ɞɚɥɟɟ. Ⱦɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɱɚɫɬɢɰɚ ɨɤɚɠɟɬɫɹ “ɡɚɩɟɪɬɨɣ” ɦɟɠɞɭ ɦɚɝɧɢɬɧɵɦɢ ɩɪɨɛɤɚɦɢ (ɜ ɚɧɝɥɨɹɡɵɱɧɨɣ ɥɢɬɟɪɚɬɭɪɟ - mirrors, ɚ ɩɪɨɛɤɨɬɪɨɧ ɧɚɡɵɜɚɸɬ mirror machine). Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɜ ɩɨɥɟ ɞɚɧɧɨɣ ɫɢɫɬɟɦɵ ɦɨɝɭɬ ɭɞɟɪɠɢɜɚɬɶɫɹ ɧɟ ɜɫɟ ɱɚɫɬɢɰɵ, ɚ ɬɨɥɶɤɨ ɬɟ, ɫɤɨɪɨɫɬɶ ɤɨɬɨɪɵɯ ɜ ɬɨɱɤɟ ɪɨɠɞɟɧɢɹ ɢɦɟɟɬ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɣ ɭɝɨɥ ɧɚɤɥɨɧɚ ɤ ɫɢɥɨɜɨɣ ɥɢɧɢɢ, ɫ ɬɟɦ, ɱɬɨɛɵ ɜ ɫɟɱɟɧɢɢ ɫ ɧɚɢɛɨɥɶɲɢɦ ɡɧɚɱɟɧɢɟɦ ȼ (ɢɥɢ ɪɚɧɶɲɟ) ɱɚɫɬɢɰɚ ɨɬɪɚɡɢɥɚɫɶ. Ɉɬɧɨɲɟɧɢɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɩɨɥɹ ȼm ɤ ɦɢɧɢɦɚɥɶɧɨɦɭ ȼ0 ɜɞɨɥɶ ɨɫɢ ɫɢɫɬɟɦɵ (ɫɦ. ɪɢɫ.2.13,ɚ), R = Bm / B0 > 1 , ɧɚɡɵɜɚɸɬ ɩɪɨɛɨɱɧɵɦ ɨɬɧɨɲɟɧɢɟɦ, ɢ ɞɥɹ ɭɞɟɪɠɚɧɢɹ ɱɚɫɬɢɰ, ɪɨɞɢɜɲɢɯɫɹ ɜ ɰɟɧɬɪɟ, ɧɟɨɛɯɨɞɢɦɨ, ɱɬɨɛɵ ɛɵɥɨ ɜɵɩɨɥɧɟɧɨ ɧɟɪɚɜɟɧɫɬɜɨ sin α ≥ 1 / R . (2.67)
Ⱦɥɹ ɜɫɟɯ ɨɫɬɚɥɶɧɵɯ ɱɚɫɬɢɰ ɜɟɥɢɱɢɧɚ sin α ɞɨɥɠɧɚ ɛɵɬɶ ɟɳɟ ɛɨɥɶɲɟ, ɱɬɨɛɵ ɨɧɢ ɨɫɬɚɜɚɥɢɫɶ ɜ ɥɨɜɭɲɤɟ. Ⱥ ɬɟ ɱɚɫɬɢɰɵ, ɞɥɹ ɤɨɬɨɪɵɯ ɜɵɩɨɥɧɟɧɨ ɨɛɪɚɬɧɨɟ ɧɟɪɚɜɟɧɫɬɜɨ sin α < 1 / R , (2.68) ɭɣɞɭɬ ɢɡ ɥɨɜɭɲɤɢ ɜɞɨɥɶ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ.
ɗɬɢ ɧɟɪɚɜɟɧɫɬɜɚ ɧɟɫɥɨɠɧɨ ɨɛɨɫɧɨɜɚɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. Ɉɛɨɡɧɚɱɢɦ ɩɨɫɪɟɞɫɬɜɨɦ αm ɭɝɨɥ ɧɚɤɥɨɧɚ ɫɤɨɪɨɫɬɢ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɫɢɥɨɜɨɣ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɨɛɥɚɫɬɢ, ɝɞɟ ɢɧɞɭɤɰɢɹ ɞɨɫɬɢɝɚɟɬ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ȼ=ȼm. ɗɬɢ ɜɟɥɢɱɢɧɵ ɞɨɥɠɧɵ ɛɵɬɶ ɫɜɹɡɚɧɵ ɫɨɨɬɧɨɲɟɧɢɟɦ, ɤɨɬɨɪɨɟ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ, ɩɪɨɫɬɨ ɡɚɦɟɧɢɜ ɜ (2.66) α ɧɚ αm ɢ ȼ ɧɚ ȼm:
sin 2 α m 2µ = . Bm mv 2 ɉɭɫɬɶ, ɞɚɥɟɟ, ȼ0 ɜɟɥɢɱɢɧɚ ɢɧɞɭɤɰɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɰɟɧɬɪɟ ɫɢɫɬɟɦɵ, ɝɞɟ ɩɟɪɜɨɧɚɱɚɥɶɧɨ ɪɚɫɩɨɥɨɠɟɧɚ ɱɚɫɬɢɰɚ. Ɍɨɝɞɚ ɫɨɨɬɧɨɲɟɧɢɟ (2.66) ɜ ɷɬɨɦ ɩɨɥɨɠɟɧɢɢ ɞɨɥɠɧɨ ɛɵɬɶ ɡɚɩɢɫɚɧɨ ɜ ɜɢɞɟ:
sin 2 α 2µ = . B0 mv 2 ɉɪɚɜɵɟ ɱɚɫɬɢ ɜ ɷɬɢɯ ɮɨɪɦɭɥɚɯ ɫɨɜɩɚɞɚɸɬ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɨɥɭɱɚɟɦ
sin 2 α m sin 2 α = , Bm B0 ɢɥɢ
sin 2 α m =
Bm sin 2 α ≡ R sin 2 α . B0
ɉɨɫɤɨɥɶɤɭ ɥɟɜɚɹ ɱɚɫɬɶ ɷɬɨɝɨ ɪɚɜɟɧɫɬɜɚ ɧɟ ɩɪɟɜɨɫɯɨɞɢɬ ɟɞɢɧɢɰɭ, ɬɨ ɜɨ ɜɫɟɯ «ɪɚɡɪɟɲɟɧɧɵɯ» ɞɥɹ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰɵ ɨɛɥɚɫɬɹɯ ɞɨɥɠɧɨ ɛɵɬɶ R sin α ≤ 1 , ɬ. ɟ. ɱɚɫɬɢɰɵ ɧɚɜɟɪɧɹɤɚ ɩɨɤɢɧɭɬ ɥɨɜɭɲɤɭ, ɟɫɥɢ ɜɵɩɨɥɧɟɧɨ ɭɫɥɨɜɢɟ (2.68). ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɜɵɩɨɥɧɟɧɨ ɭɫɥɨɜɢɟ (2.67), ɨɛɥɚɫɬɶ ɫ ɦɚɤɫɢɦɚɥɶɧɵɦ ɩɨɥɟɦ ɞɥɹ ɱɚɫɬɢɰɵ ɨɤɚɡɵɜɚɟɬɫɹ ɧɟɞɨɫɬɢɠɢɦɨɣ, ɢ ɨɧɚ ɧɟ ɦɨɠɟɬ ɩɨɤɢɧɭɬɶ ɥɨɜɭɲɤɭ. 2
Ʉɨɧɭɫ ɧɚɩɪɚɜɥɟɧɢɣ, ɜ ɩɪɟɞɟɥɚɯ ɤɨɬɨɪɨɝɨ ɱɚɫɬɢɰɵ ɩɨɤɢɞɚɸɬ ɥɨɜɭɲɤɭ, ɧɨɫɢɬ ɧɚɡɜɚɧɢɟ ɨɩɚɫɧɨɝɨ ɤɨɧɭɫɚ ɩɨɬɟɪɶ. ɋɢɫɬɟɦɵ, ɜ ɤɨɬɨɪɵɯ ɜɫɟ ɫɢɥɨɜɵɟ ɥɢɧɢɢ ɜɵɯɨɞɹɬ ɡɚ ɩɪɟɞɟɥɵ ɪɚɛɨɱɟɣ ɤɚɦɟɪɵ, ɧɚɡɵɜɚɸɬ ɨɬɤɪɵɬɵɦɢ, ɤ ɧɢɦ ɨɬɧɨɫɹɬɫɹ ɜɫɟ ɩɪɨɛɤɨɬɪɨɧɵ. ɂɡ-ɡɚ ɫɢɦɦɟɬɪɢɢ ɝɟɨɦɟɬɪɢɢ ɭɞɟɪɠɢɜɚɸɳɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɬɚɤɢɟ ɥɨɜɭɲɤɢ ɟɳɟ ɧɚɡɵɜɚɸɬ ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɵɦɢ ɥɨɜɭɲɤɚɦɢ. sin 2 α ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɭɫɥɨɜɢɟ ɭɞɟɪɠɚɧɢɹ (2.67) ɜ ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɨɣ ɥɨɜɭɲɤɟ ɹɜɥɹɟɬɫɹ ɭɧɢɜɟɪɫɚɥɶɧɵɦ − ɨɧɨ ɧɟ ɡɚɜɢɫɢɬ ɧɢ ɨɬ ɡɚɪɹɞɚ, ɧɢ ɨɬ ɦɚɫɫɵ, ɧɢ ɨɬ ɜɟɥɢɱɢɧɵ ɦɨɞɭɥɹ ɫɤɨɪɨɫɬɢ, ɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɥɢɲɶ ɨɬɧɨɲɟɧɢɟɦ ɩɪɨɞɨɥɶɧɨɣ ɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ (ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ) ɤɨɦɩɨɧɟɧɬ ɫɤɨɪɨɫɬɢ. ɉɪɚɜɞɚ, ɷɬɨ ɫɩɪɚɜɟɞɥɢɜɨ ɞɥɹ ɨɬɞɟɥɶɧɨɣ ɱɚɫɬɢɰɵ: ɪɟɚɥɶɧɨ ɜ ɩɥɚɡɦɟ ɱɚɫɬɢɰɵ ɪɚɫɫɟɢɜɚɸɬɫɹ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɹɯ, ɧɚɩɪɚɜɥɟɧɢɟ ɜɟɤɬɨɪɚ ɫɤɨɪɨɫɬɢ ɩɪɢ ɷɬɨɦ ɢɡɦɟɧɹɟɬɫɹ, ɦɨɠɟɬ ɩɨɩɚɫɬɶ ɜ ɨɩɚɫɧɵɣ ɤɨɧɭɫ ɢ ɱɚɫɬɢɰɚ ɩɨɤɢɧɟɬ ɥɨɜɭɲɤɭ. Ɇɟɞɥɟɧɧɵɟ ɱɚɫɬɢɰɵ ɪɚɫɫɟɢɜɚɸɬɫɹ ɛɵɫɬɪɟɟ 1 (ɬɚɤ ɤɚɤ ɞɥɹ ɧɢɯ ɫɟɱɟɧɢɟ ɤɭɥɨɧɨɜɫɤɨɝɨ ɪɚɫɫɟɹɧɢɹ ɛɨɥɶɲɟ, σ c ∼ 2 , ɫɦ. § 6), ɩɨɷɬɨɦɭ ɨɧɢ E ɛɵɫɬɪɟɟ ɭɯɨɞɹɬ, ɢ ɜ ɫɩɟɤɬɪɟ ɱɚɫɬɢɰ ɜɨɡɧɢɤɚɟɬ “ɩɪɨɜɚɥ” ɜ ɨɛɥɚɫɬɢ ɦɚɥɵɯ ɫɤɨɪɨɫɬɟɣ. Ʉɪɨɦɟ ɬɨɝɨ, ɫ ɩɨɜɵɲɟɧɢɟɦ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ ɜ ɢɝɪɭ ɜɫɬɭɩɚɸɬ ɫɨɛɫɬɜɟɧɧɵɟ ɩɨɥɹ ɩɥɚɡɦɵ. ɗɬɨ − ɩɪɢɱɢɧɚ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ, ɨ ɧɟɣ ɛɭɞɟɦ ɝɨɜɨɪɢɬɶ ɩɨɡɠɟ. ȿɫɥɢ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɜ ɩɪɨɛɤɟ ɧɚɪɚɫɬɚɟɬ ɜɨ ɜɪɟɦɟɧɢ, ɬɨ, ɜɫɥɟɞɫɬɜɢɟ ɫɨɯɪɚɧɟɧɢɹ ɩɨɩɟɪɟɱɧɨɝɨ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɢɧɜɚɪɢɚɧɬɚ, ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɦɨɞɭɥɶ ɩɨɩɟɪɟɱɧɨɣ ɤɨɦɩɨɧɟɧɬɵ ɫɤɨɪɨɫɬɢ v⊥ ɢ ɭɥɭɱɲɚɟɬɫɹ ɭɞɟɪɠɚɧɢɟ − ɩɪɢ ɷɬɨɦ ɢɡɦɟɧɢɬɫɹ ɩɪɨɛɨɱɧɨɟ ɨɬɧɨɲɟɧɢɟ ȼm/ȼ0, ɢ ɨɬɪɚɠɟɧɢɟ ɱɚɫɬɢɰ ɩɪɨɢɡɨɣɞɟɬ ɛɥɢɠɟ ɤ ɰɟɧɬɪɭ ɩɪɨɛɤɨɬɪɨɧɚ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɨɛɥɚɫɬɶ ɩɪɨɞɨɥɶɧɵɯ ɨɫɰɢɥɥɹɰɢɣ ɱɚɫɬɢɰ ɫɨɤɪɚɳɚɟɬɫɹ ɢ, ɫɨɝɥɚɫɧɨ (2.65), ɞɨɥɠɧɚ ɭɜɟɥɢɱɢɬɶɫɹ ɢ ɩɪɨɞɨɥɶɧɚɹ ɤɨɦɩɨɧɟɧɬɚ ɫɤɨɪɨɫɬɢ v|| ɡɚ ɫɱɟɬ ɫɛɥɢɠɟɧɢɹ ɨɬɪɚɠɚɸɳɢɯ ɱɚɫɬɢɰɭ ɭɩɪɭɝɢɯ ɫɬɟɧɨɤ. Ɍɨɱɧɨɟ ɪɟɲɟɧɢɟ ɩɨɞɨɛɧɨɣ ɡɚɞɚɱɢ ɨ ɞɜɢɠɟɧɢɢ ɱɚɫɬɢɰɵ ɜ ɩɟɪɟɦɟɧɧɨɦ ɢ ɧɟɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɹɜɥɹɟɬɫɹ ɫɥɨɠɧɨɣ ɩɪɨɛɥɟɦɨɣ.
ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɩɪɢ ɫɠɚɬɢɢ ɪɚɫɬɟɬ ɢ ɩɥɨɬɧɨɫɬɶ ɱɢɫɥɚ ɱɚɫɬɢɰ, ɬɚɤ ɤɚɤ ɩɪɢ ɪɨɫɬɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜɨɡɧɢɤɚɟɬ ɜɢɯɪɟɜɨɟ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɢ ɩɨɹɜɥɹɟɬɫɹ ɞɪɟɣɮɨɜɚɹ ɫɤɨɪɨɫɬɶ, ɧɚɩɪɚɜɥɟɧɧɚɹ ɬɚɤ, ɱɬɨ ɱɚɫɬɢɰɵ ɫɨɛɢɪɚɸɬɫɹ ɤ ɰɟɧɬɪɭ ɫɢɫɬɟɦɵ. ȼɟɥɢɱɢɧɭ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɟɣ ɫɤɨɪɨɫɬɶ ɞɪɟɣɮɚ ɦɨɠɧɨ ɨɰɟɧɢɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. Ɉɛɨɡɧɚɱɢɦ ɪɚɞɢɭɫ ɨɛɥɚɫɬɢ, ɡɚɧɹɬɨɣ ɩɥɚɡɦɨɣ, R(t), ɬɨɝɞɚ ɢɡ ɬɟɨɪɟɦɵ ɨ ɰɢɪɤɭɥɹɰɢɢ, 2π
1 ³0 Eϕ R dϕ = − c
R( t )
³ 0
∂ Bz 2π rdr , ∂t
(2.69)
ɩɨɥɭɱɚɟɦ
Eϕ = −
R dBz . 2c dt
(2.70)
ɉɪɢɛɥɢɠɟɧɧɨ ɫɱɢɬɚɟɦ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɨɞɧɨɪɨɞɧɵɦ ɜ ɩɪɟɞɟɥɚɯ ɨɤɪɭɠɧɨɫɬɢ ɫ ɪɚɞɢɭɫɨɦ R(t). Ɉɩɪɟɞɟɥɹɹ ɞɚɥɟɟ ɫɤɨɪɨɫɬɶ ɞɪɟɣɮɚ
Eϕ & & vd = c e , Bz r
(2.71)
ɩɪɢɯɨɞɢɦ ɤ ɫɨɨɬɧɨɲɟɧɢɸ
1 dBz dR =− , 2 Bz R
(2.72)
ɢɥɢ
R 2 Bz = const .
(2.73) ɗɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɜɵɪɚɠɚɟɬ ɫɨɯɪɚɧɟɧɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɬɨɤɚ, ɩɪɨɧɢɡɵɜɚɸɳɟɝɨ ɩɨɩɟɪɟɱɧɨɟ ɫɟɱɟɧɢɟ ɩɨɜɟɪɯɧɨɫɬɢ (ɱɚɫɬɨ ɧɚɡɵɜɚɟɦɨɣ ɞɪɟɣɮɨɜɨɣ ɩɨɜɟɪɯɧɨɫɬɶɸ), ɩɨ ɤɨɬɨɪɨɣ ɞɜɢɠɟɬɫɹ ɱɚɫɬɢɰɚ ɩɪɢ ɟɺ ɞɪɟɣɮɟ ɜ ɧɟɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ (ɫɦ. ɪɢɫ.2.13,ɚ,ɛ) - ɟɳɟ ɨɞɧɨɝɨ, ɬɚɤ ɧɚɡɵɜɚɟɦɨɝɨ ɬɪɟɬɶɟɝɨ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɢɧɜɚɪɢɚɧɬɚ, ɩɨɫɥɟ ɩɨɩɟɪɟɱɧɨɝɨ, ɨɬɜɟɱɚɸɳɟɝɨ ɛɵɫɬɪɨɦɭ ɜɪɚɳɟɧɢɸ ɩɨ ɥɚɪɦɨɪɨɜɫɤɨɣ ɨɤɪɭɠɧɨɫɬɢ, ɢ ɩɪɨɞɨɥɶɧɨɝɨ, ɨɬɜɟɱɚɸɳɟɝɨ ɛɨɥɟɟ ɦɟɞɥɟɧɧɵɦ ɩɪɨɞɨɥɶɧɵɦ ɨɫɰɢɥɥɹɰɢɹɦ ɱɚɫɬɢɰɵ ɦɟɠɞɭ ɩɪɨɛɤɚɦɢ. ɇɟɫɦɨɬɪɹ ɧɚ ɜɧɟɲɧɟɟ ɫɯɨɞɫɬɜɨ ɮɨɪɦɭɥ (2.59) ɢ (2.73), ɨɧɢ ɨɬɪɚɠɚɸɬ ɪɚɡɥɢɱɧɵɟ ɹɜɥɟɧɢɹ. ɋɨɝɥɚɫɧɨ ɮɨɪɦɭɥɟ (2.59) ɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤ, ɩɪɨɧɢɡɵɜɚɸɳɢɣ ɥɚɪɦɨɪɨɜɫɤɭɸ ɨɤɪɭɠɧɨɫɬɶ, ɨɩɢɫɵɜɚɟɦɭɸ ɱɚɫɬɢɰɟɣ, ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ, ɚ ɜɵɪɚɠɟɧɢɟ (2.73) ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɪɚɞɢɭɫ ɨɛɥɚɫɬɢ, ɡɚɧɹɬɨɣ ɩɥɚɡɦɨɣ, ɦɟɧɹɟɬɫɹ ɬɚɤ, ɱɬɨɛɵ ɩɨɬɨɤ ɱɟɪɟɡ ɷɬɭ ɨɛɥɚɫɬɶ ɛɵɥ ɩɨɫɬɨɹɧɧɵɦ. ɑɚɫɬɢɰɵ ɞɨɥɠɧɵ ɧɟ ɬɨɥɶɤɨ ɢɡɦɟɧɢɬɶ ɪɚɞɢɭɫ ɜɪɚɳɟɧɢɹ, ɧɨ ɢ ɩɟɪɟɦɟɫɬɢɬɶɫɹ ɩɨɩɟɪɟɤ ɩɨɥɹ.
ȿɫɥɢ ɩɨɥɧɨɟ ɱɢɫɥɨ ɱɚɫɬɢɰ N=nΩ (ɝɞɟ Ω - ɨɛɴɟɦ ɩɥɚɡɦɵ) ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ, ɬɨ, ɝɪɭɛɨ ɨɩɪɟɞɟɥɹɹ ɨɛɴɟɦ ɩɥɚɡɦɵ ɤɚɤ Ω ~ R2l, ɩɨɥɭɱɚɟɦ N = n0 R02 l0 = nR 2 l , ɢɥɢ 2 B § r0 · nl = n0 l0 ¨ ¸ = n0 l0 . (2.74) ©r¹ B0 ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɱɢɫɥɨ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɜ ɪɚɫɱɟɬɟ ɧɚ ɟɞɢɧɢɰɭ ɩɥɨɳɚɞɢ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ (ɩɨɝɨɧɧɚɹ ɩɥɨɬɧɨɫɬɶ) ɦɟɧɹɟɬɫɹ ɜɨ ɜɪɟɦɟɧɢ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ.
ɉɪɢɧɰɢɩ “ɦɢɧɢɦɭɦɚ B” ȼ ɰɟɧɬɪɚɥɶɧɨɣ ɱɚɫɬɢ ɩɪɨɛɤɨɬɪɨɧɚ (ɪɢɫ.2.13) ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɭɛɵɜɚɟɬ ɩɨ ɪɚɞɢɭɫɭ ɨɬ ɰɟɧɬɪɚ, ɩɨɷɬɨɦɭ ∇B ɧɚɩɪɚɜɥɟɧ ɤ ɰɟɧɬɪɭ. Ⱦɥɹ ɨɞɢɧɨɱɧɨɣ ɱɚɫɬɢɰɵ − ɷɬɨ ɩɪɢɱɢɧɚ ɞɪɟɣɮɚ ɩɨ ɚɡɢɦɭɬɭ ɜɨɤɪɭɝ ɨɫɢ ɫɢɫɬɟɦɵ, ɧɨ ɱɚɫɬɢɰɵ ɪɚɡɧɵɯ ɡɧɚɤɨɜ ɞɪɟɣɮɭɸɬ ɧɚɜɫɬɪɟɱɭ ɞɪɭɝ ɞɪɭɝɭ (ɫɦ. ɪɢɫ.2.13,ɛ), ɜɨɡɧɢɤɚɟɬ ɞɪɟɣɮɨɜɵɣ ɬɨɤ, ɤɨɬɨɪɵɣ, ɨɱɟɜɢɞɧɨ, ɧɚɩɪɚɜɥɟɧ ɬɚɤ, ɱɬɨ ɜɵɡɵɜɚɟɬ ɭɦɟɧɶɲɟɧɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɫɨɥɟɧɨɢɞɚ. ɉɥɚɡɦɚ ɤɚɤ ɛɵ «ɜɵɬɚɥɤɢɜɚɟɬ» ɭɞɟɪɠɢɜɚɸɳɟɟ ɟɺ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ. ȿɫɥɢ ɩɥɨɬɧɨɫɬɶ ɩɥɚɡɦɵ ɞɨɫɬɚɬɨɱɧɨ ɜɟɥɢɤɚ, ɬɨ ɷɮɮɟɤɬ ɛɭɞɟɬ ɫɭɳɟɫɬɜɟɧɧɵɦ. Ɉɧ ɪɟɚɥɶɧɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ ɢɡɦɟɪɟɧɢɹ ɞɚɜɥɟɧɢɹ ɩɥɚɡɦɵ ɩɨ ɜɟɥɢɱɢɧɟ ɜɵɬɟɫɧɹɟɦɨɝɨ ɩɨɥɹ - ɢɡɦɟɪɟɧɢɹ ɬɚɤ ɧɚɡɵɜɚɟɦɨɝɨ ɞɢɚɦɚɝɧɢɬɧɨɝɨ ɫɢɝɧɚɥɚ. ȿɫɥɢ ɫɢɫɬɟɦɚ ɢɞɟɚɥɶɧɨ ɫɢɦɦɟɬɪɢɱɧɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ, ɬɨ ɞɪɟɣɮɨɜɵɟ ɩɨɬɨɤɢ ɡɚɦɤɧɭɬɵ, ɢ ɧɚɤɨɩɥɟɧɢɹ ɡɚɪɹɞɚ ɧɟ ɩɪɨɢɫɯɨɞɢɬ. ɉɪɢ ɧɚɪɭɲɟɧɢɢ ɫɢɦɦɟɬɪɢɢ ɫɰɟɧɚɪɢɣ ɩɨɫɥɟɞɭɸɳɢɯ
ɫɨɛɵɬɢɣ ɩɪɢɨɛɪɟɬɚɟɬ ɞɪɚɦɚɬɢɱɟɫɤɢɣ ɯɚɪɚɤɬɟɪ. ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɧɚ ɛɨɤɨɜɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɩɥɚɡɦɵ ɜɨɡɧɢɤɚɟɬ ɜɵɫɬɭɩ (ɫɦ. ɪɢɫ.2.13,ɛ) – «ɩɥɚɡɦɟɧɧɵɣ ɹɡɵɤ». ɗɬɨ ɜɨɡɦɭɳɟɧɢɟ ɫɜɨɛɨɞɧɨ «ɪɚɫɬɟɤɚɟɬɫɹ» ɜɞɨɥɶ ɫɢɥɨɜɵɯ ɥɢɧɢɣ, ɜɜɢɞɭ ɨɬɫɭɬɫɬɜɢɹ ɩɪɨɬɢɜɨɞɟɣɫɬɜɢɹ ɬɚɤɨɦɭ ɪɚɫɬɟɤɚɧɢɸ, ɚ ɩɨɬɨɦɭ ɛɵɫɬɪɨ ɩɪɟɜɪɚɳɚɟɬɫɹ ɜ ɜɵɬɹɧɭɬɵɣ ɜɞɨɥɶ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɠɟɥɨɛɨɤ. ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ ɨɛɫɭɠɞɚɟɦɭɸ ɧɚɦɢ ɫɟɣɱɚɫ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ ɨɛɵɱɧɨ ɧɚɡɵɜɚɸɬ ɠɟɥɨɛɤɨɜɨɣ. ȼ ɨɛɥɚɫɬɢ ɠɟɥɨɛɤɚ ɞɪɟɣɮɨɜɵɟ ɩɨɬɨɤɢ ɧɟ ɡɚɦɤɧɭɬɵ, ɤɚɤ ɷɬɨ ɫɯɟɦɚɬɢɱɧɨ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 2.13,ɛ. ɉɨɷɬɨɦɭ ɡɞɟɫɶ ɩɪɨɢɡɨɣɞɟɬ ɪɚɡɞɟɥɟɧɢɟ ɡɚɪɹɞɨɜ ɢ ɜɨɡɧɢɤɧɟɬ ɩɨɥɹɪɢɡɚɰɢɨɧɧɨɟ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ & &ȿ, ɧɚɩɪɚɜɥɟɧɧɨɟ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨ ɪɟɡɭɥɶɬɢɪɭɸɳɢɣ ɞɪɟɣɮ ɜ ɫɤɪɟɳɟɧɧɵɯ E × B ɩɨɥɹɯ ɛɭɞɟɬ ɫɩɨɫɨɛɫɬɜɨɜɚɬɶ ɪɨɫɬɭ ɩɟɪɜɨɧɚɱɚɥɶɧɨɝɨ ɜɨɡɦɭɳɟɧɢɹ, ɡɚɜɟɪɲɚɸɳɟɝɨɫɹ ɜɵɛɪɨɫɨɦ ɩɥɚɡɦɵ ɧɚ ɫɬɟɧɤɭ ɤɚɦɟɪɵ. ɗɬɨ ɩɪɨɹɜɥɟɧɢɟ ɞɢɚɦɚɝɧɟɬɢɡɦɚ ɩɥɚɡɦɵ: ɨɧɚ ɜɫɟɝɞɚ ɫɬɪɟɦɢɬɫɹ ɩɟɪɟɣɬɢ ɜ ɨɛɥɚɫɬɶ ɛɨɥɟɟ ɫɥɚɛɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ɉɨɷɬɨɦɭ ɩɪɢ ɫɨɡɞɚɧɢɢ ɫɢɫɬɟɦ ɞɥɹ ɭɞɟɪɠɚɧɢɹ ɩɥɚɡɦɵ ɧɭɠɧɨ ɪɚɫɩɨɥɚɝɚɬɶ ɩɥɚɡɦɟɧɧɵɣ ɫɝɭɫɬɨɤ ɩɨ ɜɨɡɦɨɠɧɨɫɬɢ ɬɚɤ, ɱɬɨɛɵ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɜɨɡɪɚɫɬɚɥɨ ɨɬ ɧɟɝɨ ɜɨ ɜɫɟɯ ɧɚɩɪɚɜɥɟɧɢɹɯ, ɬ.ɟ. ɪɚɫɩɨɥɚɝɚɬɶ ɩɥɚɡɦɭ ɜ ɨɛɥɚɫɬɢ ɦɢɧɢɦɚɥɶɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ɂɦɟɧɧɨ ɩɨ ɜɨɡɦɨɠɧɨɫɬɢ, ɩɨɫɤɨɥɶɤɭ ɫɨɡɞɚɧɢɟ ɤɨɧɮɢɝɭɪɚɰɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɜ ɤɨɬɨɪɵɯ ɩɨɥɟ ɧɚɪɚɫɬɚɥɨ ɛɵ ɜɨ ɜɫɟɯ ɧɚɩɪɚɜɥɟɧɢɹɯ, ɨɱɟɜɢɞɧɨ, ɧɟɜɨɡɦɨɠɧɨ. Ɋɟɱɶ ɦɨɠɟɬ ɢɞɬɢ ɥɢɲɶ ɨ ɧɚɪɚɫɬɚɧɢɢ ɧɚɪɭɠɭ ɜ ɫɪɟɞɧɟɦ, ɤɨɝɞɚ ɜɤɥɚɞ ɭɱɚɫɬɤɨɜ ɫ ɛɥɚɝɨɩɪɢɹɬɧɨɣ ɞɥɹ ɭɞɟɪɠɚɧɢɹ ɤɪɢɜɢɡɧɨɣ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɩɪɟɜɚɥɢɪɭɟɬ ɧɚɞ ɜɤɥɚɞɨɦ ɭɱɚɫɬɤɨɜ ɫ ɧɟɛɥɚɝɨɩɪɢɹɬɧɨɣ ɤɪɢɜɢɡɧɨɣ, ɝɞɟ ɩɨɥɟ ɭɛɵɜɚɟɬ. ɗɬɨ, ɩɨ ɫɭɬɢ ɞɟɥɚ, ɢ ɜɵɪɚɠɚɟɬ ɫɨɞɟɪɠɚɧɢɟ ɩɪɢɧɰɢɩɚ «ɦɢɧɢɦɭɦɚ ȼ». ɍɩɪɨɳɟɧɧɨ (ɜ ɞɟɬɚɥɹɯ ɫɦ. [11]) ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɷɬɨɦɭ ɩɪɢɧɰɢɩɭ ɭɫɥɨɜɢɟ ɦɨɠɧɨ ɫɮɨɪɦɭɥɢɪɨɜɚɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. ȼɵɞɟɥɢɦ ɦɵɫɥɟɧɧɨ ɜ ɩɪɟɞɟɥɚɯ ɨɛɴɺɦɚ, ɡɚɧɢɦɚɟɦɨɝɨ ɩɥɚɡɦɨɣ, ɫɢɥɨɜɭɸ ɬɪɭɛɤɭ ɞɥɢɧɨɣ l ɢ ɫɟɱɟɧɢɟɦ S, ɜɵɬɹɧɭɬɭɸ ɜɞɨɥɶ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɢ ɧɚɩɨɥɧɟɧɧɭɸ ɩɥɚɡɦɨɣ. ȼ ɪɚɜɧɨɜɟɫɢɢ ɬɚɤɚɹ ɬɪɭɛɤɚ ɡɚɧɢɦɚɟɬ ɩɨɥɨɠɟɧɢɟ, ɨɬɜɟɱɚɸɳɟɟ ɦɢɧɢɦɚɥɶɧɨɣ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ. ɋɚɦɚ ɩɨ ɫɟɛɟ ɬɚɤɚɹ ɬɪɭɛɤɚ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɢɥ ɞɚɜɥɟɧɢɹ ɫɬɪɟɦɢɬɫɹ ɪɚɫɲɢɪɢɬɶɫɹ. ɉɭɫɬɶ ɞɥɹ ɩɪɨɫɬɨɬɵ ɞɚɜɥɟɧɢɟ ɩɥɚɡɦɵ ɜ ɩɪɟɞɟɥɚɯ ɷɬɨɣ ɬɪɭɛɤɢ ɩɨɫɬɨɹɧɧɨ − ɦɵ ɩɨɫɬɭɩɚɟɦɫɹ ɡɞɟɫɶ ɫɬɪɨɝɨɫɬɶɸ ɪɚɞɢ ɧɚɝɥɹɞɧɨɫɬɢ. ɂɬɚɤ, ɩɥɚɡɦɚ ɫɬɪɟɦɢɬɫɹ ɭɜɟɥɢɱɢɬɶ ɫɜɨɣ ɨɛɴɟɦ
Ω = ³ dSdl .
(2.75)
ɉɨɞɟɥɢɜ ɢ ɞɨɦɧɨɠɢɜ ɩɨɞɵɧɬɟɝɪɚɥɶɧɨɟ ɜɵɪɚɠɟɧɢɟ ɧɚ ɜɟɥɢɱɢɧɭ ɢɧɞɭɤɰɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɡɚɩɢɲɟɦ ɷɬɭ ɮɨɪɦɭɥɭ ɜ ɜɢɞɟ dl Ω = ³ ( BdS ) . (2.76) B ɉɨɫɤɨɥɶɤɭ ɩɪɨɧɢɡɵɜɚɸɳɢɣ ɷɬɭ ɬɪɭɛɤɭ ɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤ
Φ = ³ BdS
(2.77)
ɩɨɫɬɨɹɧɧɵɣ, ɬɨ ɷɬɭ (ɩɨɥɨɠɢɬɟɥɶɧɭɸ!) ɩɨɫɬɨɹɧɧɭɸ ɦɨɠɧɨ ɜɵɧɟɫɬɢ ɡɚ ɡɧɚɤ ɢɧɬɟɝɪɚɥɚ, ɢ ɦɵ ɩɨɥɭɱɚɟɦ dl Ω = Φ³ . (2.78) B ɂɧɬɟɝɪɚɥ ɡɞɟɫɶ ɛɟɪɟɬɫɹ ɜɞɨɥɶ ɫɢɥɨɜɨɣ ɥɢɧɢɢ. ɑɬɨɛɵ ɪɚɜɧɨɜɟɫɧɨɟ ɩɨɥɨɠɟɧɢɟ ɜɵɞɟɥɟɧɧɨɣ ɩɥɚɡɦɟɧɧɨɣ ɬɪɭɛɤɢ ɛɵɥɨ ɭɫɬɨɣɱɢɜɵɦ, ɨɧɚ ɞɨɥɠɧɚ ɢɦɟɬɶ ɜ ɷɬɨɦ ɩɨɥɨɠɟɧɢɢ ɦɚɤɫɢɦɚɥɶɧɵɣ ɨɛɴɟɦ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɪɢ ɥɸɛɨɦ «ɜɢɪɬɭɚɥɶɧɨɦ» ɫɦɟɳɟɧɢɢ ɬɪɭɛɤɢ ɜɚɪɢɚɰɢɹ dl δ³ <0 (2.79) B ɞɨɥɠɧɚ ɛɵɬɶ ɨɬɪɢɰɚɬɟɥɶɧɚ. ɗɬɨ ɢ ɟɫɬɶ (ɜ ɭɩɪɨɳɟɧɧɨɣ ɮɨɪɦɟ) ɫɨɞɟɪɠɚɧɢɟ ɩɪɢɧɰɢɩɚ «ɦɢɧɢɦɭɦɚ ȼ». ɉɪɟɞɥɨɠɟɧɵ ɪɚɡɥɢɱɧɵɟ ɫɩɨɫɨɛɵ ɫɨɡɞɚɧɢɹ ɦɚɝɧɢɬɧɵɯ ɩɨɥɟɣ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɯ ɷɬɨɦɭ ɩɪɢɧɰɢɩɭ: ɧɚɥɨɠɟɧɢɟ ɧɚ ɩɨɥɟ ɩɪɨɫɬɨɝɨ ɩɪɨɛɤɨɬɪɨɧɚ “ɫɬɟɪɠɧɟɣ ɂɨɮɮɟ” (ɪɢɫ.2.14) (ɧɚɡɜɚɧɧɵɯ ɬɚɤ ɩɨ ɮɚɦɢɥɢɢ ɚɜɬɨɪɚ, ɜɩɟɪɜɵɟ ɩɪɟɞɥɨɠɢɜɲɟɝɨ ɢ ɪɟɚɥɢɡɨɜɚɜɲɟɝɨ ɢɞɟɸ
ɬɚɤɨɣ ɫɬɚɛɢɥɢɡɚɰɢɢ), ɩɪɢɦɟɧɟɧɢɟ ɫɩɟɰɢɚɥɶɧɵɯ ɤɚɬɭɲɟɤ ɬɢɩɚ “ɛɟɣɫɛɨɥ” (ɪɢɫ.2.15) ɢ ɞɪ. ɋɨɛɥɸɞɟɧɢɟ ɩɪɢɧɰɢɩɚ “ɦɢɧɢɦɭɦɚ ȼ” ɨɛɹɡɚɬɟɥɶɧɨ, ɢɧɚɱɟ ɜ ɨɬɤɪɵɬɵɯ ɥɨɜɭɲɤɚɯ ɩɥɚɡɦɚ ɭɫɬɨɣɱɢɜɨ ɧɟ ɭɞɟɪɠɢɜɚɟɬɫɹ.
Ɋɢɫ.2.14. ɋɯɟɦɚ “ɦɢɧɢɦɭɦɨɦ B”
ɫɨɡɞɚɧɢɹ
ɩɨɥɹ
ɫ
Ɋɢɫ.2.15. Ɉɛɦɨɬɤɚ “ɛɟɣɫɛɨɥ”
ɉɥɚɡɦɟɧɧɵɟ ɰɟɧɬɪɢɮɭɝɢ & & ȼ ɰɢɥɢɧɞɪɢɱɟɫɤɢɯ ɫɢɫɬɟɦɚɯ ɫ ɚɤɫɢɚɥɶɧɵɦ ɩɨɥɟɦ E ɢ ɪɚɞɢɚɥɶɧɵɦ ɩɨɥɟɦ B (ɢɥɢ ɫ & & ɚɤɫɢɚɥɶɧɵɦ ɩɨɥɟɦ B ɢ ɪɚɞɢɚɥɶɧɵɦ ɩɨɥɟɦ E ) ɩɥɚɡɦɚ ɛɭɞɟɬ ɜɪɚɳɚɬɶɫɹ ɩɨ ɚɡɢɦɭɬɭ ɫ E ɞɪɟɣɮɨɜɨɣ ɫɤɨɪɨɫɬɶɸ v E = c . ȼɬɨɪɨɣ ɜɚɪɢɚɧɬ ɤɨɧɫɬɪɭɤɬɢɜɧɨ ɩɪɨɳɟ, ɟɝɨ ɞɥɹ B ɨɩɪɟɞɟɥɟɧɧɨɫɬɢ ɢ ɛɭɞɟɦ ɨɛɫɭɠɞɚɬɶ. ȼɨɡɧɢɤɚɟɬ ɰɟɧɬɪɨɛɟɠɧɚɹ ɫɢɥɚ F = mv E2 / r , ɬɟɦ ɛɨɥɶɲɚɹ, ɱɟɦ ɛɨɥɶɲɟ ɦɚɫɫɚ ɱɚɫɬɢɰɵ. ɗɬɚ ɰɟɧɬɪɨɛɟɠɧɚɹ ɫɢɥɚ ɧɚɩɪɚɜɥɟɧɚ ɩɨ ɪɚɞɢɭɫɭ ɢ ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɫɨɡɞɚɟɬ ɞɪɟɣɮɨɜɭɸ ɫɤɨɪɨɫɬɶ (ɪɚɡɧɨɝɨ ɡɧɚɤɚ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ, ɧɨ ɜ ɭɩɪɨɳɟɧɧɨɦ ɪɚɫɫɦɨɬɪɟɧɢɢ ɡɚɛɭɞɟɦ ɨɛ ɷɥɟɤɬɪɨɧɚɯ), ɫɤɥɚɞɵɜɚɸɳɭɸɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ vE. Ɍɚɤ ɤɚɤ ɩɪɢ ɡɚɞɚɧɧɨɦ ɪɚɞɢɭɫɟ ɷɬɚ ɞɨɛɚɜɤɚ ɪɚɡɧɚɹ ɞɥɹ ɱɚɫɬɢɰ ɫ ɪɚɡɧɨɣ ɦɚɫɫɨɣ, ɬɨ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ ɜɨɡɧɢɤɚɟɬ ɫɢɥɚ ɬɪɟɧɢɹ Fmɪ, ɧɚɩɪɚɜɥɟɧɧɚɹ ɩɨ ɤɚɫɚɬɟɥɶɧɨɣ ɤ ɨɤɪɭɠɧɨɫɬɢ, ɬɨɪɦɨɡɹɳɚɹ ɬɹɠɟɥɵɟ ɢ ɭɫɤɨɪɹɸɳɚɹ ɥɟɝɤɢɟ ɢɨɧɵ. ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɷɬɨɣ ɫɢɥɵ ɬɪɟɧɢɹ ɩɨɹɜɢɬɫɹ ɞɪɟɣɮ ɬɹɠɟɥɵɯ ɱɚɫɬɢɰ ɨɬ ɰɟɧɬɪɚ, ɚ ɥɟɝɤɢɯ - ɤ ɰɟɧɬɪɭ ɫɢɫɬɟɦɵ. ɂɨɧɵ ɛɭɞɭɬ ɪɚɡɞɟɥɹɬɶɫɹ ɩɨ ɦɚɫɫɚɦ, ɤɚɤ ɢ ɜ ɨɛɵɱɧɨɣ ɰɟɧɬɪɢɮɭɝɟ, ɧɨ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɛɨɥɶɲɢɦɢ, ɡɧɚɱɢɬ, ɦɨɠɟɬ ɛɵɬɶ ɛɨɥɶɲɢɦ ɢ ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɡɞɟɥɟɧɢɹ. Ɋɟɚɥɶɧɨ ɜɫɟ ɫɥɨɠɧɟɟ ɢ ɧɚɞɨ ɭɱɢɬɵɜɚɬɶ ɬɪɟɧɢɟ ɡɚ ɫɱɟɬ ɫɬɨɥɤɧɨɜɟɧɢɣ ɫ ɷɥɟɤɬɪɨɧɚɦɢ, ɬɟɪɦɨɞɢɮɮɭɡɢɸ, ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɫɨ ɫɬɟɧɤɚɦɢ ɢ ɬ.ɞ. ȼɟɞɟɬɫɹ ɦɧɨɝɨ ɢɫɫɥɟɞɨɜɚɧɢɣ ɩɨ ɩɪɢɦɟɧɟɧɢɸ ɩɨɞɨɛɧɵɯ ɰɟɧɬɪɢɮɭɝ ɞɥɹ ɪɚɡɞɟɥɟɧɢɹ ɷɥɟɦɟɧɬɨɜ (ɢɥɢ ɯɢɦɢɱɟɫɤɢɯ ɫɨɟɞɢɧɟɧɢɣ) ɢ ɞɚɠɟ ɢɡɨɬɨɩɨɜ.
§ 20. əɜɥɟɧɢɹ ɩɟɪɟɧɨɫɚ ɜ ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɟ ɉɥɚɡɦɚ, ɩɨɦɟɳɟɧɧɚɹ ɜ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɫɬɚɧɨɜɢɬɫɹ ɚɧɢɡɨɬɪɨɩɧɨɣ: ɧɚɩɪɚɜɥɟɧɢɹ ɜɞɨɥɶ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɩɨɩɟɪɟɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɨɤɚɡɵɜɚɸɬɫɹ ɧɟɪɚɜɧɨɩɪɚɜɧɵɦɢ. ɗɬɨ ɫɜɹɡɚɧɨ ɫ ɬɟɦ, ɱɬɨ ɯɚɪɚɤɬɟɪ ɞɜɢɠɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜɞɨɥɶ ɩɨɥɹ ɢ ɩɨɩɟɪɟɤ ɩɨɥɹ ɪɟɡɤɨ ɨɬɥɢɱɚɟɬɫɹ. ȼ ɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɩɪɨɞɨɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɜ ɨɬɫɭɬɫɬɜɢɢ ɞɪɭɝɢɯ ɫɢɥ ɨɫɬɚɟɬɫɹ ɫɜɨɛɨɞɧɵɦ, ɚ ɜ ɩɨɩɟɪɟɱɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɱɚɫɬɢɰɚ ɜɪɚɳɚɟɬɫɹ ɩɨ ɥɚɪɦɨɪɨɜɫɤɨɣ ɨɤɪɭɠɧɨɫɬɢ, ɪɚɞɢɭɫ ɤɨɬɨɪɨɣ ɬɟɦ ɦɟɧɶɲɟ, ɱɟɦ ɛɨɥɶɲɟ ɜɟɥɢɱɢɧɚ ɩɨɥɹ. Ɋɚɡɥɢɱɢɟ ɜ ɯɚɪɚɤɬɟɪɟ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɧɚɯɨɞɢɬ ɫɜɨɟ ɨɬɪɚɠɟɧɢɟ ɜ ɢɡɦɟɧɟɧɢɢ ɫɜɨɣɫɬɜ ɩɥɚɡɦɵ, ɜ ɱɚɫɬɧɨɫɬɢ, ɦɨɠɧɨ ɨɠɢɞɚɬɶ ɫɭɳɟɫɬɜɟɧɧɨɟ ɨɬɥɢɱɢɟ ɜ ɜɟɥɢɱɢɧɟ «ɩɪɨɞɨɥɶɧɵɯ» ɢ «ɩɨɩɟɪɟɱɧɵɯ» ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɩɟɪɟɧɨɫɚ. ɋɜɨɟɨɛɪɚɡɢɟ ɩɥɚɡɦɟɧɧɨɣ ɫɪɟɞɵ, ɨɞɧɚɤɨ, ɜ ɬɨɦ, ɱɬɨ ɨɧɚ ɡɚɱɚɫɬɭɸ ɧɟ ɫɥɟɞɭɟɬ ɩɪɨɫɬɵɦ, ɧɚ ɩɟɪɜɵɣ ɜɡɝɥɹɞ ɨɱɟɜɢɞɧɵɦ, ɫɯɟɦɚɦ. Ɍɚɤɨɜɚ, ɧɚɩɪɢɦɟɪ, ɫɢɬɭɚɰɢɹ ɫ ɩɪɨɜɨɞɢɦɨɫɬɶɸ - ɩɪɨɞɨɥɶɧɚɹ ɢ ɩɨɩɟɪɟɱɧɚɹ ɩɪɨɜɨɞɢɦɨɫɬɢ ɨɬɥɢɱɚɸɬɫɹ ɥɢɲɶ ɩɪɢɦɟɪɧɨ ɜɞɜɨɟ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɝɨɜɨɪɹɬ ɨ ɧɚɥɢɱɢɢ ɧɟɤɨɬɨɪɨɝɨ «ɦɟɯɚɧɢɡɦɚ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ», ɜɵɪɚɜɧɢɜɚɸɳɟɝɨ ɚɧɢɡɨɬɪɨɩɢɸ. Ɉɛɫɭɠɞɟɧɢɟ ɩɪɨɰɟɫɫɨɜ ɩɟɪɟɧɨɫɚ ɜ «ɡɚɦɚɝɧɢɱɟɧɧɨɣ» ɩɥɚɡɦɟ ɧɚɱɧɟɦ ɫ ɞɢɮɮɭɡɢɢ. Ⱦɢɮɮɭɡɢɹ ɋɬɨɥɤɧɨɜɟɧɢɹ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ ɨɞɧɨɝɨ ɫɨɪɬɚ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɧɟ ɩɪɢɜɨɞɹɬ ɤ ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɢɦ ɢɡɦɟɧɟɧɢɹɦ ɢɯ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ [12], ɧɟ ɩɪɢɜɨɞɹɬ, ɬɟɦ ɫɚɦɵɦ, ɤ ɞɢɮɮɭɡɢɢ. Ⱦɢɮɮɭɡɢɹ ɜɨɡɦɨɠɧɚ ɥɢɲɶ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɢ ɪɚɡɧɨɪɨɞɧɵɯ ɱɚɫɬɢɰ, ɧɚɩɪɢɦɟɪ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɩɥɚɡɦɵ. ɇɚɩɨɦɧɢɦ, ɱɬɨ ɞɢɮɮɭɡɢɨɧɧɵɣ ɩɨɬɨɤ (ɟɫɥɢ ɨɬɜɥɟɱɶɫɹ ɨɬ ɷɮɮɟɤɬɨɜ ɬɟɪɦɨɞɢɮɮɭɡɢɢ ɢ ɛɚɪɨɞɢɮɮɭɡɢɢ) ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɝɪɚɞɢɟɧɬɭ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɥɚɡɦɵ, ɩɪɢ ɷɬɨɦ ɧɚɩɪɚɜɥɟɧɢɟ ɩɨɬɨɤɚ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɝɪɚɞɢɟɧɬɭ ɤɨɧɰɟɧɬɪɚɰɢɢ, ɚ ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ ɢ ɟɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬ ɞɢɮɮɭɡɢɢ. Ʉɨɷɮɮɢɰɢɟɧɬ ɩɪɨɞɨɥɶɧɨɣ ɞɢɮɮɭɡɢɢ ɩɥɚɡɦɵ, ɩɨɦɟɳɟɧɧɨɣ ɜ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɢɦɟɟɬ ɬɚɤɭɸ ɠɟ ɜɟɥɢɱɢɧɭ, ɤɚɤ ɢ ɤɨɷɮɮɢɰɢɟɧɬ ɞɢɮɮɭɡɢɢ ɩɥɚɡɦɵ ɜ ɨɬɫɭɬɫɬɜɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ: T 1 D| | = D0 = λ vTe = e τ ei . (2.80) me 3 ɉɨɫɤɨɥɶɤɭ ɩɟɪɟɦɟɳɟɧɢɟ ɩɨɩɟɪɟɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɩɨɫɥɟ ɫɬɨɥɤɧɨɜɟɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɟɥɢɱɢɧɨɣ ɥɚɪɦɨɪɨɜɫɤɨɝɨ ɪɚɞɢɭɫɚ ρ, ɚ ɬɚɤɠɟ ɜɪɟɦɟɧɟɦ ɦɟɠɞɭ ɷɥɟɤɬɪɨɧɢɨɧɧɵɦɢ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ, τei, ɬɨ ɤɨɷɮɮɢɰɢɟɧɬ ɩɨɩɟɪɟɱɧɨɣ ɞɢɮɮɭɡɢɢ, ɤɚɤ ɷɬɨ ɫɥɟɞɭɟɬ ɢɡ ɨɛɳɟɝɨ ɨɩɪɟɞɟɥɟɧɢɹ D ~ < ( ∆x )2 > / τ (ɫɦ. §10), ɞɨɥɠɟɧ ɨɩɪɟɞɟɥɹɬɶɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ: D⊥ ~
ρ2 . τ ei
(2.81)
ɉɨɫɤɨɥɶɤɭ ɞɢɮɮɭɡɢɹ ɩɥɚɡɦɵ ɧɨɫɢɬ ɚɦɛɢɩɨɥɹɪɧɵɣ ɯɚɪɚɤɬɟɪ, ɬɨ ɜ ɤɚɱɟɫɬɜɟ ɯɚɪɚɤɬɟɪɧɨɝɨ ɪɚɡɦɟɪɚ ɜ ɮɨɪɦɭɥɭ (2.81) ɫɥɟɞɭɟɬ ɩɨɞɫɬɚɜɥɹɬɶ ɦɟɧɶɲɢɣ ɥɚɪɦɨɪɨɜɫɤɢɣ ɪɚɞɢɭɫ, ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ - ɷɥɟɤɬɪɨɧɧɵɣ. ɉɨɫɤɨɥɶɤɭ ɷɥɟɤɬɪɨɧɧɵɣ ɥɚɪɦɨɪɨɜɫɤɢɣ ɪɚɞɢɭɫ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɟɩɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ ɷɥɟɤɬɪɨɧɨɜ vTe ɢ ɷɥɟɤɬɪɨɧɧɨɣ ɰɢɤɥɨɬɪɨɧɧɨɣ ɱɚɫɬɨɬɨɣ ωȼɟ: v ρe ~ Te ,
ω Be
ɬɨ, ɩɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ ɜ (2.81), ɥɟɝɤɨ ɩɨɥɭɱɢɬɶ D|| D⊥ ≅ . (2.82) ( ωτ ei )2 ȼɟɥɢɱɢɧɚ ɩɪɨɢɡɜɟɞɟɧɢɹ ω Beτ ei ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɡɚɦɚɝɧɢɱɟɧɧɨɫɬɶ ɱɚɫɬɢɰ (ɢɧɨɝɞɚ ɟɺ ɧɚɡɵɜɚɸɬ ɩɚɪɚɦɟɬɪɨɦ ɡɚɦɚɝɧɢɱɟɧɧɨɫɬɢ), ɬ.ɟ. ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɫɬɟɩɟɧɶ ɜɥɢɹɧɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɚ ɢɯ ɞɜɢɠɟɧɢɟ. ȿɫɥɢ ɷɬɨ ɩɪɨɢɡɜɟɞɟɧɢɟ ɜɟɥɢɤɨ, ɬɨ ɱɚɫɬɢɰɚ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ ɫɨɜɟɪɲɚɟɬ ɦɧɨɝɨ ɥɚɪɦɨɪɨɜɫɤɢɯ ɨɛɨɪɨɬɨɜ. ȼɵɪɚɠɟɧɢɟ (2.82) ɩɪɢɦɟɧɢɦɨ ɤ ɫɥɭɱɚɸ ɫɢɥɶɧɨ
ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɵ, ɧɨ ɟɝɨ ɧɟɬɪɭɞɧɨ ɨɛɨɛɳɢɬɶ. ȼ ɫɥɭɱɚɟ ɫɥɚɛɨɝɨ ɩɨɥɹ ɤɨɷɮɮɢɰɢɟɧɬɵ ɩɪɨɞɨɥɶɧɨɣ ɢ ɩɨɩɟɪɟɱɧɨɣ ɞɢɮɮɭɡɢɢ ɞɨɥɠɧɵ ɫɨɜɩɚɞɚɬɶ D⊥/D||~1, ɚ ɞɥɹ ɫɢɥɶɧɨɝɨ ɩɨɥɹ, ɮɚɤɬɢɱɟɫɤɢ, D⊥ D| | ~ ( ω Beτ ei )−2 . ɉɨɷɬɨɦɭ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɞɨɥɠɧɨ ɛɵɬɶ [13]:
D⊥ ~ D||
1
. (2.83) 1 + ( ω Beτ ei )2 ȿɫɥɢ ɭɱɟɫɬɶ ɪɚɡɥɢɱɢɟ ɢɨɧɧɨɣ ɢ ɷɥɟɤɬɪɨɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪ, ɬɨ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ ɩɨɩɟɪɟɤ ɩɨɥɹ ɩɪɢɧɢɦɚɟɬ ɫɥɟɞɭɸɳɢɣ ɜɢɞ [12]: T + Ti D0 D⊥ ≅ e . Te 1 + ( ω Beτ ei )2 ȼ ɫɢɥɶɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ, ɤɨɝɞɚ ɩɚɪɚɦɟɬɪ ɡɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɜɟɥɢɤ, ɞɢɮɮɭɡɢɹ ɩɨɩɟɪɟɤ ɩɨɥɹ ɞɨɥɠɧɚ ɩɪɨɢɫɯɨɞɢɬɶ ɨɱɟɧɶ ɦɟɞɥɟɧɧɨ. ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɫɭɳɟɫɬɜɟɧɧɨ ɨɬɥɢɱɚɟɬɫɹ ɢ ɯɚɪɚɤɬɟɪ ɡɚɜɢɫɢɦɨɫɬɢ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɞɢɮɮɭɡɢɢ ɨɬ ɩɚɪɚɦɟɬɪɨɜ ɩɥɚɡɦɵ. ɋɨɝɥɚɫɧɨ ɜɵɪɚɠɟɧɢɸ (1.54), ɞɥɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɩɪɨɞɨɥɶɧɨɣ ɞɢɮɮɭɡɢɢ ɢɦɟɟɦ D0∼Ɍ5/2/n, ɚ ɬɚɤ ɤɚɤ ωȼɟ∼ȼ, τei∼T3/2/n, ɬɨ ɞɥɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɩɨɩɟɪɟɱɧɨɣ ɞɢɮɮɭɡɢɢ ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɵ ɩɨɥɭɱɚɟɦ n D⊥ ∼ 2 . (2.84) B T Ɇɵ ɜɢɞɢɦ, ɱɬɨ ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɞɨɥɶɧɨɣ ɞɢɮɮɭɡɢɢ ɭɦɟɧɶɲɚɟɬɫɹ ɫ ɪɨɫɬɨɦ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ ɢ ɪɚɫɬɟɬ ɫ ɪɨɫɬɨɦ ɟɺ ɬɟɦɩɟɪɚɬɭɪɵ, ɚ ɩɨɩɟɪɟɱɧɨɣ, ɧɚɩɪɨɬɢɜ, ɪɚɫɬɟɬ ɫ ɪɨɫɬɨɦ ɩɥɨɬɧɨɫɬɢ ɢ ɭɦɟɧɶɲɚɟɬɫɹ ɫ ɪɨɫɬɨɦ ɬɟɦɩɟɪɚɬɭɪɵ! Ɍɨɬ ɮɚɤɬ, ɱɬɨ ɤɨɷɮɮɢɰɢɟɧɬ ɩɨɩɟɪɟɱɧɨɣ ɞɢɮɮɭɡɢɢ ɛɵɫɬɪɨ ɭɛɵɜɚɟɬ ɫ ɪɨɫɬɨɦ ɜɟɥɢɱɢɧɵ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɤ ɬɨɦɭ ɠɟ ɞɨɥɠɟɧ ɭɦɟɧɶɲɚɬɶɫɹ ɩɨ ɦɟɪɟ ɧɚɝɪɟɜɚ ɩɥɚɡɦɵ, ɢ ɨɩɪɟɞɟɥɢɥɨ ɧɚɞɟɠɞɭ ɨɛɟɫɩɟɱɢɬɶ ɬɟɪɦɨɢɡɨɥɹɰɢɸ ɩɥɚɡɦɵ ɫ ɩɨɦɨɳɶɸ ɫɢɥɶɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. Ʉ ɫɨɠɚɥɟɧɢɸ, ɫɭɳɟɫɬɜɭɸɬ ɢ ɞɪɭɝɢɟ ɩɪɢɱɢɧɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɜɨɡɧɢɤɧɨɜɟɧɢɸ ɩɨɬɨɤɨɜ ɩɥɚɡɦɵ ɩɨɩɟɪɟɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɸɳɢɯ ɩɨɬɨɤɢ, ɜɵɡɵɜɚɟɦɵɟ ɤɥɚɫɫɢɱɟɫɤɨɣ ɫɬɨɥɤɧɨɜɢɬɟɥɶɧɨɣ ɞɢɮɮɭɡɢɟɣ. ɇɚɢɛɨɥɟɟ ɫɭɳɟɫɬɜɟɧɧɵɦɢ ɢɡ ɧɢɯ ɹɜɥɹɸɬɫɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ, ɨ ɧɢɯ ɛɭɞɟɦ ɝɨɜɨɪɢɬɶ ɩɨɡɠɟ. ɇɨ ɢ ɜ ɨɞɧɨɪɨɞɧɨɦ ɩɨɥɟ, ɜ ɫɩɨɤɨɣɧɨɣ ɛɟɫɬɨɤɨɜɨɣ ɩɥɚɡɦɟ ɦɨɝɭɬ ɜɨɡɧɢɤɚɬɶ ɦɟɫɬɧɵɟ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɩɨɥɹ, ɩɨɹɜɥɟɧɢɟ ɤɨɬɨɪɵɯ ɬɚɤɠɟ ɩɪɢɜɨɞɢɬ ɤ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɸ ɤɨɧɰɟɧɬɪɚɰɢɢ, ɤ ɞɢɮɮɭɡɢɢ. Ɍɚɤɢɟ ɩɪɨɰɟɫɫɵ ɩɨɥɭɱɢɥɢ ɧɚɡɜɚɧɢɟ ɬɭɪɛɭɥɟɧɬɧɨɣ ɞɢɮɮɭɡɢɢ. Ʉɚɱɟɫɬɜɟɧɧɨ ɦɨɠɧɨ ɟɟ ɨɩɢɫɚɬɶ, ɩɪɟɞɩɨɥɨɠɢɜ, ɱɬɨ ɦɚɫɲɬɚɛ ɜɨɡɧɢɤɚɸɳɢɯ ɮɥɭɤɬɭɚɰɢɨɧɧɵɯ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɨɥɟɣ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ: (2.85) elE∼T. Ⱦɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɯɚɪɚɤɬɟɪɧɚɹ ɷɧɟɪɝɢɹ, ɤɨɬɨɪɭɸ ɧɚɛɢɪɚɸɬ ɱɚɫɬɢɰɵ (ɫ ɡɚɪɹɞɨɦ ɟ) ɜ ɩɨɥɟ, ɨɤɚɡɵɜɚɟɬɫɹ ɩɨɪɹɞɤɚ ɬɟɩɥɨɜɨɣ ɷɧɟɪɝɢɢ ɩɥɚɡɦɵ. ȼ ɩɪɟɞɟɥɚɯ ɨɛɥɚɫɬɢ, ɩɪɨɬɹɠɟɧɧɨɫɬɶ ɤɨɬɨɪɨɣ ɩɨɪɹɞɤɚ l, ɩɥɚɡɦɚ ɞɪɟɣɮɭɟɬ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɤɪɟɳɟɧɧɵɯ ȿ×ȼ ɩɨɥɟɣ. ȿɫɥɢ ɧɚɩɪɚɜɥɟɧɢɟ ɩɨɥɹ ɦɟɧɹɟɬɫɹ ɯɚɨɬɢɱɟɫɤɢ, ɬɨ ɜ ɫɨɫɟɞɧɢɯ ɨɛɥɚɫɬɹɯ ɫ ɢɡɦɟɧɟɧɢɟɦ ɧɚɩɪɚɜɥɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɦɟɧɹɟɬɫɹ ɢ ɧɚɩɪɚɜɥɟɧɢɟ ɞɪɟɣɮɚ − ɩɥɚɡɦɚ ɞɜɢɠɟɬɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ
vE = c
E , B
(2.86)
ɢ ɛɟɫɩɨɪɹɞɨɱɧɨ ɦɟɧɹɟɬ ɧɚɩɪɚɜɥɟɧɢɟ ɫɜɨɟɝɨ ɞɜɢɠɟɧɢɹ. Ɏɥɭɤɬɭɚɰɢɨɧɧɵɟ ɹɱɟɣɤɢ ɠɢɜɭɬ ɤɨɪɨɬɤɨɟ ɜɪɟɦɹ, ɩɨɪɹɞɤɚ ɜɪɟɦɟɧɢ ɩɪɨɥɟɬɚ τ ~ l/vE. ɂɡɭɱɟɧɢɟ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɜ ɩɨɞɨɛɧɵɯ ɬɭɪɛɭɥɟɧɬɧɵɯ ɩɨɥɹɯ ɹɜɥɹɟɬɫɹ ɫɥɨɠɧɨɣ, ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɣ ɡɚɞɚɱɟɣ. ɍɩɪɨɳɟɧɧɨ ɟɝɨ ɦɨɠɧɨ ɬɪɚɤɬɨɜɚɬɶ ɤɚɤ ɞɢɮɮɭɡɢɸ (ɱɚɫɬɨ ɢɫɩɨɥɶɡɭɸɬ ɬɟɪɦɢɧ ɬɭɪɛɭɥɟɧɬɧɚɹ ɞɢɮɮɭɡɢɹ) ɫ ɷɮɮɟɤɬɢɜɧɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɞɢɮɮɭɡɢɢ, ɨɩɪɟɞɟɥɹɟɦɨɦ ɜɟɥɢɱɢɧɨɣ l ɢɡ (2.85) ɢ vE ɢɡ (2.86),
< ( ∆x )2 >
l2
cT (2.87) τ τ eB ɗɬɚ ɩɨɥɭɱɟɧɧɚɹ ɢɡ ɧɟɫɬɪɨɝɢɯ ɤɚɱɟɫɬɜɟɧɧɵɯ ɫɨɨɛɪɚɠɟɧɢɣ ɮɨɪɦɭɥɚ ɮɚɤɬɢɱɟɫɤɢ ɫɨɜɩɚɞɚɟɬ ɫ ɷɦɩɢɪɢɱɟɫɤɨɣ ɮɨɪɦɭɥɨɣ Ȼɨɦɚ, ɩɨɥɭɱɟɧɧɨɣ ɢɡ ɚɧɚɥɢɡɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ: 1 cT DB = . (2.88) 16 e B DɌɭ ɪ ɛ ~
~
~ vE l ~
Ʉɨɷɮɮɢɰɢɟɧɬ ɞɢɮɮɭɡɢɢ, ɨɩɪɟɞɟɥɹɟɦɵɣ ɷɬɨɣ ɮɨɪɦɭɥɨɣ, ɧɨɫɢɬ ɧɚɡɜɚɧɢɟ ɛɨɦɨɜɫɤɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ. Ɂɚɜɢɫɢɦɨɫɬɢ ɜɟɥɢɱɢɧ DB ɢ D⊥ ɨɬ ɜɟɥɢɱɢɧɵ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɪɚɡɥɢɱɧɵ. ɋɪɚɜɧɢɜɚɹ ɜɵɪɚɠɟɧɢɹ (2.82) ɢ (2.88), ɧɚɯɨɞɢɦ ɞɥɹ ɨɬɧɨɲɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɞɢɮɮɭɡɢɢ Dȼ/D⊥∼ωȼɟτɟi∼ȼT3/2/n, (2.89) ɬ.ɟ. ɜ ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɟ, ɤɨɝɞɚ ɡɚ ɜɪɟɦɹ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ ɷɥɟɤɬɪɨɧ ɭɫɩɟɜɚɟɬ ɫɨɜɟɪɲɢɬɶ ɦɧɨɝɨ ɥɚɪɦɨɪɨɜɫɤɢɯ ɨɛɨɪɨɬɨɜ, ɨɩɪɟɞɟɥɹɸɳɭɸ ɪɨɥɶ ɞɨɥɠɧɚ ɢɝɪɚɬɶ ɬɭɪɛɭɥɟɧɬɧɚɹ ɞɢɮɮɭɡɢɹ. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɬɟɦɩɟɪɚɬɭɪɵ ɤɨɷɮɮɢɰɢɟɧɬ ɤɥɚɫɫɢɱɟɫɤɨɣ ɞɢɮɮɭɡɢɢ D⊥ ɭɦɟɧɶɲɚɟɬɫɹ, ɚ ɬɭɪɛɭɥɟɧɬɧɨɣ, DɌɭɪɛ, − ɪɚɫɬɟɬ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɞɢɮɮɭɡɢɹ «ɩɨ Ȼɨɦɭ» ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɨɫɬɚɜɥɹɟɬ ɧɚɞɟɠɞ ɧɚ ɞɥɢɬɟɥɶɧɨɟ ɭɞɟɪɠɚɧɢɟ ɝɨɪɹɱɟɣ ɩɥɚɡɦɵ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ. ɇɟɨɤɥɚɫɫɢɱɟɫɤɚɹ ɞɢɮɮɭɡɢɹ ɇɟɨɛɯɨɞɢɦɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜ ɪɹɞɟ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɫɨ ɫɩɨɤɨɣɧɨɣ, ɩɪɚɤɬɢɱɟɫɤɢ ɪɚɜɧɨɜɟɫɧɨɣ, ɯɨɥɨɞɧɨɣ ɩɥɚɡɦɨɣ (ɧɚ ɬɚɤ ɧɚɡɵɜɚɟɦɵɯ Q-ɦɚɲɢɧɚɯ) ɧɟɨɞɧɨɤɪɚɬɧɨ ɧɚɛɥɸɞɚɥɚɫɶ ɞɢɮɮɭɡɢɹ, ɤɨɷɮɮɢɰɢɟɧɬ ɤɨɬɨɪɨɣ ɜɟɫɶɦɚ ɛɥɢɡɨɤ ɤ ɤɥɚɫɫɢɱɟɫɤɨɦɭ ɡɧɚɱɟɧɢɸ. ɇɚ ɞɪɭɝɢɯ ɭɫɬɚɧɨɜɤɚɯ, ɜ ɱɚɫɬɧɨɫɬɢ, ɧɚ ɫɬɟɥɥɚɪɚɬɨɪɚɯ ɢɡɦɟɪɹɟɦɨɟ ɜɪɟɦɹ ɭɞɟɪɠɚɧɢɹ ɩɥɚɡɦɵ ɫɨɨɬɜɟɬɫɬɜɨɜɚɥɨ ɤɨɷɮɮɢɰɢɟɧɬɭ ɞɢɮɮɭɡɢɢ ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɸɳɟɦɭ ɤɥɚɫɫɢɱɟɫɤɢɣ ɢ ɛɥɢɡɤɨɦɭ ɩɨ ɜɟɥɢɱɢɧɟ ɤ ɨɩɪɟɞɟɥɹɟɦɨɦɭ ɮɨɪɦɭɥɨɣ Ȼɨɦɚ. ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɢɡɦɟɪɟɧɧɵɟ ɧɚ ɭɫɬɚɧɨɜɤɚɯ ɬɢɩɚ ɬɨɤɚɦɚɤɚ, ɫɨɡɞɚɧɧɵɯ ɨɬɟɱɟɫɬɜɟɧɧɵɦɢ ɭɱɟɧɵɦɢ, ɜɟɥɢɱɢɧɵ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ ɨɤɚɡɚɥɢɫɶ ɛɨɥɶɲɟ ɤɥɚɫɫɢɱɟɫɤɨɝɨ, ɧɨ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɟ ɛɨɦɨɜɫɤɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ. ɉɪɟɜɵɲɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ ɜ ɫɬɨɥɤɧɨɜɢɬɟɥɶɧɨɦ ɪɟɠɢɦɟ ɧɚɞ ɟɝɨ ɤɥɚɫɫɢɱɟɫɤɢɦ ɡɧɚɱɟɧɢɟɦ, ɩɨɥɭɱɟɧɧɵɦ ɞɥɹ ɨɞɧɨɪɨɞɧɨɝɨ ɩɨɥɹ, ɧɚɯɨɞɢɬ ɨɛɴɹɫɧɟɧɢɟ, ɤɚɤ ɜɩɟɪɜɵɟ ɛɵɥɨ ɩɨɤɚɡɚɧɨ ɉɮɢɪɲɟɦ ɢ ɒɥɸɬɟɪɨɦ, ɜ ɢɡɦɟɧɟɧɢɢ ɝɟɨɦɟɬɪɢɢ ɩɨɥɹ. ȼ ɝɟɨɦɟɬɪɢɢ ɧɟɨɞɧɨɪɨɞɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɬɨɤɚɦɚɤɚ (ɪɢɫ. 2.16), ɫɭɳɟɫɬɜɟɧɧɭɸ ɪɨɥɶ ɢɝɪɚɸɬ ɞɪɟɣɮɵ. Ⱦɪɟɣɮɨɜɵɟ ɩɨɜɟɪɯɧɨɫɬɢ ɨɬɥɢɱɚɸɬɫɹ ɨɬ ɦɚɝɧɢɬɧɵɯ ɩɨɜɟɪɯɧɨɫɬɟɣ. ɉɪɢ ɷɬɨɦ ɫɞɜɢɝ ɦɨɠɟɬ ɩɪɟɜɵɲɚɬɶ ɜɟɥɢɱɢɧɭ ɥɚɪɦɨɪɨɜɫɤɨɝɨ ɪɚɞɢɭɫɚ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɢ ɱɚɫɬɢɰɚ ɫɦɟɳɚɟɬɫɹ ɩɨɩɟɪɟɤ ɩɨɥɹ ɧɚ ɪɚɫɫɬɨɹɧɢɟ, ɩɪɟɜɵɲɚɸɳɟɟ ɥɚɪɦɨɪɨɜɫɤɢɣ ɪɚɞɢɭɫ, ɱɬɨ ɢ ɜɵɡɵɜɚɟɬ ɷɮɮɟɤɬɢɜɧɨɟ ɭɜɟɥɢɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɩɨɩɟɪɟɱɧɨɣ ɞɢɮɮɭɡɢɢ, ɤɨɬɨɪɵɣ ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɵɦ: Dɉɒ = ( 1 + q 2 )D⊥ . (2.90) ɝɞɟ q>1 - ɤɨɷɮɮɢɰɢɟɧɬ ɡɚɩɚɫɚ ɭɫɬɨɣɱɢɜɨɫɬɢ, ɪɚɜɧɵɣ ɨɬɧɨɲɟɧɢɸ ɲɚɝɚ ɫɢɥɨɜɨɣ ɥɢɧɢɢ ɤ ɞɥɢɧɟ ɫɢɫɬɟɦɵ ɜɞɨɥɶ ɨɫɢ. Ʉɚɱɟɫɬɜɟɧɧɨ ɷɬɨɬ ɪɟɡɭɥɶɬɚɬ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. ȼ ɜɢɧɬɨɜɨɦ ɩɨɥɟ ɯɚɪɚɤɬɟɪɧɵɦ ɪɚɡɦɟɪɨɦ ɹɜɥɹɟɬɫɹ ɲɚɝ ɫɢɥɨɜɨɣ ɥɢɧɢɢ, ɩɭɫɬɶ h. ɑɚɫɬɢɰɚ, ɞɜɢɠɭɳɚɹɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ v, ɩɪɨɥɟɬɚɟɬ ɪɚɫɫɬɨɹɧɢɟ ɩɨɪɹɞɤɚ ɲɚɝɚ ɡɚ ɜɪɟɦɹ tɩɪɨɥ~h/v, ɢ ɡɚ ɷɬɨ ɜɪɟɦɹ ɫɞɪɟɣɮɨɜɵɜɚɟɬ ɩɨɩɟɪɟɤ ɩɨɥɹ ɧɚ ɪɚɫɫɬɨɹɧɢɟ ∆ɩ ɪ ɨɥ ~ v d t ɩ ɪ ɨɥ . Ɂɞɟɫɶ vd - ɫɤɨɪɨɫɬɶ ɞɪɟɣɮɚ ɩɨ ɛɢɧɨɪɦɚɥɢ, ɤɨɬɨɪɭɸ, ɝɪɭɛɨ ɫɱɢɬɚɹ v||~v⊥~vɌ, ɨɰɟɧɢɜɚɟɦ, ɫɨɝɥɚɫɧɨ (2.36), ɤɚɤ
vd =
v ⊥2 + 2 v|2| 2 Rω B
~
vT2 , Rω B
(2.91)
ɝɞɟ R – ɛɨɥɶɲɨɣ ɪɚɞɢɭɫ ɬɨɪɚ, ωȼ – ɰɢɤɥɨɬɪɨɧɧɚɹ ɱɚɫɬɨɬɚ, ɚ vɌ – ɬɟɩɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ. Ɍɨɝɞɚ
∆ɩ ɪ ɨɥ ~ v d
h v2 h ~ ~ qρB , v Rω B v
(2.92)
ɝɞɟ ρȼ -ɥɚɪɦɨɪɨɜɫɤɢɣ ɪɚɞɢɭɫ, ɚ q=h/2πR. – ɤɨɷɮɮɢɰɢɟɧɬ ɡɚɩɚɫɚ ɭɫɬɨɣɱɢɜɨɫɬɢ. ɍɜɟɥɢɱɟɧɢɟ ɜ q ɪɚɡ ɯɚɪɚɤɬɟɪɧɨɝɨ ɪɚɡɦɟɪɚ ɩɪɢɜɨɞɢɬ ɤ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦɭ ɭɜɟɥɢɱɟɧɢɸ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ, ɢ ɜ ɪɟɠɢɦɟ ɉɮɢɪɲɚ-ɒɥɸɬɟɪɚ ɞɨɥɠɧɨ ɛɵɬɶ:
Dɉɒ ~ q 2 D⊥
(2.93) Ɂɚɦɟɧɢɜ ɡɞɟɫɶ q ɧɚ 1+q , ɱɬɨɛɵ ɩɨɥɭɱɢɬɶ ɚɤɤɭɪɚɬɧɵɣ ɩɟɪɟɯɨɞ ɤ ɫɥɭɱɚɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɫ ɩɪɹɦɵɦɢ ɫɢɥɨɜɵɦɢ ɥɢɧɢɹɦɢ, ɤɨɝɞɚ q→0, ɩɪɢɯɨɞɢɦ ɤ ɮɨɪɦɭɥɟ (2.90). 2
2
ɉɨɞɱɟɪɤɧɟɦ ɟɳɟ ɪɚɡ, ɱɬɨ ɩɨɥɭɱɟɧɧɨɟ ɭɜɟɥɢɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ ɧɟ ɫɜɹɡɚɧɨ ɫ ɭɱɟɬɨɦ ɤɚɤɢɯ-ɥɢɛɨ ɬɭɪɛɭɥɟɧɬɧɵɯ ɩɭɥɶɫɚɰɢɣ, ɚ ɥɢɲɶ ɫ ɚɤɤɭɪɚɬɧɵɦ ɭɱɟɬɨɦ ɝɟɨɦɟɬɪɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ȼ ɷɬɨɦ ɩɥɚɧɟ ɮɨɪɦɭɥɚ ɉɮɢɪɲɚ-ɒɥɸɬɟɪɚ ɬɚɤɠɟ ɨɩɢɫɵɜɚɟɬ ɤɥɚɫɫɢɱɟɫɤɭɸ ɫɬɨɥɤɧɨɜɢɬɟɥɶɧɭɸ ɞɢɮɮɭɡɢɸ ɩɨɩɟɪɟɤ ɩɨɥɹ, ɧɨ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɬɨɪɨɢɞɚɥɶɧɨɣ ɝɟɨɦɟɬɪɢɢ ɩɪɢ ɧɚɥɢɱɢɢ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ. ɉɪɢ ɷɬɨɦ ɫɬɨɥɤɧɨɜɟɧɢɹ ɫɱɢɬɚɸɬɫɹ ɞɨɫɬɚɬɨɱɧɨ ɱɚɫɬɵɦɢ. ɉɨɹɫɧɢɦ, ɤɚɤ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɨɬɜɟɱɚɸɳɭɸ ɷɬɨɦɭ ɬɪɟɛɨɜɚɧɢɸ ɝɪɚɧɢɱɧɭɸ ɱɚɫɬɨɬɭ ɫɬɨɥɤɧɨɜɟɧɢɣ. Ɉɱɟɜɢɞɧɨ, ɧɟɨɛɯɨɞɢɦɨ ɫɪɚɜɧɢɬɶ ɯɚɪɚɤɬɟɪɧɨɟ ɜɪɟɦɹ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ ~ν −1 ɢ ɯɚɪɚɤɬɟɪɧɨɟ ɩɪɨɥɟɬɧɨɟ ɜɪɟɦɹ ~h/v, ɫ ɬɟɦ, ɱɬɨɛɵ ɩɨɥɭɱɢɬɶ ɞɥɹ ɪɟɠɢɦɚ ɉɮɢɪɲɚ-ɒɥɸɬɟɪɚ: v ν > ν ɉɒ ~ . (2.94) qR ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɷɬɨɝɨ ɭɫɥɨɜɢɹ ɱɚɫɬɢɰɵ ɭɫɩɟɜɚɸɬ ɫɬɨɥɤɧɭɬɶɫɹ ɪɚɧɶɲɟ, ɱɟɦ ɩɪɨɥɟɬɹɬ ɯɚɪɚɤɬɟɪɧɵɣ ɪɚɡɦɟɪ ɩɨɪɹɞɤɚ ɲɚɝɚ ɜɢɧɬɚ. ɉɪɢ ɦɟɧɶɲɢɯ ɱɚɫɬɨɬɚɯ ɫɬɨɥɤɧɨɜɟɧɢɣ, ɤɚɤ ɜɩɟɪɜɵɟ ɩɨɤɚɡɚɥɢ Ƚɚɥɟɟɜ ɢ ɋɚɝɞɟɟɜ [14], ɨɤɚɡɵɜɚɟɬɫɹ ɫɭɳɟɫɬɜɟɧɧɵɦ ɭɱɟɫɬɶ ɟɳɺ ɨɞɧɭ ɜɚɠɧɭɸ ɨɫɨɛɟɧɧɨɫɬɶ ɜ ɯɚɪɚɤɬɟɪɟ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɜ ɬɨɪɨɢɞɚɥɶɧɨɦ ɩɨɥɟ ɫ ɜɢɧɬɨɜɵɦɢ ɫɢɥɨɜɵɦɢ ɥɢɧɢɹɦɢ. ȼɢɧɬɨɜɵɟ ɫɢɥɨɜɵɟ ɥɢɧɢɢ, «ɧɚɦɨɬɚɧɧɵɟ ɧɚ ɬɨɪ», ɫɝɭɳɚɸɬɫɹ ɧɚ ɜɧɭɬɪɟɧɧɟɦ ɨɛɜɨɞɟ ɬɨɪɚ ɢ ɪɚɡɪɟɠɚɸɬɫɹ ɧɚ ɜɧɟɲɧɟɦ (ɪɢɫ. 2.16,ɚ). ɍɦɟɫɬɧɚɹ ɚɧɚɥɨɝɢɹ: ɩɪɟɞɫɬɚɜɢɦ ɫɟɛɟ ɧɚɦɨɬɚɧɧɭɸ ɫ ɩɨɫɬɨɹɧɧɵɦ ɲɚɝɨɦ ɢɡ ɝɢɛɤɨɣ ɩɪɨɜɨɥɨɤɢ ɩɪɹɦɭɸ ɫɩɢɪɚɥɶ. ȿɫɥɢ ɟɺ ɢɡɨɝɧɭɬɶ ɜ ɤɚɤɨɦ-ɥɢɛɨ ɦɟɫɬɟ, ɬɨ ɧɚ ɜɧɭɬɪɟɧɧɟɣ ɱɚɫɬɢ Ɋɢɫ.2.16. ɋɯɟɦɚ ɨɛɪɚɡɨɜɚɧɢɹ ɥɨɤɚɥɶɧɵɯ ɩɪɨɛɨɤ ɜ ɜ ɦɟɫɬɟ ɢɡɝɢɛɚ ɜɢɬɤɢ ɫɝɭɳɚɸɬɫɹ, ɚ ɧɚ ɬɨɤɚɦɚɤɚɯ (ɚ); ɫɯɟɦɚɬɢɱɟɫɤɨɟ ɢɡɨɛɪɚɠɟɧɢɟ ɜɧɟɲɧɟɣ - ɪɚɫɯɨɞɹɬɫɹ. ȼ ɦɟɫɬɚɯ ɫɝɭɳɟɧɢɹ ɩɪɨɟɤɰɢɣ ɬɪɚɟɤɬɨɪɢɣ ɡɚɩɟɪɬɵɯ ɱɚɫɬɢɰ ɧɚ ɫɟɱɟɧɢɟ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɛɨɥɶɲɟ ɢ ɬɨɤɚɦɚɤɚ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɟ ɤ ɟɝɨ ɛɨɥɶɲɨɦɭ ɩɨɷɬɨɦɭ ɡɞɟɫɶ ɪɚɫɩɨɥɚɝɚɸɬɫɹ ɥɨɤɚɥɶɧɵɟ ɞɢɚɦɟɬɪɭ (ɛ ɢ ɜ) ɩɪɨɛɤɢ ɬɚɤ ɠɟ, ɤɚɤ ɢ ɜ ɩɪɨɛɤɨɬɪɨɧɚɯ, ɫɩɨɫɨɛɧɵɟ ɨɬɪɚɠɚɬɶ ɱɚɫɬɢɰɵ, ɫɤɨɪɨɫɬɶ ɤɨɬɨɪɵɯ ɢɦɟɟɬ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɣ ɭɝɨɥ ɧɚɤɥɨɧɚ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɦɚɝɧɢɬɧɨɣ ɫɢɥɨɜɨɣ ɥɢɧɢɢ. Ʉɨɧɟɱɧɨ, ɝɟɨɦɟɬɪɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɷɬɢɯ «ɩɪɨɛɤɨɬɪɨɧɚɯ» ɫɥɨɠɧɟɟ, ɱɟɦ ɜ ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɵɯ ɥɨɜɭɲɤɚɯ, ɧɨ ɫɭɬɶ ɞɟɥɚ ɨɫɬɚɺɬɫɹ ɩɪɟɠɧɟɣ: ɱɚɫɬɶ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɫ ɦɚɥɨɣ ɩɪɨɞɨɥɶɧɨɣ ɫɤɨɪɨɫɬɶɸ ɨɬɪɚɠɚɟɬɫɹ ɜ ɩɪɨɛɤɚɯ ɢ ɨɤɚɡɵɜɚɟɬɫɹ ɡɚɯɜɚɱɟɧɧɨɣ. ɉɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɬɨɤɚɦɚɤɚɦ ɞɥɹ ɧɢɯ ɫɥɨɠɢɥɫɹ ɬɟɪɦɢɧ ɡɚɩɟɪɬɵɟ ɱɚɫɬɢɰɵ. Ɉɫɬɚɥɶɧɵɟ ɱɚɫɬɢɰɵ, ɢ ɢɯ ɩɨɞɚɜɥɹɸɳɟɟ ɛɨɥɶɲɢɧɫɬɜɨ, ɧɟ ɭɞɟɪɠɢɜɚɸɬɫɹ ɜ ɩɪɨɛɤɚɯ, ɚ ɩɨɬɨɦɭ ɧɚɡɵɜɚɸɬɫɹ ɩɪɨɥɟɬɧɵɦɢ ɱɚɫɬɢɰɚɦɢ. ȿɫɥɢ ɬɨɪ ɬɨɧɤɢɣ, ɬɚɤ ɱɬɨ ɨɬɧɨɲɟɧɢɟ ɪɚɞɢɭɫɚ ɫɟɱɟɧɢɹ ɬɨɪɚ ɤ ɪɚɞɢɭɫɭ ɬɨɪɚ ɹɜɥɹɟɬɫɹ ɦɚɥɨɣ ɜɟɥɢɱɢɧɨɣ, ε=r/R<<1, ɬɨ «ɩɪɨɛɨɱɧɨɟ ɨɬɧɨɲɟɧɢɟ» ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɟɞɢɧɢɰɵ ɥɢɲɶ ɧɚ ɦɚɥɭɸ ɜɟɥɢɱɢɧɭ ~ε. ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ, ɨɱɟɜɢɞɧɨ, ɡɚɩɟɪɬɵɦɢ ɛɭɞɭɬ ɥɢɲɶ ɬɟ ɱɚɫɬɢɰɵ (ɜɫɩɨɦɧɢɦ ɨɩɪɟɞɟɥɟɧɢɟ ɭɝɥɚ ɪɚɫɬɜɨɪɚ ɨɩɚɫɧɨɝɨ ɤɨɧɭɫɚ ɩɨɬɟɪɶ (2.67)), ɭ ɤɨɬɨɪɵɯ ɦɚɥɚ ɩɪɨɞɨɥɶɧɚɹ ɫɤɨɪɨɫɬɶ v| | v < ε << 1 . ɂɯ ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɱɢɫɥɨ ɩɨ ɩɥɨɬɧɨɫɬɢ (ɩɪɢ ɪɚɜɧɨɪɚɫɩɪɟɞɟɥɟɧɢɢ ɩɨ ɭɝɥɚɦ) ɬɚɤɠɟ, ɨɱɟɜɢɞɧɨ, ɧɟɜɟɥɢɤɨ, ɢ ɫɨɫɬɚɜɥɹɟɬ nɡɚɩ nɩ ɪ ɨɥ < ε << 1 . ȼ ɷɬɨɦ ɦɨɠɧɨ ɥɟɝɤɨ ɭɛɟɞɢɬɶɫɹ, ɨɰɟɧɢɜ ɨɛɴɟɦ ɜ ɫɤɨɪɨɫɬɧɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ, ɩɪɢɯɨɞɹɳɢɣɫɹ ɧɚ ɞɨɥɸ ɡɚɩɟɪɬɵɯ ɱɚɫɬɢɰ.
ɏɨɬɹ ɡɚɩɟɪɬɵɯ ɱɚɫɬɢɰ ɨɬɧɨɫɢɬɟɥɶɧɨ ɦɚɥɨ, ɧɨ ɨɧɢ ɞɚɸɬ ɡɚɦɟɬɧɵɣ ɜɤɥɚɞ ɜ ɞɢɮɮɭɡɢɸ. ɗɬɨ ɫɜɹɡɚɧɨ ɫ ɨɫɨɛɟɧɧɨɫɬɶɸ ɢɯ ɬɪɚɟɤɬɨɪɢɣ. ɉɨɫɤɨɥɶɤɭ ɩɪɨɞɨɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɡɚɩɟɪɬɵɯ ɱɚɫɬɢɰ ɦɚɥɚ, ɬɨ ɡɚ ɜɪɟɦɹ ɞɜɢɠɟɧɢɹ ɨɬ ɩɪɨɛɤɢ ɤ ɩɪɨɛɤɟ ɨɧɢ «ɜɵɞɪɟɣɮɨɜɵɜɚɸɬ» ɩɨɩɟɪɟɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɡɧɚɱɢɬɟɥɶɧɨ ɞɚɥɶɲɟ, ɱɟɦ ɩɪɨɥɺɬɧɵɟ ɱɚɫɬɢɰɵ. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɞɥɢɧɭ ɩɨɪɹɞɤɚ ɲɚɝɚ ɜɢɧɬɚ ɡɚɩɟɪɬɚɹ ɱɚɫɬɢɰɚ ɩɪɨɥɟɬɚɟɬ ɡɚ ɜɪɟɦɹ t ɩ ɪ ɨɥ h h t ɡɚɩ ~ ~ = , (2.95) v|| v ε ε ɢ ɫɦɟɳɚɟɬɫɹ ɡɚ ɫɱɟɬ ɞɪɟɣɮɚ ɩɨɩɟɪɟɤ ɩɨɥɹ ɧɚ ɪɚɫɫɬɨɹɧɢɟ
∆ɡɚɩ ~ v d t ɡɚɩ ~
∆ɩ ɪ ɨɥ >> ∆ɩ ɪ ɨɥ . ε
(2.96)
ɉɪɢ ɫɬɨɥɤɧɨɜɟɧɢɢ, ɢɡɦɟɧɢɜ ɫɤɨɪɨɫɬɶ, ɱɚɫɬɢɰɚ ɨɩɢɲɟɬ ɞɪɭɝɭɸ ɬɪɚɟɤɬɨɪɢɸ, ɫɦɟɫɬɢɜɲɢɫɶ ɩɪɢ ɷɬɨɦ ɩɨɩɟɪɟɤ ɩɨɥɹ ɜ ɫɪɟɞɧɟɦ ɧɚ ɪɚɫɫɬɨɹɧɢɟ (2.96), ɱɬɨ ɢ ɨɛɭɫɥɚɜɥɢɜɚɟɬ ɭɜɟɥɢɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ. Ɉɫɰɢɥɥɹɰɢɸ ɡɚɩɟɪɬɵɯ ɱɚɫɬɢɰ ɦɟɠɞɭ ɥɨɤɚɥɶɧɵɦɢ ɩɪɨɛɤɚɦɢ ɫɨɩɪɨɜɨɠɞɚɟɬ «ɜɵɞɪɟɣɮɨɜɚɧɢɟ» ɩɨɩɟɪɟɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ɉɪɢ ɷɬɨɦ ɜ ɩɪɨɟɤɰɢɢ ɧɚ ɫɟɱɟɧɢɟ ɬɨɪɚ ɩɨɩɟɪɟɱɧɨɟ ɫɦɟɳɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɪɟɞɧɟɣ ɥɢɧɢɢ ɦɟɧɹɟɬ ɡɧɚɤ, ɢ ɜ ɪɟɡɭɥɶɬɚɬɟ ɩɪɨɟɤɰɢɹ ɬɪɚɟɤɬɨɪɢɣ ɡɚɩɟɪɬɵɯ ɱɚɫɬɢɰ ɧɚ ɩɨɩɟɪɟɱɧɨɟ ɫɟɱɟɧɢɟ ɬɨɪɚ ɧɚɩɨɦɢɧɚɟɬ ɢɡɜɟɫɬɧɵɣ ɫɭɛɬɪɨɩɢɱɟɫɤɢɣ ɩɥɨɞ (ɪɢɫ.2.16,ɛ,ɜ) − ɩɨ ɷɬɨɣ ɩɪɢɱɢɧɟ ɝɨɜɨɪɹɬ ɨ ɞɢɮɮɭɡɢɢ «ɜ ɛɚɧɚɧɨɜɨɦ ɪɟɠɢɦɟ». ɗɥɟɦɟɧɬɚɪɧɚɹ ɬɟɨɪɢɹ [11] ɞɚɟɬ ɫɥɟɞɭɸɳɭɸ ɨɰɟɧɤɭ ɞɥɹ ɜɟɥɢɱɢɧɵ ɤɨɷɮɮɢɰɢɟɧɬɚ ɭɫɢɥɟɧɢɹ ɞɢɮɮɭɡɢɢ ɜ ɛɚɧɚɧɨɜɨɦ ɪɟɠɢɦɟ: 3/ 2 Dɛɚɧ § R· −3 / 2 =ε = ¨ ¸ >> 1 . (2.97) ©r¹ Dɉɒ ɋɚɦɢ «ɛɚɧɚɧɵ» ɦɨɝɭɬ ɫɭɳɟɫɬɜɨɜɚɬɶ, ɧɟ ɪɚɡɪɭɲɚɹɫɶ, ɩɨɤɚ ɱɚɫɬɨɬɚ ɫɬɨɥɤɧɨɜɟɧɢɣ ɞɨɫɬɚɬɨɱɧɨ ɦɚɥɚ v 3/ 2 ν < νɛɚɧ = ε = ν ɉɒ ε 3/ 2 . (2.98) qR ȼ ɨɛɨɢɯ ɪɟɠɢɦɚɯ ɢ ɱɚɫɬɵɯ ɫɬɨɥɤɧɨɜɟɧɢɣ, ν > ν ɉɒ , ɢ ɪɟɞɤɢɯ ɫɬɨɥɤɧɨɜɟɧɢɣ, ν < νɛɚɧ , ɤɨɷɮɮɢɰɢɟɧɬ ɞɢɮɮɭɡɢɢ, ɨɱɟɜɢɞɧɨ, ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɱɚɫɬɨɬɟ ɫɬɨɥɤɧɨɜɟɧɢɣ (ɫɦ. ɪɢɫ. 2.17), ɧɨ ɭɝɥɨɜɨɣ ɤɨɷɮɮɢɰɢɟɧɬ ɷɬɨɣ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ ɫɭɳɟɫɬɜɟɧɧɨ ɪɚɡɧɵɣ. ȼ ɩɪɨɦɟɠɭɬɨɱɧɨɣ ɨɛɥɚɫɬɢ ɱɚɫɬɨɬ, ɤɨɝɞɚ «ɛɚɧɚɧɵ» ɭɠɟ ɪɚɡɪɭɲɚɸɬɫɹ, ɧɨ ɫɬɨɥɤɧɨɜɟɧɢɹ ɟɳɺ ɪɟɞɤɢɟ, ɨɫɧɨɜɧɨɣ ɜɤɥɚɞ ɜ ɞɢɮɮɭɡɢɸ ɞɚɸɬ ɦɟɞɥɟɧɧɵɟ ɩɪɨɥɟɬɧɵɟ ɱɚɫɬɢɰɵ, ɚ ɤɨɷɮɮɢɰɢɟɧɬ ɞɢɮɮɭɡɢɢ ɩɨɱɬɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɱɚɫɬɨɬɵ ɫɬɨɥɤɧɨɜɟɧɢɣ − ɷɬɨ ɪɟɠɢɦ ɩɥɚɬɨ. ȼɟɥɢɱɢɧɭ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ ɜ ɪɟɠɢɦɟ ɩɥɚɬɨ ɦɨɠɧɨ ɨɰɟɧɢɬɶ, ɩɨɞɫɬɚɜɢɜ ɜ ɮɨɪɦɭɥɭ ɉɮɢɪɲɚ-ɒɥɸɬɟɪɚ ɜɦɟɫɬɨ ɱɚɫɬɨɬɵ ɫɬɨɥɤɧɨɜɟɧɢɣ ν = ν ɉɒ . ɉɪɟɜɵɲɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ ɧɚɞ ɟɝɨ ɤɥɚɫɫɢɱɟɫɤɢɦ ɡɧɚɱɟɧɢɟɦ ɩɨɥɭɱɢɥɨ ɧɚɡɜɚɧɢɟ ɧɟɨɤɥɚɫɫɢɱɟɫɤɨɣ ɞɢɮɮɭɡɢɢ, ɚ ɬɟɨɪɢɹ Ƚɚɥɟɟɜɚ ɢ ɋɚɝɞɟɟɜɚ, ɨɛɴɹɫɧɹɸɳɚɹ ɩɪɢɱɢɧɭ ɷɬɨɝɨ ɩɪɟɜɵɲɟɧɢɹ, ɧɚɡɵɜɚɟɬɫɹ ɧɟɨɤɥɚɫɫɢɱɟɫɤɨɣ ɬɟɨɪɢɟɣ ɞɢɮɮɭɡɢɢ, ɢɥɢ, ɤɪɚɬɤɨ, ɧɟɨɤɥɚɫɫɢɤɨɣ. ɗɤɫɩɟɪɢɦɟɧɬɵ ɩɨɞɬɜɟɪɠɞɚɸɬ ɷɬɭ ɧɟɨɤɥɚɫɫɢɱɟɫɤɭɸ ɬɟɨɪɢɸ. Ɋɢɫ. 2.17. Ɂɚɜɢɫɢɦɨɫɬɶ «ɧɟɨɤɥɚɫɫɢɱɟɫɤɨɝɨ» ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ ɨɬ ɱɚɫɬɨɬɵ ɫɬɨɥɤɧɨɜɟɧɢɣ
Ɍɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ
ɋ ɬɨɱɤɢ ɡɪɟɧɢɹ ɝɚɡɨɤɢɧɟɬɢɱɟɫɤɨɣ ɬɟɨɪɢɢ ɤɨɷɮɮɢɰɢɟɧɬ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ ɪɚɜɟɧ ɤɨɷɮɮɢɰɢɟɧɬɭ ɞɢɮɮɭɡɢɢ, ɭɦɧɨɠɟɧɧɨɦɭ ɧɚ ɩɥɨɬɧɨɫɬɶ (1.61): κ = Dn. ɗɬɨ ɩɪɚɜɢɥɨ ɦɨɠɟɬ ɛɵɬɶ ɮɨɪɦɚɥɶɧɨ ɩɪɢɦɟɧɟɧɨ ɤ ɩɥɚɡɦɟ, ɤɚɤ ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ κ||, ɬɚɤ ɢ ɞɥɹ κ⊥. ɋɥɟɞɭɟɬ ɥɢɲɶ ɭɱɟɫɬɶ, ɱɬɨ ɜ ɨɬɥɢɱɢɟ ɨɬ ɞɢɮɮɭɡɢɢ, ɜɨɡɦɨɠɧɨɣ ɥɢɲɶ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɢ ɪɚɡɧɨɪɨɞɧɵɯ ɱɚɫɬɢɰ, ɜ ɩɟɪɟɧɨɫɟ ɬɟɩɥɚ, ɧɚɩɪɨɬɢɜ, ɝɥɚɜɧɭɸ ɪɨɥɶ ɢɝɪɚɸɬ ɫɬɨɥɤɧɨɜɟɧɢɹ ɨɞɢɧɚɤɨɜɵɯ ɱɚɫɬɢɰ. ɋɥɟɞɭɟɬ ɢɦɟɬɶ ɜ ɜɢɞɭ, ɱɬɨ ɩɪɢ ɡɚɞɚɧɧɨɣ ɩɥɨɬɧɨɫɬɢ ɤɨɷɮɮɢɰɢɟɧɬ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ ɜɞɨɥɶ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ κ||, ɫɨɝɥɚɫɧɨ ɜɵɪɚɠɟɧɢɹɦ (2.80) ɢ (1.61), ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɞɥɢɧɟ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ɱɚɫɬɢɰɵ ɢ ɜ ɦɚɤɫɜɟɥɥɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɟ ɛɨɥɶɲɟ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ (ɩɪɢɦɟɪɧɨ ɜ ɤɨɪɟɧɶ ɢɡ ɨɬɧɨɲɟɧɢɹ ɦɚɫɫ, ~(mi/me)1/2, ɪɚɡ) , ɚ ɤɨɷɮɮɢɰɢɟɧɬ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ ɩɨɩɟɪɟɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɫɨɝɥɚɫɧɨ ɜɵɪɚɠɟɧɢɸ (2.82), ɛɨɥɶɲɟ ɞɥɹ ɢɨɧɨɜ (ɬɚɤɠɟ ɩɪɢɦɟɪɧɨ ɜ ɤɨɪɟɧɶ ɢɡ ɨɬɧɨɲɟɧɢɹ ɦɚɫɫ, ~(mi/me)1/2, ɪɚɡ). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɨɝɥɚɫɧɨ ɤɥɚɫɫɢɱɟɫɤɢɦ ɩɪɟɞɫɬɚɜɥɟɧɢɹɦ, ɜ ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɟ ɜɞɨɥɶ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɬɟɩɥɨ ɩɟɪɟɧɨɫɹɬ ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɷɥɟɤɬɪɨɧɵ, ɚ ɩɨɩɟɪɟɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ − ɢɨɧɵ. Ɉɬɦɟɬɢɦ, ɱɬɨ ɧɟɨɤɥɚɫɫɢɱɟɫɤɢɟ ɫɨɨɛɪɚɠɟɧɢɹ ɦɨɝɭɬ ɛɵɬɶ ɩɟɪɟɧɟɫɟɧɵ ɢ ɧɚ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ. Ɉɫɨɛɟɧɧɨɫɬɢ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɜ ɩɨɥɟ ɫɥɨɠɧɨɣ ɝɟɨɦɟɬɪɢɢ ɢ ɡɞɟɫɶ ɩɪɢɜɨɞɹɬ ɤ ɢɡɦɟɧɟɧɢɸ ɜɟɥɢɱɢɧɵ ɤɨɷɮɮɢɰɢɟɧɬɚ ɩɪɨɰɟɫɫɚ ɩɟɪɟɧɨɫɚ ɬɟɩɥɚ. ɉɪɚɜɞɚ, ɜ ɷɤɫɩɟɪɢɦɟɧɬɚɯ ɧɚ ɬɨɤɚɦɚɤɚɯ ɧɚɛɥɸɞɚɟɬɫɹ ɚɧɨɦɚɥɶɧɨ ɛɨɥɶɲɨɣ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɧɟɨɤɥɚɫɫɢɱɟɫɤɢɦ ɬɟɩɥɨɩɟɪɟɧɨɫ ɷɥɟɤɬɪɨɧɚɦɢ. ɉɪɨɜɨɞɢɦɨɫɬɶ ɩɥɚɡɦɵ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ • ɉɪɨɜɨɞɢɦɨɫɬɶ ɩɥɚɡɦɵ ɜɞɨɥɶ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ɇɚɥɨɠɟɧɢɟ ɧɚ ɩɥɚɡɦɭ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɟ ɨɤɚɡɵɜɚɟɬ ɜɥɢɹɧɢɹ ɧɚ ɞɜɢɠɟɧɢɟ ɱɚɫɬɢɰ ɜɞɨɥɶ ɩɨɥɹ ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɧɟ ɜɥɢɹɟɬ ɧɚ ɩɪɨɞɨɥɶɧɭɸ ɩɪɨɜɨɞɢɦɨɫɬɶ, ɨɩɪɟɞɟɥɹɟɦɭɸ ɫɨɫɬɚɜɥɹɸɳɟɣ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɧɚɩɪɚɜɥɟɧɧɨɣ ɩɚɪɚɥɥɟɥɶɧɨ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ: T 3/ 2 j|| = σ|| E|| , σ| | =σ 0 ~ e . (2.99)
Λ
ɝɞɟ σ0 - ɩɪɨɜɨɞɢɦɨɫɬɶ ɩɥɚɡɦɵ ɜ ɨɬɫɭɬɫɬɜɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. • ɉɨɥɹɪɢɡɚɰɢɹ ɩɥɚɡɦɵ. ȿɫɥɢ ɩɥɚɡɦɭ, ɧɚɯɨɞɹɳɭɸɫɹ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ, ɩɨɦɟɫɬɢɬɶ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ȿ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɟ ɤ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ, ɬɨ ɫɨɝɥɚɫɧɨ ɞɪɟɣɮɨɜɵɦ ɩɪɟɞɫɬɚɜɥɟɧɢɹɦ ɭ E ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ ɩɨɹɜɢɬɫɹ ɨɞɢɧɚɤɨɜɚɹ ɫɤɨɪɨɫɬɶ v E = c . ɉɨɷɬɨɦɭ ɬɨɤɚ ɧɟ ɛɭɞɟɬ, B ɨɞɧɚɤɨ, ɩɪɨɢɡɨɣɞɟɬ ɧɟɤɨɬɨɪɨɟ ɪɚɡɞɟɥɟɧɢɟ ɡɚɪɹɞɨɜ − ɩɥɚɡɦɚ ɩɨɥɹɪɢɡɭɟɬɫɹ: ɱɚɫɬɢɰɵ ɛɭɞɭɬ ɞɜɢɝɚɬɶɫɹ ɩɨ ɬɪɨɯɨɢɞɚɦ, ɫɦɟɳɚɹɫɶ ɨɬ ɩɟɪɜɨɧɚɱɚɥɶɧɨɝɨ ɩɨɥɨɠɟɧɢɹ ɧɚ ɧɟɤɨɬɨɪɵɟ ɜɟɥɢɱɢɧɵ ∆e, ∆i. ȿɫɥɢ ɩɪɟɧɟɛɪɟɱɶ ɬɟɩɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ, ɩɪɢɧɹɜ ɧɚɱɚɥɶɧɭɸ ɫɤɨɪɨɫɬɶ ɪɚɜɧɨɣ ɧɭɥɸ, ɬɨ ɬɪɨɯɨɢɞɚ ɜɵɪɨɠɞɚɟɬɫɹ ɜ ɰɢɤɥɨɢɞɭ (ɫɦ. ɪɢɫ. 2.2), ɚ ɜɟɥɢɱɢɧɚ ɫɪɟɞɧɟɝɨ ɫɦɟɳɟɧɢɹ ∆e,i ɛɭɞɟɬ ɪɚɜɧɚ ɥɚɪɦɨɪɨɜɫɤɨɦɭ ɪɚɞɢɭɫɭ, ɤɨɬɨɪɵɣ ɫɥɟɞɭɟɬ ɜɵɱɢɫɥɹɬɶ ɩɨ ɜɟɥɢɱɢɧɟ ɞɪɟɣɮɨɜɨɣ ɫɤɨɪɨɫɬɢ.
ɉɭɫɬɶ ɜɟɤɬɨɪ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ȼ ɧɚɩɪɚɜɥɟɧ ɜɞɨɥɶ ɨɫɢ Z ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ, ɚ ɜɟɤɬɨɪ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ȿ - ɜɞɨɥɶ ɨɫɢ Y (ɫɦ. ɪɢɫ.2.18). ɋɤɨɪɨɫɬɶ ɞɪɟɣɮɚ ɜ ɫɤɪɟɳɟɧɧɵɯ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɢ ɦɚɝɧɢɬɧɨɦ ɩɨɥɹɯ ɛɭɞɟɬ ɧɚɩɪɚɜɥɟɧɚ ɩɚɪɚɥɥɟɥɶɧɨ ɨɫɢ X. Ɇɨɞɭɥɢ ɫɪɟɞɧɢɯ ɫɦɟɳɟɧɢɣ ɞɥɹ ɷɥɟɤɬɪɨɧɚ <∆e> ɢ ɢɨɧɚ <∆i> ɪɚɜɧɵ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ:
< ∆e >= ρBe = ɝɞɟ
vE = c
me v E c mv c ; < ∆i >= ρ Bi = i E , eB eB
E , ɚ ɡɚɪɹɞɵ ɱɚɫɬɢɰ ɩɨ ɜɟɥɢɱɢɧɟ ɫɱɢɬɚɸɬɫɹ ɨɞɢɧɚɤɨɜɵɦɢ. B
Ɂɚɪɹɞɵ ɜ ɫɪɟɞɧɟɦ “ɪɚɡɨɣɞɭɬɫɹ” ɧɚ ɜɟɥɢɱɢɧɭ
(2.100)
( me + mi )c 2 E⊥ ∆ =< ∆e > + < ∆i >= . eB 2
(2.101)
ɍɦɧɨɠɢɜ ɷɬɭ ɜɟɥɢɱɢɧɭ ɧɚ ɡɚɪɹɞ ɢ ɧɚ ɩɥɨɬɧɨɫɬɶ, ɩɨɥɭɱɢɦ ɞɢɩɨɥɶɧɵɣ ɦɨɦɟɧɬ Ɋ ɟɞɢɧɢɰɵ ɨɛɴɟɦɚ
n( me + mi )c 2 E E P = ne∆ = = ρm c 2 2 , 2 B B
(2.102)
ɢ ɩɨɩɟɪɟɱɧɭɸ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɤɨɦɩɨɧɟɧɬɭ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɩɥɚɡɦɵ
P c2 ε ⊥ = 1 + 4π = 1 + 4πρm 2 . E B ȼ ɨɛɟɢɯ ɮɨɪɦɭɥɚɯ ρm = n( me + mi ) - ɦɚɫɫɨɜɚɹ ɩɥɨɬɧɨɫɬɶ ɩɥɚɡɦɵ.
(2.103)
Ɋɚɫɱɟɬɵ ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ ɜɟɥɢɱɢɧɚ ε⊥ ɦɨɠɟɬ ɛɵɬɶ ɛɨɥɶɲɨɣ, ɩɨɷɬɨɦɭ ɩɨɥɟ ɜ ɩɥɚɡɦɟ ɫɢɥɶɧɨ ɨɫɥɚɛɥɹɟɬɫɹ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɞɟɣɬɟɪɢɟɜɨɣ ɩɥɚɡɦɵ ɫ ɩɚɪɚɦɟɬɪɚɦɢ n=1010ɫɦ-3, ȼ=103Ƚɫ ɩɨɥɭɱɚɟɦ ε⊥≈102. ȿɫɥɢ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɦɟɞɥɟɧɧɨ ɦɟɧɹɟɬɫɹ ɜɨ ɜɪɟɦɟɧɢ, ɬɚɤ ɱɬɨ ɜɪɟɦɟɧɧɨɣ ɦɚɫɲɬɚɛ ɟɝɨ ɢɡɦɟɧɟɧɢɹ ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɟɬ ɥɚɪɦɨɪɨɜɫɤɢɣ ɩɟɪɢɨɞ, ɬɨ ɩɪɢɜɟɞɟɧɧɚɹ ɮɨɪɦɭɥɚ ɞɥɹ ε⊥ ɫɩɪɚɜɟɞɥɢɜɚ ɢ ɜ ɷɬɨɦ ɫɥɭɱɚɟ. ɇɚɩɨɦɧɢɦ, ɱɬɨ ɮɨɪɦɭɥɚ (2.103) ɪɚɧɟɟ ɛɵɥɚ ɩɨɥɭɱɟɧɚ ɩɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɩɨɥɹɪɢɡɚɰɢɨɧɧɨɝɨ ɞɪɟɣɮɚ.
Ⱦɢɷɥɟɤɬɪɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɩɥɚɡɦɵ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɩɪɟɬɟɪɩɟɜɚɸɬ ɫɭɳɟɫɬɜɟɧɧɨɟ ɢɡɦɟɧɟɧɢɟ, ɜɟɥɢɱɢɧɵ ε|| ɢ ε⊥ ɪɚɡɥɢɱɧɵ, ɢ ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɵ ɫɬɚɧɨɜɢɬɫɹ ɬɟɧɡɨɪɧɨɣ ɜɟɥɢɱɢɧɨɣ. ɉɪɢ ɷɬɨɦ ɤɨɦɩɨɧɟɧɬɚ ε|| ɨɫɬɚɟɬɫɹ ɬɚɤɨɣ ɠɟ, ɤɚɤ ɢ ɜ ɫɥɭɱɚɟ ɩɥɚɡɦɵ ɛɟɡ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. Ɉɧɚ ɡɚɜɢɫɢɬ ɨɬ ɱɚɫɬɨɬɵ ɩɚɞɚɸɳɟɣ ɜɨɥɧɵ ɢ ɩɥɨɬɧɨɫɬɢ ɱɢɫɥɚ ɱɚɫɬɢɰ ɩɥɚɡɦɵ, ɬɨɝɞɚ ɤɚɤ ɤɨɦɩɨɧɟɧɬɚ ε⊥ − ɨɬ ɦɚɫɫɨɜɨɣ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ ɢ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. • ɉɨɩɟɪɟɱɧɚɹ ɩɪɨɜɨɞɢɦɨɫɬɶ. Ʉɚɪɬɢɧɚ ɫɨ ɫɜɨɛɨɞɧɵɦ ɞɪɟɣɮɨɦ ɩɥɚɡɦɵ ɜ ɫɤɪɟɳɟɧɧɵɯ ɩɨɥɹɯ ɫɩɪɚɜɟɞɥɢɜɚ ɥɢɲɶ ɩɪɢ ɭɫɥɨɜɢɢ, ɱɬɨ ɧɟɬ ɩɪɢɱɢɧ, ɦɟɲɚɸɳɢɯ ɷɬɨɦɭ ɫɜɨɛɨɞɧɨɦɭ ɞɜɢɠɟɧɢɸ ɩɥɚɡɦɵ. Ɋɟɚɥɢɡɨɜɚɬɶ ɬɚɤɨɣ ɫɥɭɱɚɣ ɦɨɠɧɨ, ɧɚɩɪɢɦɟɪ, ɜ ɫɥɭɱɚɟ ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɨɝɨ ɫɨɥɟɧɨɢɞɚ ɫ ɞɨɩɨɥɧɢɬɟɥɶɧɵɦ ɪɚɞɢɚɥɶɧɵɦ ɷɥɟɤɬɪɢɱɟɫɤɢɦ ɩɨɥɟɦ. ȿɫɥɢ ɨɫɶ Z ɧɚɩɪɚɜɢɬɶ ɜɞɨɥɶ ɨɫɢ ɫɨɥɟɧɨɢɞɚ, ɚ ɨɫɶ Y − ɩɨ ɪɚɞɢɭɫɭ, ɬɨɝɞɚ ɨɫɶ X ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɜɪɚɳɟɧɢɸ ɩɨ ɭɝɥɭ ϕ ɜɨɤɪɭɝ ɨɫɢ ɫɨɥɟɧɨɢɞɚ. Ɍɚɤɢɟ ɫɢɫɬɟɦɵ ɫɭɳɟɫɬɜɭɸɬ, ɢ ɜ ɞɜɢɠɭɳɟɣɫɹ ɩɥɚɡɦɟ ɭɞɚɟɬɫɹ ɧɚɤɚɩɥɢɜɚɬɶ ɜɟɫɶɦɚ ɡɚɦɟɬɧɭɸ ɷɧɟɪɝɢɸ - ɩɨ ɫɭɳɟɫɬɜɭ ɫɨɡɞɚɸɬɫɹ ɩɥɚɡɦɟɧɧɵɟ ɤɨɧɞɟɧɫɚɬɨɪɵ ɫ ɛɨɥɶɲɢɦ ɡɧɚɱɟɧɢɟɦ ε⊥ . Ⱦɪɭɝɨɟ ɩɪɢɦɟɧɟɧɢɟ − ɩɥɚɡɦɟɧɧɵɟ ɰɟɧɬɪɢɮɭɝɢ − ɛɵɥɨ ɪɚɫɫɦɨɬɪɟɧɨ ɪɚɧɟɟ. ȿɫɥɢ ɠɟ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɞɪɟɣɮɚ ɜɨɡɧɢɤɚɟɬ ɤɚɤɨɟ-ɥɢɛɨ ɩɪɟɩɹɬɫɬɜɢɟ, ɬɨ ɩɪɨɢɫɯɨɞɢɬ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɥɨɬɧɨɫɬɢ ɱɚɫɬɢɰ, ɬɚɤ ɤɚɤ ɜɛɥɢɡɢ ɩɪɟɩɹɬɫɬɜɢɹ ɱɚɫɬɢɰɵ ɧɚɤɚɩɥɢɜɚɸɬɫɹ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɜɨɡɧɢɤɚɟɬ ɝɪɚɞɢɟɧɬ ɞɚɜɥɟɧɢɹ ɢ ɫɢɥɚ (ɜ ɪɚɫɱɟɬɟ ɧɚ ɨɞɧɭ ɱɚɫɬɢɰɭ) F= −∇p/n. ɗɬɚ ɫɢɥɚ ɩɪɢɜɨɞɢɬ ɤ ɩɨɹɜɥɟɧɢɸ ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɞɪɟɣɮɚ, ɩɪɢɱɟɦ ɷɥɟɤɬɪɨɧɵ ɢ ɢɨɧɵ ɞɪɟɣɮɭɸɬ ɜ ɪɚɡɧɵɟ ɫɬɨɪɨɧɵ − ɜɨɡɧɢɤɚɟɬ ɬɨɤ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜɨɫɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɩɪɨɜɨɞɢɦɨɫɬɶ ɩɨɩɟɪɺɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ȼ. ɇɚ ɪɢɫ. 2.18 ɩɨɥɟ ȼ ɧɚɩɪɚɜɥɟɧɨ ɜɞɨɥɶ Ɋɢɫ.2.18. ɋɯɟɦɚ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɩɪɨɜɨɞɢɦɨɫɬɢ ɨɫɢ Z, ɚ ɩɨɥɟ ȿ - ɜɞɨɥɶ ɨɫɢ Y ɢ ɜɨɡɧɢɤɚɟɬ ɞɪɟɣɮ ɜɞɨɥɶ ɨɫɢ X. ȿɫɥɢ ɢɦɟɟɬɫɹ ɤɚɤɨɟ-ɥɢɛɨ ɩɪɟɩɹɬɫɬɜɢɟ, ɬɨ ɜɛɥɢɡɢ ɧɟɝɨ ɩɥɨɬɧɨɫɬɶ ɩɨɜɵɲɚɟɬɫɹ; ɜɨɡɧɢɤɚɟɬ ∇p ɢ ɨɬɜɟɱɚɸɳɚɹ ɟɦɭ ɫɢɥɚ F. Ⱦɪɟɣɮ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɢɥɵ F ɧɚɩɪɚɜɥɟɧ ɞɥɹ ɢɨɧɨɜ ɜɞɨɥɶ ɨɫɢ Y, ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɚɧɬɢɩɚɪɚɥɥɟɥɶɧɨ Y. ɉɨɹɜɥɹɟɬɫɹ ɬɨɤ j, ɧɚɩɪɚɜɥɟɧɧɵɣ ɜɞɨɥɶ ɨɫɢ Y, ɬɨ ɟɫɬɶ ɜɞɨɥɶ ɜɟɤɬɨɪɚ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ - ɩɪɨɜɨɞɢɦɨɫɬɶ «ɜɨɫɫɬɚɧɚɜɥɢɜɚɟɬɫɹ». ȼɵɱɢɫɥɹɹ ɷɬɨɬ
ɬɨɤ, ɧɚɞɨ ɭɱɢɬɵɜɚɬɶ ɬɪɟɧɢɟ, ɜɨɡɧɢɤɚɸɳɟɟ ɩɪɢ ɨɬɧɨɫɢɬɟɥɶɧɨɦ ɞɜɢɠɟɧɢɢ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ.
Ɍɨɱɧɵɣ ɜɵɜɨɞ, ɫɬɪɨɝɨ ɭɱɢɬɵɜɚɸɳɢɣ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ [13], ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɩɨɩɟɪɟɱɧɚɹ ɩɪɨɜɨɞɢɦɨɫɬɶ ɧɟ ɪɚɜɧɚ ɩɪɨɞɨɥɶɧɨɣ, σ⊥≠σ||, ɬ.ɟ. ɩɪɨɜɨɞɢɦɨɫɬɶ ɩɥɚɡɦɵ ɚɧɢɡɨɬɪɨɩɧɚ. ɉɪɢ ɷɬɨɦ ɨɬɧɨɲɟɧɢɟ σ⊥/σ|| ɡɚɜɢɫɢɬ ɨɬ ɡɚɪɹɞɨɜɨɝɨ ɱɢɫɥɚ ɢɨɧɚ. Ⱦɥɹ ɢɨɧɨɜ ɫ Z=1, ɧɚɩɪɢɦɟɪ, ɞɥɹ ɜɨɞɨɪɨɞɧɨɣ ɩɥɚɡɦɵ σ ⊥ ≈ 0 ,5σ|| (2.104) ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɬɨɤ ɬɟɱɟɬ ɩɨɞ ɭɝɥɨɦ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɢ ɡɚɤɨɧ Ɉɦɚ ɞɥɹ ɩɥɚɡɦɵ ɜɵɝɥɹɞɢɬ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ [13]:
& & j|| & j 1 && + ⊥ + E′ = [ jB ] , σ || σ ⊥ enc
(2.105)
Ɂɞɟɫɶ ɫɩɪɚɜɚ ɜɵɞɟɥɟɧɵ ɜɫɟ ɫɥɚɝɚɟɦɵɟ, ɜ ɤɨɬɨɪɵɟ ɜɯɨɞɢɬ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ, ɜ ɬɨɦ ɱɢɫɥɟ ɩɨɫɥɟɞɧɟɟ ɢɡ ɧɢɯ ɨɬɜɟɱɚɟɬ ɷɮɮɟɤɬɭ ɏɨɥɥɚ, ɚ ɫɥɟɜɚ ɜ ɮɨɪɦɭɥɟ ɮɢɝɭɪɢɪɭɟɬ ɷɮɮɟɤɬɢɜɧɨɟ ɩɨɥɟ, ɪɚɜɧɨɟ
& & 1 && & 1 E ′ = E + [ VB ] + ( ∇pe − RT ) . c en
(2.106)
Ɂɞɟɫɶ ɩɟɪɜɨɟ ɫɥɚɝɚɟɦɨɟ − ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɜɬɨɪɨɟ ɭɱɢɬɵɜɚɟɬ ɷɮɮɟɤɬ ɢɧɞɭɤɰɢɢ, ɜɨɡɧɢɤɚɸɳɢɣ ɩɪɢ ɩɟɪɟɫɟɱɟɧɢɢ ɩɨɬɨɤɨɦ ɩɥɚɡɦɵ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɬɪɟɬɶɟ ɫɜɹɡɚɧɨ ɫ ɝɪɚɞɢɟɧɬɨɦ ɷɥɟɤɬɪɨɧɧɨɝɨ ɞɚɜɥɟɧɢɹ, ɚ ɩɨɫɥɟɞɧɟɟ ɭɱɢɬɵɜɚɟɬ ɜɥɢɹɧɢɟ ɬɟɪɦɨ-ɗȾɋ, ɜɨɡɧɢɤɚɸɳɟɣ ɢɡ-ɡɚ ɬɟɪɦɨɫɢɥɵ, ɜ ɫɢɥɶɧɨ ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɟ ɩɪɢɦɟɪɧɨ ɪɚɜɧɨɣ:
& & & & B & 3 ne RT = −0.71ne ( b ∇ )Te − [ b ∇Te ], b = . B 2 ω eτ ei
(2.107)
Ɏɨɪɦɭɥɚ (2.105) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ, ɩɨ ɫɭɳɟɫɬɜɭ, ɨɞɧɭ ɢɡ ɜɨɡɦɨɠɧɵɯ ɮɨɪɦ ɡɚɩɢɫɢ ɡɚɤɨɧɚ Ɉɦɚ ɞɥɹ ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɵ. ɂɡ ɧɟɺ ɫɥɟɞɭɟɬ, ɱɬɨ ɜ ɫɢɥɶɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɜɞɨɥɶ ɩɨɥɹ ɫɨɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɤɨɦɩɨɧɟɧɬɨɣ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɢ ɩɥɨɬɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ ɬɚɤɨɟ ɠɟ, ɤɚɤ ɢ ɜ ɨɬɫɭɬɫɬɜɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ
E||′ =
j||
σ
.
(2.108ɚ)
||
ɉɨɩɟɪɟɱɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ, ɨɞɧɚɤɨ, ɩɪɟɬɟɪɩɟɜɚɟɬ ɫɭɳɟɫɬɜɟɧɧɨɟ ɢɡɦɟɧɟɧɢɟ: ɷɮɮɟɤɬɢɜɧɨɟ ɩɨɥɟ ɨɤɚɡɵɜɚɟɬɫɹ ɩɪɚɤɬɢɱɟɫɤɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɵɦ ɤ ɬɨɤɭ. ɉɪɨɟɤɰɢɹ ɩɨɩɟɪɟɱɧɨɝɨ ɩɨɥɹ ɧɚ ɬɨɤ ɫɜɹɡɚɧɚ ɫ ɩɨɩɟɪɟɱɧɨɣ ɤɨɦɩɨɧɟɧɬɨɣ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ ɫɨɨɬɧɨɲɟɧɢɟɦ, ɤɨɬɨɪɨɟ ɮɚɤɬɢɱɟɫɤɢ ɧɟ ɫɢɥɶɧɨ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɩɪɟɞɵɞɭɳɟɝɨ:
E⊥′ j =
j⊥
σ⊥
.
(2.108ɛ)
ɇɨ ɞɥɹ ɩɪɨɬɟɤɚɧɢɹ ɬɨɤɚ ɩɨɩɟɪɟɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɭɠɧɚ ɫɨɫɬɚɜɥɹɸɳɚɹ ɷɮɮɟɤɬɢɜɧɨɝɨ ɩɨɥɹ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɚɹ ɢ ɤ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ, ɢ ɤ ɬɨɤɭ - ɷɬɨ ɬɚɤ ɧɚɡɵɜɚɟɦɨɟ ɯɨɥɥɨɜɫɤɨɟ ɩɨɥɟ:
ω Beτ ei & & & 1 && [ jB ] = [ jB ] . E ′ɏɨɥɥ = σ⊥ enc
(2.109)
Ɂɚɱɚɫɬɭɸ ɯɨɥɥɨɜɫɤɨɟ ɩɨɥɟ ɜɨɡɧɢɤɚɟɬ ɜ ɩɥɚɡɦɟ ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɡɚ ɫɱɟɬ ɧɟɛɨɥɶɲɨɝɨ ɧɚɪɭɲɟɧɢɹ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɢ, ɚ ɜɧɟɲɧɢɟ ɩɨɥɹ, ɤɨɬɨɪɵɟ ɧɚɞɨ ɩɪɢɤɥɚɞɵɜɚɬɶ ɤ ɩɥɚɡɦɟ, ɨɩɪɟɞɟɥɹɸɬɫɹ ɫɨɨɬɧɨɲɟɧɢɹɦɢ (2.108,ɚ) ɢ (2.108,ɛ). ɂɧɨɝɞɚ ɝɨɜɨɪɹɬ, ɱɬɨ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɧɟ ɜɥɢɹɟɬ ɧɚ ɩɪɨɜɨɞɢɦɨɫɬɶ ɩɥɚɡɦɵ. ɗɬɨ ɧɚɞɨ ɩɨɧɢɦɚɬɶ ɢɦɟɧɧɨ ɜ ɭɤɚɡɚɧɧɨɦ ɫɦɵɫɥɟ.
• Ⱦɪɟɣɮɨɜɵɟ ɬɨɤɢ. ȼɫɟɝɞɚ, ɤɨɝɞɚ ɜɨɡɧɢɤɚɟɬ ɝɪɚɞɢɟɧɬ ɞɚɜɥɟɧɢɹ, ɩɨɹɜɥɹɟɬɫɹ ɢ ɨɬɜɟɱɚɸɳɚɹ ɟɦɭ ɫɢɥɚ, ɜ & ɪɚɫɱɟɬɟ ɧɚ ɨɞɧɭ ɱɚɫɬɢɰɭ (ɷɥɟɤɬɪɨɧ ɢɥɢ ɢɨɧ), ɪɚɜɧɚɹ Fe ,i = −∇pe ,i / n . Ɉɧɚ ɜɵɡɵɜɚɟɬ ɞɪɟɣɮ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɫɨ ɫɤɨɪɨɫɬɶɸ & & & c B × ∇p c F×B & vd = = , (2.110) en B 2 e B2 ɩɪɢɱɟɦ ɱɚɫɬɢɰɵ ɫ ɡɚɪɹɞɚɦɢ ɪɚɡɧɵɯ ɡɧɚɤɨɜ ɞɪɟɣɮɭɸɬ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɟ ɫɬɨɪɨɧɵ. ɗɬɨ ɩɪɢɜɨɞɢɬ ɤ ɩɟɪɟɧɨɫɭ ɡɚɪɹɞɚ, ɬ.ɟ. ɤ ɩɪɨɜɨɞɢɦɨɫɬɢ, ɩɨɹɜɥɟɧɢɸ ɬɚɤ ɧɚɡɵɜɚɟɦɵɯ ɬɨɤɨɜ ɧɚɦɚɝɧɢɱɟɧɢɹ ɢɥɢ ɞɪɟɣɮɨɜɵɯ ɬɨɤɨɜ & B × ∇p & & . (2.111) j = ¦ nev d = c B2 e ,i
ɉɨɹɜɥɟɧɢɟ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɬɨɤɨɜ ɜɫɥɟɞɫɬɜɢɟ ɧɟɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɪɢɱɢɧ − ɫɩɟɰɢɮɢɱɟɫɤɚɹ ɨɫɨɛɟɧɧɨɫɬɶ ɩɥɚɡɦɵ, ɩɪɢɫɭɳɚɹ ɟɣ ɜɫɟɝɞɚ, ɤɨɝɞɚ ɟɫɬɶ ɤɚɤɢɟ-ɥɢɛɨ ɧɟɨɞɧɨɪɨɞɧɨɫɬɢ ɩɥɚɡɦɵ. & ɂɡ ɬɟɨɪɢɢ ɦɚɝɧɟɬɢɡɦɚ [15] ɢɡɜɟɫɬɧɨ, ɱɬɨ ɧɚɦɚɝɧɢɱɟɧɢɟ ɫɪɟɞɵ I ɢ ɩɥɨɬɧɨɫɬɶ ɦɨɥɟɤɭɥɹɪɧɵɯ ɬɨɤɨɜ & j µ ɫɜɹɡɚɧɵ ɫɨɨɬɧɨɲɟɧɢɟɦ & & jµ = c rot I . (2.112) & & ȼ ɩɥɚɡɦɟ ɧɚɦɚɝɧɢɱɟɧɢɟ ɪɚɜɧɨ ɫɭɦɦɟ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ ɱɚɫɬɢɰ ɜ ɟɞɢɧɢɰɟ ɨɛɴɟɦɚ: I = n < µ > ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (2.9),
& mv ⊥2 & I = −¦ n < > B. 2 B2 e ,i
(2.113)
Ɍɚɤ ɤɚɤ ɞɜɢɠɟɧɢɟ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɟ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ, ɢɦɟɟɬ ɞɜɟ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ, ɬɨ, ɩɪɨɢɡɜɨɞɹ ɭɫɪɟɞɧɟɧɢɟ, ɢ ɨɛɨɡɧɚɱɢɜ p⊥=nT⊥, ɩɨɥɭɱɚɟɦ
& p⊥ B & j = − c rot 2 . B
(2.114)
ȼ ɷɬɨɣ ɮɨɪɦɟ ɡɚɩɢɫɢ ɭɱɢɬɵɜɚɸɬɫɹ ɞɪɟɣɮɨɜɵɟ ɬɨɤɢ, ɜɨɡɧɢɤɚɸɳɢɟ ɜɫɥɟɞɫɬɜɢɟ ɝɪɚɞɢɟɧɬɚ ɩɥɨɬɧɨɫɬɢ ɢ ɝɪɚɞɢɟɧɬɚ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ȿɫɥɢ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɨɞɧɨɪɨɞɧɨ, ɬɨ ɮɨɪɦɭɥɚ (2.114) ɮɚɤɬɢɱɟɫɤɢ ɫɨɜɩɚɞɚɟɬ ɫ (2.111).
ȽɅȺȼȺ 3 ɆȺȽɇɂɌɈȽɂȾɊɈȾɂɇȺɆɂɑȿɋɄɂɃ ɆȿɌɈȾ ɈɉɂɋȺɇɂə ɉɅȺɁɆɕ § 21. ɂɞɟɚɥɶɧɚɹ ɨɞɧɨɠɢɞɤɨɫɬɧɚɹ ɝɢɞɪɨɞɢɧɚɦɢɤɚ ɩɥɚɡɦɵ. ɍɫɥɨɜɢɹ ɩɪɢɦɟɧɢɦɨɫɬɢ Ⱦɨ ɫɢɯ ɩɨɪ ɦɵ ɪɚɫɫɦɚɬɪɢɜɚɥɢ ɩɥɚɡɦɭ ɤɚɤ ɫɨɜɨɤɭɩɧɨɫɬɶ ɨɬɞɟɥɶɧɵɯ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɢ ɢɫɫɥɟɞɨɜɚɥɢ ɢɯ ɞɜɢɠɟɧɢɟ ɜ ɡɚɞɚɧɧɵɯ ɩɨɥɹɯ. Ɉɞɧɚɤɨ ɬɚɤɨɣ ɩɨɞɯɨɞ ɤ ɨɩɢɫɚɧɢɸ ɩɥɚɡɦɟɧɧɵɯ ɹɜɥɟɧɢɣ ɧɟ ɦɨɠɟɬ ɩɪɟɬɟɧɞɨɜɚɬɶ ɧɚ ɩɨɥɧɨɬɭ. ɉɪɢ ɞɜɢɠɟɧɢɢ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɜɨɡɧɢɤɚɸɬ ɬɨɤɢ ɢ ɨɬɜɟɱɚɸɳɟɟ ɢɦ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɜɥɢɹɸɳɟɟ ɧɚ ɞɜɢɠɟɧɢɟ ɱɚɫɬɢɰ, ɤɨɬɨɪɨɟ, ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɨɤɚɡɵɜɚɟɬɫɹ ɫɚɦɨɫɨɝɥɚɫɨɜɚɧɧɵɦ ɫ ɩɨɥɟɦ. ɉɥɚɡɦɭ ɫ ɷɬɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɫɩɥɨɲɧɭɸ ɫɪɟɞɭ, ɤɚɤ ɧɟɤɭɸ ɩɪɨɜɨɞɹɳɭɸ ɫɭɛɫɬɚɧɰɢɸ − ɩɪɨɜɨɞɹɳɢɣ ɝɚɡ. ȿɫɥɢ ɫɤɨɪɨɫɬɢ ɞɜɢɠɟɧɢɹ ɩɥɚɡɦɵ ɧɟ ɫɥɢɲɤɨɦ ɜɟɥɢɤɢ (ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɟ ɫɤɨɪɨɫɬɢ ɡɜɭɤɚ), ɬɨ ɪɨɥɶ ɫɠɢɦɚɟɦɨɫɬɢ ɷɬɨɣ ɫɭɛɫɬɚɧɰɢɢ ɧɟɡɧɚɱɢɬɟɥɶɧɚ, ɚ ɭɪɚɜɧɟɧɢɹ ɝɚɡɨɞɢɧɚɦɢɤɢ ɢ ɝɢɞɪɨɞɢɧɚɦɢɤɢ ɫɨɜɩɚɞɚɸɬ; ɬɨɝɞɚ ɩɥɚɡɦɭ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɩɪɨɜɨɞɹɳɭɸ ɠɢɞɤɨɫɬɶ. Ɍɚɤɨɣ ɩɨɞɯɨɞ ɤ ɨɩɢɫɚɧɢɸ ɞɢɧɚɦɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ ɜ ɩɥɚɡɦɟ ɩɨɥɭɱɢɥ ɧɚɡɜɚɧɢɟ ɦɚɝɧɢɬɧɨɣ ɝɢɞɪɨɞɢɧɚɦɢɤɢ ɢɥɢ ɫɨɤɪɚɳɟɧɧɨ ɆȽȾ. ȼɩɟɪɜɵɟ ɨɧ ɛɵɥ ɩɪɟɞɥɨɠɟɧ ɜ ɫɨɪɨɤɨɜɵɯ ɝɨɞɚɯ ɞɜɚɞɰɚɬɨɝɨ ɫɬɨɥɟɬɢɹ Ⱥɥɶɜɟɧɨɦ ɩɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɞɢɧɚɦɢɤɟ ɤɨɫɦɢɱɟɫɤɨɣ ɩɥɚɡɦɵ. ɉɨɜɟɞɟɧɢɟ ɩɪɨɜɨɞɹɳɟɣ ɠɢɞɤɨɫɬɢ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɜ ɛɨɥɶɲɨɣ ɫɬɟɩɟɧɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɟɟ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɜɨɞɢɦɨɫɬɶɸ, ɢɦɟɧɧɨ ɨɧɚ ɨɛɭɫɥɚɜɥɢɜɚɟɬ ɫɤɨɪɨɫɬɶ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɩɪɨɜɨɞɧɢɤ. ȼ ɢɞɟɚɥɶɧɵɣ ɩɪɨɜɨɞɧɢɤ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɤɚɤ ɢɡɜɟɫɬɧɨ, ɜɨɨɛɳɟ ɧɟ ɦɨɠɟɬ ɩɪɨɧɢɤɧɭɬɶ. Ɉɞɧɚɤɨ ɟɫɥɢ ɜ ɩɪɨɜɨɞɧɢɤɟ ɭɠɟ ɟɫɬɶ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɬɨ ɷɬɨ ɩɨɥɟ ɛɭɞɟɬ “ɜɦɨɪɨɠɟɧɨ” ɜ ɧɟɝɨ − ɩɪɢ ɫɜɨɟɦ ɞɜɢɠɟɧɢɢ ɩɪɨɜɨɞɧɢɤ ɭɜɥɟɱɟɬ ɡɚ ɫɨɛɨɣ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ. Ɋɟɚɥɶɧɨ ɩɥɚɡɦɚ ɜɫɟɝɞɚ ɢɦɟɟɬ ɤɨɧɟɱɧɭɸ ɩɪɨɜɨɞɢɦɨɫɬɶ, ɧɨ ɟɫɥɢ ɢɧɬɟɪɟɫɭɸɳɢɟ ɧɚɫ ɩɪɨɰɟɫɫɵ ɩɪɨɬɟɤɚɸɬ ɛɵɫɬɪɨ, ɡɚ ɜɪɟɦɟɧɚ, ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɢɟ ɜɪɟɦɟɧɢ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɩɥɚɡɦɭ, ɬɨ ɩɥɚɡɦɭ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɢɞɟɚɥɶɧɵɣ ɩɪɨɜɨɞɧɢɤ. Ʉɚɤ ɢɡɜɟɫɬɧɨ [15], ɜɪɟɦɹ τs (ɬɚɤ ɧɚɡɵɜɚɟɦɨɟ ɫɤɢɧɨɜɨɟ ɜɪɟɦɹ) ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɩɨɥɹ ɧɚ ɡɚɞɚɧɧɭɸ ɝɥɭɛɢɧɭ δ ɜ ɩɪɨɜɨɞɧɢɤɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ δ2 4πσ τs = 2 δ 2 = , (3.1) c Dɦɚɝ ɝɞɟ σ - ɩɪɨɜɨɞɢɦɨɫɬɶ; c2 Dɦɚɝ = (3.2) 4πσ ɤɨɷɮɮɢɰɢɟɧɬ ɦɚɝɧɢɬɧɨɣ ɞɢɮɮɭɡɢɢ ɩɨɥɹ ɜ ɩɪɨɜɨɞɧɢɤ. Ⱦɥɹ ɜɪɟɦɟɧ t<<τs ɩɥɚɡɦɭ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɢɞɟɚɥɶɧɵɣ ɩɪɨɜɨɞɧɢɤ ɫ ɜɦɨɪɨɠɟɧɧɵɦ ɜ ɧɟɝɨ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɨɞɧɨ ɢɡ ɭɫɥɨɜɢɣ ɩɪɢɦɟɧɢɦɨɫɬɢ ɩɪɢɛɥɢɠɟɧɢɹ ɢɞɟɚɥɶɧɨɣ ɝɢɞɪɨɞɢɧɚɦɢɤɢ ɤ ɩɥɚɡɦɟ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ ɞɥɢɬɟɥɶɧɨɫɬɶ ɩɪɨɰɟɫɫɚ t ɞɨɥɠɧɚ ɛɵɬɶ ɦɟɧɶɲɟ ɫɤɢɧɨɜɨɝɨ ɜɪɟɦɟɧɢ τs. Ʉɪɨɦɟ ɬɨɝɨ, ɦɚɝɧɢɬɧɭɸ ɝɢɞɪɨɞɢɧɚɦɢɤɭ ɨɛɵɱɧɨ ɩɪɢɦɟɧɹɸɬ ɤ ɨɩɢɫɚɧɢɸ ɩɥɚɡɦɵ ɜ ɞɨɫɬɚɬɨɱɧɨ ɫɢɥɶɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɢ ɜɥɢɹɧɢɟɦ ɤɨɧɟɱɧɨɫɬɢ ɥɚɪɦɨɪɨɜɫɤɨɝɨ ɪɚɞɢɭɫɚ ɩɪɟɧɟɛɪɟɝɚɸɬ. ɗɬɨ ɜɨɡɦɨɠɧɨ, ɟɫɥɢ ɯɚɪɚɤɬɟɪɧɵɣ ɪɚɡɦɟɪ ɨɛɥɚɫɬɢ, ɡɚɧɹɬɨɣ ɩɥɚɡɦɨɣ, L ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ ɥɚɪɦɨɪɨɜɫɤɨɝɨ ɪɚɞɢɭɫɚ ɢɨɧɚ. ɇɚɤɨɧɟɰ, ɧɟɨɛɯɨɞɢɦɨ ɨɛɟɫɩɟɱɢɬɶ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɶ ɩɥɚɡɦɵ. ȼɫɟ ɷɬɢ ɭɫɥɨɜɢɹ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ t<<τs, (3.3) L>>ρi Zni-ne=0.
ɍɫɬɚɧɨɜɢɜ ɬɚɤɢɟ ɨɝɪɚɧɢɱɟɧɢɹ (ɧɚ ɫɚɦɨɦ ɞɟɥɟ, ɨɧɢ ɛɨɥɟɟ ɠɟɫɬɤɢɟ), ɦɨɠɧɨ ɩɪɢɦɟɧɢɬɶ ɞɥɹ ɨɩɢɫɚɧɢɹ ɞɢɧɚɦɢɤɢ ɩɥɚɡɦɵ ɭɪɚɜɧɟɧɢɹ ɦɚɝɧɢɬɧɨɣ ɝɢɞɪɨɞɢɧɚɦɢɤɢ, ɞɨɩɨɥɧɟɧɧɵɟ ɭɪɚɜɧɟɧɢɹɦɢ Ɇɚɤɫɜɟɥɥɚ. Ɇɚɝɧɢɬɨɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɩɥɚɡɦɵ ɦɨɠɟɬ ɛɵɬɶ ɪɚɫɲɢɪɟɧɨ ɪɚɫɫɦɨɬɪɟɧɢɟɦ ɧɟ ɨɞɧɨɤɨɦɩɨɧɟɧɬɧɨɣ ɩɪɨɜɨɞɹɳɟɣ ɠɢɞɤɨɫɬɢ, ɚ ɫɦɟɫɢ ɞɜɭɯ ɤɨɦɩɨɧɟɧɬ − ɷɥɟɤɬɪɨɧɧɨɣ ɢ ɢɨɧɧɨɣ. Ɍɚɤɨɟ ɨɛɨɛɳɟɧɢɟ ɫɬɚɧɨɜɢɬɫɹ ɧɟɨɛɯɨɞɢɦɵɦ, ɤɨɝɞɚ ɜ ɩɥɚɡɦɟ ɩɪɨɬɟɤɚɟɬ ɬɨɤ ɫ ɡɚɦɟɬɧɨɣ ɩɥɨɬɧɨɫɬɶɸ ɢ ɭɠɟ ɧɟɥɶɡɹ ɫɱɢɬɚɬɶ, ɱɬɨ ɫɤɨɪɨɫɬɢ ɤɨɦɩɨɧɟɧɬ ɩɥɚɡɦɵ ɫɨɜɩɚɞɚɸɬ, ɤɚɤ ɷɬɨ ɩɪɢɧɹɬɨ ɜ ɨɞɧɨɠɢɞɤɨɫɬɧɨɣ ɝɢɞɪɨɞɢɧɚɦɢɤɟ. Ⱦɜɭɯɠɢɞɤɨɫɬɧɨɟ ɪɚɫɫɦɨɬɪɟɧɢɟ ɪɚɫɲɢɪɹɟɬ ɜɨɡɦɨɠɧɨɫɬɢ ɦɟɬɨɞɚ, ɨɞɧɚɤɨ, ɧɚ ɩɪɚɤɬɢɤɟ ɩɪɢɯɨɞɢɬɫɹ ɩɨɥɶɡɨɜɚɬɶɫɹ ɢ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢɦɢ ɢ ɤɢɧɟɬɢɱɟɫɤɢɦɢ ɩɪɟɞɫɬɚɜɥɟɧɢɹɦɢ ɫɨɜɦɟɫɬɧɨ, ɬɚɤ ɤɚɤ ɝɢɞɪɨɞɢɧɚɦɢɤɚ ɧɟ ɦɨɠɟɬ ɨɬɪɚɡɢɬɶ ɧɟɤɨɬɨɪɵɟ ɫɭɳɟɫɬɜɟɧɧɵɟ ɫɬɨɪɨɧɵ ɩɪɨɰɟɫɫɚ.
§ 22. Ɉɫɧɨɜɧɵɟ ɭɪɚɜɧɟɧɢɹ Ɉɫɧɨɜɭ ɥɸɛɨɣ ɝɢɞɪɨɞɢɧɚɦɢɤɢ ɫɨɫɬɚɜɥɹɸɬ ɬɪɢ ɡɚɤɨɧɚ ɫɨɯɪɚɧɟɧɢɹ − ɦɚɫɫɵ, ɢɦɩɭɥɶɫɚ ɢ ɷɧɟɪɝɢɢ. ɉɪɢ ɷɬɨɦ ɨɫɧɨɜɧɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɦɢ ɞɜɢɠɟɧɢɟ ɫɪɟɞɵ, ɹɜɥɹɸɬɫɹ ɦɚɫɫɨɜɚɹ ɩɥɨɬɧɨɫɬɶ, ɦɚɫɫɨɜɚɹ ɫɤɨɪɨɫɬɶ ɢ ɞɚɜɥɟɧɢɟ, ɡɚɜɢɫɹɳɢɟ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɨɬ ɜɪɟɦɟɧɢ ɢ ɤɨɨɪɞɢɧɚɬ. ȼ ɦɚɝɧɢɬɧɨɣ ɝɢɞɪɨɞɢɧɚɦɢɤɟ, ɤɪɨɦɟ ɬɨɝɨ, ɜɜɨɞɹɬ ɩɥɨɬɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ ɢ ɜɟɤɬɨɪ ɢɧɞɭɤɰɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. Ⱦɥɹ ɢɯ ɨɩɪɟɞɟɥɟɧɢɹ ɭɪɚɜɧɟɧɢɹ ɞɢɧɚɦɢɤɢ ɩɪɨɜɨɞɹɳɟɣ ɫɪɟɞɵ ɞɨɩɨɥɧɹɸɬ ɭɪɚɜɧɟɧɢɹɦɢ Ɇɚɤɫɜɟɥɥɚ. ȼɜɟɞɟɦ ɫɥɟɞɭɸɳɢɟ ɨɛɨɡɧɚɱɟɧɢɹ: • ɩɥɨɬɧɨɫɬɶ ɦɚɫɫɵ ρ = ¦ nα mα = ¦ ni mi , (α )
i
ɡɞɟɫɶ α - ɢɧɞɟɤɫ ɫɨɪɬɚ ɱɚɫɬɢɰ (ɷɥɟɤɬɪɨɧɵ, ɢɨɧɵ). Ɍɚɤ ɤɚɤ ɦɚɫɫɚ ɢɨɧɚ ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɨɫɯɨɞɢɬ ɦɚɫɫɭ ɷɥɟɤɬɪɨɧɚ, mi>>me ɬɨ ɜɤɥɚɞɨɦ ɦɚɫɫɵ ɷɥɟɤɬɪɨɧɨɜ ɜ ɩɥɨɬɧɨɫɬɶ ρ ɨɛɵɱɧɨ ɩɪɟɧɟɛɪɟɝɚɸɬ; • ɦɚɫɫɨɜɚɹ ɫɤɨɪɨɫɬɶ & 1 & & v = ¦ nα mα vα ≈ v i ,
ρ (α )
ɩɨ ɬɨɣ ɠɟ ɩɪɢɱɢɧɟ ɩɪɢɦɟɪɧɨ ɪɚɜɧɚ ɫɤɨɪɨɫɬɢ ɢɨɧɧɨɣ ɤɨɦɩɨɧɟɧɬɵ; • ɩɥɨɬɧɨɫɬɶ ɡɚɪɹɞɚ ρq = ¦ nα qα = | e|( zni − ne ) , (α )
ɝɞɟ |e| - ɚɛɫɨɥɸɬɧɚɹ ɜɟɥɢɱɢɧɚ ɡɚɪɹɞɚ ɷɥɟɤɬɪɨɧɚ; • ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ & & j = ¦ nα qα vα . (α )
ȿɫɥɢ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɫɤɨɪɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ve ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɨɫɯɨɞɢɬ ɫɤɨɪɨɫɬɶ ɢɨɧɨɜ vi, ɬɨ & & j = −| e| ne v e . ɂɫɩɨɥɶɡɭɹ ɩɪɢɧɹɬɵɟ ɨɛɨɡɧɚɱɟɧɢɹ, ɡɚɩɢɲɟɦ: • Ɂɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɦɚɫɫɵ (ɧɟɪɚɡɪɵɜɧɨɫɬɢ ɫɬɪɭɢ): ∂ρ & + div( ρv ) = 0 . (3.4) ∂t • ɍɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɟɞɢɧɢɰɵ ɨɛɴɟɦɚ ɩɥɚɡɦɵ (ɫɨɯɪɚɧɟɧɢɹ ɢɦɩɭɥɶɫɚ): & & dv 1 & & = j × B − ∇p + F , ρ (3.5) dt c ɝɞɟ p=pe+pi - ɩɨɥɧɨɟ ɞɚɜɥɟɧɢɟ ɩɥɚɡɦɵ, ɪɚɜɧɨɟ ɫɭɦɦɟ ɞɚɜɥɟɧɢɣ ɷɥɟɤɬɪɨɧɨɜ ɢ & & & dv ∂ v & & ɢɨɧɨɜ, F - ɜɧɟɲɧɹɹ ɫɢɥɚ (ɧɚɩɪɢɦɟɪ, ɫɢɥɚ ɬɹɠɟɫɬɢ), = + ( v ∇ )v − ɩɨɥɧɚɹ dt ∂ t ɩɪɨɢɡɜɨɞɧɚɹ (ɬɚɤ ɧɚɡɵɜɚɟɦɚɹ ɫɭɛɫɬɚɰɢɨɧɚɥɶɧɚɹ ɩɪɨɢɡɜɨɞɧɚɹ) ɩɨ ɜɪɟɦɟɧɢ ɨɬ ɫɤɨɪɨɫɬɢ ɩɥɚɡɦɵ. ɍɪɚɜɧɟɧɢɟ (3.5) ɦɨɠɟɬ ɛɵɬɶ ɩɨɥɭɱɟɧɨ ɫɭɦɦɢɪɨɜɚɧɢɟɦ ɭɪɚɜɧɟɧɢɣ ɞɜɢɠɟɧɢɹ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ (ɫɦ. ɮɨɪɦɭɥɭ (2.1)) ɫ ɩɨɫɥɟɞɭɸɳɢɦ ɩɪɟɧɟɛɪɟɠɟɧɢɟɦ ɤɨɧɟɱɧɨɫɬɶɸ ɢɧɟɪɰɢɢ ɷɥɟɤɬɪɨɧɨɜ. ȼɨ ɦɧɨɝɢɯ ɤɨɧɤɪɟɬɧɵɯ ɫɥɭɱɚɹɯ ɜ ɭɪɚɜɧɟɧɢɢ (3.5) ɫɢɥɨɣ F ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ.
• ɍɪɚɜɧɟɧɢɹ & Ɇɚɤɫɜɟɥɥɚ: div E = 4πρq = 4π| e|( zni − ne ) ; & div B = 0 ; (3.6) & & 1 ∂B rot E = − ; c ∂t & 4π & rot B = j. c ɉɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɜɫɟ ɩɪɨɰɟɫɫɵ ɦɟɞɥɟɧɧɵɟ ɢ ɬɨɤɚɦɢ ɫɦɟɳɟɧɢɹ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ, ɱɬɨ ɢ ɢɫɩɨɥɶɡɨɜɚɧɨ ɜ ɩɨɫɥɟɞɧɟɦ ɢɡ ɭɪɚɜɧɟɧɢɣ (3.6). • Ɂɚɤɨɧ Ɉɦɚ (ɫɨɝɥɚɫɧɨ ɪɚɛɨɬɟ [13]): & & j || & j⊥ 1 & & (3.7) j ×B, + + E′ = σ ⊥ σ|| cne| e| ɝɞɟ ȿ′ - ɷɮɮɟɤɬɢɜɧɨɟ ɩɨɥɟ, ɨɛɭɫɥɨɜɥɟɧɧɨɟ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɧɟ ɬɨɥɶɤɨ ɩɪɢɥɨɠɟɧɧɨɣ ɜɧɟɲɧɟɣ ɗȾɋ, ɧɨ ɢ ɫɚɦɢɦ ɞɜɢɠɟɧɢɟɦ ɩɥɚɡɦɵ, ɚ ɬɚɤɠɟ ɧɚɥɢɱɢɟɦ ɷɥɟɤɬɪɨɧɧɨɝɨ ɞɚɜɥɟɧɢɹ ɢ ɩɟɪɟɩɚɞɚ ɷɥɟɤɬɪɨɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ; σ||,⊥ - ɩɪɨɞɨɥɶɧɚɹ ɢ ɩɨɩɟɪɟɱɧɚɹ (ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ) ɩɪɨɜɨɞɢɦɨɫɬɶ 1 & & j × B - ɯɨɥɥɨɜɫɤɨɟ ɩɨɥɟ. ɩɥɚɡɦɵ; cne| e| ɍɩɨɬɪɟɛɢɬɟɥɶɧɨ ɧɟɫɤɨɥɶɤɨ ɪɚɡɥɢɱɧɵɯ ɮɨɪɦ ɡɚɩɢɫɢ ɡɚɤɨɧɚ Ɉɦɚ ɞɥɹ ɩɥɚɡɦɵ. ɗɬɨ ɫɜɹɡɚɧɨ ɫ ɬɟɦ, ɱɬɨ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɤɨɧɤɪɟɬɧɵɯ ɭɫɥɨɜɢɣ ɦɨɠɟɬ ɨɤɚɡɚɬɶɫɹ ɧɚɢɛɨɥɟɟ ɫɭɳɟɫɬɜɟɧɧɨɣ ɬɚ ɢɥɢ ɢɧɚɹ ɩɪɢɱɢɧɚ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɗȾɋ (ɩɨɞɪɨɛɧɟɟ ɫɦ.[13]). ɑɚɫɬɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɫɥɟɞɭɸɳɚɹ ɭɩɪɨɳɟɧɧɚɹ ɮɨɪɦɚ ɡɚɩɢɫɢ ɡɚɤɨɧɚ Ɉɦɚ: & 1 & & ½ 1 & & 1 & j = σ ®E + v × B − j ×B+ ∇pe ¾ . (3.8) c n| e| c n| e| ¯ ¿ • ɍɪɚɜɧɟɧɢɟ ɫɨɫɬɨɹɧɢɹ - ɷɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɜɢɞɚ: p = p( ρ ,T ) . (3.9) ɍɪɚɜɧɟɧɢɟ ɫɨɫɬɨɹɧɢɹ ɩɪɢɨɛɪɟɬɚɟɬ ɩɪɨɫɬɨɣ ɜɢɞ, ɟɫɥɢ ɩɥɚɡɦɭ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɢɞɟɚɥɶɧɨɣ. Ⱦɥɹ ɤɥɚɫɫɢɱɟɫɤɨɝɨ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ, ɤɚɤ ɢɡɜɟɫɬɧɨ, ɭɪɚɜɧɟɧɢɟ ɫɨɫɬɨɹɧɢɹ ɪ = nT. ɝɞɟ n – ɤɨɧɰɟɧɬɪɚɰɢɹ (ɩɥɨɬɧɨɫɬɶ ɱɢɫɥɚ ɱɚɫɬɢɰ) ɝɚɡɚ. Ⱦɥɹ ɫɦɟɫɢ ɞɜɭɯ ɢɞɟɚɥɶɧɵɯ «ɝɚɡɚ» ɷɥɟɤɬɪɨɧɨɜ ɫ ɤɨɧɰɟɧɬɪɚɰɢɟɣ ne ɢ «ɝɚɡɚ» ɢɨɧɨɜ ɫ «ɝɚɡɨɜ» − ɤɨɧɰɟɧɬɪɚɰɢɟɣ ni p = neTe+niTi. ȼ ɱɚɫɬɧɨɦ ɫɥɭɱɚɟ ɢɞɟɚɥɶɧɨɣ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɣ ɢɡɨɬɟɪɦɢɱɟɫɤɨɣ ɩɥɚɡɦɵ, ɤɨɝɞɚ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɤɨɧɰɟɧɬɪɚɰɢɢ ɟɟ ɤɨɦɩɨɧɟɧɬ ɫɨɜɩɚɞɚɸɬ Te=Ti=Ɍ, ne=ni=n, ɷɬɨ ɭɪɚɜɧɟɧɢɟ ɩɪɢɨɛɪɟɬɚɟɬ ɨɫɨɛɟɧɧɨ ɩɪɨɫɬɨɣ ɜɢɞ p = 2nT. (3.10) ɇɨ ɬɟɩɟɪɶ ɜ ɭɪɚɜɧɟɧɢɹɯ ɞɢɧɚɦɢɤɢ ɩɥɚɡɦɵ ɩɨɹɜɥɹɟɬɫɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɣ ɩɚɪɚɦɟɬɪ − ɬɟɦɩɟɪɚɬɭɪɚ, ɢ ɧɟɨɛɯɨɞɢɦɨ ɭɤɚɡɚɬɶ ɩɪɚɜɢɥɨ ɟɝɨ ɜɵɱɢɫɥɟɧɢɹ, ɜɵɪɚɠɚɸɳɟɟ ɛɚɥɚɧɫ ɬɟɩɥɚ. ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɷɬɨ ɞɨɫɬɚɬɨɱɧɨ ɫɥɨɠɧɨɟ ɭɪɚɜɧɟɧɢɟ, ɭɱɢɬɵɜɚɸɳɟɟ ɤɨɧɟɱɧɭɸ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ ɩɥɚɡɦɵ, ɜɹɡɤɨɟ ɬɟɩɥɨɜɵɞɟɥɟɧɢɟ, ɞɠɨɭɥɟɜɨ ɬɟɩɥɨ, ɨɛɭɫɥɨɜɥɟɧɧɨɟ ɩɪɨɬɟɤɚɧɢɟɦ ɩɨ ɩɥɚɡɦɟ ɬɨɤɚ ɢ ɞɪɭɝɢɟ ɢɫɬɨɱɧɢɤɢ ɧɚɝɪɟɜɚ ɢɥɢ ɨɯɥɚɠɞɟɧɢɹ ɩɥɚɡɦɵ. Ɇɵ ɧɟ ɛɭɞɟɦ ɟɝɨ ɜɵɩɢɫɵɜɚɬɶ, ɞɟɬɚɥɶɧɵɣ ɚɧɚɥɢɡ ɛɚɥɚɧɫɚ ɬɟɩɥɚ ɜ ɩɥɚɡɦɟ ɦɨɠɧɨ ɧɚɣɬɢ, ɧɚɩɪɢɦɟɪ, ɜ [13].
ɉɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɨɞɧɨɠɢɞɤɨɫɬɧɨɣ ɦɚɝɧɢɬɧɨɣ ɝɢɞɪɨɞɢɧɚɦɢɤɟ ɜ ɤɨɧɤɪɟɬɧɵɯ ɩɪɢɥɨɠɟɧɢɹɯ ɱɚɫɬɨ ɢɫɩɨɥɶɡɭɸɬɫɹ ɪɚɡɥɢɱɧɵɟ ɭɩɪɨɳɟɧɧɵɟ ɩɨɞɯɨɞɵ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɦɟɞɥɟɧɧɵɯ, ɫɭɳɟɫɬɜɟɧɧɨ ɞɨɡɜɭɤɨɜɵɯ, ɬɟɱɟɧɢɣ, ɩɥɚɡɦɭ ɩɪɢɛɥɢɠɟɧɧɨ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɧɟɫɠɢɦɚɟɦɨɣ, ρ=const , ɢ ɬɨɝɞɚ, ɫɨɝɥɚɫɧɨ ɭɪɚɜɧɟɧɢɸ ɧɟɪɚɡɪɵɜɧɨɫɬɢ (3.4), ɬɟɱɟɧɢɟ ɩɥɚɡɦɵ ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɫɥɨɜɢɸ & divv = 0 , ɚ ɞɚɜɥɟɧɢɟ ɩɥɚɡɦɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɫɥɨɜɢɟɦ ɫɨɜɦɟɫɬɢɦɨɫɬɢ ɞɢɧɚɦɢɱɟɫɤɢɯ ɭɪɚɜɧɟɧɢɣ. ȼ ɭɫɥɨɜɢɹɯ, ɤɨɝɞɚ ɬɟɩɥɨɨɛɦɟɧ ɫ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɨɣ ɧɟɫɭɳɟɫɬɜɟɧ, ɢɫɩɨɥɶɡɭɟɬɫɹ ɚɞɢɚɛɚɬɢɱɟɫɤɢɣ ɡɚɤɨɧɚ ɜɢɞɚ p ~ ρ γ . ɉɪɢ ɷɬɨɦ ɢɡɦɟɧɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɫɥɟɞɭɟɬ ɫɨɨɬɧɨɲɟɧɢɸ T ~ ρ γ −1 . Ɂɞɟɫɶ γ − ɩɨɤɚɡɚɬɟɥɶ ɚɞɢɚɛɚɬɵ, ɧɚɩɪɢɦɟɪ, ɞɥɹ ɦɨɞɟɥɢ ɨɞɧɨɚɬɨɦɧɨɝɨ ɝɚɡɚ ɪɚɜɧɵɣ γ=5/3. ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ, ɧɚɩɨɦɧɢɦ, γ = 1 + 2 N , ɝɞɟ N=1,2,3… - ɱɢɫɥɨ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ. ɂɫɩɨɥɶɡɭɹ ɩɪɢɜɟɞɟɧɧɵɟ ɭɪɚɜɧɟɧɢɹ ɦɚɝɧɢɬɧɨɣ ɝɢɞɪɨɞɢɧɚɦɢɤɢ, ɦɨɠɧɨ ɨɩɢɫɚɬɶ ɩɨɜɟɞɟɧɢɟ ɩɥɚɡɦɵ ɜɨ ɦɧɨɝɢɯ ɜɟɫɶɦɚ ɫɥɨɠɧɵɯ ɫɥɭɱɚɹɯ. ɇɟɫɨɦɧɟɧɧɵɦ ɩɪɟɢɦɭɳɟɫɬɜɨɦ ɬɚɤɨɝɨ ɩɨɞɯɨɞɚ ɤ ɨɩɢɫɚɧɢɸ ɩɥɚɡɦɵ ɹɜɥɹɟɬɫɹ ɟɝɨ ɫɪɚɜɧɢɬɟɥɶɧɚɹ ɩɪɨɫɬɨɬɚ ɢ ɧɚɝɥɹɞɧɨɫɬɶ. ɂɧɨɝɞɚ ɷɬɨ ɨɱɟɧɶ ɜɚɠɧɨ, ɧɚɩɪɢɦɟɪ, ɩɪɢ ɨɩɢɫɚɧɢɢ ɞɢɧɚɦɢɤɢ ɬɨɤɨɜɵɯ ɫɢɫɬɟɦ. ɉɪɢ ɷɬɨɦ, ɤɨɧɟɱɧɨ, ɜ ɤɚɠɞɨɦ ɤɨɧɤɪɟɬɧɨɦ ɫɥɭɱɚɟ, ɢɫɩɨɥɶɡɭɹ ɭɪɚɜɧɟɧɢɹ ɦɚɝɧɢɬɧɨɣ ɝɢɞɪɨɞɢɧɚɦɢɤɢ ɩɥɚɡɦɵ, ɧɟɨɛɯɨɞɢɦɨ ɢɦɟɬɶ ɜ ɜɢɞɭ ɭɫɥɨɜɢɹ (3.3) ɩɪɢɦɟɧɢɦɨɫɬɢ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɩɪɟɞɫɬɚɜɥɟɧɢɣ.
§ 23. Ɇɚɝɧɢɬɧɨɟ ɞɚɜɥɟɧɢɟ ȼɟɫɶɦɚ ɜɚɠɧɵɟ ɜɵɜɨɞɵ ɨɛɳɟɝɨ ɯɚɪɚɤɬɟɪɚ ɦɨɝɭɬ ɛɵɬɶ ɩɨɥɭɱɟɧɵ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɢɡ ɚɧɚɥɢɡɚ ɭɪɚɜɧɟɧɢɣ (3.4) ɢ&(3.5). ȼ ɩɪɟɧɟɛɪɟɠɟɧɢɢ ɜɧɟɲɧɢɦɢ ɫɢɥɚɦɢ F , ɞɜɢɠɟɧɢɟ ɩɥɚɡɦɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɢɥɨɣ Ⱥɦɩɟɪɚ (ɢɧɚɱɟ ɧɚɡɵɜɚɟɦɨɣ ɩɨɧɞɟɪɨɦɨɬɨɪɧɨɣ ɫɢɥɨɣ) ɢ ɝɪɚɞɢɟɧɬɨɦ ɝɚɡɨɤɢɧɟɬɢɱɟɫɤɨɝɨ ɞɚɜɥɟɧɢɹ & dv 1 & & = j × B − ∇p . ρ (3.11) dt c ɂɫɩɨɥɶɡɭɹ ɢɡɜɟɫɬɧɨɟ ɬɨɠɞɟɫɬɜɨ ɢɡ ɜɟɤɬɨɪɧɨɝɨ ɚɧɚɥɢɡɚ, ɫɩɪɚɜɟɞɥɢɜɨɟ ɞɥɹ ɞɜɭɯ & & ɥɸɛɵɯ ɜɟɤɬɨɪɨɜ a ɢ b , & & && & & & & & & ∇( ab ) = ( a∇ )b + ( b ∇ )a + a × rotb + b × rota , ɢ ɭɪɚɜɧɟɧɢɟ (3.6), ɩɨɧɞɟɪɨɦɨɬɨɪɧɭɸ ɫɢɥɭ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ: & & 1& & 1 1 & & B2 + ( B∇ )B ≡ − ∇ ⋅ p ɦɚɝ . (3.12) j×B= rotB × B = − ∇ 4π 8π 4π c ɝɞɟ ^ B2 p ɦɚɝ = (3.13) ( δ − 2 ττ ), 8π & & B − ɟɞɢɧɢɱɧɵɣ ɬɟɧɡɨɪ ɦɚɝɧɢɬɧɨɝɨ ɞɚɜɥɟɧɢɹ; δ - ɟɞɢɧɢɱɧɚɹ ɦɚɬɪɢɰɚ, ɚ τ = B ɜɟɤɬɨɪ, ɧɚɩɪɚɜɥɟɧɧɵɣ ɩɨ ɤɚɫɚɬɟɥɶɧɨɣ ɤ ɫɢɥɨɜɨɣ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ȼ & ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ ɫ ɨɫɶɸ z, ɧɚɩɪɚɜɥɟɧɧɨɣ ɜɞɨɥɶ ɜɟɤɬɨɪɚ B , ɷɬɨɬ ɬɟɧɡɨɪ ɡɚɩɢɫɵɜɚɟɬɫɹ ɜ ɜɢɞɟ ɫɥɟɞɭɸɳɟɣ ɞɢɚɝɨɧɚɥɶɧɨɣ ɬɚɛɥɢɰɵ: § B2 · 0 0 ¸ ¨ ¸ ¨ 8π 2 B ¨ 0 ¸¸ . (3.14) p ɦɚɝ = ¨ 0 8π ¨ B2 ¸ ¸ ¨ 0 0 − 8π ¹ © Ɂɧɚɤ ɤɨɦɩɨɧɟɧɬ ɬɟɧɡɨɪɚ ɦɚɝɧɢɬɧɨɝɨ ɞɚɜɥɟɧɢɹ ɧɟ ɫɥɭɱɚɟɧ: ɩɨɩɟɪɟɱɧɵɟ ɤɨɦɩɨɧɟɧɬɵ ɩɨɥɨɠɢɬɟɥɶɧɵ, ɱɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɪɚɫɬɚɥɤɢɜɚɧɢɸ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɩɨɩɟɪɟɱɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ, ɬɨɝɞɚ ɤɚɤ ɩɪɨɞɨɥɶɧɚɹ ɤɨɦɩɨɧɟɧɬɚ ɷɬɨɝɨ ɬɟɧɡɨɪɚ ɨɬɪɢɰɚɬɟɥɶɧɚ − ɜ ɩɪɨɞɨɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɫɢɥɨɜɵɟ ɥɢɧɢɢ ɧɚɬɹɧɭɬɵ. ȼɟɥɢɱɢɧɭ B2 pm = (3.15) 8π ɨɛɵɱɧɨ ɧɚɡɵɜɚɸɬ ɦɚɝɧɢɬɧɵɦ ɞɚɜɥɟɧɢɟɦ. ɉɨɥɟɡɧɨ ɬɚɤ ɩɟɪɟɩɢɫɚɬɶ ɫɨɨɬɧɨɲɟɧɢɟ (3.12), ɱɬɨɛɵ ɪɚɫɬɚɥɤɢɜɚɧɢɟ ɢ ɧɚɬɹɠɟɧɢɟ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɩɪɨɹɜɥɹɥɢɫɶ ɜ ɧɟɦ ɟɳɟ ɛɨɥɟɟ ɹɜɧɨ. Ⱦɥɹ ɷɬɨɝɨ, ɩɨɥɶɡɭɹɫɶ ɨɩɪɟɞɟɥɟɧɢɟɦ ɤɚɫɚɬɟɥɶɧɨɝɨ ɜɟɤɬɨɪɚ, ɡɚɩɢɲɟɦ
& & & & & & & & ( B∇ )B = ( Bτ ∇ )( Bτ ) = B 2 ( τ ∇ )τ + Bτ ( τ ∇B ) .
ɍɱɢɬɵɜɚɹ, ɞɚɥɟɟ, ɱɬɨ ɩɨ ɨɩɪɟɞɟɥɟɧɢɸ
&
& & & n ( τ ∇ )τ = , R
ɝɞɟ n - ɧɨɪɦɚɥɶ ɤ ɫɢɥɨɜɨɣ ɥɢɧɢɢ, ɚ
R - ɪɚɞɢɭɫ ɟɟ ɤɪɢɜɢɡɧɵ, ɩɨɥɭɱɢɦ
1& & B2 B2 & + n, j × B = −∇ ⊥ c 8π 4πR
(3.16)
ɝɞɟ ɨɛɨɡɧɚɱɟɧɨ ɞɥɹ ɤɪɚɬɤɨɫɬɢ & & ∇⊥ = ∇ − τ ( τ ∇ ) . ɉɟɪɜɨɟ ɫɥɚɝɚɟɦɨɟ ɜ (3.16) ɨɬɜɟɱɚɟɬ ɮɚɪɚɞɟɟɜɫɤɨɦɭ “ɪɚɫɬɚɥɤɢɜɚɧɢɸ”, ɚ ɜɬɨɪɨɟ, ɫɜɹɡɚɧɧɨɟ ɫ ɢɫɤɪɢɜɥɟɧɢɟɦ ɦɚɝɧɢɬɧɨɣ ɫɢɥɨɜɨɣ ɥɢɧɢɢ, ɨɩɢɫɵɜɚɟɬ ɜɥɢɹɧɢɟ ɧɚɬɹɠɟɧɢɹ ɦɚɝɧɢɬɧɵɯ ɫɢɥɨɜɵɯ ɥɢɧɢɣ, ɢɥɢ ɮɚɪɚɞɟɟɜɫɤɨɟ “ɫɨɤɪɚɳɟɧɢɟ ɞɥɢɧɵ”. ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɜ ɜɚɤɭɭɦɟ, ɬɨ ɟɫɬɶ ɜ ɨɛɥɚɫɬɢ & ɜɧɟ ɬɨɤɨɜ, ɤɨɝɞɚ j ≡ 0 , ɢɡ (3.16) ɫɥɟɞɭɟɬ ɫɨɨɬɧɨɲɟɧɢɟ
& ∇⊥ B n = , B R
ɤɨɬɨɪɨɟ ɭɠɟ ɢɫɩɨɥɶɡɨɜɚɥɨɫɶ ɧɚɦɢ ɪɚɧɟɟ ɩɪɢ ɨɛɫɭɠɞɟɧɢɢ ɞɪɟɣɮɨɜɨɝɨ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɜ ɧɟɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ. Ɉɛɟ ɮɨɪɦɵ ɡɚɩɢɫɢ (3.12) ɢ (3.16) ɜɩɨɥɧɟ ɪɚɜɧɨɡɧɚɱɧɵ, ɢ ɦɨɠɧɨ ɩɨɥɶɡɨɜɚɬɶɫɹ ɥɸɛɨɣ ɢɡ ɧɢɯ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɨɧɞɟɪɨɦɨɬɨɪɧɚɹ ɫɢɥɚ ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɚ ɜ ɜɢɞɟ ɫɭɦɦɵ ɝɪɚɞɢɟɧɬɚ ɦɚɝɧɢɬɧɨɝɨ ɞɚɜɥɟɧɢɹ ɢ ɤɨɦɩɨɧɟɧɬɵ, ɨɛɹɡɚɧɧɨɣ ɫɜɨɟɦɭ ɩɨɹɜɥɟɧɢɸ ɧɚɬɹɠɟɧɢɸ ɦɚɝɧɢɬɧɵɯ ɫɢɥɨɜɵɯ ɥɢɧɢɣ. ȼ ɨɞɧɨɪɨɞɧɨɦ ɩɨɥɟ ɢɦɟɟɦ R→∞, ɢ ɜɤɥɚɞ ɨɬ ɷɬɨɣ ɤɨɦɩɨɧɟɧɬɵ ɨɛɪɚɳɚɟɬɫɹ ɜ ɧɭɥɶ.
ȼ ɩɪɨɛɥɟɦɟ ɦɚɝɧɢɬɧɨɝɨ ɭɞɟɪɠɚɧɢɹ ɩɥɚɡɦɵ ɜɚɠɧɭɸ ɪɨɥɶ ɢɝɪɚɟɬ ɩɚɪɚɦɟɬɪ p 8πp β= = 2 , (3.17) pm B ɨɩɪɟɞɟɥɹɸɳɢɣ ɨɬɧɨɲɟɧɢɟ ɝɚɡɨɤɢɧɟɬɢɱɟɫɤɨɝɨ ɞɚɜɥɟɧɢɹ ɩɥɚɡɦɵ ɤ ɦɚɝɧɢɬɧɨɦɭ ɞɚɜɥɟɧɢɸ. ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɜɟɥɢɱɢɧɵ ɷɬɨɝɨ ɩɚɪɚɦɟɬɪɚ ɩɪɢɧɹɬɨ ɝɨɜɨɪɢɬɶ ɨ ɩɥɚɡɦɟ ɜɵɫɨɤɨɝɨ ɞɚɜɥɟɧɢɹ, ɟɫɥɢ β>1, ɢɥɢ ɨ ɩɥɚɡɦɟ ɧɢɡɤɨɝɨ ɞɚɜɥɟɧɢɹ, ɟɫɥɢ β<1. ɇɚɩɪɢɦɟɪ, ɜ ɬɨɤɚɦɚɤɚɯ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɦɨɠɟɬ ɭɞɟɪɠɢɜɚɬɶɫɹ ɬɨɥɶɤɨ ɩɥɚɡɦɚ ɧɢɡɤɨɝɨ ɞɚɜɥɟɧɢɹ, βmax<0.1. ȼ ɬɨ ɜɪɟɦɹ ɤɚɤ ɜ ɨɬɤɪɵɬɵɯ ɥɨɜɭɲɤɚɯ ɜ ɩɪɢɧɰɢɩɟ ɜɨɡɦɨɠɧɨ ɭɞɟɪɠɚɧɢɟ ɩɥɚɡɦɵ ɫ β ~1. Ɉɬɦɟɬɢɦ ɜ ɡɚɤɥɸɱɟɧɢɟ, ɱɬɨ, ɬɚɤ ɤɚɤ ɦɚɝɧɢɬɧɨɟ ɞɚɜɥɟɧɢɟ, ɨɩɪɟɞɟɥɟɧɧɨɟ ɮɨɪɦɭɥɨɣ (3.15), ɹɜɥɹɟɬɫɹ ɨɞɧɨɜɪɟɦɟɧɧɨ ɢ ɩɥɨɬɧɨɫɬɶɸ ɦɚɝɧɢɬɧɨɣ ɷɧɟɪɝɢɢ, ɬɨ pm ɢɡɦɟɪɹɟɬɫɹ ɜ ɷɪɝ/ɫɦ3, ɟɫɥɢ ɦɚɝɧɢɬɧɚɹ ɢɧɞɭɤɰɢɹ ȼ ɢɡɦɟɪɹɟɬɫɹ ɜ ɝɚɭɫɫɚɯ.
§ 24. Ɋɚɜɧɨɜɟɫɢɟ ɩɥɚɡɦɵ ɜ ɦɚɝɧɢɬɧɨɣ ɝɢɞɪɨɞɢɧɚɦɢɤɟ ȼɚɠɧɵɣ ɤɪɭɝ ɡɚɞɚɱ, ɜ ɤɨɬɨɪɵɯ ɫ ɭɫɩɟɯɨɦ ɩɪɢɦɟɧɹɟɬɫɹ ɦɚɝɧɢɬɧɚɹ ɝɢɞɪɨɞɢɧɚɦɢɤɚ, ɫɜɹɡɚɧ ɫɨ ɫɬɚɰɢɨɧɚɪɧɵɦɢ ɬɟɱɟɧɢɹɦɢ ɩɥɚɡɦɵ, ɬ.ɟ. ɫ ɬɚɤɢɦɢ, ɤɨɝɞɚ ɩɚɪɚɦɟɬɪɵ ɬɟɱɟɧɢɹ ɹɜɧɨ ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɜɪɟɦɟɧɢ ɢ ɱɚɫɬɧɵɟ ɩɪɨɢɡɜɨɞɧɵɟ ɩɨ ɜɪɟɦɟɧɢ ɜ ɭɪɚɜɧɟɧɢɹɯ (3.4) − (3.10) ɦɨɠɧɨ ɨɩɭɫɬɢɬɶ. ɑɚɫɬɧɵɦ ɫɥɭɱɚɟɦ ɫɬɚɰɢɨɧɚɪɧɵɯ ɩɪɨɰɟɫɫɨɜ ɹɜɥɹɸɬɫɹ ɫɬɚɬɢɱɟɫɤɢɟ ɪɚɜɧɨɜɟɫɢɹ, ɤɨɝɞɚ ɫɤɨɪɨɫɬɶ ɩɥɚɡɦɵ ɬɨɠɞɟɫɬɜɟɧɧɨ ɪɚɜɧɚ ɧɭɥɸ. ɗɬɨ ɢɦɟɧɧɨ ɪɚɜɧɨɜɟɫɢɹ, ɬɚɤ & & ɤɚɤ ɢɡ ɭɫɥɨɜɢɹ v = 0 ɜɵɬɟɤɚɟɬ dv dt = 0 , ɚ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɞɟɣɫɬɜɭɸɳɢɟ ɧɚ ɥɸɛɨɣ ɷɥɟɦɟɧɬɚɪɧɵɣ ɨɛɴɟɦ ɩɥɚɡɦɵ ɫɢɥɵ ɞɨɥɠɧɵ ɛɵɬɶ ɭɪɚɜɧɨɜɟɲɟɧɵ. ɉɪɢ ɷɬɨɦ, ɤɚɤ ɷɬɨ ɜɢɞɧɨ ɢɡ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ (3.5), ɞɨɥɠɧɨ ɛɵɬɶ ɜɵɩɨɥɧɟɧɨ ɭɫɥɨɜɢɟ: 1& & j × B = ∇p . (3.18) c ɗɬɨ ɭɫɥɨɜɢɟ ɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɭɪɚɜɧɟɧɢɟ ɪɚɜɧɨɜɟɫɢɹ& ɩɥɚɡɦɵ ɜ ɦɚɝɧɢɬɧɨɣ & ɝɢɞɪɨɞɢɧɚɦɢɤɟ. ɂɡ ɧɟɝɨ, ɨɱɟɜɢɞɧɨ, ɫɥɟɞɭɟɬ, ɱɬɨ ɜɟɤɬɨɪɚ j ɢ B ɥɟɠɚɬ ɧɚ ɩɨɜɟɪɯɧɨɫɬɹɯ, ɨɪɬɨɝɨɧɚɥɶɧɵɯ ɤ ɝɪɚɞɢɟɧɬɭ ɞɚɜɥɟɧɢɹ, ɬɨ ɟɫɬɶ ɧɚ ɩɨɜɟɪɯɧɨɫɬɹɯ ɩɨɫɬɨɹɧɧɨɝɨ ɞɚɜɥɟɧɢɹ p=const. ɋ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ, ɟɫɥɢ ɦɚɝɧɢɬɧɨɣ ɤɨɧɮɢɝɭɪɚɰɢɢ ɫɨɩɨɫɬɚɜɢɬɶ ɫɟɦɟɣɫɬɜɨ ɦɚɝɧɢɬɧɵɯ ɩɨɜɟɪɯɧɨɫɬɟɣ, ɧɚ ɤɨɬɨɪɵɯ ɥɟɠɚɬ ɫɢɥɨɜɵɟ ɥɢɧɢɢ, ɬɨ, ɨɱɟɜɢɞɧɨ, ɱɬɨ ɢɦɟɧɧɨ ɧɚ ɷɬɢɯ ɩɨɜɟɪɯɧɨɫɬɹɯ ɞɚɜɥɟɧɢɟ ɩɥɚɡɦɵ ɞɨɥɠɧɨ ɛɵɬɶ ɩɨɫɬɨɹɧɧɨ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɦɚɝɧɢɬɧɵɟ ɩɨɜɟɪɯɧɨɫɬɢ ɭɞɟɪɠɢɜɚɸɳɟɝɨ ɩɥɚɡɦɭ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɫ ɧɟɨɛɯɨɞɢɦɨɫɬɶɸ ɞɨɥɠɧɵ ɛɵɬɶ ɢɡɨɛɚɪɢɱɟɫɤɢɦɢ ɞɥɹ ɩɥɚɡɦɵ. ȼ ɩɪɨɫɬɟɣɲɟɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɫɢɥɨɜɵɟ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɹɜɥɹɸɬɫɹ ɩɪɹɦɨɥɢɧɟɣɧɵɦɢ ɢ ɩɚɪɚɥɥɟɥɶɧɵɦɢ ɞɪɭɝ ɞɪɭɝɭ, ɢɯ ɪɚɞɢɭɫ ɤɪɢɜɢɡɧɵ ɪɚɜɟɧ ɛɟɫɤɨɧɟɱɧɨɫɬɢ, ɬɨ ɫɨɝɥɚɫɧɨ ɜɵɪɚɠɟɧɢɸ (3.16) ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ 1& & B2 . (3.19) j × B = −∇ ⊥ c 8π ȼɵɛɪɚɜ ɧɚɩɪɚɜɥɟɧɢɟ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɡɚ ɨɫɶ z ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ, ɞɥɹ ɟɞɢɧɫɬɜɟɧɧɨɣ ɨɬɥɢɱɧɨɣ ɨɬ & ɧɭɥɹ ɤɨɦɩɨɧɟɧɬɵ ɩɨɥɹ Bz ɢɡ ɭɪɚɜɧɟɧɢɹ ɫɨɥɟɧɨɢɞɚɥɶɧɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ div B = 0 ɩɨɥɭɱɢɦ
∂ B = 0, ∂z z
ɢ ɦɚɝɧɢɬɧɚɹ ɢɧɞɭɤɰɢɹ ɦɨɠɟɬ ɦɟɧɹɬɶɫɹ ɬɨɥɶɤɨ ɩɨɩɟɪɟɤ ɧɚɩɪɚɜɥɟɧɢɹ ɫɢɥɨɜɵɯ ɥɢɧɢɣ. ȼɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶ ɩɪɟɞɫɬɚɜɥɟɧɢɟɦ (3.19) ɞɥɹ ɫɢɥɵ Ⱥɦɩɟɪɚ, ɢɡ ɭɪɚɜɧɟɧɢɹ (3.18) ɩɨɥɭɱɢɦ B2 ∂ p = 0, ∇⊥ z + ∇⊥ p = 0 , 8π ∂z ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɞɚɜɥɟɧɢɟ ɩɥɚɡɦɵ ɬɚɤɠɟ ɧɟ ɦɟɧɹɟɬɫɹ ɜɞɨɥɶ ɫɢɥɨɜɵɯ ɥɢɧɢɣ, ɚ ɩɨɩɟɪɟɤ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɞɨɥɠɧɚ ɛɵɬɶ ɩɨɫɬɨɹɧɧɚ ɫɭɦɦɚ ɞɚɜɥɟɧɢɹ ɩɥɚɡɦɵ ɢ ɦɚɝɧɢɬɧɨɝɨ ɞɚɜɥɟɧɢɹ: Bz 2 + p = const . 8π ɋɨɝɥɚɫɧɨ ɷɬɨɦɭ ɭɫɥɨɜɢɸ ɜɧɟ ɨɛɥɚɫɬɢ, ɡɚɧɹɬɨɣ ɩɥɚɡɦɨɣ, ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɹɜɥɹɟɬɫɹ ɨɞɧɨɪɨɞɧɵɦ, ɩɭɫɬɶ ɡɞɟɫɶ Bz=B0. Ɍɨɝɞɚ ɩɨɫɬɨɹɧɧɭɸ ɦɨɠɧɨ ɜɵɛɪɚɬɶ ɬɚɤ, ɱɬɨ ɜɨ ɜɫɟɦ ɩɪɨɫɬɪɚɧɫɬɜɟ ɛɭɞɟɬ Bz 2 B0 2 +p= . (3.20) 8π 8π ȼɢɞɧɨ, ɱɬɨ ɜ ɨɛɥɚɫɬɢ, ɡɚɧɹɬɨɣ ɩɥɚɡɦɨɣ, ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɦɟɧɶɲɟ ɜɧɟɲɧɟɝɨ. Ɇɨɠɧɨ ɫɤɚɡɚɬɶ, ɱɬɨ ɩɥɚɡɦɚ «ɜɵɬɚɥɤɢɜɚɟɬ» ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɤɚɤ ɢ ɥɸɛɨɣ ɞɪɭɝɨɣ ɞɢɚɦɚɝɧɟɬɢɤ. ɍɪɚɜɧɟɧɢɟ (3.20) ɞɥɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɱɚɫɬɧɨɝɨ ɫɥɭɱɚɹ ɭɫɬɚɧɚɜɥɢɜɚɟɬ ɭɫɥɨɜɢɟ ɪɚɜɧɨɜɟɫɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɫɢɫɬɟɦɵ “ɩɥɚɡɦɚ − ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ”, ɩɪɢɱɟɦ ɞɚɜɥɟɧɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜɧɟ ɩɥɚɡɦɵ ɜ ɪɚɜɧɨɜɟɫɢɢ ɞɨɥɠɧɨ ɛɵɬɶ ɛɨɥɶɲɟ ɦɚɝɧɢɬɧɨɝɨ ɞɚɜɥɟɧɢɹ
ɜɧɭɬɪɟɧɧɟɝɨ ɩɨɥɹ ɤɚɤ ɪɚɡ ɧɚ ɜɟɥɢɱɢɧɭ ɝɚɡɨɤɢɧɟɬɢɱɟɫɤɨɝɨ ɞɚɜɥɟɧɢɹ ɩɥɚɡɦɵ, ɱɬɨ ɧɚɝɥɹɞɧɨ ɞɟɦɨɧɫɬɪɢɪɭɟɬ ɢɞɟɸ ɭɞɟɪɠɚɧɢɹ ɩɥɚɡɦɵ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ. ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɜ ɭɪɚɜɧɟɧɢɹɯ ɪɚɜɧɨɜɟɫɢɹ ɧɟɬ ɤɚɤɢɯ-ɥɢɛɨ ɨɝɪɚɧɢɱɟɧɢɣ ɧɚ ɩɪɨɢɫɯɨɠɞɟɧɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɩɨɷɬɨɦɭ ɨɧɨ ɦɨɠɟɬ ɛɵɬɶ ɫɨɡɞɚɧɨ ɤɚɤ ɜɧɟɲɧɢɦɢ ɬɨɤɚɦɢ, ɬɚɤ ɢ ɬɨɤɨɦ, ɩɪɨɬɟɤɚɸɳɢɦ ɩɨ ɩɥɚɡɦɟ. ȼɦɟɫɬɟ ɫ ɬɟɦ ɭɫɥɨɜɢɟ (3.20) ɫɜɹɡɵɜɚɟɬ ɞɜɟ ɧɟɢɡɜɟɫɬɧɵɟ ɜɟɥɢɱɢɧɵ. ɉɨɷɬɨɦɭ ɞɥɹ ɨɞɧɨɡɧɚɱɧɨɝɨ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɪɚɜɧɨɜɟɫɢɹ ɧɟɨɛɯɨɞɢɦɨ ɩɪɢɜɥɟɤɚɬɶ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɭɫɥɨɜɢɹ, ɜ ɬɨɦ ɱɢɫɥɟ ɭɫɥɨɜɢɹ ɩɨɞɞɟɪɠɚɧɢɹ ɬɨɤɚ ɜ ɩɥɚɡɦɟ. ɉɪɢɦɟɪɨɦ ɤɜɚɡɢɫɬɚɰɢɨɧɚɪɧɨɝɨ ɩɪɨɰɟɫɫɚ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɪɚɜɧɨɜɟɫɧɨɟ ɫɨɫɬɨɹɧɢɟ ɫɚɦɨɫɠɢɦɚɸɳɟɝɨɫɹ ɞɥɢɧɧɨɝɨ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɫɬɨɥɛɚ ɩɥɚɡɦɵ ɫ ɩɪɨɞɨɥɶɧɵɦ ɬɨɤɨɦ - ɬɚɤ
Ɋɢɫ.3.1. ɉɥɚɡɦɟɧɧɵɣ Z-ɩɢɧɱ: ɚ − ɝɟɨɦɟɬɪɢɹ ɬɨɤɨɜɨɝɨ ɤɚɧɚɥɚ, ɛ − ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɜ −ɞɚɜɥɟɧɢɹ ɩɥɚɡɦɵ (ɪ) ɢ ɦɚɝɧɢɬɧɨɝɨ ɞɚɜɥɟɧɢɹ (pm) ɩɨ ɪɚɞɢɭɫɭ
ɧɚɡɵɜɚɟɦɵɣ Z-ɩɢɧɱ∗. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ȼ ɢ ɪ ɡɚɜɢɫɹɬ ɬɨɥɶɤɨ ɨɬ ɨɞɧɨɣ ɤɨɨɪɞɢɧɚɬɵ ɪɚɫɫɬɨɹɧɢɹ r ɨɬ ɨɫɢ ɫɬɨɥɛɚ (ɪɢɫ.3.1). ɍɪɚɜɧɟɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɩɪɢɦɟɬ ɜɢɞ: ∂p 1 − = jB . ∂r c z ϕ ȿɫɥɢ ɫɱɢɬɚɬɶ ɬɨɤ ɩɢɧɱɚ ɪɚɫɩɪɟɞɟɥɟɧɧɵɦ ɪɚɜɧɨɦɟɪɧɨ ɩɨ ɟɝɨ ɫɟɱɟɧɢɸ, ɬɨ jz=const ɢ 2 Bϕ = πrjz , ɬɚɤ ɤɚɤ ɩɨ ɬɟɨɪɟɦɟ ɨ ɰɢɪɤɭɥɹɰɢɢ c 2π 4π 4π ³ Bϕ dlϕ ≡ ³0 Bϕ rdϕ ≡ Bϕ ⋅ 2πr = c J ( r ) ≡ c πr 2 jz , ɝɞɟ r
J ( r ) = 2π ³ j z rdr = πr 2 j z 0
− ɬɨɤ ɜ ɰɢɥɢɧɞɪɟ ɫ ɪɚɞɢɭɫɨɦ r. Ⱦɥɹ ɨɛɥɚɫɬɢ ɜɧɟ ɩɢɧɱɚ, ɜɧɨɜɶ ɜɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶ ɬɟɨɪɟɦɨɣ ɨ ɰɢɪɤɭɥɹɰɢɢ, ɩɨɥɭɱɚɟɦ: 2π 4π 4π B dl ≡ ³ ϕ ϕ ³0 Bϕ rdϕ ≡ Bϕ ⋅ 2πr = c I ≡ c πa 2 jz , ∗
Ɋɚɡɪɹɞ ɫ ɝɟɨɦɟɬɪɢɟɣ Z-ɩɢɧɱɚ ɜɨɡɧɢɤɚɟɬ, ɧɚɩɪɢɦɟɪ, ɩɪɢ ɩɪɨɩɭɫɤɚɧɢɢ ɫɢɥɶɧɨɝɨ ɬɨɤɚ ɱɟɪɟɡ ɝɚɡ ɦɟɠɞɭ ɞɜɭɦɹ ɩɚɪɚɥɥɟɥɶɧɵɦɢ ɷɥɟɤɬɪɨɞɚɦɢ, ɪɚɫɩɨɥɨɠɟɧɧɵɦɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɨɫɢ z.
ɝɞɟ I - ɩɨɥɧɵɣ ɬɨɤ ɩɢɧɱɚ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɩɢɧɱɚ ɫɥɟɞɭɸɳɟɟ (ɪɢɫ. 3.1,ɛ): r ° ,r ≤ a , Bϕ ( r ) = Bϕ ( a )® a a ° ,r > a ¯r ɝɞɟ 2I Bϕ ( a ) = ca ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɧɚ ɝɪɚɧɢɰɟ ɩɥɚɡɦɵ. Ɉɬɦɟɬɢɦ ɩɨɩɭɬɧɨ ɩɨɥɟɡɧɭɸ ɩɪɚɤɬɢɱɟɫɤɭɸ ɮɨɪɦɭɥɭ ɞɥɹ ɪɚɫɱɟɬɚ ɜɟɥɢɱɢɧɵ ɷɬɨɝɨ ɩɨɥɹ:
Bϕ ( a ) =
0.2 I [ A ]
, [ Ƚɫ ] . a [ ɫɦ ] ɉɨɞɫɬɚɧɨɜɤɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨɥɹ ɜ ɭɪɚɜɧɟɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɩɪɢɜɨɞɢɬ ɤ ɫɨɨɬɧɨɲɟɧɢɸ 2π ∂p = − 2 jz 2 r . ∂r c ɂɧɬɟɝɪɢɪɭɟɦ ɢ, ɭɱɢɬɵɜɚɹ, ɱɬɨ ɧɚ ɝɪɚɧɢɰɟ ɫɬɨɥɛɚ (ɩɪɢ r=a) ɝɚɡɨɤɢɧɟɬɢɱɟɫɤɨɟ ɞɚɜɥɟɧɢɟ ɪɚɜɧɨ ɧɭɥɸ (ɪ=0), ɩɨɥɭɱɚɟɦ 2 r2 · I2 § r 2 · Bϕ ( a ) § r2 · πa 2 2 § p = 2 j ¨1 − 2 ¸ = 2 2 ¨1 − 2 ¸ ≡ ¨1 − 2 ¸ . a ¹ πa c © a ¹ a ¹ c 4π © © ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɫɭɦɦɚ ɞɚɜɥɟɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɞɚɜɥɟɧɢɹ ɩɥɚɡɦɵ Bϕ2 ( r ) Bϕ2 ( a ) § r2 · p+ = ¨ 2 − 2 ¸ ≠ const 8π 8π © a ¹ ɬɟɩɟɪɶ ɧɟ ɹɜɥɹɟɬɫɹ ɜɟɥɢɱɢɧɨɣ ɩɨɫɬɨɹɧɧɨɣ (ɫɪɚɜɧɢɦ ɫ (3.20)). Ɉɱɟɜɢɞɧɨ, ɷɬɨ ɫɜɹɡɚɧɨ ɫ ɜɤɥɚɞɨɦ ɨɬ ɧɚɬɹɠɟɧɢɹ ɫɢɥɨɜɵɯ ɥɢɧɢɣ, ɤɨɬɨɪɵɟ ɡɞɟɫɶ ɢɦɟɸɬ ɮɨɪɦɭ ɨɤɪɭɠɧɨɫɬɟɣ ɫ ɤɨɧɟɱɧɵɦ ɪɚɞɢɭɫɨɦ ɤɪɢɜɢɡɧɵ. ɉɨɫɬɨɹɧɧɨɣ ɬɟɩɟɪɶ ɹɜɥɹɟɬɫɹ ɜɟɥɢɱɢɧɚ Bϕ2 ( r ) Bϕ2 ( r ) Bϕ2 ( r ) Bϕ2 ( a ) )≡ p+ p+ −(− = = const . 8π 8π 4π 4π ȼɤɥɚɞ ɧɚɬɹɠɟɧɢɹ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɩɪɢɜɨɞɢɬ ɤ ɬɨɦɭ, ɱɬɨ ɞɚɜɥɟɧɢɟ ɩɥɚɡɦɵ ɜ ɰɟɧɬɪɟ ɬɨɤɨɜɨɝɨ ɤɚɧɚɥɚ ɨɤɚɡɵɜɚɟɬɫɹ ɪɨɜɧɨ ɜɞɜɨɟ ɛɨɥɶɲɟ ɦɚɝɧɢɬɧɨɝɨ ɞɚɜɥɟɧɢɹ ɧɚ ɟɝɨ ɝɪɚɧɢɰɟ. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɞɚɜɥɟɧɢɣ ɜ ɬɨɤɨɜɨɦ ɤɚɧɚɥɟ ɩɨɤɚɡɚɧɨ ɧɚ (ɪɢɫ. 3.1,ɜ). Ɍɚɤ ɤɚɤ p=2nT, ɬɨ, ɜɜɨɞɹ ɩɨɥɧɨɟ ɱɢɫɥɨ ɱɚɫɬɢɰ ɧɚ ɟɞɢɧɢɰɭ ɞɥɢɧɵ ɩɥɚɡɦɟɧɧɨɝɨ ɫɬɨɥɛɚ N (ɬɚɤ ɧɚɡɵɜɚɟɦɨɟ ɩɨɝɨɧɧɨɟ ɱɢɫɥɨ ɱɚɫɬɢɰ) ɢ ɫɱɢɬɚɹ ɬɟɦɩɟɪɚɬɭɪɭ ɩɥɚɡɦɵ Ɍ ɩɨɫɬɨɹɧɧɨɣ, ɨɩɪɟɞɟɥɢɦ a I2 N = 2π ³ nr dr = 2 , 4c T 0 ɨɬɤɭɞɚ ɩɨɥɭɱɚɟɦ ɫɨɨɬɧɨɲɟɧɢɟ I2 4 NT = 2 , c ɢɡɜɟɫɬɧɨɟ ɤɚɤ ɫɨɨɬɧɨɲɟɧɢɟ Ȼɟɧɧɟɬɚ. ɉɪɢ ɜɵɜɨɞɟ ɷɬɨɝɨ ɫɨɨɬɧɨɲɟɧɢɹ ɧɚɦɢ ɩɪɟɞɩɨɥɚɝɚɥɨɫɶ, ɱɬɨ ɬɟɦɩɟɪɚɬɭɪɚ ɩɥɚɡɦɵ ɩɨɫɬɨɹɧɧɚ. Ɉɞɧɚɤɨ ɩɪɨɜɨɞɢɦɨɫɬɶ ɪɟɚɥɶɧɨɣ ɩɥɚɡɦɵ ɧɟ ɛɟɫɤɨɧɟɱɧɚ, ɢ ɩɨɷɬɨɦɭ ɩɪɨɬɟɤɚɧɢɟ ɬɨɤɚ ɛɭɞɟɬ ɫɨɩɪɨɜɨɠɞɚɬɶɫɹ ɜɵɞɟɥɟɧɢɟɦ ɞɠɨɭɥɟɜɚ ɬɟɩɥɚ ɢ ɧɚɝɪɟɜɨɦ ɩɥɚɡɦɵ. ȿɫɥɢ ɷɬɨɬ ɩɪɨɰɟɫɫ ɫɱɢɬɚɬɶ ɦɟɞɥɟɧɧɵɦ, ɬɨ ɭɫɥɨɜɢɟ ɪɚɜɧɨɜɟɫɢɹ ɦɨɠɧɨ ɫɱɢɬɚɬɶ, ɩɨ ɤɪɚɣɧɟɣ ɦɟɪɟ, ɩɪɢɛɥɢɠɟɧɧɨ ɫɩɪɚɜɟɞɥɢɜɵɦ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɟɫɥɢ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɩɨɝɨɧɧɨɦ ɱɢɫɥɟ ɱɚɫɬɢɰ ɬɟɦɩɟɪɚɬɭɪɚ ɛɭɞɟɬ ɪɚɫɬɢ, ɬɨ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɧɟɨɛɯɨɞɢɦɨ ɭɜɟɥɢɱɢɜɚɬɶ ɬɨɤ.
Ʉ ɫɨɠɚɥɟɧɢɸ, ɜ ɨɛɫɭɠɞɚɟɦɨɣ ɜɵɲɟ ɝɟɨɦɟɬɪɢɢ ɪɚɡɪɹɞɚ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɭɞɚɟɬɫɹ ɞɨɜɟɫɬɢ ɩɥɚɡɦɟɧɧɵɣ ɫɬɨɥɛ ɞɨ ɪɚɜɧɨɜɟɫɧɨɝɨ ɫɨɫɬɨɹɧɢɹ, ɬɚɤ ɤɚɤ ɪɹɞ ɩɪɨɰɟɫɫɨɜ ɩɪɢɜɨɞɢɬ ɤ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ, ɢ ɫɬɨɥɛ ɩɥɚɡɦɵ ɛɵɫɬɪɨ ɪɚɡɪɭɲɚɟɬɫɹ. ɉɥɚɡɦɟɧɧɵɣ ɫɬɨɥɛ ɜ Z-ɩɢɧɱɟ ɨɩɢɪɚɟɬɫɹ ɧɚ ɷɥɟɤɬɪɨɞɵ, ɡɧɚɱɢɬ ɜɞɨɥɶ ɫɬɨɥɛɚ ɭɯɨɞ ɱɚɫɬɢɰ ɢ ɩɨɬɟɪɢ ɷɧɟɪɝɢɢ ɜ ɨɛɥɚɫɬɢ ɤɨɧɬɚɤɬɚ ɧɟɢɡɛɟɠɧɵ. ȿɫɬɟɫɬɜɟɧɧɨ ɠɟɥɚɧɢɟ ɫɜɟɪɧɭɬɶ ɫɬɨɥɛ ɩɥɚɡɦɵ ɜ ɬɨɪ − ɫɨɡɞɚɬɶ ɡɚɦɤɧɭɬɭɸ ɛɟɡɷɥɟɤɬɪɨɞɧɭɸ ɫɢɫɬɟɦɭ. Ɉɞɧɚɤɨ ɬɨɪɨɢɞɚɥɶɧɵɣ ɜɢɬɨɤ ɫ ɬɨɤɨɦ ɫɬɪɟɦɢɬɫɹ ɤ ɪɚɫɲɢɪɟɧɢɸ, ɩɨɬɨɦɭ ɱɬɨ ɞɚɜɥɟɧɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɚ ɜɧɭɬɪɟɧɧɸɸ ɩɨɜɟɪɯɧɨɫɬɶ ɜɢɬɤɚ ɛɨɥɶɲɟ, ɱɟɦ ɧɚ ɧɚɪɭɠɧɭɸ. ɇɚɩɪɢɦɟɪ, ɧɚ ɥɸɛɨɣ ɭɱɚɫɬɨɤ ɜɢɬɤɚ ∆1J ɞɟɣɫɬɜɭɟɬ ɨɬɬɚɥɤɢɜɚɸɳɚɹ ɫɢɥɚ ɨɬ ɞɢɚɦɟɬɪɚɥɶɧɨ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɝɨ ɭɱɚɫɬɤɚ ɜɢɬɤɚ ∆2J (ɪɢɫ.3.2), ɩɨɫɤɨɥɶɤɭ, ɤɚɤ ɢɡɜɟɫɬɧɨ, ɚɧɬɢɩɚɪɚɥɥɟɥɶɧɵɟ ɬɨɤɢ ɨɬɬɚɥɤɢɜɚɸɬɫɹ. ɑɬɨɛɵ ɨɛɟɫɩɟɱɢɬɶ ɪɚɜɧɨɜɟɫɢɟ ɩɥɚɡɦɟɧɧɨɝɨ ɜɢɬɤɚ, ɟɝɨ ɦɨɠɧɨ ɛɵɥɨ ɛɵ ɩɨɦɟɫɬɢɬɶ ɜ ɜɟɪɬɢɤɚɥɶɧɨɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ȼz, ɧɚɩɪɚɜɥɟɧɧɨɟ ɩɨ ɨɫɢ z, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ ɩɥɨɫɤɨɫɬɢ ɜɢɬɤɚ (ɩɥɨɫɤɨɫɬɢ ɪɢɫ.3.2). Ɍɨɝɞɚ ɫɢɥɵ, ɪɚɫɬɹɝɢɜɚɸɳɢɟ ɜɢɬɨɤ F1∼J2, ɦɨɝɭɬ ɛɵɬɶ ɫɤɨɦɩɟɧɫɢɪɨɜɚɧɵ ɫɢɥɚɦɢ, ɫɠɢɦɚɸɳɢɦɢ ɟɝɨ, F2∼Jȼz. Ɋɚɫɱɟɬɵ [10] ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ ɩɪɢ ɷɬɨɦ ɪɚɜɧɨɜɟɫɢɟ ɞɨɫɬɢɝɚɟɬɫɹ, ɟɫɥɢ J § 8R 1· Bz = − ¸, ¨ ln cR © a 2 ¹ ɝɞɟ J - ɩɨɥɧɵɣ ɬɨɤ ɜ ɩɥɚɡɦɟɧɧɨɦ ɜɢɬɤɟ. Ɋɚɜɧɨɜɟɫɧɨɟ ɫɨɫɬɨɹɧɢɟ ɜɢɬɤɚ ɦɨɠɟɬ ɛɵɬɶ ɩɨɥɭɱɟɧɨ ɬɚɤɠɟ (ɧɚ ɜɪɟɦɟɧɚɯ ɦɚɫɲɬɚɛɚ ɫɤɢɧɨɜɵɯ), ɟɫɥɢ ɟɝɨ ɩɨɦɟɫɬɢɬɶ ɜ ɯɨɪɨɲɨ ɩɪɨɜɨɞɹɳɢɣ ɦɟɬɚɥɥɢɱɟɫɤɢɣ ɤɨɠɭɯ. ɋɦɟɳɟɧɢɟ ɜɢɬɤɚ ɩɪɢɜɨɞɢɬ ɤ ɜɨɡɧɢɤɧɨɜɟɧɢɸ ɬɨɤɨɜ Ɏɭɤɨ ɜ ɤɨɠɭɯɟ, ɢ ɦɚɝɧɢɬɧɵɟ ɩɨɥɹ ɷɬɢɯ ɬɨɤɨɜ ɢɝɪɚɸɬ ɪɨɥɶ ɩɨɥɹ ȼz. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɜɪɟɦɹ ɫɭɳɟɫɬɜɨɜɚɧɢɹ ɪɚɜɧɨɜɟɫɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɡɚɜɢɫɢɬ ɨɬ ɫɨɨɬɧɨɲɟɧɢɹ ɪɚɞɢɭɫɚ ɩɥɚɡɦɟɧɧɨɝɨ ɲɧɭɪɚ a, ɪɚɞɢɭɫɚ ɤɚɦɟɪɵ ɬɨɪɚ R, ɩɪɨɜɨɞɢɦɨɫɬɢ ɢ ɬɨɥɳɢɧɵ ∆r ɩɪɨɜɨɞɹɳɟɝɨ ɤɨɠɭɯɚ. ɋɬɚɛɢɥɢɡɚɰɢɹ ɩɨɥɨɠɟɧɢɹ ɩɥɚɡɦɟɧɧɨɝɨ ɜɢɬɤɚ ɫ ɬɨɤɨɦ ɜɟɪɬɢɤɚɥɶɧɵɦ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ ɢ ɩɪɨɜɨɞɹɳɢɦ ɦɚɫɫɢɜɧɵɦ Ɋɢɫ.3.2. Ƚɟɨɦɟɬɪɢɹ ɦɟɬɚɥɥɢɱɟɫɤɢɦ ɤɨɠɭɯɨɦ ɪɟɚɥɶɧɨ ɢɫɩɨɥɶɡɨɜɚɥɢɫɶ ɜ ɬɨɤɚɦɚɤɚɯ ɬɨɪɨɢɞɚɥɶɧɨɝɨ ɜɢɬɤɚ ɩɥɚɡɦɵ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɩɨ ɛɨɥɶɲɨɦɭ ɪɚɞɢɭɫɭ ɬɨɪɚ. Ɋɚɜɧɨɜɟɫɢɟ ɩɨ ɦɚɥɨɦɭ ɪɚɞɢɭɫɭ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ (ɜ ɫɨɜɨɤɭɩɧɨɫɬɢ ɫ ɩɨɥɟɦ ɬɨɤɚ) ɫɢɥɶɧɵɦ ɬɨɪɨɢɞɚɥɶɧɵɦ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ. Ɇɚɝɧɢɬɨɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢɣ ɦɟɬɨɞ ɪɚɫɫɦɨɬɪɟɧɢɹ ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɤɚɱɟɫɬɜɟɧɧɨ ɢ ɧɚɝɥɹɞɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɭɫɥɨɜɢɹ ɪɚɜɧɨɜɟɫɢɹ ɩɥɚɡɦɟɧɧɨɝɨ ɲɧɭɪɚ ɪɚɡɥɢɱɧɨɣ ɝɟɨɦɟɬɪɢɢ, ɚ ɪɚɫɱɟɬɵ ɩɨɡɜɨɥɹɸɬ ɨɰɟɧɢɬɶ ɧɟɨɛɯɨɞɢɦɵɟ ɫɨɨɬɧɨɲɟɧɢɹ ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ.
§ 25. Ȼɵɫɬɪɵɟ ɩɪɨɰɟɫɫɵ ȼ ɭɪɚɜɧɟɧɢɢ (3.18) ɢɧɟɪɰɢɟɣ ɩɥɚɡɦɵ ɩɪɟɧɟɛɪɟɝɚɟɦ. Ɉɞɧɚɤɨ ɩɪɢ ɛɵɫɬɪɵɯ ɩɪɨɰɟɫɫɚɯ ɷɬɨ ɧɟɞɨɩɭɫɬɢɦɨ. Ȼɨɥɟɟ ɬɨɝɨ, ɨɩɵɬ ɩɨɤɚɡɚɥ, ɱɬɨ ɧɚ ɩɟɪɜɵɯ ɫɬɚɞɢɹɯ ɪɚɡɜɢɬɢɹ ɢɦɩɭɥɶɫɧɨɝɨ ɪɚɡɪɹɞɚ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ ɝɚɡɨɤɢɧɟɬɢɱɟɫɤɢɦ ɞɚɜɥɟɧɢɟɦ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɢɧɟɪɰɢɨɧɧɵɦ ɱɥɟɧɨɦ. ɉɪɢ ɛɵɫɬɪɨɦ ɩɪɨɰɟɫɫɟ ɩɪɨɛɨɣ ɝɚɡɚ ɩɪɨɢɫɯɨɞɢɬ ɩɟɪɜɨɧɚɱɚɥɶɧɨ ɩɨ ɩɟɪɢɮɟɪɢɢ ɪɚɡɪɹɞɧɨɣ ɤɚɦɟɪɵ. ȼ ɮɨɪɦɢɪɨɜɚɧɢɢ ɩɥɚɡɦɟɧɧɨɣ ɨɛɨɥɨɱɤɢ ɫɭɳɟɫɬɜɟɧɧɭɸ ɪɨɥɶ ɢɝɪɚɸɬ ɷɥɟɦɟɧɬɚɪɧɵɟ ɩɪɨɰɟɫɫɵ − ɢɨɧɢɡɚɰɢɹ, ɪɟɤɨɦɛɢɧɚɰɢɹ ɢ ɩɟɪɟɡɚɪɹɞɤɚ. ɇɚ ɷɬɨɣ ɫɬɚɞɢɢ ɨɛɪɚɡɭɟɬɫɹ ɬɨɧɤɢɣ ɩɪɨɜɨɞɹɳɢɣ ɰɢɥɢɧɞɪ ɩɥɚɡɦɵ. ɉɨ ɦɟɪɟ ɪɚɡɨɝɪɟɜɚ ɢ ɪɨɫɬɚ ɬɨɤɚ ɷɬɚ ɩɥɚɡɦɟɧɧɚɹ ɨɛɨɥɨɱɤɚ ɨɬɪɵɜɚɟɬɫɹ ɨɬ ɫɬɟɧɤɢ ɤɚɦɟɪɵ, ɫɠɢɦɚɟɬɫɹ ɤ ɰɟɧɬɪɭ, ɢɨɧɢɡɭɟɬ ɢ “ɫɝɪɟɛɚɟɬ” ɩɪɢ ɫɠɚɬɢɢ ɧɚɯɨɞɹɳɢɣɫɹ ɜɧɭɬɪɢ ɧɟɟ ɧɟɣɬɪɚɥɶɧɵɣ ɢɥɢ ɫɥɚɛɨ ɢɨɧɢɡɨɜɚɧɧɵɣ ɝɚɡ, ɜɨɜɥɟɤɚɹ ɟɝɨ ɜ ɞɜɢɠɟɧɢɟ ɤ ɰɟɧɬɪɭ. Ɍɚɤɨɣ ɩɪɨɰɟɫɫ ɩɨɥɭɱɢɥ ɧɚɡɜɚɧɢɟ ɞɜɢɠɭɳɟɣɫɹ ɦɚɝɧɢɬɧɨɣ ɫɬɟɧɤɢ (ɜ ɚɧɝɥɢɣɫɤɨɣ ɥɢɬɟɪɚɬɭɪɟ ɫɥɨɠɢɥɫɹ ɬɟɪɦɢɧ snow-plow − ɫɧɟɠɧɵɣ ɩɥɭɝ) ɢ ɬɟɨɪɟɬɢɱɟɫɤɢ ɛɵɥ ɪɚɫɫɦɨɬɪɟɧ ɜ ɋɋɋɊ Ʌɟɨɧɬɨɜɢɱɟɦ ɢ Ɉɫɨɜɰɨɦ [16], ɚ ɜ ɋɒȺ Ɋɨɡɟɧɛɥɸɬɨɦ. ɉɨɫɥɟ ɫɯɨɠɞɟɧɢɹ ɩɥɚɡɦɟɧɧɨɣ ɨɛɨɥɨɱɤɢ ɤ ɨɫɢ ɜ ɰɟɧɬɪɟ ɤɚɦɟɪɵ ɨɛɪɚɡɭɟɬɫɹ ɰɢɥɢɧɞɪɢɱɟɫɤɢɣ ɩɥɚɡɦɟɧɧɵɣ «ɫɬɨɥɛ», ɫɠɢɦɚɸɳɢɣɫɹ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɫɨɛɫɬɜɟɧɧɨɝɨ ɬɨɤɚ ɢ, ɜ ɪɟɡɭɥɶɬɚɬɟ, ɛɵɫɬɪɨ ɪɚɡɨɝɪɟɜɚɸɳɢɣɫɹ - ɩɨ ɷɬɨɣ ɩɪɢɱɢɧɟ ɩɪɟɧɟɛɪɟɱɶ ɞɚɜɥɟɧɢɟɦ ɩɥɚɡɦɵ ɭɠɟ ɧɟɥɶɡɹ. ɉɨ ɦɟɪɟ ɪɚɡɨɝɪɟɜɚ ɞɚɜɥɟɧɢɟ ɩɥɚɡɦɵ ɪɚɫɬɟɬ ɢ ɬɨɪɦɨɡɢɬ ɩɪɨɰɟɫɫ ɞɚɥɶɧɟɣɲɟɝɨ ɫɠɚɬɢɹ. ɗɬɚ ɫɬɚɞɢɹ ɡɚɜɟɪɲɚɟɬɫɹ ɨɛɪɚɡɨɜɚɧɢɟɦ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɬɨɤɨɜɨɝɨ ɤɚɧɚɥɚ, ɩɨɱɬɢ ɪɚɜɧɨɜɟɫɧɨɝɨ, ɧɨ, ɤɚɤ ɩɨɤɚɡɚɥɢ ɷɤɫɩɟɪɢɦɟɧɬɵ, ɧɟɭɫɬɨɣɱɢɜɨɝɨ, ɜɫɤɨɪɟ ɪɚɡɪɭɲɚɸɳɟɝɨɫɹ, ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ, ɡɚ ɫɱɟɬ ɪɚɡɜɢɬɢɹ ɩɟɪɟɬɹɠɟɤ, ɜɟɞɭɳɢɯ ɤ ɨɛɪɵɜɭ ɬɨɤɚ, ɢ ɢɡɝɢɛɨɜ-ɡɦɟɟɤ, ɪɚɡɪɭɲɚɸɳɢɯ ɬɨɤɨɜɵɣ ɤɚɧɚɥ. ɇɚ ɡɚɤɥɸɱɢɬɟɥɶɧɨɣ ɫɬɚɞɢɢ ɪɚɡɪɹɞɚ, ɤɨɝɞɚ ɬɨɤɨɜɵɣ ɤɚɧɚɥ ɪɚɡɪɭɲɚɟɬɫɹ, ɜɨɡɧɢɤɚɸɬ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ ɩɨɥɹ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɭɫɤɨɪɟɧɢɸ ɱɚɫɬɢ ɱɚɫɬɢɰ ɩɥɚɡɦɵ, ɜɫɩɥɟɫɤɭ ɪɟɧɬɝɟɧɨɜɫɤɨɝɨ ɢɡɥɭɱɟɧɢɹ ɢ ɧɟɣɬɪɨɧɧɨɦɭ ɢɡɥɭɱɟɧɢɸ, ɟɫɥɢ ɪɚɡɪɹɞ ɩɪɨɢɡɜɨɞɢɬɫɹ ɜ ɞɟɣɬɟɪɢɢ. Ɇɨɳɧɵɣ ɢɦɩɭɥɶɫɧɵɣ ɪɚɡɪɹɞ, ɜ ɤɨɬɨɪɨɦ ɪɟɚɥɢɡɭɟɬɫɹ ɨɩɢɫɚɧɧɚɹ ɜɵɲɟ (ɜɟɫɶɦɚ ɮɪɚɝɦɟɧɬɚɪɧɨ!) ɫɨɜɨɤɭɩɧɨɫɬɶ ɫɨɛɵɬɢɣ, ɩɨɥɭɱɢɥ ɧɚɡɜɚɧɢɟ Z-ɩɢɧɱ, ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɡɚ ɫɱɟɬ ɝɟɨɦɟɬɪɢɢ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɪɚɡɪɹɞɧɨɣ ɤɚɦɟɪɵ, ɨɫɶ ɤɨɬɨɪɨɣ ɩɪɢɧɹɬɨ ɨɛɵɱɧɨ ɜɵɛɢɪɚɬɶ ɡɚ ɨɫɶ z ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ. ɇɚ ɮɚɡɟ ɞɜɢɠɟɧɢɹ ɩɥɚɡɦɟɧɧɨɣ ɨɛɨɥɨɱɤɢ ɤ ɨɫɢ, ɫɨɩɪɨɜɨɠɞɚɸɳɟɦɫɹ ɫɝɪɟɛɚɧɢɟɦ ɝɚɡɚ ɢ ɪɨɫɬɨɦ ɦɚɫɫɵ ɩɥɚɡɦɵ, ɪɚɞɢɚɥɶɧɚɹ ɤɨɨɪɞɢɧɚɬɚ ɩɥɚɡɦɟɧɧɨɣ ɨɛɨɥɨɱɤɢ, ɤɨɬɨɪɚɹ ɫɱɢɬɚɟɬɫɹ ɬɨɧɤɨɣ, ɫɨɝɥɚɫɧɨ ɬɟɨɪɢɢ Ʌɟɨɧɬɨɜɢɱɚ − Ɉɫɨɜɰɚ [16], ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ: Bϕ2 d § dr · 1 & & (3.21) ⋅ 2πr , ¨ m ¸ = ( j × B )r ⋅ 2πr ≡ − dt © dt ¹ c 8π ɝɞɟ m - ɦɚɫɫɚ ɟɞɢɧɢɰɵ ɞɥɢɧɵ ɲɧɭɪɚ ɩɥɚɡɦɵ r2 m = m0 ( 1 − 2 ), m0 = πρa 2 , a ɝɞɟ ɚ - ɧɚɱɚɥɶɧɵɣ ɪɚɞɢɭɫ ɨɛɨɥɨɱɤɢ, m0 - ɧɚɱɚɥɶɧɚɹ ɦɚɫɫɚ ɝɚɡɚ ɜ ɪɚɡɪɹɞɧɨɣ ɤɚɦɟɪɟ ɧɚ ɟɞɢɧɢɰɭ ɞɥɢɧɵ ɜɞɨɥɶ ɨɫɢ; 2 I( t ) Bϕ = cr ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɬɨɤɚ ɫɧɚɪɭɠɢ ɨɬ ɩɥɚɡɦɟɧɧɨɣ ɨɛɨɥɨɱɤɢ. ȼɧɭɬɪɢ ɨɛɨɥɨɱɤɢ ɩɪɢ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɫɢɦɦɟɬɪɢɢ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɨɱɟɜɢɞɧɨ, ɪɚɜɧɨ ɧɭɥɸ. ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ ɜ ɩɪɚɜɨɣ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ (3.21), ɩɪɟɞɫɬɚɜɥɹɸɳɟɣ ɫɨɛɨɣ ɪɚɞɢɚɥɶɧɭɸ ɫɢɥɭ, ɞɟɣɫɬɜɭɸɳɭɸ ɧɚ ɨɛɨɥɨɱɤɭ ɜ ɪɚɫɱɟɬɟ ɧɚ ɟɞɢɧɢɰɭ ɟɟ ɞɥɢɧɵ ɜɞɨɥɶ ɨɫɢ, ɡɧɚɤ ɨɛɹɡɚɬɟɥɶɧɨ ɞɨɥɠɟɧ ɛɵɬɶ ɨɬɪɢɰɚɬɟɥɶɧɵɦ! ɂɧɨɝɞɚ ɜ ɥɟɜɭɸ ɱɚɫɬɶ (3.21) ɜɜɨɞɹɬ ɞɨɩɨɥɧɢɬɟɥɶɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ k, ɭɱɢɬɵɜɚɸɳɢɣ ɞɨɥɸ ɡɚɯɜɚɬɵɜɚɟɦɨɣ ɦɚɫɫɵ ɢ ɪɚɜɧɵɣ ɟɞɢɧɢɰɟ ɩɪɢ ɩɨɥɧɨɦ ɫɝɪɟɛɚɧɢɢ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɜɟɥɢɱɢɧɵ ɪɚɡɪɹɞɧɨɝɨ ɬɨɤɚ I(t) ɧɟɨɛɯɨɞɢɦɨ ɞɨɩɨɥɧɢɬɟɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ - ɷɥɟɤɬɪɨɬɟɯɧɢɱɟɫɤɨɟ ɭɪɚɜɧɟɧɢɟ ɰɟɩɢ ɞɥɹ ɪɚɡɪɹɞɧɨɝɨ ɤɨɧɬɭɪɚ. ɗɬɨ, ɤɨɧɟɱɧɨ, ɭɫɥɨɠɧɹɟɬ ɪɟɲɟɧɢɟ. ɇɨ ɧɚ ɧɚɱɚɥɶɧɨɣ ɫɬɚɞɢɢ ɦɨɠɧɨ ɩɨɥɚɝɚɬɶ, ɱɬɨ ɬɨɤ ɪɚɫɬɟɬ ɥɢɧɟɣɧɨ ɩɨ ɜɪɟɦɟɧɢ, ɬɚɤ ɱɬɨ
I ( t ) = I0 t , ɝɞɟ I0 - ɬɟɦɩ ɧɚɪɚɫɬɚɧɢɹ ɬɨɤɚ (ɡɞɟɫɶ ɩɨɫɬɨɹɧɧɚɹ ɜɟɥɢɱɢɧɚ), ɨɩɪɟɞɟɥɹɟɦɵɣ ɷɥɟɤɬɪɨɬɟɯɧɢɱɟɫɤɢɦɢ ɩɚɪɚɦɟɬɪɚ ɪɚɡɪɹɞɧɨɣ ɰɟɩɢ. Ɋɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ (3.21) ɞɥɹ ɥɢɧɟɣɧɨ ɧɚɪɚɫɬɚɸɳɟɝɨ ɬɨɤɚ ɞɚɧɨ ɜ [12]. Ɉɧɨ ɩɪɟɞɫɤɚɡɵɜɚɟɬ, ɱɬɨ ɜ ɨɩɪɟɞɟɥɟɧɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t = t ɨɫɨɛ = 1.5 ( ac / I0 )1 / 2 m01 / 4 , (3.22) ɧɚɡɵɜɚɟɦɵɣ ɦɨɦɟɧɬɨɦ ɨɫɨɛɟɧɧɨɫɬɢ, ɩɥɚɡɦɟɧɧɚɹ ɨɛɨɥɨɱɤɚ ɫɯɥɨɩɵɜɚɟɬɫɹ ɧɚ ɨɫɢ ɫɢɫɬɟɦɵ. Ɇɨɦɟɧɬ ɨɫɨɛɟɧɧɨɫɬɢ ɪɟɚɥɶɧɨ ɧɚɛɥɸɞɚɟɬɫɹ ɧɚ ɷɤɫɩɟɪɢɦɟɧɬɟ (ɧɨ, ɤɨɧɟɱɧɨ, ɫɠɚɬɢɹ ɞɨ ɧɭɥɟɜɨɝɨ ɪɚɞɢɭɫɚ ɧɟ ɩɪɨɢɫɯɨɞɢɬ), ɩɪɢɱɟɦ ɩɪɟɞɫɤɚɡɚɧɢɹ ɫ ɩɨɦɨɳɶɸ (3.22) ɭɞɢɜɢɬɟɥɶɧɨ ɬɨɱɧɨ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɧɚɛɥɸɞɟɧɢɹɦ (ɩɨɞɪɨɛɧɟɟ ɫɦ. [12], ɬɢɩɢɱɧɵɟ ɡɧɚɱɟɧɢɹ tɨɫɨɛ ɫɨɫɬɚɜɥɹɸɬ 2 - 10 ɦɤɫ). Ɂɚɦɟɬɢɦ, ɱɬɨ ɜɟɥɢɱɢɧɚ tɨɫɨɛ ɨɩɪɟɞɟɥɹɟɬɫɹ, ɮɚɤɬɢɱɟɫɤɢ, ɬɨɥɶɤɨ ɧɚɱɚɥɶɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɜɟɥɢɱɢɧ.
Ɋɢɫ. 3.3. Ɋɚɡɧɨɜɢɞɧɨɫɬɢ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ (ɚ,ɛ) ɢ ɧɟɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ (ɜ,ɝ) Z-ɩɢɧɱɚ: ɚ − ɤɥɚɫɫɢɱɟɫɤɢɣ Z-ɩɢɧɱ, ɛ − ɦɢɤɪɨɩɢɧɱ, ɜ − ɩɥɚɡɦɟɧɧɵɣ ɮɨɤɭɫ Ɏɢɥɢɩɩɨɜɚ, ɝ − ɩɭɲɤɚ Ɇɟɣɡɟɪɚ. Ɋ −ɪɚɡɪɹɞɧɢɤ, ɋ − ɛɚɬɚɪɟɹ ɤɨɧɞɟɧɫɚɬɨɪɨɜ, ɫɬɪɟɥɤɚ − ɧɚɩɪɚɜɥɟɧɢɟ ɬɨɤɚ
ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɢɡɭɱɟɧɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɰɟɥɨɟ ɫɟɦɟɣɫɬɜɨ ɪɚɡɥɢɱɧɵɯ ɦɨɞɢɮɢɤɚɰɢɣ Z-ɩɢɧɱɚ, ɧɟɤɨɬɨɪɵɟ ɢɡ ɩɪɟɞɫɬɚɜɢɬɟɥɟɣ ɤɨɬɨɪɨɝɨ ɫɯɟɦɚɬɢɱɧɨ ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ. 3.3. Ɇɧɨɝɨɨɛɪɚɡɢɟ ɦɨɞɢɮɢɤɚɰɢɣ ɪɚɡɪɹɞɧɵɯ ɭɫɬɪɨɣɫɬɜ ɬɚɤɨɝɨ ɬɢɩɚ ɧɟ ɫɥɭɱɚɣɧɨ: ɩɨ ɫɭɬɢ ɞɟɥɚ, ɜɫɹ ɢɫɬɨɪɢɹ ɢɫɫɥɟɞɨɜɚɧɢɣ ɜ ɨɛɥɚɫɬɢ ɭɩɪɚɜɥɹɟɦɨɝɨ ɬɟɪɦɨɹɞɟɪɧɨɝɨ ɫɢɧɬɟɡɚ ɛɟɪɟɬ ɧɚɱɚɥɨ ɨɬ ɦɨɳɧɵɯ ɢɦɩɭɥɶɫɧɵɯ ɪɚɡɪɹɞɨɜ ɜ ɝɚɡɟ, ɜ ɤɨɬɨɪɵɯ ɜɩɟɪɜɵɟ ɛɵɥɢ ɨɛɧɚɪɭɠɟɧɵ «ɬɟɪɦɨɹɞɟɪɧɵɟ» ɧɟɣɬɪɨɧɵ ɢ ɤɨɬɨɪɵɟ ɞɥɢɬɟɥɶɧɨɟ ɜɪɟɦɹ ɛɵɥɢ ɪɟɤɨɪɞɫɦɟɧɚɦɢ ɩɨ ɩɚɪɚɦɟɬɪɭ nτ - ɩɪɨɢɡɜɟɞɟɧɢɸ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɥɚɡɦɵ ɧɚ ɜɪɟɦɹ ɭɞɟɪɠɚɧɢɹ. Ɇɧɨɝɢɟ ɫɜɨɢ ɩɨɡɢɰɢɢ ɜɜɢɞɭ ɰɟɥɨɝɨ ɪɹɞɚ ɭɧɢɤɚɥɶɧɵɯ ɫɜɨɣɫɬɜ ɩɢɧɱɢ ɧɟ ɭɬɪɚɬɢɥɢ ɞɨ ɫɢɯ ɩɨɪ.
§ 26. ȼɡɚɢɦɧɨɟ ɩɪɨɧɢɤɧɨɜɟɧɢɟ ɩɥɚɡɦɵ ɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ Ɇɚɝɧɢɬɧɨɟ ɞɚɜɥɟɧɢɟ ɞɟɣɫɬɜɭɟɬ ɧɚ ɩɪɨɜɨɞɧɢɤ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɦ ɤ ɦɚɝɧɢɬɧɵɦ ɫɢɥɨɜɵɦ ɥɢɧɢɹɦ, ɜ ɬɟɱɟɧɢɟ ɜɪɟɦɟɧɢ, ɦɟɧɶɲɟɦ ɫɤɢɧɨɜɨɝɨ ɜɪɟɦɟɧɢ t<τs. Ɂɚ ɜɪɟɦɹ, ɛɨɥɶɲɟɟ ɫɤɢɧɨɜɨɝɨ t>τs, ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɭɫɩɟɜɚɟɬ “ɩɪɨɫɨɱɢɬɶɫɹ” ɜ ɩɪɨɜɨɞɧɢɤ ɢ ɜɟɥɢɱɢɧɵ ɢɧɞɭɤɰɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜɧɭɬɪɢ ɢ ɜɧɟ ɩɪɨɜɨɞɧɢɤɚ ɜɵɪɚɜɧɢɜɚɸɬɫɹ. ȼ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɩɪɨɧɢɤɧɨɜɟɧɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɩɥɚɡɦɭ, ɧɭɠɧɨ ɭɱɢɬɵɜɚɬɶ, ɱɬɨ ɩɪɨɰɟɫɫ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɜɡɚɢɦɧɵɣ − ɧɟ ɬɨɥɶɤɨ ɩɨɥɟ ɩɪɨɧɢɤɚɟɬ ɜ ɩɥɚɡɦɭ, ɧɨ ɢ ɩɥɚɡɦɚ ɩɪɨɧɢɤɚɟɬ ɜ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɧɚɩɪɢɦɟɪ, ɡɚ ɫɱɟɬ ɞɢɮɮɭɡɢɢ, ɢɦɟɸɳɟɣ ɦɟɫɬɨ ɢ ɜ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɨɞɧɨɪɨɞɧɨ. ɉɪɨɧɢɤɧɨɜɟɧɢɟ ɩɨɥɹ ɜ ɩɪɨɜɨɞɧɢɤ ɫ ɩɨɫɬɨɹɧɧɨɣ ɩɪɨɜɨɞɢɦɨɫɬɶɸ σ, ɢɥɢ, ɱɬɨ ɬɨ ɠɟ ɫɚɦɨɟ, ɜ ɨɞɧɨɪɨɞɧɭɸ ɧɟɩɨɞɜɢɠɧɭɸ ɩɥɚɡɦɭ ɫ ɩɨɫɬɨɹɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ, ɮɨɪɦɚɥɶɧɨ ɚɧɚɥɨɝɢɱɧɨ ɞɢɮɮɭɡɢɢ, ɬɚɤ ɤɚɤ ɨɩɢɫɵɜɚɟɬɫɹ (ɩɪɢɛɥɢɠɟɧɧɨ) ɫɯɨɞɧɵɦ ɭɪɚɜɧɟɧɢɟɦ: & ∂ & B = Dɦɚɝ ∆B , (3.23) ∂t ɫ ɤɨɷɮɮɢɰɢɟɧɬ ɦɚɝɧɢɬɧɨɣ ɞɢɮɮɭɡɢɢ Dɦɚɝ, ɨɩɪɟɞɟɥɹɟɦɵɦ ɮɨɪɦɭɥɨɣ (3.2). ɏɨɪɨɲɨ ɢɡɜɟɫɬɧɨ, ɱɬɨ ɷɬɨ ɭɪɚɜɧɟɧɢɟ ɨɩɢɫɵɜɚɟɬ ɨɛɵɱɧɵɣ ɫɤɢɧ-ɷɮɮɟɤɬ. Ƚɥɭɛɢɧɚ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɩɨɥɹ lm ɪɚɫɬɟɬ ɫɨ ɜɪɟɦɟɧɟɦ ɩɨ ɡɚɤɨɧɭ l m ~ Dɦɚɝ t . ȼ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɩɥɚɡɦɚ ɩɨɦɟɳɟɧɚ ɜ ɩɨɫɬɨɹɧɧɨɟ ɨɞɧɨɪɨɞɧɨɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɟɟ ɝɪɚɧɢɰɚ ɩɨɫɬɟɩɟɧɧɨ ɪɚɡɦɵɜɚɟɬɫɹ ɢ ɷɬɨ ɪɚɡɦɵɬɢɟ ɝɪɚɧɢɰɵ ɩɥɚɡɦɵ ɫɜɹɡɚɧɨ ɫ ɞɜɢɠɟɧɢɟɦ ɱɚɫɬɢɰ ɩɨɩɟɪɟɤ ɩɨɥɹ. Ⱥ ɷɬɨ ɜɨɡɦɨɠɧɨ ɬɨɥɶɤɨ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɢ ɱɚɫɬɢɰ, ɬ.ɟ. ɜ ɩɪɨɰɟɫɫɟ ɩɨɩɟɪɟɱɧɨɣ ɞɢɮɮɭɡɢɢ. ɗɬɨɬ ɩɪɨɰɟɫɫ ɨɩɢɫɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ
∂ n = div( D⊥ ∇n ) , ∂t
(3.24)
ɝɞɟ D⊥ =
< ρe > 2
τ ei
.
(3.25)
ȼɟɥɢɱɢɧɚ ɪɚɡɦɵɬɢɹ ɝɪɚɧɢɰɵ ɩɥɚɡɦɵ lp ɡɚ ɜɪɟɦɹ t ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɟɩɟɪɶ ɜɵɪɚɠɟɧɢɟɦ: l p ~ D⊥ t . Ʌɸɛɨɩɵɬɧɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɮɨɪɦɚɥɶɧɨ ɢɦɟɟɬ ɦɟɫɬɨ ɫɨɨɬɧɨɲɟɧɢɟ [17] 1 D⊥ = βDɦɚɝ , (3.26) 2 ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɡɚ ɬɨɠɟ ɫɚɦɨɟ ɜɪɟɦɹ ɬɨɥɳɢɧɚ ɫɥɨɹ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɩɥɚɡɦɵ ɧɢɡɤɨɝɨ ɞɚɜɥɟɧɢɹ ɫ β<1 ɜ ɨɞɧɨɪɨɞɧɨɟ ɩɨɥɟ ɨɤɚɡɵɜɚɟɬɫɹ ɜ β / 2 ɪɚɡ ɦɟɧɶɲɟ ɬɨɥɳɢɧɵ ɫɥɨɹ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɩɨɥɹ ɜ ɨɞɧɨɪɨɞɧɭɸ ɧɟɩɨɞɜɢɠɧɭɸ ɩɥɚɡɦɭ. ȼɚɠɧɨ ɜɵɹɫɧɢɬɶ, ɤɚɤɨɣ ɩɪɨɰɟɫɫ ɹɜɥɹɟɬɫɹ ɞɨɦɢɧɢɪɭɸɳɢɦ, ɤɨɝɞɚ ɢɦɟɟɬ ɦɟɫɬɨ ɜɡɚɢɦɧɚɹ ɞɢɮɮɭɡɢɹ ɩɥɚɡɦɵ ɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɬ.ɟ. ɜ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɢ ɩɥɚɡɦɚ ɢ ɩɨɥɟ ɹɜɥɹɸɬɫɹ ɧɟɨɞɧɨɪɨɞɧɵɦɢ. ȼ ɨɛɳɟɦ ɜɢɞɟ ɷɬɨ ɫɥɨɠɧɚɹ ɡɚɞɚɱɚ, ɧɨ ɞɨɫɬɚɬɨɱɧɨ ɩɪɨɫɬɨɟ ɟɟ ɪɟɲɟɧɢɟ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ, ɟɫɥɢ ɨɝɪɚɧɢɱɢɬɶɫɹ ɫɥɭɱɚɟɦ ɩɥɚɡɦɵ ɧɢɡɤɨɝɨ ɞɚɜɥɟɧɢɹ. ɉɪɨɰɟɫɫ ɞɢɮɮɭɡɢɢ ɹɜɥɹɟɬɫɹ ɧɟɫɬɚɰɢɨɧɚɪɧɵɦ, ɧɨ ɨɛɵɱɧɨ ɟɝɨ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɦɟɞɥɟɧɧɵɦ ɧɚ ɦɚɫɲɬɚɛɚɯ ɜɪɟɦɟɧ ɭɫɬɚɧɨɜɥɟɧɢɹ
ɪɚɜɧɨɜɟɫɢɹ ɩɥɚɡɦɵ. ɂɧɵɦɢ ɫɥɨɜɚɦɢ, ɨɩɢɫɵɜɚɹ ɞɢɮɮɭɡɢɸ, ɜ ɭɪɚɜɧɟɧɢɢ ɞɜɢɠɟɧɢɹ (3.11) ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ ɢɧɟɪɰɢɟɣ, ɢ ɩɪɢɧɹɬɶ, ɱɬɨ 1& & (3.27) j × B − ∇p ≈ 0 . c ɋɱɢɬɚɹ ɷɬɨ ɭɫɥɨɜɢɟ ɜɵɩɨɥɧɟɧɧɵɦ, ɢɡ ɡɚɤɨɧɚ Ɉɦɚ (3.8) ɩɨɥɭɱɢɦ ɜɟɥɢɱɢɧɭ ɧɚɩɪɹɠɟɧɧɨɫɬɢ & ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ & j 1& & 1 E = − v ×B+ ∇p . (3.28) σ c 2 n| e| ɋɬɪɟɦɹɫɶ ɦɚɤɫɢɦɚɥɶɧɨ ɭɩɪɨɫɬɢɬɶ ɨɩɢɫɚɧɢɟ, ɨɝɪɚɧɢɱɢɦɫɹ ɫɥɭɱɚɟɦ ɞɢɮɮɭɡɢɢ ɩɥɚɡɦɵ ɫ ɩɨɫɬɨɹɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ Ɍ=const ɜ ɧɟɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɫ ɩɪɹɦɵɦɢ ɫɢɥɨɜɵɦɢ ɥɢɧɢɹɦɢ, ɨɪɢɟɧɬɢɪɨɜɚɧɧɵɦɢ ɜɞɨɥɶ ɨɫɢ z ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ. ɋɱɢɬɚɟɦ, ɱɬɨ ɜɞɨɥɶ ɷɬɨɝɨ ɧɚɩɪɚɜɥɟɧɢɹ ɩɨɥɟ ɢ ɩɥɚɡɦɚ ɨɞɧɨɪɨɞɧɵ. ȼ & ɷɬɢɯ ɭɫɥɨɜɢɹɯ ɩɨɞɫɬɚɧɨɜɤɚ ɩɨɥɹ E ɢɡ (3.28) ɜ ɡɚɤɨɧ ɢɧɞɭɤɰɢɢ & & 1 ∂B rot E = − , c ∂t ɫ ɩɨɫɥɟɞɭɸɳɢɦ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɭɪɚɜɧɟɧɢɹ ɧɟɩɪɟɪɵɜɧɨɫɬɢ (3.4), ɤɨɬɨɪɨɟ ɡɞɟɫɶ ɭɞɨɛɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ 1 dn & (3.29) = − div v , n dt ɩɪɢɜɨɞɢɬ ɤ ɫɨɨɬɧɨɲɟɧɢɸ d § Bz · ∆Bz . (3.30) ¨ ¸ = Dɦɚɝ dt © n ¹ n ɍɱɬɟɦ ɞɚɥɟɟ, ɱɬɨ (3.27) ɷɤɜɢɜɚɥɟɧɬɧɨ ɫɥɟɞɭɸɳɟɦɭ ɭɫɥɨɜɢɸ Bz 2 1& & j × B − ∇p = −∇ ⊥ ( + p) ≈ 0 . c 8π Ɉɧɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɫɭɦɦɚɪɧɨɟ ɞɚɜɥɟɧɢɟ ɩɥɚɡɦɵ ɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɩɨɞɞɟɪɠɢɜɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ: Bz 2 B0 2 +p= , (3.31) 8π 8π ɝɞɟ ȼ0 ɫɱɢɬɚɟɬɫɹ ɡɚɞɚɧɧɨɣ ɜɟɥɢɱɢɧɨɣ. Ɂɚɦɟɬɢɦ, ɱɬɨ ɩɪɢ ɜɵɜɨɞɟ (3.29) − (3.31) ɹɜɧɨ ɧɢɤɚɤ ɧɟ ɢɫɩɨɥɶɡɨɜɚɥɚɫɶ ɩɪɟɞɩɨɥɚɝɚɟɦɚɹ ɦɚɥɨɫɬɶ ɜɟɥɢɱɢɧɵ β, ɬɚɤ ɱɬɨ ɜ ɷɬɨɦ ɩɥɚɧɟ ɨɧɢ ɹɜɥɹɸɬɫɹ ɩɨɤɚ ɬɨɱɧɵɦɢ. ɍɱɬɟɦ ɷɬɭ ɦɚɥɨɫɬɶ, ɬɨɝɞɚ, ɜɜɟɞɹ ɞɥɹ ɭɞɨɛɫɬɜɚ ɩɪɨɦɟɠɭɬɨɱɧɨɟ ɨɛɨɡɧɚɱɟɧɢɟ, 8πp β0 = 2 << 1 , B0 ɢɡ (3.30) ɩɪɢɛɥɢɠɟɧɧɨ ɩɨɥɭɱɚɟɦ ɜɟɥɢɱɢɧɭ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ 1 Bz ≅ B0 ( 1 − β0 ) . (3.32) 2 ɉɨɫɤɨɥɶɤɭ ɜɟɥɢɱɢɧɚ β0 ɡɞɟɫɶ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɥɚɡɦɵ, ɬɨ, ɢɫɩɨɥɶɡɭɹ ɷɬɨ ɫɨɨɬɧɨɲɟɧɢɟ, ɦɨɠɧɨ ɩɨɤɚɡɚɬɶ (ɩɪɟɞɥɚɝɚɟɦ ɱɢɬɚɬɟɥɸ ɜ ɤɚɱɟɫɬɜɟ ɭɩɪɚɠɧɟɧɢɹ ɩɪɨɞɟɥɚɬɶ ɷɬɨɬ ɧɟɫɥɨɠɧɵɣ ɜɵɜɨɞ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ), ɱɬɨ ɭɪɚɜɧɟɧɢɹ (3.29), (3.30) ɫɜɨɞɹɬɫɹ ɤ ɨɞɧɨɦɭ 1 ∂ n = div( β0 Dɦɚɝ ∇n ) , (3.33) ∂t 2 ɮɨɪɦɚɥɶɧɨ ɫɨɜɩɚɞɚɸɳɟɦɭ ɫ ɭɪɚɜɧɟɧɢɟɦ ɞɢɮɮɭɡɢɢ ɩɥɚɡɦɵ ɜ ɨɞɧɨɪɨɞɧɨɦ ɩɨɥɟ (3.24). Ɍɟɩɟɪɶ, ɨɞɧɚɤɨ, ɜ ɫɢɥɭ (3.32), ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɨɞɧɨɡɧɚɱɧɨ ɫɜɹɡɚɧɨ ɫ
ɩɥɨɬɧɨɫɬɶɸ ɩɥɚɡɦɵ, ɩɨɷɬɨɦɭ ɦɨɠɧɨ ɫɤɚɡɚɬɶ, ɱɬɨ ɨɧɨ «ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɩɨɞɫɬɪɚɢɜɚɟɬɫɹ» ɩɨɞ ɦɟɞɥɟɧɧɨ ɦɟɧɹɸɳɭɸɫɹ ɡɚ ɫɱɟɬ ɞɢɮɮɭɡɢɢ ɩɥɨɬɧɨɫɬɶ ɩɥɚɡɦɵ. ɍɪɚɜɧɟɧɢɟ (3.33) ɹɜɥɹɟɬɫɹ ɧɟɥɢɧɟɣɧɵɦ, ɟɝɨ ɪɟɲɟɧɢɟ - ɧɟɩɪɨɫɬɚɹ ɡɚɞɚɱɚ. Ⱦɥɹ ɢɥɥɸɫɬɪɚɰɢɢ ɜɡɚɢɦɧɨɝɨ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɩɥɚɡɦɵ ɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɪɚɫɫɦɨɬɪɢɦ ɱɚɫɬɧɵɣ ɫɥɭɱɚɣ
ɚ)
ɛ)
Ɋɢɫ. 3.4. Ⱦɢɮɮɭɡɢɨɧɧɨɟ ɪɚɫɩɥɵɜɚɧɢɟ ɫɤɚɱɤɚ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ: ɚ − ɚɜɬɨɦɨɞɟɥɶɧɵɟ ɩɪɨɮɢɥɢ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɡɧɚɱɟɧɢɣ ɜɟɥɢɱɢɧɵ ɫɤɚɱɤɚ (ɩɭɧɤɬɢɪ |ξ|1/2); ɛ − ɷɜɨɥɸɰɢɹ ɫɤɚɱɤɚ ɩɥɨɬɧɨɫɬɢ ɫ ɪɨɫɬɨɦ ɜɪɟɦɟɧɢ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɪɚɫɩɥɵɜɚɧɢɹ ɡɚɞɚɧɧɨɝɨ ɨɞɧɨɦɟɪɧɨɝɨ ɫɤɚɱɤɚ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ. ɍɩɪɨɳɟɧɢɟ ɞɨɫɬɢɝɚɟɬɫɹ ɡɞɟɫɶ ɡɚ ɫɱɟɬ ɬɨɝɨ, ɱɬɨ ɜɫɟ ɬɨɱɤɢ ɩɪɨɮɢɥɹ ɩɥɨɬɧɨɫɬɢ ɞɜɢɠɭɬɫɹ ɩɨ ɩɨɞɨɛɧɵɦ ɬɪɚɟɤɬɨɪɢɹɦ, ɩɨ ɡɚɤɨɧɭ ɞɢɮɮɭɡɢɢ ɞɨɥɠɧɨ ɛɵɬɶ x ~ ɚɜɬɨɦɨɞɟɥɶɧɭɸ ɩɟɪɟɦɟɧɧɭɸ,
ξ=
x 1 D β t 2 ɦɚɝ max
t , ɢ ɦɨɠɧɨ ɜɜɟɫɬɢ, ɤɚɤ ɝɨɜɨɪɹɬ,
,
ɝɞɟ βmax - ɧɨɪɦɢɪɨɜɤɚ, ɬɚɤɚɹ ɱɬɨ β ( x ,t ) = f ( ξ )βmax .
(3.34)
(3.35)
ɉɪɨɮɢɥɶ f(ξ), ɤɚɤ ɫɥɟɞɭɟɬ ɢɡ (3.33), ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɪɚɜɧɟɧɢɸ
df d ξ df (f )+ =0, dξ dξ 2 dξ
ɪɟɲɟɧɢɹ ɤɨɬɨɪɨɝɨ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɡɧɚɱɟɧɢɣ ɜɟɥɢɱɢɧɵ ɫɤɚɱɤɚ ɩɥɨɬɧɨɫɬɢ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 3.4. ɉɪɨɢɡɜɨɥɶɧɵɣ ɫɤɚɱɨɤ ɩɥɨɬɧɨɫɬɢ ɩɨɫɬɟɩɟɧɧɨ ɪɚɡɦɵɜɚɟɬɫɹ ɫ ɬɟɱɟɧɢɟɦ ɜɪɟɦɟɧɢ (ɪɢɫ. 3.4,ɛ). Ɂɚɦɟɬɢɦ, ɱɬɨ ɫɤɚɱɨɤ ɪɚɡɦɵɜɚɟɬɫɹ ɜ ɨɛɟ ɫɬɨɪɨɧɵ ɨɬ ɟɝɨ ɧɚɱɚɥɶɧɨɝɨ ɩɨɥɨɠɟɧɢɹ, ɬɨɥɶɤɨ ɟɫɥɢ ɩɥɨɬɧɨɫɬɶ ɩɥɚɡɦɵ ɩɟɪɜɨɧɚɱɚɥɶɧɨ ɛɵɥɚ ɧɟ ɧɭɥɟɜɨɣ ɩɨ ɨɛɟ ɫɬɨɪɨɧɵ ɨɬ ɧɟɝɨ. ȿɫɥɢ ɠɟ ɩɥɨɬɧɨɫɬɶ ɩɥɚɡɦɵ ɬɨɠɞɟɫɬɜɟɧɧɨ ɪɚɜɧɚ ɧɭɥɸ ɫ ɨɞɧɨɣ ɫɬɨɪɨɧɵ ɨɬ ɫɤɚɱɤɚ (ɧɚɩɪɢɦɟɪ, ɫɩɪɚɜɚ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 3.4,ɚ), ɬɨ ɩɪɨɧɢɤɧɨɜɟɧɢɟ ɩɥɚɡɦɵ ɜ ɷɬɭ ɨɛɥɚɫɬɶ ɨɤɚɡɵɜɚɟɬɫɹ ɧɟɜɨɡɦɨɠɧɵɦ. ɗɬɨ ɧɟɭɞɢɜɢɬɟɥɶɧɨ, ɬɚɤ ɤɚɤ ɩɪɢ ɧɭɥɟɜɨɣ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ ɤɨɷɮɮɢɰɢɟɧɬ ɩɨɩɟɪɟɱɧɨɣ ɞɢɮɮɭɡɢɢ ɬɨɠɞɟɫɬɜɟɧɧɨ ɨɛɪɚɳɚɟɬɫɹ ɜ ɧɭɥɶ ɢ, ɜ ɪɚɦɤɚɯ ɩɪɢɦɟɧɢɦɨɫɬɢ ɭɪɚɜɧɟɧɢɹ (3.33), ɞɢɮɮɭɡɢɹ ɨɤɚɡɵɜɚɟɬɫɹ ɧɟɜɨɡɦɨɠɧɨɣ. ȼ ɷɬɢɯ ɭɫɥɨɜɢɹɯ ɩɪɟɞɩɨɥɨɠɟɧɢɹ, ɡɚɥɨɠɟɧɧɵɟ ɩɪɢ ɜɵɜɨɞɟ (3.33), ɨɱɟɜɢɞɧɨ, ɞɨɥɠɧɵ ɛɵɬɶ ɭɬɨɱɧɟɧɵ.
ȽɅȺȼȺ 4 ɄɈɅȿȻȺɇɂə ɂ ȼɈɅɇɕ ȼ ɉɅȺɁɆȿ. ɇȿɍɋɌɈɃɑɂȼɈɋɌɂ ɉɅȺɁɆɕ ɗɬɨ ɨɱɟɧɶ ɢɧɬɟɪɟɫɧɵɣ, ɧɨ ɜɟɫɶɦɚ ɫɥɨɠɧɵɣ ɪɚɡɞɟɥ ɮɢɡɢɤɢ ɩɥɚɡɦɵ. ɉɥɚɡɦɚ ɢɦɟɟɬ ɦɧɨɝɨ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ, ɟɟ ɫɜɨɣɫɬɜɚ ɫɢɥɶɧɨ ɦɟɧɹɸɬɫɹ ɩɪɢ ɧɚɥɨɠɟɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ (ɜɨɡɧɢɤɚɟɬ ɫɢɥɶɧɚɹ ɚɧɢɡɨɬɪɨɩɢɹ). ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ ɫɩɟɤɬɪ ɜɨɡɦɨɠɧɵɯ ɜ ɧɟɣ ɤɨɥɟɛɚɧɢɣ ɢ ɜɨɥɧ ɹɜɥɹɟɬɫɹ ɜɟɫɶɦɚ ɲɢɪɨɤɢɦ. Ɇɵ ɪɚɫɫɦɨɬɪɢɦ ɥɢɲɶ ɧɟɤɨɬɨɪɵɟ, ɧɚɢɛɨɥɟɟ ɯɚɪɚɤɬɟɪɧɵɟ ɩɪɢɦɟɪɵ ɞɥɹ ɢɡɨɬɪɨɩɧɨɣ (ɧɟɡɚɦɚɝɧɢɱɟɧɧɨɣ) ɩɥɚɡɦɵ ɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɩɪɨɫɬɟɣɲɢɯ ɬɢɩɨɜ ɜɨɥɧ ɜ ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɟ. Ȼɨɥɟɟ ɩɨɞɪɨɛɧɨɟ ɢɡɥɨɠɟɧɢɟ ɦɨɠɧɨ ɧɚɣɬɢ, ɧɚɩɪɢɦɟɪ, ɜ [18,19]. Ɉɛɵɱɧɨ ɤɥɚɫɫɢɮɢɤɚɰɢɹ ɬɢɩɨɜ ɜɨɥɧ ɧɚɱɢɧɚɟɬɫɹ ɫ ɪɚɡɞɟɥɟɧɢɹ ɢɯ ɧɚ ɩɪɨɞɨɥɶɧɵɟ ɢ ɩɨɩɟɪɟɱɧɵɟ ɜɨɥɧɵ. Ⱦɥɹ ɦɟɯɚɧɢɱɟɫɤɢɯ ɜɨɥɧ ɩɪɨɞɨɥɶɧɨɫɬɶ ɢɥɢ ɩɨɩɟɪɟɱɧɨɫɬɶ ɜɨɥɧɵ ɫɜɹɡɵɜɚɸɬ ɫ ɯɚɪɚɤɬɟɪɨɦ ɞɜɢɠɟɧɢɹ ɜ ɧɟɣ ɱɚɫɬɢɰ − ɜɞɨɥɶ ɢɥɢ ɩɨɩɟɪɟɤ ɧɚɩɪɚɜɥɟɧɢɹ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜɨɥɧɵ. ɇɚɩɪɢɦɟɪ, ɡɜɭɤɨɜɵɟ ɜɨɥɧɵ, ɫ ɩɨɦɨɳɶɸ ɤɨɬɨɪɵɯ ɥɟɤɬɨɪ ɞɨɜɨɞɢɬ ɞɨ ɫɜɨɢɯ ɫɥɭɲɚɬɟɥɟɣ ɢɧɮɨɪɦɚɰɢɸ ɨɛ ɨɛɫɭɠɞɚɟɦɨɦ ɩɪɟɞɦɟɬɟ, ɹɜɥɹɸɬɫɹ ɩɪɨɞɨɥɶɧɵɦɢ ɫɝɭɳɟɧɢɹ ɢ ɪɚɡɪɟɠɟɧɢɹ ɝɚɡɚ, ɩɨ ɫɭɬɢ ɞɟɥɚ ɢ ɩɪɟɞɫɬɚɜɥɹɸɳɢɟ ɫɨɛɨɣ ɡɜɭɤɨɜɭɸ ɜɨɥɧɭ, ɩɪɨɢɫɯɨɞɹɬ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ. Ⱦɥɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɜɨɥɧɵ ɟɟ ɩɪɨɞɨɥɶɧɨɫɬɶ ɢɥɢ ɩɨɩɟɪɟɱɧɨɫɬɶ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɡɚɢɦɧɨɣ ɨɪɢɟɧɬɚɰɢɟɣ ɜɟɤɬɨɪɚ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜɨɥɧɵ (ɜɨɥɧɨɜɨɝɨ ɜɟɤɬɨɪɚ) ɢ ɜɟɤɬɨɪɚ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜɨɥɧɵ. ȿɫɥɢ ɜɨɥɧɨɜɨɣ ɜɟɤɬɨɪ ɢ ɜɟɤɬɨɪ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜɨɥɧɵ ɤɨɥɥɢɧɟɚɪɧɵɟ, ɬɨ ɬɚɤɚɹ ɜɨɥɧɚ ɹɜɥɹɟɬɫɹ ɩɪɨɞɨɥɶɧɨɣ. ȿɫɥɢ ɠɟ ɩɥɨɫɤɨɫɬɶ ɤɨɥɟɛɚɧɢɣ ɜɟɤɬɨɪɚ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɚ ɧɚɩɪɚɜɥɟɧɢɸ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜɨɥɧɵ, ɬɨ ɬɚɤɚɹ ɜɨɥɧɚ ɹɜɥɹɟɬɫɹ ɩɨɩɟɪɟɱɧɨɣ. ɉɪɢɦɟɪɨɦ ɫɬɪɨɝɨ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɵ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ ɜɨɥɧɚ - ɫɜɟɬ - ɜ ɜɚɤɭɭɦɟ. Ⱦɥɹ ɩɨɩɟɪɟɱɧɵɯ ɜɨɥɧ ɜ ɩɨɩɟɪɟɱɧɨɣ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜɨɥɧɵ ɩɥɨɫɤɨɫɬɢ, ɨɱɟɜɢɞɧɨ, ɦɨɠɧɨ ɜɜɟɫɬɢ ɞɜɚ ɧɟɡɚɜɢɫɢɦɵɯ ɜɡɚɢɦɧɨ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɵɯ ɧɚɩɪɚɜɥɟɧɢɹ. ɋɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɝɨɜɨɪɹɬ ɨ ɞɜɭɯ ɧɟɡɚɜɢɫɢɦɵɯ ɩɨɥɹɪɢɡɚɰɢɹɯ ɜɨɥɧɵ. ȼ ɩɥɚɡɦɟ, ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɧɚɥɢɱɢɹ ɢɥɢ ɨɬɫɭɬɫɬɜɢɹ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɜɨɡɦɨɠɧɨ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɢ ɩɪɨɞɨɥɶɧɵɯ ɢ ɩɨɩɟɪɟɱɧɵɯ ɜɨɥɧ, ɩɪɢɱɟɦ ɩɪɢ ɧɚɥɢɱɢɢ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜɨɡɦɨɠɧɨ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɢ ɩɪɨɞɨɥɶɧɵɯ ɢ ɩɨɩɟɪɟɱɧɵɯ ɜɨɥɧ ɤɚɤ ɜɞɨɥɶ, ɬɚɤ ɢ ɩɨɩɟɪɟɤ ɷɬɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ȼ ɫɜɹɡɢ ɫ ɷɬɢɦ ɜɚɠɧɨ ɧɟ ɩɭɬɚɬɶ ɯɚɪɚɤɬɟɪ ɜɨɥɧɵ − ɩɪɨɞɨɥɶɧɚɹ ɨɧɚ ɢɥɢ ɩɨɩɟɪɟɱɧɚɹ − ɢ ɯɚɪɚɤɬɟɪ ɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ: ɜɞɨɥɶ ɢɥɢ ɩɨɩɟɪɟɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɜ ɤɨɬɨɪɨɟ ɩɨɦɟɳɟɧɚ ɩɥɚɡɦɚ. ɋ ɜɨɡɧɢɤɧɨɜɟɧɢɟɦ ɢ ɪɚɫɤɚɱɤɨɣ ɤɨɥɟɛɚɧɢɣ ɢ ɜɨɥɧ ɜ ɩɥɚɡɦɟ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɫɜɹɡɚɧɵ ɦɧɨɝɢɟ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɩɥɚɡɦɵ, ɤɨɬɨɪɵɟ ɛɭɞɭɬ ɨɛɫɭɠɞɚɬɶɫɹ ɜ ɡɚɤɥɸɱɢɬɟɥɶɧɨɦ ɪɚɡɞɟɥɟ ɷɬɨɣ ɝɥɚɜɵ. § 27. Ⱦɢɫɩɟɪɫɢɨɧɧɵɟ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɩɪɨɞɨɥɶɧɵɯ ɢ ɩɨɩɟɪɟɱɧɵɯ ɜɨɥɧ ɦɚɥɨɣ ɚɦɩɥɢɬɭɞɵ ɇɚɩɨɦɧɢɦ ɤɪɚɬɤɨ ɨɫɧɨɜɧɵɟ ɫɜɟɞɟɧɢɹ ɢɡ ɮɢɡɢɤɢ ɜɨɥɧɨɜɵɯ ɩɪɨɰɟɫɫɨɜ. Ɉɫɧɨɜɧɵɦ ɫɨɨɬɧɨɲɟɧɢɟɦ, ɨɩɪɟɞɟɥɹɸɳɢɦ ɭɫɥɨɜɢɹ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜɨɥɧɵ ɜ ɞɚɧɧɨɣ ɫɪɟɞɟ, ɹɜɥɹɟɬɫɹ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ, ɭɫɬɚɧɚɜɥɢɜɚɸɳɢɣ ɫɜɹɡɶ ɱɚɫɬɨɬɵ ɤɨɥɟɛɚɧɢɣ ɢ ɜɨɥɧɨɜɨɝɨ ɜɟɤɬɨɪɚ: & ω = ω( k ) . (4.1) Ɂɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɩɨɡɜɨɥɹɟɬ ɨɩɪɟɞɟɥɢɬɶ ɮɚɡɨɜɭɸ ɫɤɨɪɨɫɬɶ ɜɨɥɧɵ & & ω( k ) k & vɮ = ⋅ , (4.2) k k ɢ ɟɟ ɝɪɭɩɩɨɜɭɸ ɫɤɨɪɨɫɬɶ & ∂ω ( k ) & & . vɝ ɪ = (4.3) ∂k
Ƚɪɭɩɩɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɨɥɧɵ ɨɩɪɟɞɟɥɹɟɬ ɩɟɪɟɧɨɫ ɜɨɥɧɨɜɨɣ ɷɧɟɪɝɢɢ ɢ ɩɨɷɬɨɦɭ ɧɢɤɨɝɞɚ ɧɟ ɦɨɠɟɬ ɩɪɟɜɵɲɚɬɶ ɫɤɨɪɨɫɬɶ ɫɜɟɬɚ ɜ ɜɚɤɭɭɦɟ vɝ ɪ < c . Ɏɚɡɨɜɚɹ ɫɤɨɪɨɫɬɶ − ɫɤɨɪɨɫɬɶ ɩɟɪɟɦɟɳɟɧɢɹ ɜ ɜɨɥɧɟ ɬɨɱɟɤ ɫ ɩɨɫɬɨɹɧɧɨɣ ɮɚɡɨɣ − ɧɟ ɫɜɹɡɚɧɚ ɫ ɩɟɪɟɧɨɫɨɦ ɜɨɥɧɨɣ ɷɧɟɪɝɢɢ, ɚ ɩɨɬɨɦɭ ɧɟ ɨɝɪɚɧɢɱɟɧɚ ɜɟɥɢɱɢɧɨɣ ɫɤɨɪɨɫɬɢ ɫɜɟɬɚ. ȼ ɩɪɢɧɰɢɩɟ, ɨɧɚ ɦɨɠɟɬ ɛɵɬɶ ɥɸɛɨɣ ɩɨ ɜɟɥɢɱɢɧɟ, ɜ ɬɨɦ ɱɢɫɥɟ ɢ ɛɨɥɶɲɟ ɫɤɨɪɨɫɬɢ ɫɜɟɬɚ, ɟɫɥɢ ɷɬɨ ɩɨɡɜɨɥɹɟɬ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ. Ⱦɢɫɩɟɪɫɢɨɧɧɵɟ ɫɜɨɣɫɬɜɚ ɞɚɧɧɨɣ ɫɪɟɞɵ, ɟɫɥɢ ɨɝɪɚɧɢɱɢɬɶɫɹ ɨɛɥɚɫɬɶɸ ɜɨɥɧ ɦɚɥɨɣ ɚɦɩɥɢɬɭɞɵ, ɦɨɠɧɨ ɭɫɬɚɧɨɜɢɬɶ, ɪɚɫɫɦɚɬɪɢɜɚɹ ɨɬɤɥɢɤ ɫɪɟɞɵ ɧɚ ɦɚɥɨɟ ɜɨɡɞɟɣɫɬɜɢɟ. Ⱦɥɹ ɜɨɥɧ ɤɨɧɟɱɧɨɣ ɚɦɩɥɢɬɭɞɵ ɫɢɬɭɚɰɢɹ ɫɥɨɠɧɟɟ: ɬɚɤɢɟ ɜɨɥɧɵ ɢɡɦɟɧɹɸɬ ɫɜɨɣɫɬɜɚ ɫɪɟɞɵ, ɜ ɤɨɬɨɪɨɣ ɪɚɫɩɪɨɫɬɪɚɧɹɸɬɫɹ. ɍɩɪɨɳɟɧɧɨ ɷɬɨ ɦɨɠɧɨ ɬɪɚɤɬɨɜɚɬɶ ɤɚɤ ɩɨɹɜɥɟɧɢɟ ɡɚɜɢɫɢɦɨɫɬɢ ɱɚɫɬɨɬɵ ɤɨɥɟɛɚɧɢɣ ɨɬ ɚɦɩɥɢɬɭɞɵ ɜɨɥɧɵ ɚ: & ω = ω( k ,a ) . (4.4) Ɍɚɤɨɜɚ ɫɢɬɭɚɰɢɹ ɞɥɹ ɫɥɚɛɨ ɧɟɥɢɧɟɣɧɵɯ ɜɨɥɧ, ɧɚɩɪɢɦɟɪ, ɥɟɧɝɦɸɪɨɜɫɤɢɯ ɫɨɥɢɬɨɧɨɜ [17]. Ɉɝɪɚɧɢɱɢɦɫɹ ɡɞɟɫɶ ɪɚɫɫɦɨɬɪɟɧɢɟɦ ɜɨɥɧ ɦɚɥɨɣ ɚɦɩɥɢɬɭɞɵ. ɍɧɢɜɟɪɫɚɥɶɧɵɣ ɩɨɞɯɨɞ, ɫɩɪɚɜɟɞɥɢɜɵɣ ɞɥɹ ɜɨɥɧ ɥɸɛɨɣ ɩɪɢɪɨɞɵ, ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɫɥɟɞɭɸɳɟɦ. ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɨɟ ~& ~& ɩɨɥɟ ɜɨɥɧɵ E , B ɫɥɟɞɭɟɬ ɨɩɪɟɞɟɥɹɬɶ ɢɡ ɭɪɚɜɧɟɧɢɣ Ɇɚɤɫɜɟɥɥɚ: ~& 1 ∂B ~& rot E = − , c ∂t ~& ~& 4π ~& 1 ∂E rot B = j+ , (4.5) c c ∂t ~& div E = 4πρ~q , ~& div B = 0 . ~& Ɂɞɟɫɶ ρ~q , j − ɧɚɜɟɞɟɧɧɚɹ ɜ ɫɪɟɞɟ ɩɨɥɟɦ ɜɨɥɧɵ ɩɥɨɬɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɡɚɪɹɞɚ ɢ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ. ɗɬɢ ɜɟɥɢɱɢɧɵ ɧɟ ɹɜɥɹɸɬɫɹ ɩɨɥɧɨɫɬɶɸ ɧɟɡɚɜɢɫɢɦɵɦɢ, ɚ, ɤɚɤ ɷɬɨ ɫɥɟɞɭɟɬ ɢɡ (4.5), ɫɜɹɡɚɧɵ ɫɨɨɬɧɨɲɟɧɢɟɦ ∂ρ~q ~& = − div j , (4.6) ∂t ɜɵɪɚɠɚɸɳɟɦ ɫɨɛɨɣ ɡɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɡɚɪɹɞɚ. ȼ ɷɬɨɦ ɧɟɬɪɭɞɧɨ ɭɛɟɞɢɬɶɫɹ, ɩɪɢɦɟɧɢɜ ɨɩɟɪɚɰɢɸ ɞɢɜɟɪɝɟɧɰɢɢ ɤɨ ɜɬɨɪɨɦɭ ɭɪɚɜɧɟɧɢɸ ɫɢɫɬɟɦɵ (4.5). ɉɨɫɤɨɥɶɤɭ ɤɨɷɮɮɢɰɢɟɧɬɵ ɭɪɚɜɧɟɧɢɣ (4.5), (4.6) ɹɜɧɨ ɧɟ ɫɨɞɟɪɠɚɬ ɤɨɨɪɞɢɧɚɬ ɢ ɜɪɟɦɟɧɢ, ɦɨɠɧɨ ɢɫɤɚɬɶ ɪɟɲɟɧɢɟ ɜ && ɜɢɞɟ ɝɚɪɦɨɧɢɱɟɫɤɨɣ ɜɨɥɧɵ ~ exp( − iωt + ikr ) . Ɍɚɤ ɤɚɤ ɩɪɨɢɡɜɨɞɧɵɟ ɩɨ ɜɪɟɦɟɧɢ ɢ ɤɨɨɪɞɢɧɚɬɚɦ ɨɬ ɝɚɪɦɨɧɢɱɟɫɤɨɣ ɜɨɥɧɵ ɬɚɤɨɝɨ ɜɢɞɚ ɫɜɨɞɹɬɫɹ ɤ ɚɥɝɟɛɪɚɢɱɟɫɤɨɦɭ & ɞɨɦɧɨɠɟɧɢɸ ɧɚ ( −iω ) ɢ ( ik ) ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, && && ∂ exp( − iωt + ikr ) = ( − iω ) exp( − iωt + ikr ) , ∂t && & && ∂ & exp( − iωt + ikr ) = ( ik ) exp( − iωt + ikr ) , ∂r ɬɨ ɭɪɚɜɧɟɧɢɹ (4.5) ɩɪɢ ɬɚɤɨɣ ɩɨɞɫɬɚɧɨɜɤɟ ɩɪɟɜɪɚɳɚɸɬɫɹ ɜ ɚɥɝɟɛɪɚɢɱɟɫɤɢɟ: & ~& ω ~& k ×E = B , c & ~& 4π ~& iω ~& ik × B = j− E, (4.7) c c & ~& ik E = 4πρ~q , & ~& kB =0. ɉɟɪɜɨɟ ɢɡ ɷɬɢɯ ɫɨɨɬɧɨɲɟɧɢɣ ɜɵɪɚɠɚɟɬ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɜɨɥɧɵ ɱɟɪɟɡ ɷɥɟɤɬɪɢɱɟɫɤɨɟ
~& c & ~& B = k ×E ,
ω
ɢ ɩɪɢ ɬɚɤɨɦ ɨɩɪɟɞɟɥɟɧɢɢ, ɨɱɟɜɢɞɧɨ, ɩɨɫɥɟɞɧɟɟ ɢɡ ɫɨɨɬɧɨɲɟɧɢɣ (4.7) ɫɬɚɧɨɜɢɬɫɹ ɬɨɠɞɟɫɬɜɨɦ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɨɨɬɧɨɲɟɧɢɹ (4.7) ɫɜɨɞɹɬɫɹ ɤ ɫɥɟɞɭɸɳɢɦ: c & & ~& 4π ~& iω ~& E, i k ×( k × E ) = j− (4.8) c ω c & ~& ik E = 4πρ~q . Ⱦɨ ɫɢɯ ɩɨɪ ɦɵ ɧɟ ɜɵɫɤɚɡɵɜɚɥɢ ɧɢɤɚɤɢɯ ɩɪɟɞɩɨɥɨɠɟɧɢɣ ɨ ɫɜɹɡɢ ɧɚɜɟɞɟɧɧɨɣ ɜɨɥɧɨɣ ɜ ɫɪɟɞɟ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ (ɢɥɢ ɡɚɪɹɞɚ) ɢ ɟɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. Ʉɚɤ ɷɬɨ ɩɪɢɧɹɬɨ, ɞɥɹ ɜɨɥɧ ɦɚɥɨɣ ɚɦɩɥɢɬɭɞɵ ɷɬɚ ɫɜɹɡɶ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ ɥɢɧɟɣɧɨɣ: & & & j = σ( ω , k )E , (4.9) ɚ ɧɚɛɨɪ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ ɫɨɫɬɚɜɥɹɟɬ ɬɟɧɡɨɪ ɩɪɨɜɨɞɢɦɨɫɬɢ σ , ɡɚɜɢɫɹɳɢɣ ɨɬ ɫɜɨɣɫɬɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɫɪɟɞɵ, ɚ ɬɚɤɠɟ, ɜɨɨɛɳɟ ɝɨɜɨɪɹ, ɨɬ ɱɚɫɬɨɬɵ ɜɨɥɧɵ ɢ ɜɨɥɧɨɜɨɝɨ ɜɟɤɬɨɪɚ. ɉɨ ɨɩɪɟɞɟɥɟɧɢɸ ɷɬɨɬ ɬɟɧɡɨɪ ɫɜɹɡɚɧ ɫ ɬɟɧɡɨɪɨɦ & ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ε( ω , k ) ɫɪɟɞɵ ɫɨɨɬɧɨɲɟɧɢɟɦ: & & 4πi ε( ω , k ) = δ + σ( ω , k ) , (4.10)
ω
ɝɞɟ ɩɟɪɜɨɟ ɫɥɚɝɚɟɦɨɟ − ɟɞɢɧɢɱɧɚɹ ɞɢɚɝɨɧɚɥɶɧɚɹ ɦɚɬɪɢɰɚ. ɉɨɫɤɨɥɶɤɭ, ɜ ɫɢɥɭ (4.6), ɧɚɜɟɞɟɧɧɚɹ ɩɥɨɬɧɨɫɬɶ ɡɚɪɹɞɚ ɞɨɥɠɧɚ ɛɵɬɶ ɫɜɹɡɚɧɚ ɫ ɧɚɜɟɞɟɧɧɨɣ ɩɥɨɬɧɨɫɬɶɸ ɬɨɤɚ ɫɨɨɬɧɨɲɟɧɢɟɦ & ~& ωρ~q = k j , ɬɨ ɜɬɨɪɨɟ ɢɡ ɫɨɨɬɧɨɲɟɧɢɣ (4.8) ɮɚɤɬɢɱɟɫɤɢ ɹɜɥɹɟɬɫɹ ɫɥɟɞɫɬɜɢɟɦ ɩɟɪɜɨɝɨ. ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ, ɫ ɭɱɟɬɨɦ ɨɩɪɟɞɟɥɟɧɢɹ ɬɟɧɡɨɪɚ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ, ɩɨɫɥɟ ɩɪɨɫɬɵɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɩɪɢɯɨɞɢɦ ɤ ɨɞɧɨɪɨɞɧɨɣ ɚɥɝɟɛɪɚɢɱɟɫɤɨɣ ɡɚɞɚɱɟ: εij ki k j ( 2 − δij + 2 )E j = 0 , (4.11) N k ɝɞɟ ɜɟɥɢɱɢɧɚ 2 § kc · 2 N =¨ ¸ (4.12) ©ω¹ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɤɜɚɞɪɚɬ ɩɨɤɚɡɚɬɟɥɹ ɩɪɟɥɨɦɥɟɧɢɹ ɜɨɥɧɵ. Ɉɞɧɨɪɨɞɧɚɹ ɡɚɞɚɱɚ (4.11), ɤɚɤ ɢɡɜɟɫɬɧɨ, ɢɦɟɟɬ ɧɟɧɭɥɟɜɨɟ ɪɟɲɟɧɢɟ ɧɟ ɜɫɟɝɞɚ, ɚ ɬɨɥɶɤɨ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɭɫɥɨɜɢɹ. Ⱥ ɢɦɟɧɧɨ, & ɞɟɬɟɪɦɢɧɚɧɬ ɜɯɨɞɹɳɟɣ ɜ (4.11) ɦɚɬɪɢɰɵ ɞɨɥɠɟɧ ɛɵɬɶ ɪɚɜɟɧ ɧɭɥɸ: εij ( ω , k ) ki k j δ Det ( − + ) = 0. (4.13) ij N2 k2 ɗɬɨ ɭɫɥɨɜɢɟ ɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɞɢɫɩɟɪɫɢɨɧɧɨɟ ɭɪɚɜɧɟɧɢɟ, ɨɩɪɟɞɟɥɹɸɳɟɟ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ (4.1) ɜɨɥɧ, ɫɩɨɫɨɛɧɵɯ ɫɭɳɟɫɬɜɨɜɚɬɶ ɜ ɞɚɧɧɨɣ ɫɪɟɞɟ. ȿɫɥɢ ɞɢɫɩɟɪɫɢɨɧɧɨɟ ɭɪɚɜɧɟɧɢɟ ɢɦɟɟɬ ɧɟɫɤɨɥɶɤɨ ɪɟɲɟɧɢɣ, ɬɨ ɨ ɧɢɯ ɝɨɜɨɪɹɬ ɤɚɤ ɨ ɜɟɬɜɹɯ ɢɥɢ ɨ ɦɨɞɚɯ ɫɨɛɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ. ȿɫɥɢ ɫɪɟɞɚ, ɜ ɤɨɬɨɪɨɣ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɜɨɥɧɵ, ɢɡɨɬɪɨɩɧɚ, ɬɚɤ ɱɬɨ ɟɞɢɧɫɬɜɟɧɧɵɦ ɜɵɞɟɥɟɧɧɵɦ ɧɚɩɪɚɜɥɟɧɢɟɦ ɹɜɥɹɟɬɫɹ ɧɚɩɪɚɜɥɟɧɢɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɫɚɦɨɣ ɜɨɥɧɵ, ɬɨ ɫɪɟɞɢ ɜɫɟɯ ɤɨɦɩɨɧɟɧɬ ɬɟɧɡɨɪɚ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɨɬɥɢɱɧɵ ɨɬ ɧɭɥɹ ɥɢɲɶ ɞɜɟ ɤɨɦɩɨɧɟɧɬɵ − ɩɪɨɞɨɥɶɧɚɹ εl ɢ ɩɨɩɟɪɟɱɧɚɹ εtr ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜɨɥɧɵ (ɡɞɟɫɶ ɢɧɞɟɤɫɵ l ɢ tr – ɧɚɱɚɥɶɧɵɟ ɛɭɤɜɵ ɚɧɝɥɢɣɫɤɢɯ ɬɟɪɦɢɧɨɜ longitudinal – ɩɪɨɞɨɥɶɧɵɣ ɢ transversal - ɩɨɩɟɪɟɱɧɵɣ). ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɷɬɨɬ ɬɟɧɡɨɪ ɨɤɚɡɵɜɚɟɬɫɹ ɫɥɟɞɭɸɳɢɦ: ki k j ki k j εij = εtr ( δij − 2 ) + εl 2 , (4.14) k k ɚ ɞɢɫɩɟɪɫɢɨɧɧɨɟ ɭɪɚɜɧɟɧɢɟ, ɤɚɤ ɥɟɝɤɨ ɩɪɨɜɟɪɢɬɶ, ɩɪɢɜɨɞɢɬɫɹ ɤ ɜɢɞɭ:
&
εij ( ω , k )
ki k j
εl § εtr
2
· 2 2 2 ¨ 2 − 1¸ = 0 . © ¹ N k N N Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɤɚɤ ɦɵ ɜɢɞɢɦ, ɫɭɳɟɫɬɜɭɸɬ ɞɜɟ ɜɨɡɦɨɠɧɨɫɬɢ ɜɵɩɨɥɧɢɬɶ ɷɬɨ ɭɫɥɨɜɢɟ: εl = 0 , (4.15) 2 εtr = N . (4.16) ɉɟɪɜɚɹ ɢɡ ɧɢɯ ɨɬɜɟɱɚɟɬ ɩɪɨɞɨɥɶɧɵɦ ɜɨɥɧɚɦ, ɚ ɜɬɨɪɚɹ − ɩɨɩɟɪɟɱɧɵɦ. ɉɨɥɟɡɧɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɟɫɥɢ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɚɹ ɞɢɫɩɟɪɫɢɹ (ɬ.ɟ. ɡɚɜɢɫɢɦɨɫɬɶ ɤɨɦɩɨɧɟɧɬ ɬɟɧɡɨɪɚ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɨɬ ɜɨɥɧɨɜɨɝɨ ɜɟɤɬɨɪɚ) ɧɟɫɭɳɟɫɬɜɟɧɧɚ, ɬɨ ɩɪɨɞɨɥɶɧɚɹ ɢ ɩɨɩɟɪɟɱɧɚɹ ɤɨɦɩɨɧɟɧɬɵ ɫɨɜɩɚɞɚɸɬ εl = εtr ≡ ε , ɢ ɦɨɠɧɨ ɝɨɜɨɪɢɬɶ ɥɢɲɶ ɨɛ ɨɞɧɨɣ ɜɟɥɢɱɢɧɟ ε - ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɫɪɟɞɵ. Ɉɧɚ ɢ ɨɩɪɟɞɟɥɹɟɬ ɞɢɫɩɟɪɫɢɨɧɧɵɟ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɩɪɨɞɨɥɶɧɵɯ ε = 0, (4.17) ɢ ɩɨɩɟɪɟɱɧɵɯ ɜɨɥɧ ε = N2. (4.18) ɇɚɩɪɢɦɟɪ, ɜ ɜɚɤɭɭɦɟ, ɤɨɝɞɚ, ɨɱɟɜɢɞɧɨ, ɩɪɨɜɨɞɢɦɨɫɬɶ ɪɚɜɧɚ ɧɭɥɸ, ɩɨɥɭɱɚɟɦ ɢɡ (4.10) εɜɚɤ = 1 , ɩɨɷɬɨɦɭ, ɫɨɝɥɚɫɧɨ (4.17), ɩɪɨɞɨɥɶɧɵɟ ɜɨɥɧɵ ɧɟɜɨɡɦɨɠɧɵ, ɚ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɩɨɩɟɪɟɱɧɵɯ ɜɨɥɧ, ɤɚɤ ɷɬɨ ɫɥɟɞɭɟɬ ɢɡ (4.18) ɢ (4.12), ɨɤɚɡɵɜɚɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ω = kc . ɇɚɩɨɦɧɢɦ, ɱɬɨ ɩɨɩɟɪɟɱɧɵɟ ɜɨɥɧɵ ɦɨɝɭɬ ɢɦɟɬɶ ɞɜɚ ɧɟɡɚɜɢɫɢɦɵɯ ɧɚɩɪɚɜɥɟɧɢɹ ɩɨɥɹɪɢɡɚɰɢɢ. ɉɨɞɱɟɪɤɧɟɦ ɜ ɡɚɤɥɸɱɟɧɢɟ, ɱɬɨ ɟɫɥɢ ɩɥɚɡɦɚ ɚɧɢɡɨɬɪɨɩɧɚ, ɧɚɩɪɢɦɟɪ, ɩɨɦɟɳɟɧɚ ɜ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɢɥɢ ɜ ɧɟɣ ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ ɩɭɱɨɤ ɱɚɫɬɢɰ, ɬɚɤ ɱɬɨ ɫɭɳɟɫɬɜɭɟɬ ɹɜɧɨ ɜɵɞɟɥɟɧɧɨɟ ɧɚɩɪɚɜɥɟɧɢɟ, ɬɨ ɩɪɟɞɫɬɚɜɥɟɧɢɟ (4.14) ɞɥɹ ɬɟɧɡɨɪɚ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɧɟ ɫɩɪɚɜɟɞɥɢɜɨ, ɧɨ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɞɥɹ ɩɪɨɞɨɥɶɧɵɯ (ɢɥɢ, ɬɨɱɧɟɟ, «ɩɨɱɬɢ» ɩɪɨɞɨɥɶɧɵɯ, ɩɨɞɪɨɛɧɟɟ ɫɦ. [20]) ɜɨɥɧ ɩɨ-ɩɪɟɠɧɟɦɭ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ (4.15), ɟɫɥɢ ɩɨɞ «ɩɪɨɞɨɥɶɧɨɣ» ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɶɸ ɩɨɧɢɦɚɬɶ ɜɟɥɢɱɢɧɭ ki k j εl ≡ 2 εij . k
Det (
− δij +
)=
§ 28. Ɇɟɬɨɞ ɦɚɥɵɯ ɤɨɥɟɛɚɧɢɣ. Ⱦɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɧɟɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɵ Ʉɚɤ ɫɥɟɞɭɟɬ ɢɡ ɢɡɥɨɠɟɧɧɨɝɨ ɜ ɩɪɟɞɵɞɭɳɟɦ ɩɚɪɚɝɪɚɮɟ, ɜɫɟ ɫɜɨɣɫɬɜɚ ɜɨɥɧ, ɫɩɨɫɨɛɧɵɯ ɪɚɫɩɪɨɫɬɪɚɧɹɬɶɫɹ ɜ ɞɚɧɧɨɣ ɫɪɟɞɟ, ɜ ɬɨɦ ɱɢɫɥɟ ɢ ɜ ɩɥɚɡɦɟ, ɨɩɪɟɞɟɥɹɸɬɫɹ ɟɟ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɶɸ. ɉɨɷɬɨɦɭ ɧɚɲɚ ɛɥɢɠɚɣɲɚɹ ɰɟɥɶ − ɭɫɬɚɧɨɜɢɬɶ ɢ ɢɫɫɥɟɞɨɜɚɬɶ ɞɢɷɥɟɤɬɪɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɩɥɚɡɦɵ. ɉɪɟɠɞɟ ɱɟɦ ɩɟɪɟɣɬɢ ɤ ɪɚɫɫɦɨɬɪɟɧɢɸ ɤɨɧɤɪɟɬɧɵɯ ɩɥɚɡɦɟɧɧɵɯ ɜɨɥɧ ɧɚɩɨɦɧɢɦ ɞɜɚ ɪɟɡɭɥɶɬɚɬɚ, ɤɨɬɨɪɵɟ ɦɵ ɭɠɟ ɨɛɫɭɠɞɚɥɢ ɪɚɧɟɟ. ȼɨ-ɩɟɪɜɵɯ, ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɯɨɥɨɞɧɨɣ ɩɥɚɡɦɵ ɞɨɥɠɧɚ ɨɩɪɟɞɟɥɹɬɶɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ (ɫɦ. § 11):
(
)
2
ε = 1 − ωp / ω ,
ω p2 = ω pe2 + ω pi2
(4.19)
ɝɞɟ ω − ɱɚɫɬɨɬɚ ɤɨɥɟɛɚɧɢɣ, ɚ ω p − ɥɟɧɝɦɸɪɨɜɫɤɚɹ (ɢɥɢ ɩɥɚɡɦɟɧɧɚɹ) ɱɚɫɬɨɬɚ. ȼɨɡɧɢɤɚɟɬ ɜɨɩɪɨɫ, ɤɚɤɭɸ ɩɥɚɡɦɭ ɦɨɠɧɨ ɧɚɡɜɚɬɶ ɯɨɥɨɞɧɨɣ? Ⱦɥɹ ɨɬɜɟɬɚ ɧɚ ɷɬɨɬ ɜɨɩɪɨɫ, ɨɱɟɜɢɞɧɨ, ɧɚɞɨ ɫɨɩɨɫɬɚɜɢɬɶ ɯɚɪɚɤɬɟɪɧɵɟ ɫɤɨɪɨɫɬɢ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɢ ɮɚɡɨɜɵɟ ɫɤɨɪɨɫɬɢ ɩɥɚɡɦɟɧɧɵɯ ɜɨɥɧ. Ⱦɥɹ ɪɚɜɧɨɜɟɫɧɨɣ ɩɥɚɡɦɵ ɯɚɪɚɤɬɟɪɧɚɹ ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ (ɜ ɨɬɫɭɬɫɬɜɢɟ ɜɨɥɧɵ!) − ɷɬɨ ɬɟɩɥɨɜɚɹ ɫɤɨɪɨɫɬɶ (ɛɨɥɶɲɚɹ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɩɥɚɡɦɵ), ɩɨɷɬɨɦɭ, ɢɡɭɱɚɹ ɭɫɥɨɜɢɹ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜɨɥɧ, ɩɥɚɡɦɭ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɯɨɥɨɞɧɨɣ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɭɫɥɨɜɢɹ:
vɮ ≡
ω
>> vTe , vTi . (4.20) k ɉɨɫɤɨɥɶɤɭ ɷɬɨ ɭɫɥɨɜɢɟ ɨɝɪɚɧɢɱɢɜɚɟɬ ɱɚɫɬɨɬɭ ɜɨɥɧ ɫɧɢɡɭ, ɬɨ ɨɧɨ ɨɬɜɟɱɚɟɬ ɜɵɫɨɤɨɱɚɫɬɨɬɧɨɦɭ ɩɪɟɞɟɥɭ, ɚ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɮɨɪɦɭɥɚ (4.19) ɨɩɪɟɞɟɥɹɟɬ ɞɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɥɚɡɦɵ ɜ ɜɵɫɨɤɨɱɚɫɬɨɬɧɨɦ ɩɪɟɞɟɥɟ. ȼɨ-ɜɬɨɪɵɯ, ɧɚɩɨɦɧɢɦ, ɱɬɨ ɩɪɢ ɨɛɫɭɠɞɟɧɢɢ ɞɟɛɚɟɜɫɤɨɣ ɞɥɢɧɵ ɷɤɪɚɧɢɪɨɜɚɧɢɹ (ɫɦ. §3 ɢ §11) ɛɵɥɨ ɩɨɥɭɱɟɧɨ ɭɪɚɜɧɟɧɢɟ ɷɤɪɚɧɢɪɨɜɤɢ
∆ϕ =
ϕ
, (4.21) rD2 ɝɞɟ rD - ɪɚɞɢɭɫ Ⱦɟɛɚɹ ɞɥɹ ɩɥɚɡɦɵ. ɗɤɪɚɧɢɪɨɜɤɚ ɡɞɟɫɶ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɤɚɤ ɫɬɚɬɢɱɟɫɤɢɣ ɩɪɨɰɟɫɫ, ɩɨɷɬɨɦɭ ɭɪɚɜɧɟɧɢɟ (4.21) ɨɬɪɚɠɚɟɬ ɞɢɷɥɟɤɬɪɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɩɥɚɡɦɵ ɜ ɫɬɚɬɢɱɟɫɤɨɦ ɩɪɟɞɟɥɟ. ɉɨɥɚɝɚɹ ɜ (4.21) && ϕ ~ e ikr , ɩɪɢɯɨɞɢɦ ɤ ɫɥɟɞɭɸɳɟɦɭ ɪɟɡɭɥɶɬɚɬɭ: 1 1 1 1 ε =1+ 2 2 , (4.22) 2 ≡ 2 + 2 , k rD rD rDe rDi ɨɩɪɟɞɟɥɹɸɳɟɦɭ ɞɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɥɚɡɦɵ ɜ ɫɬɚɬɢɱɟɫɤɨɦ ɩɪɟɞɟɥɟ, ɫɩɪɚɜɟɞɥɢɜɨɦ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɭɫɥɨɜɢɹ, ɨɛɪɚɬɧɨɝɨ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ (4.19):
vɮ ≡
ω
<< vTi , vTe . (4.23) k ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɜ ɨɛɨɢɯ ɩɪɟɞɟɥɶɧɵɯ ɫɥɭɱɚɹɯ ɫɬɪɭɤɬɭɪɚ ε ɨɤɚɡɵɜɚɟɬɫɹ ɫɥɟɞɭɸɳɟɣ: ε = 1 + δεe + δεi . ɉɟɪɜɨɟ ɫɥɚɝɚɟɦɨɟ ɡɞɟɫɶ − ɟɞɢɧɢɰɚ − ɜɤɥɚɞ ɜɚɤɭɭɦɚ, ɚ ɨɫɬɚɥɶɧɵɟ ɞɜɚ ɨɬɜɟɱɚɸɬ ɜɤɥɚɞɭ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ȼɤɥɚɞ ɪɚɡɥɢɱɧɵɯ ɤɨɦɩɨɧɟɧɬ ɨɤɚɡɵɜɚɟɬɫɹ ɚɞɞɢɬɢɜɧɵɦ ɜɫɥɟɞɫɬɜɢɟ ɨɬɫɭɬɫɬɜɢɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɟɠɞɭ ɧɢɦɢ. ɑɬɨɛɵ ɫɨɫɬɚɜɢɬɶ ɛɨɥɟɟ ɩɨɥɧɭɸ ɤɚɪɬɢɧɭ ɞɢɷɥɟɤɬɪɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɧɟɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɵ, ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɦɟɬɨɞɨɦ ɦɚɥɵɯ ɤɨɥɟɛɚɧɢɣ. Ⱦɥɹ ɭɩɪɨɳɟɧɢɹ, ɢ ɡɞɟɫɶ ɫɥɟɞɭɟɬ ɫɪɚɡɭ ɨɝɨɜɨɪɢɬɶɫɹ, ɛɭɞɟɦ ɩɪɟɧɟɛɪɟɝɚɬɶ ɷɮɮɟɤɬɚɦɢ ɪɟɡɨɧɚɧɫɧɵɯ ɫ ɜɨɥɧɨɣ ɱɚɫɬɢɰ. Ɋɟɡɨɧɚɧɫɧɵɟ ɷɮɮɟɤɬɵ ɢɝɪɚɸɬ ɩɪɢɧɰɢɩɢɚɥɶɧɭɸ ɪɨɥɶ ɜɨ ɦɧɨɝɢɯ ɩɥɚɡɦɟɧɧɵɯ ɹɜɥɟɧɢɹɯ - ɧɚɩɪɢɦɟɪ, ɜ ɦɟɯɚɧɢɡɦɟ ɛɟɫɫɬɨɥɤɧɨɜɢɬɟɥɶɧɨɝɨ ɡɚɬɭɯɚɧɢɹ Ʌɚɧɞɚɭ, ɧɨ ɢɯ ɭɱɟɬ ɬɪɟɛɭɟɬ ɭɫɥɨɠɧɟɧɢɹ ɨɩɢɫɚɧɢɹ ɩɥɚɡɦɵ, ɩɨɷɬɨɦɭ ɩɨɤɚ ɢɯ ɧɟ ɛɭɞɟɦ ɡɚɬɪɚɝɢɜɚɬɶ.
ɋɭɬɶ ɦɟɬɨɞɚ ɦɚɥɵɯ ɤɨɥɟɛɚɧɢɣ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɫɥɟɞɭɸɳɟɦ. ɉɪɢ ɜɨɡɞɟɣɫɬɜɢɢ ɧɚ ɩɟɪɜɨɧɚɱɚɥɶɧɨ ɧɟɜɨɡɦɭɳɟɧɧɭɸ ɩɥɚɡɦɭ ɜɨɥɧɵ ɦɚɥɨɣ ɚɦɩɥɢɬɭɞɵ ɥɨɝɢɱɧɨ ɨɠɢɞɚɬɶ ɩɨɹɜɥɟɧɢɹ ɦɚɥɨɝɨ ɨɬɤɥɢɤɚ, ɩɨɷɬɨɦɭ ɦɨɠɧɨ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɪɚɡɥɨɠɟɧɢɟɦ ɜɟɥɢɱɢɧɵ ɷɬɨɝɨ ɨɬɤɥɢɤɚ ɩɨ ɚɦɩɥɢɬɭɞɟ ɜɨɥɧɵ, ɩɪɟɧɟɛɪɟɝɚɹ ɧɟɥɢɧɟɣɧɵɦɢ ɷɮɮɟɤɬɚɦɢ. Ʉɪɨɦɟ ɬɨɝɨ, ɛɟɡ ɭɱɟɬɚ ɪɟɡɨɧɚɧɫɧɵɯ ɷɮɮɟɤɬɨɜ, ɞɜɢɠɟɧɢɟ ɱɚɫɬɢɰ ɩɥɚɡɦɵ, ɢɧɞɭɰɢɪɭɟɦɨɟ ɜɨɥɧɨɣ, ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɫ ɩɨɦɨɳɶɸ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɭɪɚɜɧɟɧɢɣ, ɡɚɩɢɫɚɜ ɞɥɹ ɤɚɠɞɨɝɨ ɫɨɪɬɚ ɱɚɫɬɢɰ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɢ ɭɪɚɜɧɟɧɢɹ ɫɨɯɪɚɧɟɧɢɹ ɜɟɳɟɫɬɜɚ. Ɋɚɫɫɦɨɬɪɢɦ ɩɪɨɫɬɟɣɲɢɣ ɩɪɢɦɟɪ: ɢɞɟɚɥɶɧɭɸ ɯɨɥɨɞɧɭɸ ɩɥɚɡɦɭ ɛɟɡ ɩɭɱɤɨɜ. ɗɬɨ ɡɧɚɱɢɬ, ɱɬɨ ɦɵ ɩɪɟɧɟɛɪɟɠɟɦ ɬɟɩɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ ɱɚɫɬɢɰ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫɨ ɫɤɨɪɨɫɬɶɸ, ɩɪɢɨɛɪɟɬɚɟɦɨɣ ɢɦɢ ɜ ɫɚɦɨɫɨɝɥɚɫɨɜɚɧɵɯ ɩɨɥɹɯ. ɗɬɨɬ ɩɪɨɫɬɨɣ ɩɪɢɦɟɪ ɹɜɥɹɟɬɫɹ ɭɞɨɛɧɨɣ ɨɬɩɪɚɜɧɨɣ ɬɨɱɤɨɣ ɞɥɹ ɛɨɥɟɟ ɫɥɨɠɧɵɯ ɫɢɬɭɚɰɢɣ. ȼ ɧɟɜɨɡɦɭɳɟɧɧɨɦ ɪɚɜɧɨɜɟɫɧɨɦ ɫɨɫɬɨɹɧɢɢ ɩɨɥɚɝɚɟɦ, ɱɬɨ ɩɥɨɬɧɨɫɬɶ ɩɥɚɡɦɵ ɨɞɧɨɪɨɞɧɚɹ noe=Znoi=no=const, ɧɟɬ ɜɧɟɲɧɟɝɨ & & ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ Eo=0 ɢ ɩɨɬɨɤɨɜ ɱɚɫɬɢɰ v oe = v oi = 0 . ɉɨɞ ɜɨɡɞɟɣɫɬɜɢɟɦ ɩɨɥɹ ɜɨɥɧɵ ɱɚɫɬɢɰɵ ɩɥɚɡɦɵ ɩɪɢɞɭɬ ɜ ɞɜɢɠɟɧɢɟ, ɩɨɥɭɱɢɜ ɭɫɤɨɪɟɧɢɟ, ɨɩɪɟɞɟɥɹɟɦɨɟ ɭɪɚɜɧɟɧɢɹɦɢ ɞɜɢɠɟɧɢɹ: & ∂~ ve ~& = − e n0 e E , me n0 e (4.24) ∂t & ∂~ vi ~& = Z e n0 i E . mi n0 i ∂t ɉɪɢ ɡɚɩɢɫɢ (4.24) ɭɱɥɢ, ɱɬɨ ɩɨɥɟ ɢɦɟɟɬ ɦɚɥɭɸ ɚɦɩɥɢɬɭɞɭ, ɩɨɷɬɨɦɭ ɜɫɟ ɧɟɥɢɧɟɣɧɵɟ ɫɥɚɝɚɟɦɵɟ ɨɩɭɳɟɧɵ. ɉɨ ɷɬɨɣ ɠɟ ɩɪɢɱɢɧɟ ɜ ɩɪɚɜɵɯ ɱɚɫɬɹɯ ɮɢɝɭɪɢɪɭɟɬ ɥɢɲɶ ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɱɚɫɬɢɰɵ ɫɢɥɚ, ɨɛɭɫɥɨɜɥɟɧɧɚɹ ɷɥɟɤɬɪɢɱɟɫɤɢɦ ɩɨɥɟɦ ɜɨɥɧɵ. Ⱦɟɣɫɬɜɭɹ ɩɨ ɪɟɰɟɩɬɭ, ɩɪɟɞɥɨɠɟɧɧɨɦɭ ɜ ɩɪɟɞɵɞɭɳɟɦ ɩɚɪɚɝɪɚɮɟ, ɫɱɢɬɚɟɦ ɩɨɥɟ ɜɨɥɧɵ ɢ ɫɤɨɪɨɫɬɢ ɝɚɪɦɨɧɢɱɟɫɤɢɦɢ, && ~& & E ,~ v e ,i ~ e − iωt +ikr . Ⱦɚɥɟɟ, ɫ ɩɨɦɨɳɶɸ (4.24) ɜɵɱɢɫɥɹɟɦ ɫɤɨɪɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ, ɚ ɡɚɬɟɦ ɢ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ, ɢɧɞɭɰɢɪɭɟɦɨɝɨ ɜɨɥɧɨɣ. Ɋɟɡɭɥɶɬɚɬ ɨɤɚɡɵɜɚɟɬɫɹ ɫɥɟɞɭɸɳɢɦ: i e 2 n0 e Z 2 e 2 n0 i ~& ~& & & 2 ~ ~ j ≡ e ( Z n0 i v i − n0 e v e ) = ( )E . + mi ω me Ʉɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ ɦɟɠɞɭ ɩɥɨɬɧɨɫɬɶɸ ɬɨɤɚ ɢ ɧɚɩɪɹɠɟɧɧɨɫɬɶɸ ɩɨɥɹ ɜɨɥɧɵ ɞɚɟɬ ɜɟɥɢɱɢɧɭ ɩɪɨɜɨɞɢɦɨɫɬɢ ɩɥɚɡɦɵ, ɤɨɬɨɪɚɹ ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɩɪɟɞɟɥɟ ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɨɣ i e2 n Z 2 e 2 n0 i σ = ( 0e + ). (4.25) ω me mi ȼɤɥɚɞ ɜ ɩɪɨɜɨɞɢɦɨɫɬɶ ɞɚɸɬ ɨɛɟ ɤɨɦɩɨɧɟɧɬɵ ɩɥɚɡɦɵ, ɧɨ, ɟɫɬɟɫɬɜɟɧɧɨ, ɧɟ ɜ ɪɚɜɧɨɣ ɦɟɪɟ. Ɉɛɵɱɧɨ ɷɥɟɤɬɪɨɧɧɵɣ ɜɤɥɚɞ ɹɜɥɹɟɬɫɹ ɞɨɦɢɧɢɪɭɸɳɢɦ. ȼɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶ ɬɟɩɟɪɶ ɨɩɪɟɞɟɥɟɧɢɟɦ (4.10), ɦɨɠɧɨ ɜɵɱɢɫɥɢɬɶ ɞɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ, ɤɨɬɨɪɚɹ, ɤɚɤ ɧɟɬɪɭɞɧɨ ɩɪɨɜɟɪɢɬɶ, ɫɨɜɩɚɞɟɬ ɫ ɩɪɢɜɟɞɟɧɧɨɣ ɜɵɲɟ ɜɟɥɢɱɢɧɨɣ (4.19). ɍɫɥɨɠɧɢɦ ɦɨɞɟɥɶ ɩɥɚɡɦɵ, ɜɜɨɞɹ ɜ ɪɚɫɫɦɨɬɪɟɧɢɟ ɜɨɡɦɨɠɧɨɫɬɶ ɩɟɪɟɞɚɱɢ ɢɦɩɭɥɶɫɚ ɜ ɫɬɨɥɤɧɨɜɟɧɢɹɯ ɦɟɠɞɭ ɢɨɧɚɦɢ ɢ ɷɥɟɤɬɪɨɧɚɦɢ. ɍɱɟɬ ɷɬɨɝɨ ɷɮɮɟɤɬɚ ɩɪɢɜɨɞɢɬ ɤ ɩɨɹɜɥɟɧɢɸ ɜ ɭɪɚɜɧɟɧɢɹɯ ɞɜɢɠɟɧɢɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɫɥɚɝɚɟɦɵɯ, ɩɪɨɢɫɯɨɠɞɟɧɢɟ ɤɨɬɨɪɵɯ − ɜɡɚɢɦɧɨɟ ɬɪɟɧɢɟ ɤɨɦɩɨɧɟɧɬ ɩɥɚɡɦɵ:
& & & ~ ∂~ ve ve − ~ vi ~& me n0 e = − e n0 e E − n0 e me , ∂t τ ei & & & ~ ∂~ vi ve − ~ vi ~& mi n0 i = Z e n0 i E + n0 e me . ∂t τ ei
(4.26)
ȼɵɱɢɫɥɟɧɢɟ ɫɤɨɪɨɫɬɟɣ ɤɨɦɩɨɧɟɧɬ ɩɥɚɡɦɵ ɬɟɩɟɪɶ ɧɟɫɤɨɥɶɤɨ ɭɫɥɨɠɧɹɟɬɫɹ, ɧɨ ɟɝɨ ɦɨɠɧɨ ɭɩɪɨɫɬɢɬɶ, ɟɫɥɢ ɭɱɟɫɬɶ ɫɥɟɞɭɸɳɟɟ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ. Ɂɚɦɟɬɢɦ, ɱɬɨ ɥɸɛɨɣ ɜɵɞɟɥɟɧɧɵɣ ɟɞɢɧɢɱɧɵɣ ɨɛɴɟɦ ɩɥɚɡɦɵ ɜ ɧɚɲɟɣ ɦɨɞɟɥɢ ɹɜɥɹɟɬɫɹ ɧɟɣɬɪɚɥɶɧɵɦ ɩɨ ɡɚɪɹɞɭ. ɉɨɷɬɨɦɭ ɞɟɣɫɬɜɭɸɳɢɟ ɧɚ ɧɟɝɨ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɫɢɥɵ ɤɨɦɩɟɧɫɢɪɭɸɬ ɞɪɭɝ ɞɪɭɝɚ. Ʉɪɨɦɟ ɬɨɝɨ, ɩɟɪɟɞɚɱɚ ɢɦɩɭɥɶɫɚ ɦɟɠɞɭ ɢɨɧɚɦɢ ɢ ɷɥɟɤɬɪɨɧɚɦɢ ɧɟ ɦɟɧɹɟɬ ɜ ɰɟɥɨɦ ɢɦɩɭɥɶɫɚ ɜɵɞɟɥɟɧɧɨɝɨ ɨɛɴɟɦɚ ɩɥɚɡɦɵ! ɉɨɷɬɨɦɭ, ɟɫɥɢ ɢɦɩɭɥɶɫ ɷɬɨɝɨ ɟɞɢɧɢɱɧɨɝɨ ɨɛɴɟɦɚ ɩɟɪɜɨɧɚɱɚɥɶɧɨ ɛɵɥ ɧɭɥɟɜɵɦ, ɬɨ ɨɧ ɨɫɬɚɟɬɫɹ ɬɚɤɨɜɵɦ ɢ ɜ ɞɚɥɶɧɟɣɲɟɦ:
& & me n0 e ~ ve + mi n0 i ~ vi = 0 . ɗɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɩɨɡɜɨɥɹɟɬ ɜɵɪɚɡɢɬɶ ɨɞɧɭ ɫɤɨɪɨɫɬɶ ɱɟɪɟɡ ɞɪɭɝɭɸ, ɧɚɩɪɢɦɟɪ ɢɨɧɧɭɸ ɫɤɨɪɨɫɬɶ ɱɟɪɟɡ ɷɥɟɤɬɪɨɧɧɭɸ ɫɤɨɪɨɫɬɶ:
mn & Zm & & ~ vi = − e 0 e ~ ve = − e ~ v . mi n0 i mi e ɍɪɚɜɧɟɧɢɹ (4.26) ɜ ɪɟɡɭɥɶɬɚɬɟ ɫɜɨɞɹɬɫɹ ɤ ɨɞɧɨɦɭ, ɧɚɩɪɢɦɟɪ, ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɛɭɞɟɬ ɫɥɟɞɭɸɳɢɦ:
& ∂~ 1 + Zme / mi ~& ve ~& = − e n0 e E − n0 e me me n0 e ve , ∂t τ ei
ɢ ɬɟɩɟɪɶ ɭɠɟ ɧɟɫɥɨɠɧɨ ɜɵɱɢɫɥɢɬɶ ɫɤɨɪɨɫɬɢ ɢ ɫ ɢɯ ɩɨɦɨɳɶɸ ɩɥɨɬɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ. Ⱦɥɹ ɝɚɪɦɨɧɢɱɟɫɤɨɣ ɜɨɥɧɵ ɨɧɚ ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɨɣ:
~& ~& j = σE ,
σ=
i( 1 + Zme / mi ) e 2 n0 , ω + iνei ( 1 + Zme / mi ) me −1
(4.27)
ɢ ɜɧɨɜɶ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɣ ɩɨɥɸ ɜɨɥɧɵ. Ɂɞɟɫɶ νei = τ ei − ɱɚɫɬɨɬɚ ɷɥɟɤɬɪɨɧ-ɢɨɧɧɵɯ ɫɬɨɥɤɧɨɜɟɧɢɣ, ɩɪɨɜɨɞɢɦɨɫɬɶ ɩɥɚɡɦɵ. Ⱦɥɹ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɩɨɥɭɱɚɟɦ:
ε =1−
ω p2 ω [ ω + iνei ( 1 + Zme / mi )]
.
σ
−
(4.28)
Ʉɚɤ ɦɵ ɜɢɞɢɦ, ɨɧɚ ɫɬɚɧɨɜɢɬɫɹ ɜɟɥɢɱɢɧɨɣ ɤɨɦɩɥɟɤɫɧɨɣ. ɗɬɨ ɹɜɥɹɟɬɫɹ ɫɥɟɞɫɬɜɢɟɦ ɬɨɝɨ, ɱɬɨ ɫɬɨɥɤɧɨɜɟɧɢɹ ɩɪɢɜɨɞɹɬ ɤ ɡɚɬɭɯɚɧɢɸ ɤɨɥɟɛɚɧɢɣ, ɬɨ ɟɫɬɶ ɤ ɞɢɫɫɢɩɚɰɢɢ ɷɧɟɪɝɢɢ. Ɂɚɦɟɬɢɦ, ɱɬɨ ɜ (4.28) ɬɟɩɟɪɶ ɭɠɟ ɧɟɥɶɡɹ ɜɵɞɟɥɢɬɶ ɨɬɞɟɥɶɧɨ ɜɤɥɚɞ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ - ɚɞɞɢɬɢɜɧɨɫɬɶ ɜɤɥɚɞɨɜ ɧɚɪɭɲɚɟɬɫɹ ɢɡ-ɡɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɤɨɦɩɨɧɟɧɬ ɩɥɚɡɦɵ. ɉɨɞɱɟɪɤɧɟɦ ɟɳɟ ɨɞɧɨ ɜɚɠɧɨɟ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ. ɂɫɩɨɥɶɡɨɜɚɧɧɵɟ ɜ (4.26) ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɩɥɨɬɧɨɫɬɢ ɫɢɥ ɜɡɚɢɦɧɨɝɨ ɬɪɟɧɢɹ ɦɟɠɞɭ ɷɥɟɤɬɪɨɧɚɦɢ ɢ ɢɨɧɚɦɢ
f ei = − n0 e me
& & ~ ve − ~ vi
τ ei
,
ɢɥɢ ɦɟɠɞɭ ɢɨɧɚɦɢ ɢ ɷɥɟɤɬɪɨɧɚɦɢ
f ie = n0 e me
& & ~ ve − ~ vi
τ ei
,
ɨɬɥɢɱɚɸɬɫɹ ɩɨ ɡɧɚɤɭ − ɬɚɤ ɢ ɞɨɥɠɧɨ ɛɵɬɶ ɞɥɹ ɫɨɯɪɚɧɟɧɢɹ ɢɦɩɭɥɶɫɚ ɜ ɰɟɥɨɦ ɜ ɢɨɧ-ɷɥɟɤɬɪɨɧɧɨɣ ɫɢɫɬɟɦɟ, ɧɨ, ɧɚ ɩɟɪɜɵɣ ɜɡɝɥɹɞ, ɧɟɫɢɦɦɟɬɪɢɱɧɵ ɩɪɢ «ɛɭɤɜɟɧɧɨɣ» ɩɟɪɟɫɬɚɧɨɜɤɟ ɦɚɫɫ, ɡɚɪɹɞɨɜ ɢ ɤɨɧɰɟɧɬɪɚɰɢɣ ɱɚɫɬɢɰ. ȼ ɞɟɣɫɬɜɢɬɟɥɶɧɨɫɬɢ, ɧɟɨɛɯɨɞɢɦɚɹ ɫɢɦɦɟɬɪɢɹ ɢɦɟɟɬ ɦɟɫɬɨ. Ⱦɨɫɬɚɬɨɱɧɨ ɜɫɩɨɦɧɢɬɶ, ɱɬɨ, ɤɚɤ ɷɬɨ ɛɵɥɨ ɩɨɤɚɡɚɧɨ ɜ § 9, ɷɬɢ ɩɚɪɚɦɟɬɪɵ ɞɨɥɠɧɵ ɜɯɨɞɢɬɶ ɜ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɜɪɟɦɟɧɢ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
τ ei ~
me µei me mi . , µei = 2 2 ee ei n0 i me + mi
Ɍɟɩɟɪɶ, ɩɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ ɜ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɩɥɨɬɧɨɫɬɟɣ ɫɢɥ ɬɪɟɧɢɹ, ɬɪɟɛɭɟɦɚɹ ɫɢɦɦɟɬɪɢɹ ɫɬɚɧɨɜɢɬɫɹ ɨɱɟɜɢɞɧɨɣ.
ȼ ɭɪɚɜɧɟɧɢɹɯ (4.24), (4.26) ɦɵ ɩɪɟɧɟɛɪɟɝɥɢ ɷɮɮɟɤɬɚɦɢ, ɫɜɹɡɚɧɧɵɦɢ ɫ ɤɨɧɟɱɧɨɫɬɶɸ ɬɟɦɩɟɪɚɬɭɪɵ ɩɥɚɡɦɵ, ɱɬɨ ɫɩɪɚɜɟɞɥɢɜɨ ɜ ɜɵɫɨɤɨɱɚɫɬɨɬɧɨɣ ɨɛɥɚɫɬɢ, ɤɨɝɞɚ ɜɵɩɨɥɧɟɧɨ ɭɫɥɨɜɢɟ (4.20). ɑɬɨɛɵ ɩɪɨɞɜɢɧɭɬɶɫɹ ɜ ɨɛɥɚɫɬɶ ɦɟɧɶɲɢɯ ɱɚɫɬɨɬ, ɤɨɝɞɚ ɮɚɡɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɨɥɧɵ ɨɤɚɡɵɜɚɟɬɫɹ ɨɞɧɨɝɨ ɩɨɪɹɞɤɚ ɫ ɬɟɩɥɨɜɵɦɢ ɫɤɨɪɨɫɬɹɦɢ ɱɚɫɬɢɰ, ɧɟɨɛɯɨɞɢɦɨ ɭɫɥɨɠɧɢɬɶ ɦɨɞɟɥɶ ɩɥɚɡɦɵ, ɜɤɥɸɱɚɹ ɷɮɮɟɤɬɵ ɤɨɧɟɱɧɨɝɨ ɞɚɜɥɟɧɢɹ, ɱɬɨ ɦɵ ɢ ɫɨɛɢɪɚɟɦɫɹ ɬɟɩɟɪɶ ɫɞɟɥɚɬɶ. ȼɦɟɫɬɟ ɫ ɬɟɦ ɞɥɹ ɭɩɪɨɳɟɧɢɹ ɛɭɞɟɦ ɩɪɟɧɟɛɪɟɝɚɬɶ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ. ɗɬɨ ɜɨɡɦɨɠɧɨ, ɟɫɥɢ ɬɟɦɩɟɪɚɬɭɪɚ ɞɨɫɬɚɬɨɱɧɨ ɜɟɥɢɤɚ. ɇɚɩɨɦɧɢɦ, ɱɬɨ ɱɚɫɬɨɬɚ ɢɨɧ-ɷɥɟɤɬɪɨɧɧɵɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɛɵɫɬɪɨ ɭɛɵɜɚɟɬ ɫ ɪɨɫɬɨɦ ɬɟɦɩɟɪɚɬɭɪɵ: νei ~ Te−3 / 2 . ȿɫɥɢ ɬɟɦɩɟɪɚɬɭɪɚ ɩɥɚɡɦɵ ɤɨɧɟɱɧɚɹ, ɬɨ ɜ ɩɪɚɜɵɟ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɣ ɞɜɢɠɟɧɢɹ (4.24) ɧɟɨɛɯɨɞɢɦɨ ɞɨɛɚɜɢɬɶ ɫɥɚɝɚɟɦɵɟ ɫ ɝɪɚɞɢɟɧɬɨɦ ɞɚɜɥɟɧɢɹ. ɉɭɫɬɶ ɬɟɦɩɟɪɚɬɭɪɚ ɤɨɦɩɨɧɟɧɬ ɩɥɚɡɦɵ ɩɨɫɬɨɹɧɧɚɹ, ɬɨɝɞɚ ɝɪɚɞɢɟɧɬ ɞɚɜɥɟɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɝɪɚɞɢɟɧɬɨɦ ɜɨɡɦɭɳɟɧɢɹ ɩɥɨɬɧɨɫɬɢ: ∇~ pe ,i = Te ,i ∇n~e ,i ,
ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɞɨɩɨɥɧɢɬɶ ɭɪɚɜɧɟɧɢɹɦɢ, ɨɩɪɟɞɟɥɹɸɳɢɦɢ ɜɨɡɦɭɳɟɧɢɟ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ. ȿɫɥɢ ɱɢɫɥɨ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɫɨɯɪɚɧɹɟɬɫɹ, ɬɨ ɧɟɨɛɯɨɞɢɦɵɟ ɧɚɦ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɫɨɨɬɧɨɲɟɧɢɹ ɞɚɸɬ ɭɪɚɜɧɟɧɢɹ ɧɟɩɪɟɪɵɜɧɨɫɬɢ. Ⱦɥɹ ɦɚɥɵɯ ɜɨɡɦɭɳɟɧɢɣ ɧɚ ɮɨɧɟ ɨɞɧɨɪɨɞɧɨɣ ɩɥɚɡɦɵ ɷɬɨ ɭɪɚɜɧɟɧɢɹ ɜɢɞɚ: ∂n~e ,i & v e ,i ) . = − div( n0 e ,i ~ ∂t Ʉɪɨɦɟ ɦɨɞɟɥɢ ɩɥɚɡɦɵ ɫ ɩɨɫɬɨɹɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ, ɱɚɫɬɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɦɨɞɟɥɶ ɩɨɥɢɬɪɨɩɵ, ɜ ɤɨɬɨɪɨɣ ɞɚɜɥɟɧɢɟ ɢ ɬɟɦɩɟɪɚɬɭɪɚ ɩɥɚɡɦɵ ɩɪɟɞɩɨɥɚɝɚɸɬɫɹ ɫɬɟɩɟɧɧɵɦɢ ɮɭɧɤɰɢɹɦɢ ɩɥɨɬɧɨɫɬɢ: γ pe ,i = ne ,iTe ,i ~ ne ,ei,i , ɝɞɟ γ e ,i = const ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɩɨɤɚɡɚɬɟɥɶ ɩɨɥɢɬɪɨɩɵ. Ⱦɥɹ ɷɬɨɝɨ ɫɥɭɱɚɹ ɝɪɚɞɢɟɧɬ ɞɚɜɥɟɧɢɹ ɞɥɹ ɦɚɥɵɯ ɜɨɡɦɭɳɟɧɢɣ ɛɭɞɟɬ ɪɚɜɟɧ ∇~ pe ,i = γ e ,iTe ,i ∇n~e ,i . Ɉɛɴɟɞɢɧɹɹ ɜɦɟɫɬɟ ɜɫɟ ɜɵɲɟ ɫɤɚɡɚɧɧɨɟ, ɩɪɢɯɨɞɢɦ ɤ ɫɥɟɞɭɸɳɟɣ ɦɨɞɟɥɢ ɞɥɹ «ɬɟɩɥɨɣ ɩɥɚɡɦɵ»: & ∂~ vα ~& = eα n0α E − γ α T0α ∇n~α , mα n0α (4.29) ∂t ∂n~α & = − div( n0α ~ vα ) . ∂t Ɂɞɟɫɶ ɢɧɞɟɤɫ α = e , i ɨɛɨɡɧɚɱɚɟɬ «ɫɨɪɬ» ɱɚɫɬɢɰ ɩɥɚɡɦɵ − ɢɨɧ ɢɥɢ ɷɥɟɤɬɪɨɧ. Ɍɚɤ, ɧɚɩɪɢɦɟɪ, ee = − e − ɡɚɪɹɞ ɷɥɟɤɬɪɨɧɚ, ɚ ei = Z e − ɡɚɪɹɞ ɢɨɧɚ. ȼɧɨɜɶ ɩɪɟɞɩɨɥɚɝɚɹ ɜɨɥɧɵ ɝɚɪɦɨɧɢɱɟɫɤɢɦɢ, ɜɵɱɢɫɥɹɟɦ ɜɨɡɦɭɳɟɧɢɟ ɩɥɨɬɧɨɫɬɢ ɢ ɫɤɨɪɨɫɬɢ ɤɨɦɩɨɧɟɧɬ ɩɥɚɡɦɵ: &~& & ~& kv ie kE α α , n~α = n0α = ω mα ω 2 − k 2 cs2α & & & ~& k k ~& 2~ 2 2 ieα ω E − k csα ( E − k ( k E )) T & ~ vα = ; cs2α ≡ γ α 0α , 2 2 2 ωmα ω − k csα mα ɝɞɟ, ɩɨ ɚɧɚɥɨɝɢɢ ɫ ɝɚɡɨɦ, ɞɥɹ ɤɪɚɬɤɨɫɬɢ ɜɜɟɞɟɧɨ ɨɛɨɡɧɚɱɟɧɢɟ csα ɞɥɹ «ɫɤɨɪɨɫɬɢ ɡɜɭɤɚ» ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɤɨɦɩɨɧɟɧɬɵ ɩɥɚɡɦɵ. ɍɦɧɨɠɢɜ ɧɚɣɞɟɧɧɵɟ ɫɤɨɪɨɫɬɢ ɤɨɦɩɨɧɟɧɬ ɩɥɚɡɦɵ ɧɚ ɡɚɪɹɞ ɢ ɧɟɜɨɡɦɭɳɟɧɧɭɸ ɩɥɨɬɧɨɫɬɶ, ɩɪɨɫɭɦɦɢɪɨɜɚɜ ɡɚɬɟɦ ɪɟɡɭɥɶɬɚɬ ɩɨ ɫɨɪɬɚɦ ɱɚɫɬɢɰ, ɜɵɱɢɫɥɹɟɦ ɩɥɨɬɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ: & & & ~& k k ~& 2~ 2 2 n e 2 ω E − k csα ( E − k ( k E )) i ~& & j = ¦ eα n0α ~ vα = ¦ 0 α α . ω α =e ,i mα ω 2 − k 2 cs2α α = e ,i ȼɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶ, ɞɚɥɟɟ, ɨɩɪɟɞɟɥɟɧɢɹɦɢ (4.9), (4.10) ɩɨɥɭɱɚɟɦ ɬɟɧɡɨɪ ɩɪɨɜɨɞɢɦɨɫɬɢ: k p kq k p kq & n0α eα2 i ω2 σ p ,q ( k ,ω ) = ¦ ( δ p ,q − 2 + 2 ), (4.30) ω α =e ,i mα k ω − k 2 cs2α k 2 ɚ ɡɚɬɟɦ ɢ ɬɟɧɡɨɪ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ: ω p2α ω p2 k p kq k p kq & & 4πi ε p ,q ( k ,ω ) ≡ δ p ,q + σ p ,q ( k ,ω ) = ( 1 − 2 )( δ p ,q − 2 ) + ( 1 − ¦ 2 . (4.31) 2 2 ) ω k k2 ω α = e ,i ω − k c sα ȼ ɮɨɪɦɭɥɚɯ (4.30), (4.31) ɢɧɞɟɤɫɵ p, q ɧɭɦɟɪɭɸɬ ɤɨɦɩɨɧɟɧɬɵ ɬɟɧɡɨɪɨɜ. ɉɨɫɤɨɥɶɤɭ ɨɛɫɭɠɞɚɟɦɚɹ ɧɚɦɢ ɫɟɣɱɚɫ ɦɨɞɟɥɶ ɩɥɚɡɦɵ ɜ ɨɬɫɭɬɫɬɜɢɟ ɜɨɥɧɵ ɹɜɥɹɟɬɫɹ ɢɡɨɬɪɨɩɧɨɣ − ɧɟɬ ɧɢɤɚɤɨɝɨ ɜɵɞɟɥɟɧɧɨɝɨ ɧɚɩɪɚɜɥɟɧɢɹ, ɬɨ ɫɬɪɭɤɬɭɪɚ ɬɟɧɡɨɪɚ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɫɨɜɩɚɞɚɟɬ ɫ ɩɪɟɞɫɤɚɡɵɜɚɟɦɨɣ ɮɨɪɦɭɥɨɣ (4.14). ɂɡ ɫɨɩɨɫɬɚɜɥɟɧɢɹ ɫ ɷɬɨɣ ɮɨɪɦɭɥɨɣ ɩɨɥɭɱɚɟɦ ɩɪɨɞɨɥɶɧɭɸ
εl = 1 −
¦ω
α = e ,i
ω p2α 2
(4.32)
− k 2 cs2α
ɢ ɩɨɩɟɪɟɱɧɭɸ
ω p2 εtr = 1 − 2 ω
(4.33)
ɞɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ. Ɉɧɢ ɪɚɡɧɵɟ, ɩɨɫɤɨɥɶɤɭ ɭɱɟɬ ɬɟɩɥɨɜɨɝɨ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɩɪɢɜɨɞɢɬ ɤ ɩɨɹɜɥɟɧɢɸ ɹɜɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɨɬ ɜɨɥɧɨɜɨɝɨ ɱɢɫɥɚ. ɋɪɚɜɧɢɜ (4.32), (4.33) ɫ ɮɨɪɦɭɥɨɣ (4.19) ɞɥɹ ɯɨɥɨɞɧɨɣ ɩɥɚɡɦɵ, ɦɵ ɜɢɞɢɦ, ɱɬɨ ɢɡɦɟɧɟɧɢɟ ɩɪɟɬɟɪɩɟɜɚɟɬ ɬɨɥɶɤɨ ɩɪɨɞɨɥɶɧɚɹ ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ, ɩɨɩɟɪɟɱɧɚɹ ɨɫɬɚɟɬɫɹ ɧɟɢɡɦɟɧɧɨɣ! ɗɬɨ ɫɜɹɡɚɧɨ ɫ ɬɟɦ, ɱɬɨ ɩɨɩɟɪɟɱɧɚɹ ɝɚɪɦɨɧɢɱɟɫɤɚɹ ɜɨɥɧɚ ɦɚɥɨɣ ɚɦɩɥɢɬɭɞɵ ɧɟ ɢɡɦɟɧɹɟɬ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɧɟ ɩɨɹɜɥɹɟɬɫɹ ɝɪɚɞɢɟɧɬ ɞɚɜɥɟɧɢɹ, ɢ ɤɨɧɟɱɧɨɫɬɶ ɬɟɦɩɟɪɚɬɭɪɵ ɧɟɫɭɳɟɫɬɜɟɧɧɚ. ȼ ɫɬɚɬɢɱɟɫɤɨɦ ɩɪɟɞɟɥɟ, ɬɨ ɟɫɬɶ ɜ ɩɪɟɞɟɥɟ ω → 0 , ɩɪɨɞɨɥɶɧɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɨɣ ω p2α 4πn0α eα2 1 § 1 1 · ε l ω →0 = 1 + ¦ 2 2 ≡ 1 + ¦ 2 ≡1+ 2 ¨ 2 + (4.34) ¸, k © γ e rDe γ i rDi2 ¹ α = e ,i k c sα α = e ,i k γ α Tα ɱɬɨ ɫɨɜɩɚɞɚɟɬ ɫ (4.22), ɟɫɥɢ ɩɪɢɧɹɬɶ γ e = γ i = 1 , ɬɨ ɟɫɬɶ ɫɱɢɬɚɬɶ ɤɨɦɩɨɧɟɧɬɵ ɩɥɚɡɦɵ ɢɡɨɬɟɪɦɢɱɟɫɤɢɦɢ. ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ, ɫɬɪɨɝɨ ɝɨɜɨɪɹ, ɭɱɟɬ ɬɟɩɥɨɜɨɝɨ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɬɪɟɛɭɟɬ ɤɢɧɟɬɢɱɟɫɤɨɝɨ ɨɩɢɫɚɧɢɹ. ɉɨɷɬɨɦɭ ɩɪɢɜɟɞɟɧɧɵɟ ɪɟɡɭɥɶɬɚɬɵ ɞɚɸɬ ɤɚɱɟɫɬɜɟɧɧɨ ɩɪɚɜɢɥɶɧɭɸ, ɧɨ ɭɩɪɨɳɟɧɧɭɸ ɤɚɪɬɢɧɭ ɞɢɷɥɟɤɬɪɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɩɥɚɡɦɵ. Ɇɨɠɧɨ ɞɨɛɢɬɶɫɹ ɥɭɱɲɟɝɨ ɫɨɝɥɚɫɢɹ ɫ ɬɨɱɧɵɦɢ ɪɟɡɭɥɶɬɚɬɚɦɢ, ɟɫɥɢ ɜɯɨɞɹɳɢɟ ɜ ɩɪɢɜɟɞɟɧɧɵɟ ɮɨɪɦɭɥɵ ɩɨɤɚɡɚɬɟɥɢ γ e ,γ i ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɜ ɤɚɱɟɫɬɜɟ «ɩɨɞɝɨɧɨɱɧɵɯ ɩɚɪɚɦɟɬɪɨɜ», ɨɬɛɢɪɚɹ ɢɯ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɤɨɧɤɪɟɬɧɨɣ ɪɟɲɚɟɦɨɣ ɡɚɞɚɱɢ. ɇɚɩɪɢɦɟɪ, ɜ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɬɟɩɥɨɜɵɟ ɩɨɩɪɚɜɤɢ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɦɚɥɵɦɢ, ɧɨ ɤɨɧɟɱɧɵɦɢ, ɢɡ ɮɨɪɦɭɥɵ (4.32) ɩɪɢɛɥɢɠɟɧɧɨ ɩɨɥɭɱɚɟɦ:
ω p2α § k2 γ T · εl ≈ 1 − ¦ 2 ¨ 1 + 2 α α ¸ , ω mα ¹ α = e ,i ω © ɱɬɨ ɫɨɜɩɚɞɚɟɬ ɫ ɪɟɡɭɥɶɬɚɬɨɦ ɤɢɧɟɬɢɱɟɫɤɨɣ ɬɟɨɪɢɢ [18] ɩɪɢ ɜɵɛɨɪɟ
(4.35)
γα = 3.
§ 29. ɉɨɩɟɪɟɱɧɵɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ ɜɨɥɧɵ ɜ ɧɟɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɟ ȼɨɨɪɭɠɢɜɲɢɫɶ ɩɨɥɭɱɟɧɧɵɦɢ ɜ ɩɪɟɞɵɞɭɳɟɦ ɩɚɪɚɝɪɚɮɟ ɪɟɡɭɥɶɬɚɬɚɦɢ, ɪɚɫɫɦɨɬɪɢɦ ɩɪɨɰɟɫɫ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɜɨɥɧ ɜ ɩɥɚɡɦɟ. Ʉɚɤ ɦɵ ɭɠɟ ɡɧɚɟɦ (ɫɦ. § 27) ɡɚɞɚɱɚ ɫɜɨɞɢɬɫɹ ɤ ɪɟɲɟɧɢɸ ɞɢɫɩɟɪɫɢɨɧɧɵɯ ɭɪɚɜɧɟɧɢɣ εl = 0 , ɢɥɢ εtr = N 2 ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɬɨɝɨ, ɤɚɤɨɣ ɤɨɧɤɪɟɬɧɨ ɬɢɩ ɜɨɥɧɵ ɧɚɫ ɢɧɬɟɪɟɫɭɟɬ: ɱɢɫɬɨ ɩɪɨɞɨɥɶɧɵɟ ɢɥɢ ɱɢɫɬɨ ɩɨɩɟɪɟɱɧɵɟ ɜɨɥɧɵ. ɉɨɫɥɟɞɧɢɣ ɫɥɭɱɚɣ ɨɫɨɛɟɧɧɨ ɩɪɨɫɬ. ɋ ɧɟɝɨ ɢ ɧɚɱɧɟɦ ɨɛɫɭɠɞɟɧɢɟ ɩɥɚɡɦɟɧɧɵɯ ɜɨɥɧ. ɉɨɫɤɨɥɶɤɭ ɞɥɹ ɩɨɩɟɪɟɱɧɵɯ ɜɨɥɧ ɞɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɥɚɡɦɵ ɨɩɪɟɞɟɥɹɟɬ ɫɨɨɬɧɨɲɟɧɢɟ (4.33), ɬɨ ɞɢɫɩɟɪɫɢɨɧɧɨɟ ɭɪɚɜɧɟɧɢɟ ɛɭɞɟɬ ɬɚɤɢɦ: ω p2 k 2c2 1− 2 = N2 ≡ 2 .
ω
ω
Ɋɟɲɟɧɢɟɦ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ, ɨɱɟɜɢɞɧɨ, ɹɜɥɹɟɬɫɹ ω = ω p2 + c 2 k 2 .
Ɋɢɫ. 4.1. Ɂɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɵ ɜ ɩɥɚɡɦɟ. ɉɭɧɤɬɢɪ - ω = kc
(4.36)
ɗɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɢ ɨɩɪɟɞɟɥɹɟɬ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɵ ɜ ɩɥɚɡɦɟ (ɪɢɫ. 4.1). Ɉɛɪɚɬɢɦ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɞɥɹ ɤɨɪɨɬɤɢɯ ɜɨɥɧ, ɤɨɝɞɚ k→∞, ɩɨɥɭɱɚɟɦ ω→kc, ɬɚɤ ɱɬɨ ɜ ɷɬɨɦ ɩɪɟɞɟɥɟ ɜɨɥɧɚ (4.36) ɫɬɚɧɨɜɢɬɫɹ ɨɛɵɱɧɨɣ ɫɜɟɬɨɜɨɣ ɜɨɥɧɨɣ. Ⱦɥɹ ɞɥɢɧɧɵɯ ɜɨɥɧ, ɤɨɝɞɚ k→0, ɩɪɢɛɥɢɠɟɧɧɨ § c2k 2 · ¨ ¸. ω ≈ ω p ¨1 + 2ω p2 ¸¹ © Ɂɚɦɟɬɢɦ ɬɚɤɠɟ, ɱɬɨ ɞɥɹ ɮɚɡɨɜɨɣ ɫɤɨɪɨɫɬɢ ɜɨɥɧɵ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ (4.36) ɞɚɟɬ ɡɧɚɱɟɧɢɟ vɮ = c 1 +
ω02
> c, k 2c2 ɛɨɥɶɲɟ ɫɤɨɪɨɫɬɢ ɫɜɟɬɚ. ɉɨɷɬɨɦɭ ɞɥɹ ɬɚɤɢɯ ɜɨɥɧ ɧɟɫɭɳɟɫɬɜɟɧɧɵ ɪɟɡɨɧɚɧɫɧɵɟ ɷɮɮɟɤɬɵ. ɉɪɨɫɬɨ ɩɨɬɨɦɭ, ɱɬɨ ɢɯ ɮɚɡɨɜɚɹ ɫɤɨɪɨɫɬɶ ɡɚɜɟɞɨɦɨ ɩɪɟɜɵɲɚɟɬ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰ ɩɥɚɡɦɵ, ɜɫɟɝɞɚ ɦɟɧɶɲɢɯ ɫɤɨɪɨɫɬɢ ɫɜɟɬɚ. ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɝɪɭɩɩɨɜɚɹ ɫɤɨɪɨɫɬɶ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɵ, ɨɬɜɟɱɚɸɳɚɹ ɡɚ ɩɟɪɟɧɨɫ ɜɨɥɧɨɜɨɣ ɷɧɟɪɝɢɢ, c ∂ω vɝ ɪ = = < c, ∂k ω02 1+ 2 2 k c ɨɤɚɡɵɜɚɟɬɫɹ, ɤɚɤ ɷɬɨ ɢ ɞɨɥɠɧɨ ɛɵɬɶ, ɦɟɧɶɲɟ ɫɤɨɪɨɫɬɢ ɫɜɟɬɚ ɜ ɜɚɤɭɭɦɟ.
§ 30. əɜɥɟɧɢɟ ɨɬɫɟɱɤɢ ɧɢɡɤɨɱɚɫɬɨɬɧɨɣ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɵ Ʉɚɤ ɦɵ ɜɢɞɢɦ ɢɡ ɮɨɪɦɭɥɵ (4.36), ɱɚɫɬɨɬɚ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɵ ɜ ɩɥɚɡɦɟ ɜɫɟɝɞɚ ɛɨɥɶɲɟ ɩɥɚɡɦɟɧɧɨɣ ɱɚɫɬɨɬɵ, ɩɨɷɬɨɦɭ ɩɨɩɟɪɟɱɧɵɟ ɜɨɥɧɵ, ɱɚɫɬɨɬɚ ɤɨɬɨɪɵɯ ɦɟɧɶɲɟ ɩɥɚɡɦɟɧɧɨɣ ɱɚɫɬɨɬɵ, ɧɟ ɦɨɝɭɬ ɜ ɧɟɣ ɪɚɫɩɪɨɫɬɪɚɧɹɬɶɫɹ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɩɚɞɚɸɳɚɹ ɢɡ ɜɚɤɭɭɦɚ ɧɚ ɝɪɚɧɢɰɭ ɩɥɚɡɦɵ ɩɨɩɟɪɟɱɧɚɹ ɜɨɥɧɚ ɫ ɦɚɥɨɣ ɱɚɫɬɨɬɨɣ ɞɨɥɠɧɚ ɨɬɪɚɠɚɬɶɫɹ. ɂɦɟɟɬ ɦɟɫɬɨ, ɤɚɤ ɝɨɜɨɪɹɬ ɹɜɥɟɧɢɟ ɨɬɫɟɱɤɢ ɜɨɥɧɵ (ɜ ɚɧɝɥɢɣɫɤɨɣ ɥɢɬɟɪɚɬɭɪɟ - cut off). Ʉɪɢɬɢɱɟɫɤɚɹ ɱɚɫɬɨɬɚ − ɱɚɫɬɨɬɚ ɨɬɫɟɱɤɢ,
ωɤ ɪ = ω p ≡
4πn0 e 2 § Zme · ¨1 + ¸, me © mi ¹
(4.37)
ɡɚɜɢɫɢɬ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɥɚɡɦɵ. Ɍɚɤ ɱɬɨ, ɢɡɦɟɪɹɹ ɤɪɢɬɢɱɟɫɤɭɸ ɱɚɫɬɨɬɭ, ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɤɨɧɰɟɧɬɪɚɰɢɸ ɩɥɚɡɦɵ. ɗɬɨ ɨɞɢɧ ɢɡ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɯ ɦɟɬɨɞɨɜ ɞɢɚɝɧɨɫɬɢɤɢ ɩɥɚɡɦɵ. ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɧɢɡɤɨɱɚɫɬɨɬɧɨɣ ɜɨɥɧɵ ɱɚɫɬɢɱɧɨ ɜɫɟ ɠɟ ɩɪɨɧɢɤɚɟɬ ɜ ɩɥɚɡɦɭ, ɧɨ ɟɝɨ ɚɦɩɥɢɬɭɞɚ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨ ɭɦɟɧɶɲɚɟɬɫɹ ɜɝɥɭɛɶ ɩɥɚɡɦɵ. Ƚɥɭɛɢɧɚ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɜ ɩɥɚɡɦɭ ɩɨɥɹ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɵ ɫ ɧɢɡɤɨɣ ɱɚɫɬɨɬɨɣ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɨɥɳɢɧɨɣ ɜɚɤɭɭɦɧɨɝɨ ɫɤɢɧ-ɫɥɨɹ, ɤɨɬɨɪɚɹ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɩɥɚɡɦɟɧɧɨɣ ɱɚɫɬɨɬɟ: c . (4.38) δɜɚɤ =
ωp
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɝɥɭɛɢɧɚ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɜɨɥɧɵ ɜ ɩɥɚɡɦɭ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɧɟɪɰɢɟɣ ɟɟ ɱɚɫɬɢɰ, ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ - ɷɥɟɤɬɪɨɧɨɜ. ȼ ɩɪɟɧɟɛɪɟɠɟɧɢɢ ɢɧɟɪɰɢɟɣ ɝɥɭɛɢɧɚ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɩɨɥɹ ɛɵɥɚ ɛɵ ɧɭɥɟɜɨɣ. ɉɪɨɢɥɥɸɫɬɪɢɪɭɟɦ ɫɤɚɡɚɧɧɨɟ ɩɪɨɫɬɵɦ ɩɪɢɦɟɪɨɦ. ɉɭɫɬɶ ɢɡ ɜɚɤɭɭɦɚ ɧɚ ɩɥɨɫɤɭɸ ɝɪɚɧɢɰɭ ɩɥɚɡɦɵ ɩɚɞɚɟɬ ɧɢɡɤɨɱɚɫɬɨɬɧɚɹ ɜɨɥɧɚ, ɫɥɟɜɚ ɧɚɩɪɚɜɨ, ɤɚɤ ɷɬɨ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 4.2. ɋɥɟɜɚ ɢ ɫɩɪɚɜɚ ɨɬ ɝɪɚɧɢɰɵ ɪɚɡɞɟɥɚ ɡɚɤɨɧɵ ɞɢɫɩɟɪɫɢɢ ɜɨɥɧɵ ɪɚɡɧɵɟ:
ω 2 , x > 0 , ω 2 − k 2c2 = ® p ¯ 0 , x < 0.
ɗɬɢ ɫɨɨɬɧɨɲɟɧɢɹ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɦ ɜɢɞɟ. ɉɭɫɬɶ ɱɚɫɬɨɬɚ ɜɨɥɧɵ ɮɢɤɫɢɪɨɜɚɧɚ, ɡɚɦɟɧɢɜ k → − i∂x , ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɹ
ω p2 − ω 2 f , x > 0, °° 2 2 c ∂x f = ® 2 ° − ω f , x < 0, °¯ c2 Ɋɢɫ. 4.2. Ɉɬɫɟɱɤɚ ɧɢɡɤɨɱɚɫɬɨɬɧɨɣ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɵ ɧɚ ɝɪɚɧɢɰɟ ɩɥɚɡɦɵ
(4.39)
ɝɞɟ ɮɭɧɤɰɢɹ f ɡɚɞɚɟɬ ɩɨɥɟ ɜɨɥɧɵ: ɧɚɩɪɢɦɟɪ, ɷɬɨ ɦɨɠɟɬ ɛɵɬɶ ɤɨɦɩɨɧɟɧɬɚ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. ɇɚ ɝɪɚɧɢɰɟ ɪɚɡɞɟɥɚ ɩɨɬɪɟɛɭɟɦ ɜɵɩɨɥɧɟɧɢɹ ɭɫɥɨɜɢɣ ɧɟɩɪɟɪɵɜɧɨɫɬɢ:
∂x f |x =+0 = ∂x f |x =−0 ,
(4.40)
f |x =+0 = f |x =−0 .
ɇɟɬɪɭɞɧɨ ɧɚɣɬɢ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ (4.39), (4.40), ɭɞɨɜɥɟɬɜɨɪɹɸɳɟɟ ɷɬɢɦ ɭɫɥɨɜɢɹɦ. ɉɪɟɞɥɚɝɚɟɦ ɱɢɬɚɬɟɥɸ ɩɪɨɜɟɪɢɬɶ, ɱɬɨ ɬɚɤɨɜɵɦ ɹɜɥɹɟɬɫɹ ɪɟɲɟɧɢɟ, ɜ ɤɨɬɨɪɨɦ ɜ ɨɛɥɚɫɬɢ ɜɚɤɭɭɦɚ ɩɨɥɟ ɫɤɥɚɞɵɜɚɟɬɫɹ ɢɡ ɩɨɥɹ ɩɚɞɚɸɳɟɣ ɢ ɨɬɪɚɠɟɧɧɨɣ ɜɨɥɧɵ, ɚ ɜ ɨɛɥɚɫɬɢ ɩɥɚɡɦɵ ɜɨɥɧɨɜɨɟ ɩɨɥɟ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨ ɡɚɬɭɯɚɟɬ:
§ ω °exp¨ i f = f0 ® © c °¯
· § ω · x ¸ + α exp¨ − i x ¸ , x < 0 , ¹ © c ¹ β exp( − κx ) , x > 0,
ɝɞɟ ɨɛɨɡɧɚɱɟɧɨ
κ=
ω p2 − ω 2 c2
>0
(4.41)
- ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɝɨ ɡɚɬɭɯɚɧɢɹ ɩɨɥɹ ɜɨɥɧɵ ɜ ɩɥɚɡɦɟ, f0 − ɚɦɩɥɢɬɭɞɚ ɩɚɞɚɸɳɟɣ ɧɚ ɝɪɚɧɢɰɭ ɪɚɡɞɟɥɚ ɜɨɥɧɵ. Ⱥɦɩɥɢɬɭɞɧɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ α ɞɥɹ ɨɬɪɚɠɟɧɧɨɣ ɜɨɥɧɵ ɢ β ɞɥɹ ɩɨɥɹ ɜ ɩɥɚɡɦɟ, ɤɚɤ ɷɬɨ ɜɵɬɟɤɚɟɬ ɢɡ ɭɫɥɨɜɢɣ ɧɟɩɪɟɪɵɜɧɨɣ ɫɲɢɜɤɢ (4.40), ɨɤɚɡɵɜɚɸɬɫɹ ɪɚɜɧɵɦɢ:
α=
ω − i κc 2ω . , β= ω + i κc ω + iκc
Ɉɛɪɚɬɢɦ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɱɢɫɥɢɬɟɥɶ ɢ ɡɧɚɦɟɧɚɬɟɥɶ ɩɟɪɜɨɣ ɮɨɪɦɭɥɵ ɹɜɥɹɸɬɫɹ ɤɨɦɩɥɟɤɫɧɨ-ɫɨɩɪɹɠɟɧɧɵɦɢ. ɉɨɷɬɨɦɭ ɩɨɥɭɱɚɟɦ |α | = 1 , ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɚɦɩɥɢɬɭɞɵ ɩɚɞɚɸɳɟɣ ɜɨɥɧɵ ɢ ɨɬɪɚɠɟɧɧɨɣ ɫɨɜɩɚɞɚɸɬ. ɗɬɨ ɢ ɨɡɧɚɱɚɟɬ ɧɚɥɢɱɢɟ ɩɨɥɧɨɝɨ ɨɬɪɚɠɟɧɢɹ ɩɚɞɚɸɳɟɣ ɧɚ ɩɥɚɡɦɭ ɜɨɥɧɵ. ȼ ɩɪɟɞɟɥɟ ɫɨɜɫɟɦ ɧɢɡɤɢɯ ɱɚɫɬɨɬ, ɤɨɝɞɚ ω → 0 , ɩɨɥɭɱɚɟɦ ɩɪɢɛɥɢɠɟɧɧɨ
α ≈ −1 − 2 i
ω ω −1 → − 1, β = − 2 i → 0 , κ ≈ δɜɚɤ , ωp ωp
ɢ ɞɥɢɧɚ ɡɚɬɭɯɚɧɢɹ ɩɨɥɹ ɜ ɩɥɚɡɦɟ ɫɨɜɩɚɞɚɟɬ ɫ ɞɥɢɧɨɣ ɜɚɤɭɭɦɧɨɝɨ ɫɤɢɧ-ɫɥɨɹ.
§ 31. Ʌɟɧɝɦɸɪɨɜɫɤɢɟ ɤɨɥɟɛɚɧɢɹ ɢ ɜɨɥɧɵ ɜ ɩɥɚɡɦɟ. ɉɥɚɡɦɨɧɵ Ɋɚɫɫɦɨɬɪɢɦ ɬɟɩɟɪɶ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɯ ɩɪɨɞɨɥɶɧɵɯ ɩɥɚɡɦɟɧɧɵɯ ɜɨɥɧ ɫ ɱɚɫɬɨɬɨɣ ɜ ɨɛɥɚɫɬɢ ɥɟɧɝɦɸɪɨɜɫɤɨɣ ɱɚɫɬɨɬɵ. Ɉɧɢ ɢɡɜɟɫɬɧɵ ɤɚɤ ɥɟɧɝɦɸɪɨɜɫɤɢɟ ɜɨɥɧɵ ɢ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɜɚɠɧɟɣɲɢɣ ɬɢɩ ɜɨɡɦɭɳɟɧɢɣ, ɫɩɨɫɨɛɧɵɯ ɫɭɳɟɫɬɜɨɜɚɬɶ ɢ ɪɚɫɩɪɨɫɬɪɚɧɹɬɶɫɹ ɜ ɩɥɚɡɦɟ. Ɂɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɩɪɨɞɨɥɶɧɵɯ ɜɨɥɧ ɨɩɪɟɞɟɥɹɟɬ, ɤɚɤ ɛɵɥɨ ɩɨɤɚɡɚɧɨ ɜɵɲɟ, ɭɪɚɜɧɟɧɢɟ εl = 0 , ɜ ɤɨɬɨɪɨɟ ɫɥɟɞɭɟɬ ɩɨɞɫɬɚɜɢɬɶ ɩɪɨɞɨɥɶɧɭɸ ɤɨɦɩɨɧɟɧɬɭ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ. ȿɫɥɢ ɩɥɚɡɦɭ ɫɱɢɬɚɬɶ ɯɨɥɨɞɧɨɣ, ɬɨ ɞɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɫɥɟɞɭɟɬ ɨɩɪɟɞɟɥɹɬɶ ɩɨ ɮɨɪɦɭɥɟ (4.19), ɢ ɦɵ ɩɪɢɯɨɞɢɦ ɤ ɭɪɚɜɧɟɧɢɸ
ω p2 1− 2 = 0. ω Ɉɧɨ ɢɦɟɟɬ ɞɜɚ ɪɟɲɟɧɢɹ, ɨɬɥɢɱɚɸɳɢɟɫɹ ɡɧɚɤɨɦ. ɉɨɥɨɠɢɬɟɥɶɧɵɣ ɤɨɪɟɧɶ ɪɚɜɟɧ ω = ωp
(4.42)
Ʉɚɤ ɦɵ ɜɢɞɢɦ, ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɫɥɭɱɚɟ ɱɚɫɬɨɬɚ ɜɨɥɧɵ ɫɨɜɩɚɞɚɟɬ ɫ ɥɟɧɝɦɸɪɨɜɫɤɨɣ ɱɚɫɬɨɬɨɣ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɜɟɥɢɱɢɧɵ ɜɨɥɧɨɜɨɝɨ ɱɢɫɥɚ. Ɏɚɡɨɜɚɹ ɫɤɨɪɨɫɬɶ ɬɚɤɢɯ ɜɨɥɧ vɮ ≡
ω
=
ωp
(4.43) k k ɭɦɟɧɶɲɚɟɬɫɹ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɜɨɥɧɨɜɨɝɨ ɱɢɫɥɚ, ɚ ɝɪɭɩɩɨɜɚɹ ɫɤɨɪɨɫɬɶ ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɨɣ ɧɭɥɸ: ∂ω ∂ω p & vɝ ɪ ≡ & = & ≡ 0 . (4.44) ∂k ∂k Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɯɨɥɨɞɧɨɣ ɩɥɚɡɦɟ ɥɟɧɝɦɸɪɨɜɫɤɢɟ ɜɨɥɧɵ ɧɟ ɦɨɝɭɬ ɩɟɪɟɧɨɫɢɬɶ ɷɧɟɪɝɢɸ: ɮɚɤɬɢɱɟɫɤɢ ɷɬɨ ɨɛɵɱɧɵɟ ɤɨɥɟɛɚɧɢɹ ɩɥɨɬɧɨɫɬɢ ɡɚɪɹɞɚ, ɜɨɡɧɢɤɚɸɳɢɟ ɜɫɥɟɞɫɬɜɢɟ ɧɚɪɭɲɟɧɢɹ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɢ ɩɥɚɡɦɵ. ȿɫɥɢ ɠɟ ɦɵ ɭɱɬɟɦ ɬɟɩɟɪɶ ɬɟɩɥɨɜɨɟ ɞɜɢɠɟɧɢɟ ɱɚɫɬɢɰ ɩɥɚɡɦɵ, ɬɨ ɫɢɬɭɚɰɢɹ ɢɡɦɟɧɢɬɫɹ ɤɚɪɞɢɧɚɥɶɧɨ. Ⱦɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɨɩɪɟɞɟɥɹɟɬ ɬɟɩɟɪɶ ɮɨɪɦɭɥɚ (4.32) ɢ ɞɢɫɩɟɪɫɢɨɧɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɩɪɨɞɨɥɶɧɵɯ ɜɨɥɧ ɫɬɚɧɨɜɢɬɫɹ ɬɚɤɢɦ:
εl = 1 −
¦ω
α = e ,i
ω p2α 2
− k 2 cs2α
= 0,
ɢɥɢ
ω pe2
ω pi2
Te ,i . (4.45) ω −k c ω −k c me ,i ɗɬɨ ɭɪɚɜɧɟɧɢɟ ɧɟɫɥɨɠɧɨ ɪɟɲɢɬɶ ɜ ɨɛɳɟɦ ɜɢɞɟ. ɇɨ ɜ ɢɧɬɟɪɟɫɭɸɳɟɣ ɧɚɫ ɫɟɣɱɚɫ ɜɵɫɨɤɨɱɚɫɬɨɬɧɨɣ ɨɛɥɚɫɬɢ ɫɥɟɞɭɟɬ ɭɱɟɫɬɶ, ɱɬɨ ɢɨɧɵ ɩɥɚɡɦɵ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɧɟɩɨɞɜɢɠɧɵɦɢ, ɚ ɩɨɬɨɦɭ ɢɯ ɜɤɥɚɞ ɜ ɞɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɛɭɞɟɬ ɩɪɟɧɟɛɪɟɠɢɦɨ ɦɚɥɵɦ. Ɏɨɪɦɚɥɶɧɨ ɷɬɨ ɨɬɜɟɱɚɟɬ ɩɪɟɞɟɥɭ mi→∞, ɢ ɭɪɚɜɧɟɧɢɟ (4.45) ɭɩɪɨɳɚɟɬɫɹ: ω pe2 T 1− 2 cs2e = γ e e . 2 2 = 0, ω − k cse me Ɍɟɩɟɪɶ ɟɝɨ ɭɠɟ ɧɟ ɫɥɨɠɧɨ ɪɟɲɢɬɶ, ɢ ɦɵ, ɜɧɨɜɶ ɜɵɛɢɪɚɹ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɤɨɪɟɧɶ, ɩɨɥɭɱɚɟɦ: ω = ω pe2 + k 2 cse2 . (4.46) 1−
2
2 2 se
−
2
2 2 si
= 0 , cs2e ,i = γ e ,i
ɗɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɢ ɨɩɪɟɞɟɥɹɟɬ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɥɟɧɝɦɸɪɨɜɫɤɨɣ ɜɨɥɧɵ ɜ ɩɥɚɡɦɟ ɫ ɤɨɧɟɱɧɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ.
Ʌɸɛɨɩɵɬɧɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɷɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɩɨ ɜɢɞɭ ɨɤɚɡɵɜɚɟɬɫɹ ɜɩɨɥɧɟ ɚɧɚɥɨɝɢɱɧɵɦ ɢɡɜɟɫɬɧɨɣ ɮɨɪɦɭɥɟ, ɨɩɪɟɞɟɥɹɸɳɟɣ ɫɜɹɡɶ ɷɧɟɪɝɢɢ ɢ ɢɦɩɭɥɶɫɚ ɪɟɥɹɬɢɜɢɫɬɫɤɨɣ ɱɚɫɬɢɰɵ:
ε=
( mc )
2 2
+ p2c2 .
ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ ɨ ɡɚɤɨɧɟ ɞɢɫɩɟɪɫɢɢ (4.46) ɝɨɜɨɪɹɬ ɤɚɤ ɨ «ɱɚɫɬɢɰɟ-ɩɨɞɨɛɧɨɦ», ɚ ɥɟɧɝɦɸɪɨɜɫɤɢɟ ɜɨɥɧɵ ɜ ɷɬɨɦ ɩɥɚɧɟ ɹɜɥɹɸɬɫɹ «ɤɜɚɡɢɱɚɫɬɢɰɚɦɢ», ɤɨɬɨɪɵɟ ɩɪɢɧɹɬɨ ɧɚɡɵɜɚɬɶ ɩɥɚɡɦɨɧɚɦɢ. ɉɨɥɟɡɧɨ ɨɬɦɟɬɢɬɶ ɬɚɤɠɟ, ɱɬɨ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ (4.46) ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ: ω = ω pe 1 + γ e k 2 rDe2 . (4.47) ȼɬɨɪɨɟ ɫɥɚɝɚɟɦɨɟ ɩɨɞ ɤɨɪɧɟɦ ɛɭɞɟɬ ɛɨɥɶɲɟ ɢɥɢ ɩɨɪɹɞɤɚ ɟɞɢɧɢɰɵ, ɤɨɝɞɚ ɞɥɢɧɚ ɜɨɥɧɵ ɛɭɞɟɬ ɦɟɧɶɲɟ ɞɟɛɚɟɜɫɤɨɝɨ ɪɚɞɢɭɫɚ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɥɟɧɝɦɸɪɨɜɫɤɚɹ ɜɨɥɧɚ ɫɢɥɶɧɨ ɩɨɝɥɨɳɚɟɬɫɹ ɡɚ ɫɱɟɬ ɦɟɯɚɧɢɡɦɚ ɛɟɫɫɬɨɥɤɧɨɜɢɬɟɥɶɧɨɝɨ ɩɨɝɥɨɳɟɧɢɹ Ʌɚɧɞɚɭ, ɬɚɤ ɤɚɤ ɨɤɚɡɵɜɚɟɬɫɹ ɪɟɡɨɧɚɧɫɧɨɣ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɷɥɟɤɬɪɨɧɚɦ ɩɥɚɡɦɵ, v ɮ ~ vTe . ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ ɥɟɧɝɦɸɪɨɜɫɤɢɟ ɜɨɥɧɵ ɦɨɝɭɬ ɫɭɳɟɫɬɜɨɜɚɬɶ ɜ ɩɥɚɡɦɟ ɛɟɡ ɫɭɳɟɫɬɜɟɧɧɨɝɨ ɩɨɝɥɨɳɟɧɢɹ ɥɢɲɶ ɜ ɨɛɪɚɬɧɨɦ ɩɪɟɞɟɥɟ, ɤɨɝɞɚ ɢɯ ɞɥɢɧɚ ɜɨɥɧɵ ɦɟɧɶɲɟ ɞɟɛɚɟɜɫɤɨɝɨ ɪɚɞɢɭɫɚ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɜ (4.47) ɜɬɨɪɨɟ ɫɥɚɝɚɟɦɨɟ ɩɨɞ ɤɨɪɧɟɦ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɦɚɥɵɦ ɢ ɪɚɡɥɨɠɢɬɶ ɩɨ ɷɬɨɣ ɦɚɥɨɫɬɢ: γ · § ω ≈ ω pe ¨ 1 + e k 2 rDe2 ¸ , k 2 rDe2 << 1 . ¹ © 2 Ⱥɧɚɥɨɝɢɹ ɫ ɷɧɟɪɝɢɟɣ ɱɚɫɬɢɰɵ ɨɩɹɬɶ ɨɫɬɚɟɬɫɹ ɜ ɫɢɥɟ, ɧɨ ɬɟɩɟɪɶ ɜ ɧɟɪɟɥɹɬɢɜɢɫɬɫɤɨɦ ɩɪɟɞɟɥɟ, ɤɨɝɞɚ ɷɧɟɪɝɢɹ ɫɜɹɡɚɧɚ ɫ ɢɦɩɭɥɶɫɨɦ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: p2 ε ≈ mc 2 + . 2m ȼ ɨɛɥɚɫɬɢ ɱɚɫɬɨɬ ɥɟɧɝɦɸɪɨɜɫɤɢɯ ɜɨɥɧ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɟ ɨɩɢɫɚɧɢɟ, ɫɥɟɞɫɬɜɢɟɦ ɤɨɬɨɪɨɝɨ ɮɚɤɬɢɱɟɫɤɢ ɹɜɥɹɟɬɫɹ ɡɚɤɨɧ (4.47), ɛɭɞɟɬ ɚɞɟɤɜɚɬɧɵɦ ɩɪɢ ɜɵɛɨɪɟ γe = 3. ɉɨɞɫɬɚɜɢɜ ɷɬɨ ɡɧɚɱɟɧɢɟ ɜ (4.47), ɩɨɥɭɱɢɦ ɨɤɨɧɱɚɬɟɥɶɧɨ 3 § · ω ≈ ω pe ¨ 1 + k 2 rDe2 ¸ , k 2 rDe2 << 1 . (4.48) © ¹ 2 ɂɦɟɧɧɨ ɨɛ ɷɬɨɦ ɫɨɨɬɧɨɲɟɧɢɢ ɢ ɝɨɜɨɪɹɬ ɨɛɵɱɧɨ ɤɚɤ ɨ ɡɚɤɨɧɟ ɞɢɫɩɟɪɫɢɢ ɥɟɧɝɦɸɪɨɜɫɤɢɯ ɜɨɥɧ ɜ ɩɥɚɡɦɟ. ɋɬɪɨɝɨ ɝɨɜɨɪɹ, ɨɧ ɫɩɪɚɜɟɞɥɢɜ, ɤɚɤ ɦɵ ɜɢɞɟɥɢ, ɥɢɲɶ ɩɪɢ 2 ɜɵɩɨɥɧɟɧɢɢ ɫɢɥɶɧɨɝɨ ɧɟɪɚɜɟɧɫɬɜɚ k 2 rDe << 1 . Ɉɞɧɚɤɨ ɤɚɱɟɫɬɜɟɧɧɨ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ (4.48) ɨɫɬɚɟɬɫɹ ɜ ɫɢɥɟ ɢ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɛɨɥɟɟ ɦɹɝɤɨɝɨ ɭɫɥɨɜɢɹ, ɤɨɝɞɚ ɞɥɢɧɚ ɜɨɥɧɵ ɫɨɫɬɚɜɥɹɟɬ ɧɟɫɤɨɥɶɤɨ ɞɟɛɚɟɜɫɤɢɯ ɪɚɞɢɭɫɨɜ. ȼɬɨɪɨɟ ɫɥɚɝɚɟɦɨɟ ɜ ɫɤɨɛɤɚɯ ɜ ɮɨɪɦɭɥɟ (4.48) ɩɪɢɧɹɬɨ ɧɚɡɵɜɚɬɶ ɬɟɩɥɨɜɨɣ ɩɨɩɪɚɜɤɨɣ. ɍɱɟɬ ɷɬɨɣ ɩɨɩɪɚɜɤɢ ɩɪɢɜɨɞɢɬ ɤ ɬɨɦɭ, ɱɬɨ ɝɪɭɩɩɨɜɚɹ ɫɤɨɪɨɫɬɶ ɥɟɧɝɦɸɪɨɜɫɤɨɣ ɜɨɥɧɵ, ɜ ɨɬɥɢɱɢɟ ɨɬ ɫɥɭɱɚɹ ɯɨɥɨɞɧɨɣ ɩɥɚɡɦɵ, ɫɬɚɧɨɜɢɬɫɹ ɧɟɧɭɥɟɜɨɣ (ɫɦ. ɪɢɫ.4.3): & 2 ∂ω & v ɝ ɪ = & = 3ω pe krDe , v ɝ ɪ = 3vTe krDe , (4.49) ∂k ɮɚɡɨɜɚɹ ɠɟ ɫɤɨɪɨɫɬɶ ɩɪɢɛɥɢɠɟɧɧɨ ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɨɪɦɭɥɨɣ vTe ω ω pe vɮ = ≈ = . (4.50) k k 3 krDe Ɋɢɫ.4.3 Ɂɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɥɟɧɝɦɸɪɨɜɫɤɨɣ ɜɨɥɧɵ
ɉɪɢ ɭɱɟɬɟ ɬɟɩɥɨɜɨɝɨ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɥɟɧɝɦɸɪɨɜɫɤɢɟ ɜɨɥɧɵ ɩɨɥɭɱɚɸɬ ɜɨɡɦɨɠɧɨɫɬɶ ɪɚɫɩɪɨɫɬɪɚɧɹɬɶɫɹ ɜ ɩɥɚɡɦɟ, ɩɟɪɟɧɨɫɹ ɷɧɟɪɝɢɸ.
§ 32. ɂɨɧɧɵɟ ɥɟɧɝɦɸɪɨɜɫɤɢɟ ɜɨɥɧɵ. ɂɨɧɧɨ-ɡɜɭɤɨɜɵɟ ɜɨɥɧɵ ɜ ɩɥɚɡɦɟ ȼɟɪɧɟɦɫɹ ɜɧɨɜɶ ɤ ɞɢɫɩɟɪɫɢɨɧɧɨɦɭ ɭɪɚɜɧɟɧɢɸ (4.45). Ⱦɥɹ ɪɚɫɫɦɨɬɪɟɧɧɵɯ ɜɵɲɟ ɥɟɧɝɦɸɪɨɜɫɤɢɯ ɜɨɥɧ ɝɪɭɩɩɨɜɚɹ ɢ ɮɚɡɨɜɚɹ ɫɤɨɪɨɫɬɢ ɭɞɨɜɥɟɬɜɨɪɹɸɬ ɧɟɪɚɜɟɧɫɬɜɭ v ɝ ɪ < vTe < v ɮ . Ɍɟɩɟɪɶ ɪɚɫɫɦɨɬɪɢɦ ɜɨɡɦɨɠɧɨɫɬɶ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜ ɩɥɚɡɦɟ ɜɨɥɧ, ɮɚɡɨɜɚɹ ɫɤɨɪɨɫɬɶ ɤɨɬɨɪɵɯ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɟ ɬɟɩɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ: v ɮ << vTe . ȿɫɥɢ ɷɬɨ ɭɫɥɨɜɢɟ ɜɵɩɨɥɧɟɧɨ, ɬɨ ɜ ɭɪɚɜɧɟɧɢɢ (4.45) ɜ ɡɧɚɦɟɧɚɬɟɥɟ ɜɬɨɪɨɝɨ ɫɥɚɝɚɟɦɨɝɨ ɦɨɠɧɨ ɨɩɭɫɬɢɬɶ ω 2 ɢ ɬɨɝɞɚ ɷɬɨ ɭɪɚɜɧɟɧɢɟ ɩɪɢɜɨɞɢɬɫɹ ɤ ɜɢɞɭ ω pe2 ω pi2 Te ,i . cs2e ,i = γ e ,i 1+ 2 2 − 2 2 2 = 0, k cse ω − k csi me ,i Ɍɟɩɟɪɶ ɭɠɟ ɧɟ ɫɥɨɠɧɨ ɧɚɣɬɢ ɢɧɬɟɪɟɫɭɸɳɟɟ ɧɚɫ ɪɟɲɟɧɢɟ:
ω =k c + 2
2 2 si
ω pi2 . ω pe2
1+
k 2 cse2 ɍɱɬɟɦ ɬɟɩɟɪɶ, ɱɬɨ ɩɨ ɨɩɪɟɞɟɥɟɧɢɸ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɜɟɥɢɱɢɧ ɢɦɟɟɬ ɦɟɫɬɨ ɫɨɨɬɧɨɲɟɧɢɟ: γ eTe me cse2 2 ≡ γ e rDe . 2 ≡ ω pe 4πe 2 nei me Ɍɨɝɞɚ ɩɨɥɭɱɟɧɧɵɣ ɧɚɦɢ ɪɟɡɭɥɶɬɚɬ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ
ω =k c + 2
2 2 si
ω pi2
. (4.51) 1 1+ γ e k 2 rDe2 Ⱦɥɹ ɤɨɪɨɬɤɢɯ ɜɨɥɧ, ɤɨɝɞɚ ɞɥɢɧɚ ɜɨɥɧɵ ɦɟɧɶɲɟ ɷɥɟɤɬɪɨɧɧɨɝɨ ɞɟɛɚɟɜɫɤɨɝɨ ɪɚɞɢɭɫɚ, ɡɧɚɦɟɧɚɬɟɥɶ ɜɨ ɜɬɨɪɨɦ ɫɥɚɝɚɟɦɨɦ ɩɪɢɦɟɪɧɨ ɪɚɜɟɧ ɟɞɢɧɢɰɟ, ɢ ɦɵ ɩɨɥɭɱɚɟɦ: § · γT ω 2 ≅ k 2 csi2 + ω pi2 ≡ ω pi2 ¨ 1 + i i k 2 rDe2 ¸ , k 2 rDe2 << 1 . (4.52) ZTe © ¹ ɑɚɫɬɨɬɚ ɷɬɢɯ ɜɨɥɧ ɨɤɚɡɵɜɚɟɬɫɹ ɩɨɪɹɞɤɚ ɢɨɧɧɨɣ ɥɟɧɝɦɸɪɨɜɫɤɨɣ ɱɚɫɬɨɬɵ. ɉɨ ɚɧɚɥɨɝɢɢ ɫ (4.46), ɷɬɢ ɜɨɥɧɵ ɧɚɡɵɜɚɸɬ ɢɨɧɧɵɦɢ ɥɟɧɝɦɸɪɨɜɫɤɢɦɢ ɜɨɥɧɚɦɢ. Ʉɚɤ ɩɪɚɜɢɥɨ, ɟɫɥɢ ɬɟɦɩɟɪɚɬɭɪɚ ɢɨɧɨɜ ɧɟ ɦɚɥɚ, ɨɧɢ ɫɢɥɶɧɨ ɡɚɬɭɯɚɸɬ ɜ ɩɥɚɡɦɟ, ɬɚɤ ɤɚɤ ɨɤɚɡɵɜɚɸɬɫɹ ɪɟɡɨɧɚɧɫɧɵɦɢ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɢɨɧɚɦ. ȼ ɨɛɪɚɬɧɨɦ ɩɪɟɞɟɥɟ ɞɥɢɧɧɵɯ ɜɨɥɧ, ɞɥɢɧɚ ɜɨɥɧɵ ɤɨɬɨɪɵɯ ɩɪɟɜɵɲɚɟɬ ɷɥɟɤɬɪɨɧɧɵɣ ɞɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ, ɜ ɡɧɚɦɟɧɚɬɟɥɟ ɜɬɨɪɨɝɨ ɫɥɚɝɚɟɦɨɝɨ ɜ ɮɨɪɦɭɥɟ (4.51) ɝɥɚɜɧɵɦ, ɧɚɩɪɨɬɢɜ, ɹɜɥɹɟɬɫɹ ɜɬɨɪɨɣ ɱɥɟɧ, ɢ ɦɵ ɩɨɥɭɱɚɟɦ: ω 2 ≅ k 2 csi2 + γ e k 2 rDe2 ω pi2 ≡ k 2 cs2 , k 2 rDe2 << 1 . (4.53) ɝɞɟ ɨɛɨɡɧɚɱɟɧɨ
Zγ eTe + γ iTi . (4.54) mi ɋɪɚɜɧɢɜ (4.54) ɫ ɬɨɱɧɵɦ ɪɟɡɭɥɶɬɚɬɨɦ ɤɢɧɟɬɢɱɟɫɤɨɣ ɬɟɨɪɢɢ [18], ɡɚɤɥɸɱɚɟɦ, ɱɬɨ ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɞɢɚɩɚɡɨɧɟ ɱɚɫɬɨɬ ɤɢɧɟɬɢɤɚ ɢ ɝɢɞɪɨɞɢɧɚɦɢɤɚ, ɢɫɩɨɥɶɡɨɜɚɧɧɚɹ ɧɚɦɢ, ɞɚɸɬ ɫɨɜɩɚɞɚɸɳɢɟ ɪɟɡɭɥɶɬɚɬɵ ɩɪɢ ɜɵɛɨɪɟ 2 cs2 ≡ csi2 + γ e rDe ω pi2 =
γ e = 1, γ i = 3 , ɬɚɤ ɱɬɨ (4.54) ɫɥɟɞɭɟɬ ɡɚɩɢɫɵɜɚɬɶ ɜ ɜɢɞɟ:
ZTe + 3Ti . (4.55) mi ȼɵɬɟɤɚɸɳɢɣ ɢɡ ɫɨɨɬɧɨɲɟɧɢɹ (4.53) ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ω = kc s , (4.56) ɫɨɝɥɚɫɧɨ ɤɨɬɨɪɨɦɭ ɱɚɫɬɨɬɚ ɜɨɥɧɵ ɨɤɚɡɵɜɚɟɬɫɹ ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɣ ɜɨɥɧɨɜɨɦɭ ɱɢɫɥɭ, ɬɢɩɢɱɟɧ ɞɥɹ ɡɜɭɤɨɜɵɯ ɜɨɥɧ (ɧɚɩɨɦɧɢɦ, ɱɬɨ ɦɵ ɨɛɫɭɠɞɚɟɦ ɫɟɣɱɚɫ ɩɪɨɞɨɥɶɧɵɟ ɜɨɥɧɵ!). ɇɚɩɪɢɦɟɪ, ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɡɜɭɤɚ ɜ ɨɛɵɱɧɨɦ Ɋɢɫ. 4.4. ɂɨɧɧɨ-ɡɜɭɤɨɜɵɟ ɜɨɥɧɵ ɜ ɝɚɡɟ ɩɥɚɡɦɟ ∂p γT ω = kcs , cs = = , ∂ρ M ɝɞɟ Ɍ - ɬɟɦɩɟɪɚɬɭɪɚ, ɚ Ɇ - ɦɚɫɫɚ ɦɨɥɟɤɭɥ ɝɚɡɚ. ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ ɜɨɥɧɵ ɫ ɡɚɤɨɧɨɦ ɞɢɫɩɟɪɫɢɢ (4.55), (4.56) ɩɪɢɧɹɬɨ ɧɚɡɵɜɚɬɶ ɢɨɧɧɨ-ɡɜɭɤɨɜɵɦɢ ɜɨɥɧɚɦɢ. ɇɚɪɹɞɭ ɫ ɥɟɧɝɦɸɪɨɜɫɤɢɦɢ ɜɨɥɧɚɦɢ, ɷɬɨ ɜɚɠɧɟɣɲɢɣ ɬɢɩ ɫɩɨɫɨɛɧɵɯ ɪɚɫɩɪɨɫɬɪɚɧɹɬɶɫɹ ɜ ɩɥɚɡɦɟ ɜɨɥɧ (ɫɦ. ɪɢɫ.4.4). Ɉɱɟɜɢɞɧɨ, ɮɚɡɨɜɚɹ ɢ ɝɪɭɩɩɨɜɚɹ ɫɤɨɪɨɫɬɢ ɢɨɧɧɨ-ɡɜɭɤɨɜɨɣ ɜɨɥɧɵ ɫɨɜɩɚɞɚɸɬ: ZTe + 3Ti v ɮ = v ɝ ɪ = cs = . (4.57) mi ȼɟɥɢɱɢɧɚ ɷɬɢɯ ɫɤɨɪɨɫɬɟɣ ɫɭɳɟɫɬɜɟɧɧɨ ɡɚɜɢɫɢɬ ɨɬ ɫɨɨɬɧɨɲɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪ ɤɨɦɩɨɧɟɧɬ ɩɥɚɡɦɵ. ɉɪɢ ɷɬɨɦ ɟɫɥɢ Ti ≥ Te , ɬɨ ɮɚɡɨɜɚɹ ɫɤɨɪɨɫɬɶ ɢɨɧɧɨ-ɡɜɭɤɨɜɨɣ ɜɨɥɧɵ ɛɭɞɟɬ ɩɨ ɜɟɥɢɱɢɧɟ ɩɨɪɹɞɤɚ ɬɟɩɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɢɨɧɨɜ. Ɍɚɤɢɟ ɜɨɥɧɵ ɞɨɥɠɧɵ ɫɢɥɶɧɨ ɩɨɝɥɨɳɚɬɶɫɹ ɜ ɩɥɚɡɦɟ, ɬɚɤ ɤɚɤ ɨɧɢ ɫɬɚɧɨɜɹɬɫɹ ɪɟɡɨɧɚɧɫɧɵɦɢ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɢɨɧɚɦ. ɉɨɷɬɨɦɭ ɢɨɧɧɨ-ɡɜɭɤɨɜɚɹ ɜɨɥɧɚ ɦɨɠɟɬ ɫɭɳɟɫɬɜɨɜɚɬɶ ɬɨɥɶɤɨ ɜ ɫɢɥɶɧɨ ɧɟɢɡɨɬɟɪɦɢɱɟɫɤɨɣ ɩɥɚɡɦɟ, ɤɨɝɞɚ ɷɥɟɤɬɪɨɧɧɚɹ ɤɨɦɩɨɧɟɧɬɚ ɫɢɥɶɧɨ «ɩɟɪɟɝɪɟɬɚ» ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɢɨɧɧɨɣ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɜɤɥɚɞ ɬɟɦɩɟɪɚɬɭɪɵ ɢɨɧɨɜ ɜ ɮɨɪɦɭɥɟ (4.57) ɹɜɥɹɟɬɫɹ ɦɚɥɵɦ, ɢ ɩɨɷɬɨɦɭ ɫɤɨɪɨɫɬɶ ɢɨɧɧɨ-ɡɜɭɤɨɜɨɣ ɜɨɥɧɵ ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɟɦɩɟɪɚɬɭɪɨɣ ɷɥɟɤɬɪɨɧɨɜ: ZTe cs ≅ , Te >> Ti . (4.58) mi ȼ ɷɬɨɦ ɫɥɭɱɚɟ, ɩɨɫɤɨɥɶɤɭ ɜ ɮɨɪɦɭɥɭ ɞɥɹ ɫɤɨɪɨɫɬɢ ɡɜɭɤɚ ɜ ɤɚɱɟɫɬɜɟ ɦɟɪɵ ɬɟɩɥɨɜɨɣ ɷɧɟɪɝɢɢ ɜɯɨɞɢɬ ɷɥɟɤɬɪɨɧɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ, ɚ ɜ ɤɚɱɟɫɬɜɟ ɢɧɟɪɰɢɨɧɧɨɝɨ ɮɚɤɬɨɪɚ ɜɯɨɞɢɬ ɦɚɫɫɚ ɢɨɧɨɜ, ɩɪɢɧɹɬɨ ɷɬɢ ɜɨɥɧɵ ɧɚɡɵɜɚɬɶ «ɢɨɧɧɵɦ ɡɜɭɤɨɦ ɫ ɷɥɟɤɬɪɨɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ». ɋɨɛɢɪɚɹ ɜɦɟɫɬɟ ɜɫɟ ɭɤɚɡɚɧɧɵɟ ɜɵɲɟ ɧɟɪɚɜɟɧɫɬɜɚ, ɩɨɥɭɱɢɦ ɨɛɥɚɫɬɶ ɮɚɡɨɜɵɯ ɫɤɨɪɨɫɬɟɣ, ɜ ɤɨɬɨɪɨɣ ɜɨɡɦɨɠɧɨ ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɢɨɧɧɨ-ɡɜɭɤɨɜɵɯ ɜɨɥɧ: 3Ti ZTe 3Te vTi = << v ɮ ~ cs ≅ << vTe = . (4.59) mi mi me cs2 =
ȼɡɹɜ ɬɟɩɟɪɶ ɷɬɢ ɧɟɪɚɜɟɧɫɬɜɚ ɜ ɤɚɱɟɫɬɜɟ ɨɬɩɪɚɜɧɨɣ ɬɨɱɤɢ, ɦɨɠɧɨ ɫɭɳɟɫɬɜɟɧɧɨ ɭɩɪɨɫɬɢɬɶ ɜɵɜɨɞ ɡɚɤɨɧɚ ɞɢɫɩɟɪɫɢɢ ɞɥɹ ɢɨɧɧɨɝɨ ɡɜɭɤɚ. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɩɨɫɤɨɥɶɤɭ ɮɚɡɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɨɥɧɵ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ ɦɚɥɨɣ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɬɟɩɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ ɷɥɟɤɬɪɨɧɨɜ, ɢɧɟɪɰɢɹ ɩɨɫɥɟɞɧɢɯ
ɫɬɚɧɨɜɢɬɫɹ ɧɟɫɭɳɟɫɬɜɟɧɧɨɣ, ɩɨ ɷɬɨɣ ɩɪɢɱɢɧɟ ɷɥɟɤɬɪɨɧɧɚɹ ɩɨɞɫɢɫɬɟɦɚ ɦɨɠɟɬ ɫɱɢɬɚɬɶɫɹ ɤɜɚɡɢɪɚɜɧɨɜɟɫɧɨɣ, ɚ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɞɟɣɫɬɜɭɸɳɢɟ ɜ ɷɬɨɣ ɩɨɞɫɢɫɬɟɦɟ ɫɢɥɵ − ɫɢɥɚ ɫɨ ɫɬɨɪɨɧɵ ɩɨɥɹ ɜɨɥɧɵ ɢ ɫɢɥɚ, ɨɛɭɫɥɨɜɥɟɧɧɚɹ ɝɪɚɞɢɟɧɬɨɦ ɷɥɟɤɬɪɨɧɧɨɝɨ ɞɚɜɥɟɧɢɹ, − ɞɨɥɠɧɵ ɛɵɬɶ ɭɪɚɜɧɨɜɟɲɟɧɵ. ɉɨɫɤɨɥɶɤɭ ɩɪɨɞɨɥɶɧɚɹ ɜɨɥɧɚ ɜɫɟɝɞɚ ɹɜɥɹɟɬɫɹ ɩɨɬɟɧɰɢɚɥɶɧɨɣ, ɜɜɟɞɟɦ ɩɨɬɟɧɰɢɚɥ ɩɨɥɹ ɜɨɥɧɵ ɫɨɝɥɚɫɧɨ
~& E = −∇ϕ .
Ɍɨɝɞɚ ɛɚɥɚɧɫ ɭɤɚɡɚɧɧɵɯ ɫɢɥ, ɩɪɟɞɩɨɥɚɝɚɹ ɷɥɟɤɬɪɨɧɧɭɸ ɬɟɦɩɟɪɚɬɭɪɭ ɩɨɫɬɨɹɧɧɨɣ, ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɬɚɤ: | e| ne ∇ϕ − Te ∇ne = 0 , (4.60) ɢ, ɤɚɤ ɦɵ ɜɢɞɢɦ, ɤɨɧɰɟɧɬɪɚɰɢɹ ɷɥɟɤɬɪɨɧɨɜ ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ ɩɨɬɟɧɰɢɚɥɚ ɩɨɥɹ ɜɨɥɧɵ. Ɇɨɠɧɨ ɫɤɚɡɚɬɶ ɢ ɬɚɤ: «ɛɟɡɵɧɟɪɰɢɨɧɧɵɟ» ɷɥɟɤɬɪɨɧɵ ɦɝɧɨɜɟɧɧɨ ɩɨɞɫɬɪɚɢɜɚɸɬɫɹ ɩɨɞ ɩɪɨɮɢɥɶ ɩɨɥɹ, ɫɨɡɞɚɜɚɟɦɵɣ ɜɨɥɧɨɣ, ɫɤɚɩɥɢɜɚɹɫɶ ɜ ɬɟɯ ɨɛɥɚɫɬɹɯ, ɝɞɟ ɩɨɬɟɧɰɢɚɥ ɩɨɥɹ ɛɨɥɶɲɟ:
§ | e|ϕ · ne = ne0 exp¨ ¸. © Te ¹ Ɂɞɟɫɶ n e0 - ɧɟɜɨɡɦɭɳɟɧɧɚɹ ɩɨɥɟɦ ɜɨɥɧɵ ɤɨɧɰɟɧɬɪɚɰɢɹ ɷɥɟɤɬɪɨɧɨɜ (ɜ ɨɛɥɚɫɬɢ ɧɭɥɟɜɨɝɨ ɩɨɬɟɧɰɢɚɥɚ). ɉɨɥɭɱɟɧɧɵɣ ɪɟɡɭɥɶɬɚɬ, ɤɚɤ ɦɵ ɜɢɞɢɦ, ɫɨɜɩɚɞɚɟɬ ɫ ɢɡɜɟɫɬɧɨɣ ɮɨɪɦɭɥɨɣ Ȼɨɥɶɰɦɚɧɚ ɞɥɹ ɪɚɜɧɨɜɟɫɧɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɱɚɫɬɢɰ, ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ ɷɥɟɤɬɪɨɧɨɜ, ɜɨ ɜɧɟɲɧɟɦ ɩɨɥɟ. Ⱦɥɹ ɢɨɧɧɨɣ ɩɨɞɫɢɫɬɟɦɵ ɩɥɚɡɦɵ ɫɢɬɭɚɰɢɹ ɩɪɨɬɢɜɨɩɨɥɨɠɧɚɹ. ɉɨɫɤɨɥɶɤɭ ɮɚɡɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɨɥɧɵ ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɟɬ ɬɟɩɥɨɜɭɸ ɫɤɨɪɨɫɬɶ ɢɨɧɨɜ, ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ ɤɨɧɟɱɧɨɫɬɶɸ ɢɨɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ, ɫɱɢɬɚɹ ɢɨɧɵ ɯɨɥɨɞɧɵɦɢ, ɧɨ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɭɱɟɫɬɶ ɢɧɟɪɰɢɸ ɢɨɧɨɜ, ɨɝɪɚɧɢɱɢɜɚɸɳɭɸ ɱɚɫɬɨɬɭ ɤɨɥɟɛɚɧɢɣ. Ⱦɥɹ ɯɨɥɨɞɧɵɯ Z-ɤɪɚɬɧɨ ɢɨɧɢɡɨɜɚɧɧɵɯ ɢɨɧɨɜ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɜɵɝɥɹɞɢɬ ɬɚɤ:
& dvi mi = − Z| e| ∇ϕ . dt
(4.61)
ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɩɨɥɹ ɜɨɥɧɵ ɢɨɧɵ ɩɥɚɡɦɵ ɩɪɢɯɨɞɹɬ ɜ ɞɜɢɠɟɧɢɟ, ɢ ɢɯ ɤɨɧɰɟɧɬɪɚɰɢɹ ɧɚɱɢɧɚɟɬ ɢɡɦɟɧɹɬɶɫɹ, ɬɚɤ ɤɚɤ ɫɨɝɥɚɫɧɨ ɭɪɚɜɧɟɧɢɸ ɧɟɩɪɟɪɵɜɧɨɫɬɢ
∂ni & + div( ni vi ) = 0 . ∂t
(4.62)
ȼ ɤɚɱɟɫɬɜɟ ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɭɫɥɨɜɢɹ, ɡɚɦɵɤɚɸɳɟɝɨ ɫɢɫɬɟɦɭ (4.60) − (4.61), ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɬɪɟɛɨɜɚɧɢɟɦ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɢ ɩɥɚɡɦɵ ne = Zni , (4.63) ɤɨɬɨɪɨɟ, ɨɱɟɜɢɞɧɨ, ɞɨɥɠɧɨ ɜɵɩɨɥɧɹɬɶɫɹ, ɬɚɤ ɤɚɤ ɞɥɢɧɚ ɜɨɥɧɵ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɸɳɟɣ ɷɥɟɤɬɪɨɧɧɵɣ ɞɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ. ȼ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɜɨɥɧɵ ɤɨɪɨɬɤɢɟ, ɭɫɥɨɜɢɟ (4.63) ɫɥɟɞɭɟɬ ɡɚɦɟɧɢɬɶ ɭɪɚɜɧɟɧɢɟɦ ɉɭɚɫɫɨɧɚ
∆ϕ = 4π| e|( ne − Zni ) .
ɇɟɥɢɧɟɣɧɵɟ ɭɪɚɜɧɟɧɢɹ (4.60) − (4.63) ɫɩɪɚɜɟɞɥɢɜɵ, ɜ ɪɚɦɤɚɯ ɜɵɫɤɚɡɚɧɧɵɯ ɜɵɲɟ ɩɪɟɞɩɨɥɨɠɟɧɢɣ, ɞɥɹ ɢɨɧɧɨ-ɡɜɭɤɨɜɵɯ ɜɨɥɧ ɥɸɛɨɣ ɚɦɩɥɢɬɭɞɵ. Ɉɝɪɚɧɢɱɢɦɫɹ ɜɨɥɧɚɦɢ ɦɚɥɨɣ ɚɦɩɥɢɬɭɞɵ. ɉɨɥɚɝɚɟɦ & ϕ = ϕ~ , ne ,i = ne ,i 0 + n~e ,i , v&i = ~ vi , ɝɞɟ ɡɧɚɤɨɦ ɬɢɥɶɞɚ ɩɨɦɟɱɟɧɵ ɦɚɥɵɟ ɜɨɡɦɭɳɟɧɢɹ. ɉɨɞɫɬɚɜɢɦ ɷɬɨ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɜ ɭɪɚɜɧɟɧɢɹ (4.60) − (4.63), ɪɚɡɥɨɠɢɦ ɡɚɬɟɦ ɩɨ ɚɦɩɥɢɬɭɞɟ ɢ, ɨɩɭɫɬɢɜ ɧɟɥɢɧɟɣɧɵɟ ɫɥɚɝɚɟɦɵɟ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɩɨɥɭɱɢɦ | e| ne0 ∇ϕ~ − Te ∇n~e = 0 ,
& vi ∂~ mi = − Z| e|∇ϕ~ , ∂t ∂n~i & + div ( ni 0 v i ) = 0 , ∂t n~e = Zn~i , ne0 = Zni 0 .
(4.64)
ȼɵɪɚɡɢɜ ɬɟɩɟɪɶ ɜɫɟ ɜɟɥɢɱɢɧɵ ɱɟɪɟɡ ɨɞɧɭ ɢɡ ɧɢɯ, ɧɚɩɪɢɦɟɪ, ɱɟɪɟɡ ɩɨɬɟɧɰɢɚɥ ɩɨɥɹ ɜɨɥɧɵ, ɩɨɥɭɱɢɦ ɜɨɥɧɨɜɨɟ ɭɪɚɜɧɟɧɢɟ
∂2 ~ 2 ~ ZT cs2 = e 2 ϕ − c s ∆ϕ = 0 , ∂t mi
,
(4.65)
ɫɥɟɞɫɬɜɢɟɦ ɤɨɬɨɪɨɝɨ, ɤɚɤ ɧɟɬɪɭɞɧɨ ɩɪɨɜɟɪɢɬɶ, ɹɜɥɹɟɬɫɹ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ (4.56), ɩɪɢɱɟɦ ɜɟɥɢɱɢɧɚ ɜɯɨɞɹɳɟɣ ɜ ɧɟɝɨ ɫɤɨɪɨɫɬɢ ɡɜɭɤɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɨɪɦɭɥɨɣ (4.58).
Ɇɵ ɪɚɫɫɦɨɬɪɟɥɢ ɫɚɦɵɟ ɩɪɨɫɬɵɟ ɞɢɫɩɟɪɫɢɨɧɧɵɟ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɧɟɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɵ. Ⱦɥɹ ɭɞɨɛɫɬɜɚ ɱɢɬɚɬɟɥɟɣ, ɧɚɢɛɨɥɟɟ ɜɚɠɧɵɟ ɢɡ ɧɢɯ ɫɜɟɞɟɧɵ ɜ ɧɢɠɟɫɥɟɞɭɸɳɭɸ ɬɚɛɥɢɰɭ 4.1: Ɍɚɛɥɢɰɚ 4.1 Ɍɢɩ ɜɨɥɧɵ ɗɥɟɤɬɪɨɧɧɚɹ ɥɟɧɝɦɸɪɨɜɫɤɚɹ ɜɨɥɧɚ ɜ ɯɨɥɨɞɧɨɣ ɩɥɚɡɦɟ ɗɥɟɤɬɪɨɧɧɚɹ ɥɟɧɝɦɸɪɨɜɫɤɚɹ ɜɨɥɧɚ ɜ «ɬɟɩɥɨɣ» ɩɥɚɡɦɟ ɂɨɧɧɨ-ɡɜɭɤɨɜɚɹ ɜɨɥɧɚ ɉɨɩɟɪɟɱɧɚɹ ɩɥɚɡɦɟɧɧɚɹ ɜɨɥɧɚ
Ɂɚɤɨɧ ɞɢɫɩɟɪɫɢɢ
ω Le § ©
ω Le ¨ 1 +
3 2 2· k rDe ¸ ¹ 2
kcs
Ɏɚɡɨɜɚɹ ɫɤɨɪɨɫɬɶ
ω Le k
Ƚɪɭɩɩɨɜɚɹ ɫɤɨɪɨɫɬɶ
ɉɪɢɦɟɱɚɧɢɟ
0
krDe → 0
≈ ω Le k
vTe ( kvTe ω Le )
krDe << 1
cs
cs
cs ≅
ZTe , Te >> Ti mi
krDe << 1
ω Le2 + k 2 c 2
c 1 + ω Le2 k 2 c 2
c
1 + ω Le2 k 2 c 2
§ 33. Ȼɟɫɫɬɨɥɤɧɨɜɢɬɟɥɶɧɨɟ ɡɚɬɭɯɚɧɢɟ ɜɨɥɧ ɜ ɩɥɚɡɦɟ ȼɵɲɟ ɩɪɢ ɨɛɫɭɠɞɟɧɢɢ ɤɨɧɤɪɟɬɧɵɯ ɬɢɩɨɜ ɜɨɥɧ, ɫɩɨɫɨɛɧɵɯ ɪɚɫɩɪɨɫɬɪɚɧɹɬɶɫɹ ɜ ɩɥɚɡɦɟ, ɦɵ ɧɟɨɞɧɨɤɪɚɬɧɨ ɫɫɵɥɚɥɢɫɶ ɧɚ ɪɟɡɨɧɚɧɫɧɵɟ ɷɮɮɟɤɬɵ, ɢɦɟɸɳɢɟ ɦɟɫɬɨ, ɤɨɝɞɚ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɫɨɜɩɚɞɚɸɬ ɫ ɮɚɡɨɜɨɣ ɫɤɨɪɨɫɬɶɸ ɜɨɥɧɵ. Ɂɞɟɫɶ, ɧɟ ɜɞɚɜɚɹɫɶ ɜ ɩɨɞɪɨɛɧɨɫɬɢ ɞɨɫɬɚɬɨɱɧɨ ɫɥɨɠɧɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɜɵɤɥɚɞɨɤ (ɫɦ. [20]), ɨɛɫɭɞɢɦ ɤɪɚɬɤɨ ɮɢɡɢɱɟɫɤɭɸ ɫɬɨɪɨɧɭ ɦɟɯɚɧɢɡɦɚ ɛɟɫɫɬɨɥɤɧɨɜɢɬɟɥɶɧɨɝɨ ɡɚɬɭɯɚɧɢɹ ɜɨɥɧ ɜ ɩɥɚɡɦɟ, ɜɩɟɪɜɵɟ ɩɪɟɞɫɤɚɡɚɧɧɨɝɨ Ʌɚɧɞɚɭ. Ʉɨɝɞɚ ɝɨɜɨɪɹɬ ɨ ɪɟɡɨɧɚɧɫɧɨɦ ɜɡɚɢɦɨɞɟɣɫɬɜɢɢ ɜɨɥɧ ɢ ɱɚɫɬɢɰ ɩɥɚɡɦɵ, ɬɨ, ɩɨ ɫɭɬɢ ɞɟɥɚ, ɪɟɱɶ ɢɞɟɬ ɨ ɱɟɪɟɧɤɨɜɫɤɨɦ ɪɟɡɨɧɚɧɫɟ & ω − kv& = 0 . (4.66) Ɏɚɡɨɜɚɹ ɫɤɨɪɨɫɬɶ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɵ ɜ ɢɡɨɬɪɨɩɧɨɣ ɩɥɚɡɦɟ, ɤɚɤ ɦɵ ɜɢɞɟɥɢ ɪɚɧɶɲɟ, ɩɪɟɜɵɲɚɟɬ ɫɤɨɪɨɫɬɶ ɫɜɟɬɚ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɷɬɨ ɭɫɥɨɜɢɟ ɡɚɜɟɞɨɦɨ ɧɟ ɦɨɠɟɬ ɜɵɩɨɥɧɹɬɶɫɹ ɢ ɪɟɡɨɧɚɧɫɧɵɟ ɷɮɮɟɤɬɵ ɬɚɤɨɝɨ ɪɨɞɚ, ɤɚɤ ɦɨɠɧɨ ɨɠɢɞɚɬɶ, ɛɭɞɭɬ ɧɟɫɭɳɟɫɬɜɟɧɧɵ. ɂɦɟɟɬ ɫɦɵɫɥ ɩɨɷɬɨɦɭ ɪɚɫɫɦɨɬɪɟɬɶ ɪɟɡɨɧɚɧɫɧɨɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɫ ɩɪɨɞɨɥɶɧɵɦɢ ɜɨɥɧɚɦɢ, ɮɚɡɨɜɚɹ ɫɤɨɪɨɫɬɶ ɤɨɬɨɪɵɯ ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɶɲɟ ɫɤɨɪɨɫɬɢ ɫɜɟɬɚ, ɬɚɤ ɱɬɨ ɜɵɩɨɥɧɟɧɢɟ ɭɫɥɨɜɢɹ ɪɟɡɨɧɚɧɫɚ ɜɨɡɦɨɠɧɨ. ɉɭɫɬɶ ɞɥɹ ɩɪɨɫɬɨɬɵ ɩɪɨɞɨɥɶɧɚɹ ɜɨɥɧɚ ɛɭɞɟɬ ɨɞɧɨɦɟɪɧɨɣ (ɩɥɨɫɤɨɣ). Ɉɛɵɱɧɨ ɦɟɯɚɧɢɡɦ ɛɟɫɫɬɨɥɤɧɨɜɢɬɟɥɶɧɨɝɨ ɩɨɝɥɨɳɟɧɢɹ ɷɧɟɪɝɢɢ ɜɨɥɧ ɱɚɫɬɢɰɚɦɢ ɩɥɚɡɦɵ ɩɨɹɫɧɹɸɬ ɫ ɩɨɦɨɳɶɸ ɫɥɟɞɭɸɳɟɣ ɧɚɝɥɹɞɧɨɣ ɤɚɪɬɢɧɤɢ, ɢɡɨɛɪɚɠɟɧɧɨɣ ɧɚ ɪɢɫ. 4.5, ɢɞɟɸ ɤɨɬɨɪɨɣ ɦɵ ɡɚɢɦɫɬɜɨɜɚɥɢ ɢɡ ɤɧɢɝɢ [21].
Ɋɢɫ. 4.5. Ʉ ɦɟɯɚɧɢɡɦɭ ɪɟɡɨɧɚɧɫɧɨɝɨ ɩɨɝɥɨɳɟɧɢɹ ɜɨɥɧ ɜ ɩɥɚɡɦɟ. ȼɜɟɪɯɭ: «ɝɨɪɛɵ ɢ ɜɩɚɞɢɧɵ» ɩɨɬɟɧɰɢɚɥɚ ɩɨɥɹ ɜɨɥɧɵ ɜ ɫɢɫɬɟɦɟ ɟɟ ɩɨɤɨɹ; ɫɬɪɟɥɤɚɦɢ ɩɨɤɚɡɚɧɵ ɧɚɩɪɚɜɥɟɧɢɹ ɫɤɨɪɨɫɬɟɣ ɨɩɟɪɟɠɚɸɳɢɯ (1) ɢ ɨɬɫɬɚɸɳɢɯ (2) ɝɪɭɩɩ ɱɚɫɬɢɰ. ȼɧɢɡɭ: ɮɭɧɤɰɢɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɱɚɫɬɢɰ ɩɨ ɫɤɨɪɨɫɬɹɦ ɜ ɧɟɩɨɞɜɢɠɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ. ȼɵɛɪɚɧɧɚɹ ɜɨɥɧɚ ɛɟɠɢɬ ɫɥɟɜɚ ɧɚɩɪɚɜɨ
ȼ ɞɜɢɠɭɳɟɣɫɹ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ, ɨɬɧɨɫɢɬɟɥɶɧɨ ɤɨɬɨɪɨɣ ɜɨɥɧɚ ɩɨɤɨɢɬɫɹ, ɧɚɝɥɹɞɧɨ ɦɨɠɧɨ ɟɟ ɩɪɟɞɫɬɚɜɥɹɬɶ ɤɚɤ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɝɨɪɛɨɜ ɢ ɹɦ ɩɨɬɟɧɰɢɚɥɚ. ɑɚɫɬɢɰɵ, ɫɤɚɬɵɜɚɸɳɢɟɫɹ ɜ ɹɦɵ, ɭɫɤɨɪɹɸɬɫɹ, ɚ ɱɚɫɬɢɰɵ, ɡɚɤɚɬɵɜɚɸɳɢɟɫɹ ɧɚ ɝɨɪɛɵ, ɧɚɩɪɨɬɢɜ, ɡɚɦɟɞɥɹɸɬɫɹ ɩɨɥɟɦ ɜɨɥɧɵ. ȼɵɞɟɥɢɦ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 3.5, ɞɜɟ ɝɪɭɩɩɵ ɱɚɫɬɢɰ, ɨɬɜɟɱɚɸɳɢɯ ɨɞɧɨɦɭ ɢ ɬɨɦɭ ɠɟ ɢɧɬɟɪɜɚɥɭ ∆v ɫɩɪɚɜɚ (ɝɪɭɩɩɚ (1)) ɢ ɫɥɟɜɚ (ɝɪɭɩɩɚ (2)) ɨɬ ɫɤɨɪɨɫɬɢ, ɫɨɜɩɚɞɚɸɳɟɣ ɩɨ ɜɟɥɢɱɢɧɟ ɢ ɧɚɩɪɚɜɥɟɧɢɸ ɫ ɮɚɡɨɜɨɣ ɫɤɨɪɨɫɬɶɸ ɜɨɥɧɵ. ȼ ɞɜɢɠɭɳɟɣɫɹ ɫ ɮɚɡɨɜɨɣ ɫɤɨɪɨɫɬɶɸ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ ɩɟɪɜɵɟ, ɨɱɟɜɢɞɧɨ, ɨɛɝɨɧɹɸɬ ɜɨɥɧɭ, ɚ ɜɬɨɪɵɟ ɨɬɫɬɚɸɬ ɨɬ ɧɟɟ (ɞɥɹ ɧɚɝɥɹɞɧɨɫɬɢ ɢɡɨɛɪɚɠɟɧɨ ɪɚɡɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɤɪɭɠɨɱɤɨɜ). ȿɫɥɢ ɜ ɤɚɱɟɫɬɜɟ ɬɚɤɢɯ ɝɪɭɩɩ ɱɚɫɬɢɰ ɜɡɹɬɶ ɬɟ, ɤɨɬɨɪɵɟ ɧɚ ɪɢɫɭɧɤɟ ɭɫɥɨɜɧɨ ɢɡɨɛɪɚɠɟɧɵ ɱɟɪɧɵɦɢ ɬɨɱɤɚɦɢ, ɬɨ ɨɛɟ ɝɪɭɩɩɵ ɱɚɫɬɢɰ ɬɨɪɦɨɡɹɬɫɹ, ɬɚɤ ɤɚɤ ɢɯ ɫɤɨɪɨɫɬɢ ɜ ɞɚɧɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɧɚɩɪɚɜɥɟɧɵ ɤ «ɝɨɪɛɚɦ» ɩɨɬɟɧɰɢɚɥɚ, ɧɚ ɤɨɬɨɪɵɟ ɩɨɷɬɨɦɭ ɨɧɢ ɜɵɧɭɠɞɟɧɵ ɡɚɛɢɪɚɬɶɫɹ. Ɉɞɧɚɤɨ ɞɜɢɠɭɳɢɟɫɹ ɧɚɩɪɚɜɨ ɩɪɢ ɷɬɨɦ ɤɚɤ ɛɵ «ɩɨɞɬɚɥɤɢɜɚɸɬ» ɝɨɪɛ ɜɩɟɪɟɞ, ɚ ɞɜɢɠɭɳɢɟɫɹ ɧɚɥɟɜɨ, ɧɚɩɪɨɬɢɜ, «ɬɨɥɤɚɸɬ» ɟɝɨ ɧɚɡɚɞ. ȿɫɥɢ ɠɟ ɜ ɤɚɱɟɫɬɜɟ ɬɚɤɢɯ ɝɪɭɩɩ ɱɚɫɬɢɰ ɜɡɹɬɶ ɬɟ, ɤɨɬɨɪɵɟ ɭɫɥɨɜɧɨ ɢɡɨɛɪɚɠɟɧɵ ɫɜɟɬɥɵɦɢ ɬɨɱɤɚɦɢ, ɬɨ ɩɨɫɤɨɥɶɤɭ ɩɪɢ ɬɨɦ ɠɟ ɫɚɦɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰɵ ɨɛɟɢɯ ɝɪɭɩɩ ɬɟɩɟɪɶ ɫɤɚɬɵɜɚɸɬɫɹ ɫ «ɩɨɬɟɧɰɢɚɥɶɧɵɯ ɝɨɪɨɤ», ɨɛɟ ɨɧɢ ɞɨɥɠɧɵ ɭɫɤɨɪɹɬɶɫɹ. ɇɨ ɷɮɮɟɤɬ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɫ ɜɨɥɧɨɣ, ɨɱɟɜɢɞɧɨ, ɧɟ ɞɨɥɠɟɧ ɡɚɜɢɫɟɬɶ ɨɬ ɬɨɝɨ, ɤɚɤ ɦɵ ɜɵɛɟɪɟɦ ɪɚɫɩɨɥɨɠɟɧɢɟ ɩɨ ɤɨɨɪɞɢɧɚɬɟ ɷɬɢɯ ɝɪɭɩɩ ɱɚɫɬɢɰ! Ɉɱɟɜɢɞɧɨ, ɷɬɢ ɧɚɝɥɹɞɧɵɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɧɟ ɞɚɸɬ ɩɨɥɧɨɣ ɤɚɪɬɢɧɵ.
Ⱦɟɬɚɥɶɧɨ ɦɟɯɚɧɢɡɦ ɛɟɫɫɬɨɥɤɧɨɜɢɬɟɥɶɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɪɚɡɨɛɪɚɧ ɜ ɤɧɢɝɟ [19]. ȼ ɨɛɦɟɧɟ ɷɧɟɪɝɢɟɣ ɫ ɩɨɥɟɦ ɭɱɚɫɬɜɭɸɬ ɱɚɫɬɢɰɵ ɫɨ ɫɤɨɪɨɫɬɹɦɢ, ɛɥɢɡɤɢɦɢ ɤ ɮɚɡɨɜɨɣ ɫɤɨɪɨɫɬɢ ɜɨɥɧɵ. ɉɪɢɱɟɦ ɱɚɫɬɢɰɵ, ɞɜɢɠɭɳɢɟɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ ɦɟɧɶɲɟɣ, ɱɟɦ ɮɚɡɨɜɚɹ ɫɤɨɪɨɫɬɶ, ɩɨɥɭɱɚɸɬ ɷɧɟɪɝɢɸ ɨɬ ɜɨɥɧɵ, ɚ ɬɟ ɱɚɫɬɢɰɵ, ɮɚɡɨɜɚɹ ɫɤɨɪɨɫɬɶ ɤɨɬɨɪɵɯ ɛɨɥɶɲɟ ɮɚɡɨɜɨɣ ɫɤɨɪɨɫɬɢ, ɨɬɞɚɸɬ ɷɧɟɪɝɢɸ ɜɨɥɧɟ. ȿɫɥɢ ɩɟɪɜɵɯ ɧɟɫɤɨɥɶɤɨ ɛɨɥɶɲɟ, ɱɟɦ ɜɬɨɪɵɯ, ɬ.ɟ. ɩɪɨɢɡɜɨɞɧɚɹ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨ ɫɤɨɪɨɫɬɢ ɨɬɪɢɰɚɬɟɥɶɧɚɹ, ɬɨ ɜɨɥɧɚ ɛɭɞɟɬ ɬɟɪɹɬɶ ɷɧɟɪɝɢɸ. ɂɦɟɧɧɨ ɬɚɤɨɜɚ ɫɢɬɭɚɰɢɹ ɞɥɹ ɪɚɜɧɨɜɟɫɧɨɣ ɦɚɤɫɜɟɥɥɨɜɫɤɨɣ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ, ɩɨɷɬɨɦɭ ɜ ɩɥɚɡɦɟ ɫ ɬɚɤɨɣ ɮɭɧɤɰɢɟɣ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɫɟ ɜɨɥɧɵ ɞɨɥɠɧɵ ɡɚɬɭɯɚɬɶ.
§ 34. Ⱦɢɷɥɟɤɬɪɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɦɚɝɧɢɬɨɚɤɬɢɜɧɨɣ ɩɥɚɡɦɵ ɉɨɦɟɳɟɧɢɟ ɩɥɚɡɦɵ ɜ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɨɱɟɧɶ ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɹɟɬ ɟɟ ɫɜɨɣɫɬɜɚ: ɩɥɚɡɦɚ ɫɬɚɧɨɜɢɬɫɹ ɚɧɢɡɨɬɪɨɩɧɨɣ. ɉɨɷɬɨɦɭ ɜɨɥɧɵ ɜ ɩɥɚɡɦɟ ɩɪɢ ɧɚɥɢɱɢɢ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɩɪɨɹɜɥɹɸɬ ɡɧɚɱɢɬɟɥɶɧɨɟ ɪɚɡɧɨɨɛɪɚɡɢɟ: ɫɤɨɪɨɫɬɶ ɢɯ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɢ ɯɚɪɚɤɬɟɪ ɞɢɫɩɟɪɫɢɢ ɫɭɳɟɫɬɜɟɧɧɨ ɡɚɜɢɫɹɬ ɨɬ ɧɚɩɪɚɜɥɟɧɢɹ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜɨɥɧɵ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɨɬ ɜɡɚɢɦɧɨɣ ɨɪɢɟɧɬɚɰɢɢ ɩɥɨɫɤɨɫɬɢ ɤɨɥɟɛɚɧɢɣ ɜɟɤɬɨɪɚ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜɨɥɧɵ ɢ «ɨɫɧɨɜɧɨɝɨ» ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɜ ɤɨɬɨɪɨɟ ɩɨɦɟɳɟɧɚ ɩɥɚɡɦɚ. ɉɨɦɟɳɟɧɧɭɸ ɜ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɩɥɚɡɦɭ ɢɧɨɝɞɚ ɧɚɡɵɜɚɸɬ ɦɚɝɧɢɬɨɚɤɬɢɜɧɨɣ. ɋɬɪɨɝɨɟ ɪɚɫɫɦɨɬɪɟɧɢɟ ɜ ɦɚɝɧɢɬɨɚɤɬɢɜɧɨɣ ɩɥɚɡɦɟ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɤɨɥɟɛɚɧɢɣ ɢ ɜɨɥɧ ɪɚɡɥɢɱɧɨɝɨ ɬɢɩɚ ɜ ɩɪɨɢɡɜɨɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɜ ɦɟɧɹɸɳɟɦɫɹ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɩɪɟɞɫɬɚɜɥɹɟɬ ɨɱɟɧɶ ɛɨɥɶɲɢɟ ɬɪɭɞɧɨɫɬɢ. Ɇɵ ɪɚɫɫɦɨɬɪɢɦ ɡɞɟɫɶ, ɟɫɬɟɫɬɜɟɧɧɨ, ɥɢɲɶ ɧɚɢɛɨɥɟɟ ɩɪɨɫɬɵɟ ɫɥɭɱɚɢ. Ȼɭɞɟɦ ɫɱɢɬɚɬɶ, ɱɬɨ ɜɧɟɲɧɟɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɜ ɤɨɬɨɪɨɟ ɩɨɦɟɳɟɧɚ ɩɥɚɡɦɚ, ɩɨɫɬɨɹɧɧɨ ɢ ɜɨ ɜɪɟɦɟɧɢ ɢ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ. ɑɬɨ ɨɧɨ ɞɨɫɬɚɬɨɱɧɨ ɜɟɥɢɤɨ, ɬɚɤ ɱɬɨ ɩɥɚɡɦɚ ɡɚɦɚɝɧɢɱɟɧɚ (ɧɚɩɨɦɧɢɦ, ɱɬɨ ɩɥɚɡɦɚ ɧɚɡɵɜɚɟɬɫɹ ɡɚɦɚɝɧɢɱɟɧɧɨɣ, ɟɫɥɢ ɯɚɪɚɤɬɟɪɧɨɟ ɜɪɟɦɹ ɦɟɠɱɚɫɬɢɱɧɵɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɟɬ ɩɟɪɢɨɞɵ ɜɪɚɳɟɧɢɹ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɩɨ ɥɚɪɦɨɪɨɜɫɤɢɦ ɨɪɛɢɬɚɦ). ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɩɥɚɡɦɭ ɛɭɞɟɦ ɫɱɢɬɚɬɶ ɯɨɥɨɞɧɨɣ, ɩɪɟɧɟɛɪɟɝɚɹ ɬɟɦ ɫɚɦɵɦ ɬɟɩɥɨɜɵɦ ɞɜɢɠɟɧɢɟɦ ɱɚɫɬɢɰ. Ɍɚɤɨɣ ɩɨɞɯɨɞ ɩɨɡɜɨɥɹɟɬ ɨɯɜɚɬɢɬɶ ɧɟ ɜɫɟ, ɤɨɧɟɱɧɨ, ɧɨ ɧɚɢɛɨɥɟɟ ɜɚɠɧɵɟ ɬɢɩɵ ɜɨɥɧ ɦɚɥɨɣ ɚɦɩɥɢɬɭɞɵ ɜ ɦɚɝɧɢɬɨɚɤɬɢɜɧɨɣ ɩɥɚɡɦɟ. Ɉɬɦɟɬɢɦ ɧɟɫɤɨɥɶɤɨ ɩɨɥɟɡɧɵɯ ɮɨɪɦɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ. • ɉɪɨɞɨɥɶɧɵɟ (ɜɞɨɥɶ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ) ɞɢɷɥɟɤɬɪɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɩɥɚɡɦɵ. ɉɪɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɢ ɜ ɩɥɚɡɦɟ ɩɪɨɞɨɥɶɧɨɣ ɜɨɥɧɵ ɜɞɨɥɶ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɨɱɟɜɢɞɧɨ, ɞɢɷɥɟɤɬɪɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɩɥɚɡɦɵ ɬɚɤɢɟ ɠɟ, ɤɚɤ ɢ ɜ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɷɬɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɟɬ. Ʉɨɥɟɛɚɧɢɹ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜɨɥɧɵ ɩɪɨɢɫɯɨɞɹɬ ɜɞɨɥɶ ɦɚɝɧɢɬɧɵɯ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɚ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɧɚɥɢɱɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɚ ɷɬɢ ɤɨɥɟɛɚɧɢɹ ɧɢɤɚɤ ɧɟ ɫɤɚɡɵɜɚɟɬɫɹ. ɉɨɷɬɨɦɭ ɨɱɟɜɢɞɧɨ, ɱɬɨ (ɞɥɹ ɯɨɥɨɞɧɨɣ ɩɥɚɡɦɵ) ɤɨɦɩɨɧɟɧɬɚ ɬɟɧɡɨɪɚ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɜɞɨɥɶ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɛɭɞɟɬ ɬɚɤɚɹ ɠɟ, ɤɚɤ ɢ ɜ ɫɥɭɱɚɟ ɛɟɡ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ: 2 4πnα eα2 §ω · ε|| = ε0 = 1 − ¨ 0 ¸ , ω02 = ¦ ≡ ¦ ω L2α , ©ω¹ mα α = e ,i α = e ,i ɝɞɟ ω Le,i ɥɟɧɝɦɸɪɨɜɫɤɢɟ ɱɚɫɬɨɬɵ ɱɚɫɬɢɰ ɩɥɚɡɦɵ. ɉɭɫɬɶ ɬɟɩɟɪɶ ɧɚ ɜɦɨɪɨɠɟɧɧɭɸ ɜ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɩɥɚɡɦɭ ɩɚɞɚɟɬ ɩɨɩɟɪɟɱɧɚɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ ɜɨɥɧɚ, ɬɚɤ, ɱɬɨ ɜɟɤɬɨɪ ɫɤɨɪɨɫɬɢ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɜɨɥɧɵ ɩɟɪɩɟɧɞɢɤɭɥɹɪɟɧ ɜɟɤɬɨɪɭ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɚ ɜɟɤɬɨɪ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɷɬɨɣ ɜɨɥɧɵ ȿ ɤɨɥɥɢɧɟɚɪɟɧ (ɩɚɪɚɥɥɟɥɟɧ ɢɥɢ ɚɧɬɢɩɚɪɚɥɥɟɥɟɧ) ɜɟɤɬɨɪɭ B0 (ɪɢɫ.4.6). ȼɧɟɲɧɟɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɛɭɞɟɦ ɩɨɦɟɱɚɬɶ ɢɧɞɟɤɫɨɦ «0», ɱɬɨɛɵ ɨɬɥɢɱɚɬɶ ɟɝɨ ɨɬ ɫɨɛɫɬɜɟɧɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜɨɥɧɵ. ȼɧɨɜɶ Ɋɢɫ.4.6. ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ ɜɨɥɧɚ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɜɨɥɧɵ ɜɨɡɞɟɣɫɬɜɭɟɬ ɬɨɥɶɤɨ ɧɚ ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɤ & & & ɞɜɢɠɟɧɢɟ ɱɚɫɬɢɰ ɜɞɨɥɶ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɧɚ ɤɨɬɨɪɨɟ B0 ɢ ɟɟ ɜɟɤɬɨɪ ȿ || B0 ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɧɟ ɫɤɚɡɵɜɚɟɬɫɹ. ɉɨɷɬɨɦɭ ɬɚɤɚɹ ɜɨɥɧɚ ɛɭɞɟɬ ɪɚɫɩɪɨɫɬɪɚɧɹɬɶɫɹ ɜ ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɟ ɬɚɤ ɠɟ, ɤɚɤ ɨɧɚ ɪɚɫɩɪɨɫɬɪɚɧɹɥɚɫɶ ɛɵ ɜ ɩɥɚɡɦɟ, ɫɜɨɛɨɞɧɨɣ ɨɬ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ɗɬɨ ɜɚɠɧɨɟ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɜ ɞɢɚɝɧɨɫɬɢɤɟ ɩɥɚɡɦɵ.
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ȼɦɨɪɨɠɟɧɧɨɫɬɶ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɢɞɟɚɥɶɧɨ ɩɪɨɜɨɞɹɳɭɸ ɩɥɚɡɦɭ.
Ʉɚɤ ɢɡɜɟɫɬɧɨ, ɡɚɤɨɧ Ɉɦɚ ɞɥɹ ɫɪɟɞɵ ɫɥɟɞɭɟɬ ɡɚɩɢɫɵɜɚɬɶ ɜ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ, ɨɬɧɨɫɢɬɟɥɶɧɨ ɤɨɬɨɪɨɣ ɨɧɚ ɩɨɤɨɢɬɫɹ. ɉɨɷɬɨɦɭ ɜ ɩɪɨɫɬɟɣɲɟɦ ɫɥɭɱɚɟ ɨɞɧɨɪɨɞɧɨɣ ɩɥɚɡɦɵ, ɩɟɪɟɫɟɤɚɸɳɟɣ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɩɪɢ ɞɜɢɠɟɧɢɢ ɫɢɥɨɜɵɟ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɡɚɤɨɧ Ɉɦɚ ɞɨɥɠɟɧ ɛɵɬɶ ɡɚɩɢɫɚɧ ɜ ɜɢɞɟ: & & & 1& & & j = σE ∗ , E ∗ ≡ E + v × B , (4.67) c ɝɞɟ σ - ɩɪɨɜɨɞɢɦɨɫɬɶ ɫɪɟɞɵ. ȿɫɥɢ ɫɪɟɞɚ – ɢɞɟɚɥɶɧɵɣ ɩɪɨɜɨɞɧɢɤ, σ→∞, ɬɨ ɜ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ, ɜ ɤɨɬɨɪɨɣ ɨɧɚ ɩɨɤɨɢɬɫɹ, ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɨɬɫɭɬɫɬɜɭɟɬ. ɉɨɷɬɨɦɭ ɭɫɥɨɜɢɟ ɢɞɟɚɥɶɧɨɣ ɩɪɨɜɨɞɢɦɨɫɬɢ ɨɤɚɡɵɜɚɟɬɫɹ ɫɥɟɞɭɸɳɢɦ: & & 1& & (4.68) E ∗ = E + v × B = 0. c ɉɨɞɫɬɚɜɢɜ ɨɩɪɟɞɟɥɹɟɦɭɸ ɷɬɢɦ ɭɫɥɨɜɢɟɦ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜ ɭɪɚɜɧɟɧɢɟ ɢɧɞɭɤɰɢɢ & 1∂ & B = rotE , − c ∂t ɩɪɢɯɨɞɢɦ ɤ ɭɪɚɜɧɟɧɢɸ ɜɦɨɪɨɠɟɧɧɨɫɬɢ: ∂ & & & B = rot ( v × B). (4.69) ∂t ɗɬɨ ɭɪɚɜɧɟɧɢɟ ɨɛɥɚɞɚɟɬ ɫɥɟɞɭɸɳɢɦ ɡɚɦɟɱɚɬɟɥɶɧɵɦ ɫɜɨɣɫɬɜɨɦ. ȼɵɞɟɥɢɦ ɜ ɩɥɚɡɦɟ ɧɟɤɨɬɨɪɵɣ ɤɨɧɬɭɪ, ɩɪɨɧɢɡɵɜɚɟɦɵɣ ɫɢɥɨɜɵɦɢ ɥɢɧɢɹɦɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ (ɪɢɫ. 4.7), ɢ ɫɦɟɳɚɸɳɢɣɫɹ ɜɦɟɫɬɟ ɫ ɩɥɚɡɦɨɣ. ɉɨɬɨɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɱɟɪɟɡ ɷɬɨɬ ɤɨɧɬɭɪ ɩɨ ɨɩɪɟɞɟɥɟɧɢɸ ɪɚɜɟɧ ɢɧɬɟɝɪɚɥɭ ɨɬ ɜɟɤɬɨɪɚ ɢɧɞɭɤɰɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɩɨ ɩɥɨɳɚɞɢ, ɨɯɜɚɬɵɜɚɟɦɨɣ ɷɬɢɦ ɤɨɧɬɭɪɨɦ: & & Φ = ³ BdS = ³ Bn dS , (4.70) S
S
ɝɞɟ ȼn – ɩɪɨɟɤɰɢɹ ɜɟɤɬɨɪɚ ɢɧɞɭɤɰɢɢ ɧɚ ɧɚɩɪɚɜɥɟɧɢɟ Ɋɢɫ. 4.7. Ʉ ɬɟɨɪɟɦɟ ɜɦɨɪɨɠɟɧɧɨɫɬɢ ɧɨɪɦɚɥɢ. ɉɪɨɢɧɬɟɝɪɢɪɨɜɚɜ ɭɪɚɜɧɟɧɢɟ (4.69) ɩɨ ɷɬɨɦɭ ɤɨɧɬɭɪɭ, ɦɵ ɨɛɧɚɪɭɠɢɦ, ɱɬɨ ɩɨɬɨɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɩɪɨɧɢɡɵɜɚɸɳɟɝɨ ɤɨɧɬɭɪ, ɫɨɯɪɚɧɹɟɬɫɹ: dΦ = 0. (4.71) dt ɋɨɯɪɚɧɟɧɢɟ ɩɨɬɨɤɚ ɢ ɫɨɫɬɚɜɥɹɟɬ ɫɨɞɟɪɠɚɧɢɟ ɬɚɤ ɧɚɡɵɜɚɟɦɨɣ ɬɟɨɪɟɦɵ ɜɦɨɪɨɠɟɧɧɨɫɬɢ. ɉɨɫɤɨɥɶɤɭ ɷɬɨ ɭɬɜɟɪɠɞɟɧɢɟ ɫɩɪɚɜɟɞɥɢɜɨ ɞɥɹ ɥɸɛɨɝɨ ɤɨɧɬɭɪɚ, ɞɜɢɠɭɳɟɝɨɫɹ ɜɦɟɫɬɟ ɫ ɜɟɳɟɫɬɜɨɦ, ɬɨ ɷɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɫɢɥɨɜɵɟ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɤɚɤ ɛɵ «ɩɪɢɤɥɟɟɧɵ» ɤ ɢɞɟɚɥɶɧɨ ɩɪɨɜɨɞɹɳɟɣ ɫɪɟɞɟ. ɉɨɷɬɨɦɭ ɫɦɟɳɟɧɢɟ ɢɥɢ ɞɟɮɨɪɦɚɰɢɹ ɤɨɧɬɭɪɚ ɩɪɢ ɞɜɢɠɟɧɢɢ ɩɥɚɡɦɵ ɩɪɢɜɨɞɢɬ ɤ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦɭ ɢɫɤɚɠɟɧɢɸ ɤɚɪɬɢɧɵ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ.
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ɉɨɩɟɪɟɱɧɵɟ ɞɢɷɥɟɤɬɪɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɩɥɚɡɦɵ. ɑɬɨɛɵ ɩɨɧɹɬɶ, ɤɚɤɨɜɚ ɞɨɥɠɧɚ ɛɵɬɶ ɫɬɪɭɤɬɭɪɚ ɱɢɫɬɨ ɩɨɩɟɪɟɱɧɨɣ ɤɨɦɩɨɧɟɧɬɵ ɬɟɧɡɨɪɚ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɩɥɚɡɦɵ, ɪɚɫɫɦɨɬɪɢɦ ɞɜɚ ɩɪɟɞɟɥɶɧɵɯ ɫɥɭɱɚɹ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɤɨɝɞɚ ɩɨɥɟ ɜɨɥɧɵ ɜɵɫɨɤɨɱɚɫɬɨɬɧɨɟ, ɫ ɱɚɫɬɨɬɨɣ ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɸɳɟɣ ɰɢɤɥɨɬɪɨɧɧɵɟ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ, ɬɨ ɧɚɥɢɱɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɟɫɭɳɟɫɬɜɟɧɧɨ. ɉɨɷɬɨɦɭ ɜ ɷɬɨɦ ɩɪɟɞɟɥɟ ɞɨɥɠɧɨ ɛɵɬɶ 2
§ω · ε⊥ ω >>ω Be ,i ≈ε|| = ε0 = 1 − ¨ 0 ¸ . ©ω¹
(4.72)
ȼ ɨɛɪɚɬɧɨɦ ɩɪɟɞɟɥɟ ɧɢɡɤɢɯ ɱɚɫɬɨɬ, ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɜ ɩɥɚɡɦɟ ɩɨɩɟɪɟɱɧɨɣ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɜɨɥɧɵ ɫ ɜɟɤɬɨɪɨɦ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɧɚɩɪɚɜɥɟɧɧɵɦ ɫɬɪɨɝɨ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɤ ɜɟɤɬɨɪɭ ɢɧɞɭɤɰɢɢ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ (ɪɢɫ.4.8), ɜɩɨɥɧɟ ɚɧɚɥɨɝɢɱɧɨ ɩɨɦɟɳɟɧɢɸ ɩɥɚɡɦɵ ɜ ɫɤɪɟɳɟɧɧɵɟ ɩɨɥɹ − ɦɟɞɥɟɧɧɨ ɦɟɧɹɸɳɟɟɫɹ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɜɨɥɧɵ ɢ ɨɞɧɨɪɨɞɧɨɟ ɜɧɟɲɧɟɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɜ ɤɨɬɨɪɨɟ ɩɨɦɟɳɟɧɚ ɩɥɚɡɦɚ.
Ɋɢɫ.4.8. ɇɚɩɪɚɜɥɟɧɢɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɜɨɥɧɵ & & & ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɤ B0 ɢ ɟɟ ɜɟɤɬɨɪ ȿ⊥B0
Ɋɢɫ. 4.9. ɉɨɥɹɪɢɡɚɰɢɹ ɩɥɚɡɦɵ ɜ ɩɨɥɟ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɵ
ȼ ɷɬɢɯ ɭɫɥɨɜɢɹɯ, ɨɱɟɜɢɞɧɨ, ɦɵ ɦɨɠɟɦ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɞɪɟɣɮɨɜɵɦ ɩɪɢɛɥɢɠɟɧɢɟɦ, ɢɡɥɨɠɟɧɧɵɦ ɜ § 17. ɑɚɫɬɢɰɵ ɩɥɚɡɦɵ ɞɨɥɠɧɵ ɞɪɟɣɮɨɜɚɬɶ ɜ ɧɚɩɪɚɜɥɟɧɢɢ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɦ ɤ ɷɥɟɤɬɪɢɱɟɫɤɨɦɭ ɢ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ, ɫɨ ɫɤɨɪɨɫɬɶɸ (ɪɢɫ. 4.9) E ue = ui = c . B ɉɪɢ ɷɬɨɦ, ɩɨɫɤɨɥɶɤɭ ɫɦɟɳɟɧɢɹ ɨɬ ɪɚɜɧɨɜɟɫɧɵɯ ɩɨɥɨɠɟɧɢɣ ɜɞɨɥɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɩɨɥɨɠɢɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɵɯ ɢɨɧɨɜ ɢ ɨɬɪɢɰɚɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɢɦɟɸɬ ɪɚɡɧɵɣ ɡɧɚɤ, ɬɨ ɩɥɚɡɦɚ ɞɨɥɠɧɚ ɩɨɥɹɪɢɡɨɜɚɬɶɫɹ, ɤɚɤ ɷɬɨ ɭɠɟ ɨɛɫɭɠɞɚɥɨɫɶ ɜ § 20. Ɍɚɦ ɠɟ ɛɵɥɚ ɪɚɫɫɱɢɬɚɧɚ ɜɟɥɢɱɢɧɚ ɩɨɥɹɪɢɡɚɰɢɢ ɩɥɚɡɦɵ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɟɣ ɩɨɩɟɪɟɱɧɚɹ ɤɨɦɩɨɧɟɧɬɚ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ (2.103). ȼɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶ ɷɬɢɦ ɪɟɡɭɥɶɬɚɬɨɦ, ɩɨɥɭɱɚɟɦ, ɱɬɨ ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɧɢɡɤɨɱɚɫɬɨɬɧɨɦ ɩɪɟɞɟɥɟ
ε⊥
ω <<ωBe ,i
ω L2α = 1+ ¦ 2 . α = e ,i ω Bα
(4.73)
ɉɨɫɤɨɥɶɤɭ ɦɚɫɫɚ ɢɨɧɨɜ ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɨɫɯɨɞɢɬ ɩɨ ɜɟɥɢɱɢɧɟ ɦɚɫɫɭ ɷɥɟɤɬɪɨɧɨɜ, ɬɨ ɨɫɧɨɜɧɨɣ ɜɤɥɚɞ ɜ ɞɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɞɚɸɬ ɢɨɧɵ ɩɥɚɡɦɵ (ɷɬɨ ɫɜɹɡɚɧɨ ɫ ɬɟɦ, ɱɬɨ ɥɚɪɦɨɪɨɜɫɤɢɣ ɪɚɞɢɭɫ ɛɨɥɟɟ ɦɚɫɫɢɜɧɵɯ ɢɨɧɨɜ ɦɧɨɝɨ ɛɨɥɶɲɟ ɥɚɪɦɨɪɨɜɫɤɨɝɨ ɪɚɞɢɭɫɚ ɷɥɟɤɬɪɨɧɨɜ). Ʉɚɤ ɦɵ ɜɢɞɢɦ, ɜ ɷɬɨɦ ɩɪɟɞɟɥɟ ɩɥɚɡɦɚ ɜɵɫɬɭɩɚɟɬ ɜ ɪɨɥɢ ɨɛɵɱɧɨɝɨ ɞɢɷɥɟɤɬɪɢɤɚ. ȿɫɥɢ ɩɥɨɬɧɨɫɬɶ ɩɥɚɡɦɵ ɧɟ ɹɜɥɹɟɬɫɹ ɱɪɟɡɦɟɪɧɨ ɦɚɥɨɣ, ɬɨ ɩɥɚɡɦɚ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɜ § 20, ɹɜɥɹɟɬɫɹ ɜɟɫɶɦɚ ɯɨɪɨɲɢɦ ɞɢɷɥɟɤɬɪɢɤɨɦ ɫ ɛɨɥɶɲɨɣ ɩɨ ɜɟɥɢɱɢɧɟ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɨɫɬɨɹɧɧɨɣ, ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟɣ, ɱɟɦ ɭ ɜɫɟɯ ɢɡɜɟɫɬɧɵɯ ɨɛɵɱɧɵɯ ɞɢɷɥɟɤɬɪɢɱɟɫɤɢɯ ɦɚɬɟɪɢɚɥɨɜ. Ɉɛɴɟɞɢɧɹɹ ɞɜɚ ɩɪɟɞɟɥɶɧɵɯ ɫɥɭɱɚɹ (4.72) ɢ (4.73), ɢ, ɭɱɢɬɵɜɚɹ ɜɨɡɦɨɠɧɨɫɬɶ ɪɟɡɨɧɚɧɫɚ ɩɪɢ ɫɨɜɩɚɞɟɧɢɢ ɱɚɫɬɨɬɵ ɜɨɥɧɵ ɢ ɰɢɤɥɨɬɪɨɧɧɵɯ ɱɚɫɬɨɬ, ɭɠɟ ɧɟɬɪɭɞɧɨ ɩɪɟɞɜɢɞɟɬɶ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɫɥɟɞɭɸɳɢɣ ɪɟɡɭɥɶɬɚɬ:
ω L2α ε⊥ == 1 − ¦ 2 2 . α = e ,i ω − ω Bα
(4.74)
ɗɬɨ ɩɨɞɬɜɟɪɠɞɚɟɬɫɹ ɞɟɬɚɥɶɧɵɦɢ ɪɚɫɱɟɬɚɦɢ[18]. ȼ ɡɚɤɥɸɱɟɧɢɟ ɩɪɢɜɟɞɟɦ (ɞɥɹ ɫɩɪɚɜɨɤ) ɛɟɡ ɜɵɜɨɞɚ ɩɨɥɧɭɸ ɫɬɪɭɤɬɭɪɭ ɬɟɧɡɨɪɚ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɯɨɥɨɞɧɨɣ ɩɥɚɡɦɵ: § ε⊥ ig 0 · ¨ ¸ (4.75) ε = ¨ − ig ε⊥ 0 ¸ , © 0 0 ε|| ¹ ɞɢɚɝɨɧɚɥɶɧɵɟ ɤɨɦɩɨɧɟɧɬɵ ɡɞɟɫɶ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɪɢɜɟɞɟɧɧɵɦɢ ɜɵɲɟ ɮɨɪɦɭɥɚɦɢ, ɚ «ɤɨɫɵɟ» ɤɨɦɩɨɧɟɧɬɵ ɨɩɪɟɞɟɥɹɸɬɫɹ ɜɟɥɢɱɢɧɨɣ:
ω Bα ω L2α . 2 2 α = e ,i ω ( ω − ω Bα )
g == − ¦
(4.76)
ɉɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɫɢɫɬɟɦɚ ɤɨɨɪɞɢɧɚɬ ɜɵɛɪɚɧɚ ɬɚɤ, ɱɬɨ ɟɟ ɨɫɶ z ɩɚɪɚɥɥɟɥɶɧɚ ɜɟɤɬɨɪɭ ɢɧɞɭɤɰɢɢ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ.
§ 35. ȼɨɥɧɵ ɜ ɦɚɝɧɢɬɨɚɤɬɢɜɧɨɣ ɩɥɚɡɦɟ ȿɫɥɢ ɜ ɩɥɚɡɦɟ ɛɟɡ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɫɩɟɤɬɪ ɜɨɡɦɨɠɧɵɯ ɜɨɥɧ ɩɨ ɫɭɳɟɫɬɜɭ ɨɝɪɚɧɢɱɢɜɚɟɬɫɹ ɩɪɨɞɨɥɶɧɵɦɢ ɥɟɧɝɦɸɪɨɜɫɤɢɦɢ ɢ ɢɨɧɧɨ-ɡɜɭɤɨɜɵɦɢ ɜɨɥɧɚɦɢ (ɜɨɡɦɨɠɧɚ ɟɳɟ ɬɚɤ ɧɚɡɵɜɚɟɦɚɹ «ɷɧɬɪɨɩɢɣɧɚɹ» ɜɨɥɧɚ – ɫɜɨɟɨɛɪɚɡɧɚɹ «ɹɦɤɚ ɞɚɜɥɟɧɢɹ») ɢ ɩɨɩɟɪɟɱɧɨɣ ɩɥɚɡɦɟɧɧɨɣ ɜɨɥɧɨɣ, ɬɨ ɜ ɦɚɝɧɢɬɨɚɤɬɢɜɧɨɣ ɩɥɚɡɦɟ ɩɨɦɢɦɨ ɷɬɢɯ ɜɨɥɧ ɩɨɹɜɥɹɟɬɫɹ ɦɧɨɠɟɫɬɜɨ ɧɨɜɵɯ. ɗɬɨ − ɩɨɩɟɪɟɱɧɵɟ ɚɥɶɜɟɧɨɜɫɤɢɟ ɜɨɥɧɵ, ɦɚɝɧɢɬɨɡɜɭɤɨɜɵɟ ɜɨɥɧɵ (ɢɥɢ ɦɚɝɧɢɬɧɵɣ ɡɜɭɤ, ɤɪɚɬɤɨ ɷɬɢ ɜɨɥɧɵ ɱɚɫɬɨ ɨɛɨɡɧɚɱɚɸɬ ɚɛɛɪɟɜɢɚɬɭɪɨɣ ɆɁȼ), ɚ ɬɚɤɠɟ ɢɯ ɪɚɡɧɨɜɢɞɧɨɫɬɢ, ɬɚɤɢɟ ɤɚɤ ɛɵɫɬɪɚɹ ɆɁȼ, ɦɟɞɥɟɧɧɚɹ ɆɁȼ, «ɤɨɫɚɹ» ɆɁȼ, ɰɢɤɥɨɬɪɨɧɧɵɟ ɪɟɡɨɧɚɧɫɵ ɢ ɰɢɤɥɨɬɪɨɧɧɵɟ ɜɨɥɧɵ, ɜɤɥɸɱɚɹ ɢɨɧɧɨ-ɰɢɤɥɨɬɪɨɧɧɵɟ ɢ ɷɥɟɤɬɪɨɧɧɨɰɢɤɥɨɬɪɨɧɧɵɟ ɜɨɥɧɵ, ɧɢɠɧɟɝɢɛɪɢɞɧɵɟ ɜɨɥɧɵ ɢ ɜɟɪɯɧɟɝɢɛɪɢɞɧɵɟ ɜɨɥɧɵ, ɝɟɥɢɤɨɧɵ (ɫɩɢɪɚɥɶɧɵɟ ɜɨɥɧɵ) ɢɥɢ «ɫɜɢɫɬɹɳɢɟ ɚɬɦɨɫɮɟɪɢɤɢ» ɢ ɞɪɭɝɢɟ. Ʉɚɤ ɭɠɟ ɨɬɦɟɱɚɥɨɫɶ ɜɵɲɟ, ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɜɨɥɧɵ ɢ ɟɟ ɯɚɪɚɤɬɟɪ ɫɭɳɟɫɬɜɟɧɧɨ ɡɚɜɢɫɹɬ ɨɬ ɜɡɚɢɦɧɨɣ ɨɪɢɟɧɬɚɰɢɢ ɧɚɩɪɚɜɥɟɧɢɹ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜɨɥɧɵ, ɬ.ɟ. ɟɟ ɜɨɥɧɨɜɨɝɨ ɜɟɤɬɨɪɚ & & & k , ɜɟɤɬɨɪɚ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ B ɢ ɜɟɤɬɨɪɚ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜɨɥɧɵ E . ɉɨɷɬɨɦɭ ɩɪɨɫɬɟɣɲɚɹ ɤɥɚɫɫɢɮɢɤɚɰɢɹ ɜɨɥɧ ɜ ɦɚɝɧɢɬɨɚɤɬɢɜɧɨɣ ɩɥɚɡɦɟ ɫɜɨɞɢɬɫɹ ɤ ɩɟɪɟɛɨɪɭ ɜɫɟɯ ɜɨɡɦɨɠɧɵɯ ɜɡɚɢɦɧɵɯ ɨɪɢɟɧɬɚɰɢɣ ɷɬɢɯ ɬɪɟɯ ɜɟɤɬɨɪɨɜ, ɧɟɤɨɬɨɪɵɟ ɢɡ ɤɨɬɨɪɵɯ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 4.10. Ɋɚɫɫɦɨɬɪɢɦ ɩɪɨɫɬɟɣɲɢɟ ɫɥɭɱɚɢ. ɉɪɨɞɨɥɶɧɨɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɜɨɥɧɵ, ɜɨɥɧɨɜɨɣ ɜɟɤɬɨɪ ɩɚɪɚɥɥɟɥɟɧ ɜɧɟɲɧɟɦɭ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ & & & ɉɪɨɞɨɥɶɧɵɟ ɜɨɥɧɵ ( E || k || B0 , ɪɢɫ. 4.10,ɚ) Ʉɚɤ ɨɬɦɟɱɟɧɨ ɜ ɩɪɟɞɵɞɭɳɟɦ ɩɚɪɚɝɪɚɮɟ, ɩɨɤɚ ɪɟɱɶ ɢɞɟɬ ɨ ɜɨɥɧɚɯ ɦɚɥɨɣ ɚɦɩɥɢɬɭɞɵ, ɚ ɩɥɚɡɦɚ ɢ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɩɪɟɞɩɨɥɚɝɚɸɬɫɹ ɨɞɧɨɪɨɞɧɵɦɢ, «ɡɚɦɚɝɧɢɱɢɜɚɧɢɟ» ɩɥɚɡɦɵ ɜɥɢɹɧɢɹ ɧɟ ɨɤɚɡɵɜɚɟɬ ɢ ɜ ɩɥɚɡɦɟ ɜɨɡɦɨɠɧɵ ɨɛɵɱɧɵɟ ɥɟɧɝɦɸɪɨɜɫɤɢɟ ɢ ɢɨɧɧɨ-ɡɜɭɤɨɜɵɟ
•
Ɋɢɫ. 4.10. Ʉɥɚɫɫɢɮɢɤɚɰɢɹ ɜɨɥɧ ɜ ɦɚɝɧɢɬɨɚɤɬɢɜɧɨɣ ɩɥɚɡɦɟ: ɚ − ɩɪɨɞɨɥɶɧɚɹ ɜɨɥɧɚ; ɛ − ɩɨɩɟɪɟɱɧɚɹ (ɨɛɵɤɧɨɜɟɧɧɚɹ) ɜɨɥɧɚ; ɜ −ɚɥɶɜɟɧɨɜɫɤɚɹ ɜɨɥɧɚ (ɩɨɩɟɪɟɱɧɚɹ); ɝ − ɦɚɝɧɢɬɨɡɜɭɤɨɜɚɹ ɜɨɥɧɚ (ɩɨɩɟɪɟɱɧɚɹ).
(ɟɫɥɢ ɬɟɦɩɟɪɚɬɭɪɚ ɩɥɚɡɦɵ ɫɱɢɬɚɟɬɫɹ ɧɟɧɭɥɟɜɨɣ) ɜɨɥɧɵ (ɫɦ. §§ 31,32). & & & Ⱥɥɶɜɟɧɨɜɫɤɚɹ ɜɨɥɧɚ ( E ⊥ k || B0 , ɪɢɫ. 4.10,ɜ) Ɍɚɤ ɤɚɤ ɜɨɥɧɨɜɨɣ ɜɟɤɬɨɪ ɢ ɜɟɤɬɨɪ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜɨɥɧɵ ɜɡɚɢɦɧɨ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɵ, ɬɨ ɪɟɱɶ ɢɞɟɬ ɨ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɟ, ɪɚɫɩɪɨɫɬɪɚɧɹɸɳɟɣɫɹ ɜɞɨɥɶ ɜɧɟɲɧɟɝɨ ɩɨɥɹ. Ⱦɢɫɩɟɪɫɢɨɧɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɵ (ɫɦ. § 27) ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɫɜɨɞɢɬɫɹ ɤ k 2c2 ε⊥ = N 2 , N 2 ≡ 2 ≡ vΦ2 . •
ω
Ɉɧɨ ɨɫɨɛɟɧɧɨ ɩɪɨɫɬɨɟ ɜ ɧɢɡɤɨɱɚɫɬɨɬɧɨɦ ɩɪɟɞɟɥɟ, ɤɨɝɞɚ ɫɨɝɥɚɫɧɨ (4.73) ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɨɫɬɨɹɧɧɚ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɱɚɫɬɨɬɵ. Ɂɚɦɟɬɢɦ, ɱɬɨ ɮɨɪɦɭɥɭ (4.73) ɦɨɠɧɨ ɩɟɪɟɩɢɫɚɬɶ ɜ ɜɢɞɟ:
c2 ε⊥ = 1 + 2 , cA ɝɞɟ ɜɜɟɞɟɧɨ ɭɞɨɛɧɨɟ ɨɛɨɡɧɚɱɟɧɢɟ B cA = 4πn( mi + me )
(4.77)
(4.78)
ɞɥɹ ɯɚɪɚɤɬɟɪɧɨɣ, ɬɚɤ ɧɚɡɵɜɚɟɦɨɣ ɚɥɶɜɟɧɨɜɫɤɨɣ ɫɤɨɪɨɫɬɢ (ɏ. Ⱥɥɶɜɟɧ, 1942). Ɉɧɚ ɜɨɡɪɚɫɬɚɟɬ ɫ ɪɨɫɬɨɦ ɜɟɥɢɱɢɧɵ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ ɢ ɭɦɟɧɶɲɚɟɬɫɹ ɫ ɪɨɫɬɨɦ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ. Ɋɟɲɚɹ ɞɢɫɩɟɪɫɢɨɧɧɨɟ ɭɪɚɜɧɟɧɢɟ, ɩɨɥɭɱɢɦ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɞɥɹ ɷɬɢɯ ɜɨɥɧ c Ac vΦ = v ɝ ɪ = . (4.79) c 2 + c A2 ȿɫɥɢ ɩɥɚɡɦɚ ɪɟɞɤɚɹ, ɬɚɤ ɱɬɨ ɫȺ>>c, ɬɨ ɷɬɚ ɜɨɥɧɚ ɩɪɟɜɪɚɳɚɟɬɫɹ ɜ ɨɛɵɱɧɭɸ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɭɸ ɜɨɥɧɭ, ɪɚɫɩɪɨɫɬɪɚɧɹɸɳɭɸɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ ɫɜɟɬɚ. ȼ ɫɥɭɱɚɟ ɩɥɨɬɧɨɣ ɩɥɚɡɦɵ, ɤɨɝɞɚ cA<
ɜɪɚɳɚɸɬɫɹ ɜ ɪɚɡɧɵɯ ɧɚɩɪɚɜɥɟɧɢɹɯ, ɬɨ ɦɵ ɜɩɪɚɜɟ ɨɠɢɞɚɬɶ ɩɨɹɜɥɟɧɢɟ ɨɫɨɛɟɧɧɨɫɬɢ ɩɨɤɚɡɚɬɟɥɹ ɩɪɟɥɨɦɥɟɧɢɹ − ɚɧɨɦɚɥɶɧɨɣ ɞɢɫɩɟɪɫɢɢ. ɗɬɨ ɢ ɧɚɛɥɸɞɚɟɬɫɹ (ɫɦ. ɪɢɫ. 4.12). ɉɨɩɟɪɟɱɧɨɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɜɨɥɧɵ, ɜɨɥɧɨɜɨɣ ɜɟɤɬɨɪ ɩɟɪɩɟɧɞɢɤɭɥɹɪɟɧ ɜɧɟɲɧɟɦɭ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ & & & Ɉɛɵɤɧɨɜɟɧɧɵɟ ɩɨɩɟɪɟɱɧɵɟ ɜɨɥɧɵ ( k ⊥ E || B0 , ɪɢɫ. 4.10,ɛ) ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɧɟ ɨɤɚɡɵɜɚɟɬ ɜɥɢɹɧɢɹ ɧɚ ɞɢɫɩɟɪɫɢɸ ɜɨɥɧ, ɢ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɨɤɚɡɵɜɚɟɬɫɹ ɬɚɤɢɦ ɠɟ, ɤɚɤ ɜ ɫɥɭɱɚɟ ɩɥɚɡɦɵ ɛɟɡ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ: ε|| = N 2 , ω 2 = ω Le2 + k 2 c 2 . (4.82)
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& & & Ɇɚɝɧɢɬɨɡɜɭɤɨɜɵɟ ɜɨɥɧɵ ( k ⊥ E ⊥ B0 , ɪɢɫ. 4.10,ɝ)
ȼ ɨɛɥɚɫɬɢ ɧɢɡɤɢɯ ɱɚɫɬɨɬ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɷɬɢɯ ɜɨɥɧ ɮɨɪɦɚɥɶɧɨ ɬɚɤɨɣ ɠɟ, ɤɚɤ ɢ ɚɥɶɜɟɧɨɜɫɤɢɯ: vΦ = v ɝ ɪ ≅ c A , (4.83) ɧɨ ɮɢɡɢɤɚ ɢɧɚɹ: ɜɨɥɧɭ ɦɨɠɧɨ ɢɧɬɟɪɩɪɟɬɢɪɨɜɚɬɶ ɤɚɤ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɫɠɚɬɢɣ ɢ ɪɚɡɪɟɠɟɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ (ɫɦ. ɪɢɫ. 4.13) ɉɥɨɫɤɢɟ ɜɨɥɧɵ ɫɠɚɬɢɹ-ɪɚɡɪɹɠɟɧɢɹ ɪɚɫɩɪɨɫɬɪɚɧɹɸɬɫɹ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɤ ɦɚɝɧɢɬɧɨɦɭ
Ɋɢɫ. 4.13. Ʉɚɱɟɫɬɜɟɧɧɚɹ ɤɚɪɬɢɧɚ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɦɚɝɧɢɬɨɡɜɭɤɨɜɨɣ ɜɨɥɧɵ: ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɪɚɡɪɟɠɟɧɢɣ ɢ ɫɠɚɬɢɣ ɜɟɥɢɱɢɧɵ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ
Ɋɢɫ. 4.14. Ʉɚɱɟɫɬɜɟɧɧɵɣ ɯɚɪɚɤɬɟɪ ɞɢɫɩɟɪɫɢɢ ɦɚɝɧɢɬɨɡɜɭɤɨɜɵɯ ɜɨɥɧ ɜ ɨɛɥɚɫɬɢ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬ: 1 – ɨɛɥɚɫɬɶ ɦɚɝɧɢɬɧɨɝɨ ɡɜɭɤɚ, 2 – ɧɢɠɧɟɝɢɛɪɢɞɧɵɟ ɜɨɥɧɵ, 3 – ɜɟɪɯɧɟɝɢɛɪɢɞɧɵɟ ɜɨɥɧɵ, 4 − ȼɑ-ɜɨɥɧɵ
ɩɨɥɸ, ɬ.ɟ. ɨɧɢ ɩɨɩɟɪɟɱɧɵɟ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ ɢ ɩɪɨɞɨɥɶɧɵɟ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ, ɢ ɩɨɩɟɪɟɱɧɵɟ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɨɪɢɟɧɬɚɰɢɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɢ ɜɨɥɧɨɜɨɝɨ ɜɟɤɬɨɪɚ. ɗɬɢ ɜɨɥɧɵ ɜɩɨɥɧɟ ɚɧɚɥɨɝɢɱɧɵ ɡɜɭɤɨɜɵɦ, ɱɚɫɬɨ ɢɯ ɩɨ ɚɧɚɥɨɝɢɢ ɧɚɡɵɜɚɸɬ ɦɚɝɧɢɬɧɵɦ ɡɜɭɤɨɦ, ɧɨ ɧɟɨɛɯɨɞɢɦɨ ɩɨɞɱɟɪɤɧɭɬɶ, ɱɬɨ ɜɟɳɟɫɬɜɨ ɜ ɜɨɥɧɟ ɞɜɢɠɟɬɫɹ ɧɟ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ȿ, ɤɚɤ ɦɨɠɟɬ ɩɨɤɚɡɚɬɶɫɹ, ɚ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɤɨɥɟɛɚɧɢɣ, ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɜɨɥɧɵ, ɬ.ɟ. ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɤ ȿ ɢ ȼ (ɤɚɤ ɷɬɨ ɢɦɟɟɬ ɦɟɫɬɨ ɩɪɢ ɞɪɟɣɮɨɜɨɦ ɞɜɢɠɟɧɢɢ ɜ ɫɤɪɟɳɟɧɧɵɯ ȿ ɢ ȼ ɩɨɥɹɯ). ɉɨ ɫɭɳɟɫɬɜɭ ɷɬɨ ɢ ɟɫɬɶ ɞɪɟɣɮɨɜɨɟ ɞɜɢɠɟɧɢɟ, ɬɚɤ ɤɚɤ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɞɜɢɠɟɧɢɟ ɦɚɫɫɵ, ɚ ɨɧɚ ɫɨɫɪɟɞɨɬɨɱɟɧɚ ɜ ɢɨɧɚɯ. ȿɫɥɢ ɧɚɞɨ ɭɱɢɬɵɜɚɬɶ ɢ ɞɚɜɥɟɧɢɟ ɝɚɡɚ ɩɪɢ ɫɠɚɬɢɢ, ɬɨ ɭɪɚɜɧɟɧɢɟ (4.83) ɢɡɦɟɧɢɬɫɹ: B2 p B2 § 1 · v2 = (4.84) +γ = ¨ 1 + γβ ¸ . nmi 4πnmi © 4πnmi 2 ¹
ȿɫɥɢ ɜɬɨɪɵɦ ɱɥɟɧɨɦ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ (ɬ.ɟ., ɟɫɥɢ β→0), ɬɨ ɨɫɬɚɟɬɫɹ ɱɢɫɬɨ ɦɚɝɧɢɬɧɵɣ ɡɜɭɤ; ɩɪɟɞɟɥ ɩɥɚɡɦɵ ɧɢɡɤɨɝɨ ɞɚɜɥɟɧɢɹ, β→0, ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɨɩɪɟɞɟɥɟɧɢɟ ɩɪɢɛɥɢɠɟɧɢɹ ɯɨɥɨɞɧɨɣ ɩɥɚɡɦɵ. Ɉɬɫɭɬɫɬɜɢɟ ɞɢɫɩɟɪɫɢɢ, ɬɚɤ ɠɟ ɤɚɤ ɢ ɜ ɫɥɭɱɚɟ ɚɥɶɜɟɧɨɜɫɤɨɣ ɜɨɥɧɵ, ɢɦɟɟɬ ɦɟɫɬɨ ɬɨɥɶɤɨ ɩɪɢ ɱɚɫɬɨɬɚɯ, ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɶɲɢɯ, ɱɟɦ ɢɨɧɧɚɹ ɰɢɤɥɨɬɪɨɧɧɚɹ ɱɚɫɬɨɬɚ. ɉɪɢ ɛɨɥɶɲɢɯ ɱɚɫɬɨɬɚɯ ɜɨɡɧɢɤɚɟɬ ɚɧɨɦɚɥɶɧɚɹ ɞɢɫɩɟɪɫɢɹ (ɪɢɫ. 4.14). ɇɨ ɬɟɩɟɪɶ ɧɟɥɶɡɹ ɨɠɢɞɚɬɶ ɪɟɡɨɧɚɧɫɚ ɬɨɥɶɤɨ ɧɚ ɢɨɧɧɨɣ ɢɥɢ ɬɨɥɶɤɨ ɧɚ ɷɥɟɤɬɪɨɧɧɨɣ ɰɢɤɥɨɬɪɨɧɧɨɣ ɱɚɫɬɨɬɟ: ɜ ɮɨɪɦɢɪɨɜɚɧɢɢ ɜɨɥɧɵ ɩɪɢɧɢɦɚɸɬ ɭɱɚɫɬɢɟ ɨɞɧɨɜɪɟɦɟɧɧɨ ɨɛɚ ɫɨɪɬɚ ɱɚɫɬɢɰ ɩɥɚɡɦɵ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɱɚɫɬɨɬɵ, ɨɬɜɟɱɚɸɳɢɟ ɩɨɹɜɥɟɧɢɸ ɚɧɨɦɚɥɶɧɨɣ ɞɢɫɩɟɪɫɢɢ, ɡɚɜɢɫɹɬ ɨɬ ɰɢɤɥɨɬɪɨɧɧɵɯ ɱɚɫɬɨɬ ɨɛɨɢɯ ɫɨɪɬɨɜ ɱɚɫɬɢɰ ɩɥɚɡɦɵ. ɗɬɨ ɬɚɤ ɧɚɡɵɜɚɟɦɚɹ ɧɢɠɧɟɝɢɛɪɢɞɧɚɹ ɱɚɫɬɨɬɚ, ɨɩɪɟɞɟɥɹɟɦɚɹ ɞɥɹ ɩɥɨɬɧɨɣ ɩɥɚɡɦɵ ɩɪɢɛɥɢɠɟɧɧɨ ɫɨɨɬɧɨɲɟɧɢɟɦ ω ɇȽ ≅ |ω Beω Bi|, (4.85) ɬɨ ɟɫɬɶ ɨɧɚ ɫɨɜɩɚɞɚɟɬ ɫɨ ɫɪɟɞɧɢɦ ɝɟɨɦɟɬɪɢɱɟɫɤɢɦ ɢɡ ɰɢɤɥɨɬɪɨɧɧɵɯ ɱɚɫɬɨɬ, ɚ ɬɚɤɠɟ ɜɟɪɯɧɟɝɢɛɪɢɞɧɚɹ ɱɚɫɬɨɬɚ, ɩɪɢɛɥɢɠɟɧɧɨ ɪɚɜɧɚɹ (ɩɨɞɪɨɛɧɟɟ ɫɦ. [18]) ω ȼȽ ≅ ω Le2 + ω Be2 . (4.86) ȼ ɨɛɥɚɫɬɢ ɱɚɫɬɨɬ ω < ω ɇȽ ɜ ɩɥɚɡɦɟ ɜɨɡɦɨɠɧɨ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɦɚɝɧɢɬɨɡɜɭɤɨɜɵɯ ɜɨɥɧ, ɜ ɨɛɥɚɫɬɢ ɱɚɫɬɨɬ ω > ω ɇȽ ɜɨɡɦɨɠɧɨ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɯ ɜɨɥɧ, ɜ ɨɛɥɚɫɬɢ ɱɚɫɬɨɬ ω ɇȽ < ω << ω ȼȽ ɱɢɫɬɨ ɩɨɩɟɪɟɱɧɨɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɜɨɥɧ ɧɟɜɨɡɦɨɠɧɨ.
§ 36. ɇɟɭɫɬɨɣɱɢɜɨɫɬɢ ɩɥɚɡɦɵ ɉɥɚɡɦɚ, ɫ ɤɨɬɨɪɨɣ ɩɪɢɯɨɞɢɬɫɹ ɢɦɟɬɶ ɞɟɥɨ ɜ ɥɚɛɨɪɚɬɨɪɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɚɯ, ɤɚɤ ɩɪɚɜɢɥɨ, ɫɢɥɶɧɨ ɧɟɪɚɜɧɨɜɟɫɧɚɹ ɢ ɨɛɥɚɞɚɟɬ ɜɵɫɨɤɨɣ ɩɥɨɬɧɨɫɬɶɸ ɷɧɟɪɝɢɢ, ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɸɳɟɣ ɩɥɨɬɧɨɫɬɶ ɷɧɟɪɝɢɢ ɜ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɟ. ɉɨ ɡɚɤɨɧɚɦ ɬɟɪɦɨɞɢɧɚɦɢɤɢ ɬɚɤɨɣ ɧɟɪɚɜɧɨɜɟɫɧɵɣ ɨɛɴɟɤɬ, ɛɭɞɭɱɢ ɩɪɟɞɨɫɬɚɜɥɟɧ ɫɚɦ ɫɟɛɟ, ɞɨɥɠɟɧ ɫɬɪɟɦɢɬɶɫɹ ɤ ɪɚɜɧɨɜɟɫɢɸ ɫ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɨɣ, ɚ, ɡɧɚɱɢɬ, ɨɯɥɚɠɞɚɬɶɫɹ. Ɋɟɥɚɤɫɚɰɢɹ ɤ ɪɚɜɧɨɜɟɫɢɸ ɦɨɠɟɬ ɩɪɨɢɫɯɨɞɢɬɶ ɫɪɚɜɧɢɬɟɥɶɧɨ ɫɩɨɤɨɣɧɨ: ɩɪɢ ɧɚɥɢɱɢɢ ɧɟɛɨɥɶɲɢɯ ɝɪɚɞɢɟɧɬɨɜ, ɧɚɩɪɢɦɟɪ, ɤɨɧɰɟɧɬɪɚɰɢɢ ɢɥɢ ɬɟɦɩɟɪɚɬɭɪɵ, ɜɨɡɧɢɤɚɸɬ ɩɨɬɨɤɢ ɜɟɳɟɫɬɜɚ ɢ ɷɧɟɪɝɢɢ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵɟ ɷɬɢɦ ɝɪɚɞɢɟɧɬɚɦ ɢ ɫɬɪɟɦɹɳɢɟɫɹ ɭɫɬɪɚɧɢɬɶ ɢɦɟɸɳɭɸɫɹ ɧɟɨɞɧɨɪɨɞɧɨɫɬɶ, ɜɨɡɧɢɤɚɸɬ ɩɟɪɟɧɨɫɵ, ɤɨɬɨɪɵɟ ɦɵ ɨɛɫɭɠɞɚɥɢ ɤɪɚɬɤɨ ɜ § 10. Ⱦɥɹ ɩɨɞɞɟɪɠɚɧɢɹ ɫɭɳɟɫɬɜɨɜɚɧɢɹ ɧɟɪɚɜɧɨɜɟɫɧɨɝɨ ɫɨɫɬɨɹɧɢɹ, ɟɫɬɟɫɬɜɟɧɧɨ, ɞɨɥɠɧɵ ɩɪɢɫɭɬɫɬɜɨɜɚɬɶ ɜɧɟɲɧɢɟ ɢɫɬɨɱɧɢɤɢ ɬɟɩɥɚ ɢ ɱɚɫɬɢɰ, ɤɨɦɩɟɧɫɢɪɭɸɳɢɟ ɩɨɬɟɪɢ ɢ ɨɛɟɫɩɟɱɢɜɚɸɳɢɟ ɫɬɚɰɢɨɧɚɪɧɨɟ ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɩɥɚɡɦɵ. ɂɦɟɧɧɨ ɬɚɤɨɜɚ ɫɢɬɭɚɰɢɹ ɜ ɫɬɚɰɢɨɧɚɪɧɵɯ ɝɚɡɨɜɵɯ ɪɚɡɪɹɞɚɯ: ɫɥɚɛɨɬɨɱɧɵɣ ɧɟɫɚɦɨɫɬɨɹɬɟɥɶɧɵɣ ɝɚɡɨɜɵɣ ɪɚɡɪɹɞ ɜ ɩɪɨɦɟɠɭɬɤɟ ɦɟɠɞɭ ɞɜɭɦɹ ɷɥɟɤɬɪɨɞɚɦɢ ɫ ɡɚɞɚɧɧɨɣ ɪɚɡɧɨɫɬɶɸ ɩɨɬɟɧɰɢɚɥɨɜ, ɤɨɝɞɚ ɡɚ ɫɨɡɞɚɧɢɟ ɡɚɪɹɠɟɧɧɨɣ ɤɨɦɩɨɧɟɧɬɵ ɨɬɜɟɱɚɟɬ ɜɧɟɲɧɢɣ ɢɨɧɢɡɚɬɨɪ, ɦɨɠɟɬ ɞɥɢɬɟɥɶɧɨɟ ɜɪɟɦɹ ɫɭɳɟɫɬɜɨɜɚɬɶ ɩɪɢ ɧɚɥɢɱɢɢ ɬɚɤɨɝɨ ɢɨɧɢɡɚɬɨɪɚ, ɧɨ ɩɪɟɤɪɚɳɚɟɬɫɹ ɩɪɢ ɟɝɨ ɜɵɤɥɸɱɟɧɢɢ. Ⱥɧɚɥɨɝɢɱɧɚ, ɩɨ ɫɭɳɟɫɬɜɭ, ɫɢɬɭɚɰɢɹ ɢ ɜ ɫɥɭɱɚɟ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɚɡɪɹɞɚ, ɜ ɤɨɬɨɪɨɦ ɜɤɥɸɱɚɟɬɫɹ ɦɟɯɚɧɢɡɦ ɫɚɦɨɩɨɞɞɟɪɠɚɧɢɹ ɩɥɚɡɦɵ, ɬɚɤ ɱɬɨ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɜɨ ɜɧɟɲɧɟɦ ɢɨɧɢɡɚɬɨɪɟ ɨɬɩɚɞɚɟɬ, ɧɨ ɫɬɚɰɢɨɧɚɪɧɨɟ ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɩɥɚɡɦɵ, ɟɫɬɟɫɬɜɟɧɧɨ, ɩɨɞɞɟɪɠɢɜɚɟɬɫɹ ɜɧɟɲɧɢɦ ɢɫɬɨɱɧɢɤɨɦ, ɡɚɞɚɸɳɢɦ ɪɚɡɧɨɫɬɶ ɩɨɬɟɧɰɢɚɥɨɜ ɢ ɨɛɟɫɩɟɱɢɜɚɸɳɢɦ ɩɪɨɬɟɤɚɧɢɟ ɬɨɤɚ, ɧɟɨɛɯɨɞɢɦɨɝɨ ɞɥɹ ɩɨɞɞɟɪɠɚɧɢɹ ɪɚɡɪɹɞɚ. Ɇɢɥɥɢɨɧɵ ɢ ɦɢɥɥɢɚɪɞɵ ɥɟɬ ɫɜɟɬɹɬ ɡɜɟɡɞɵ, ɭɫɬɨɣɱɢɜɨɟ ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɤɨɬɨɪɵɯ ɨɛɟɫɩɟɱɢɜɚɟɬ ɛɚɥɚɧɫ ɞɚɜɥɟɧɢɹ ɜɟɳɟɫɬɜɚ ɢ ɝɪɚɜɢɬɚɰɢɢ, ɤɨɧɬɪɨɥɢɪɭɟɦɵɣ ɜɵɞɟɥɟɧɢɟɦ ɷɧɟɪɝɢɢ ɜ ɹɞɟɪɧɵɯ ɪɟɚɤɰɢɹɯ ɫɢɧɬɟɡɚ ɜ ɧɟɞɪɚɯ ɡɜɟɡɞɵ ɢ ɟɟ ɢɡɥɭɱɟɧɢɟɦ. Ʉɚɤ ɢ ɭ ɩɥɚɡɦɵ ɝɚɡɨɜɵɯ ɪɚɡɪɹɞɨɜ, ɬɚɤ ɢ ɭ ɩɥɚɡɦɵ ɡɜɟɡɞ, ɜɨɡɦɨɠɧɵ ɪɚɡɧɵɟ ɫɨɫɬɨɹɧɢɹ ɭɫɬɨɣɱɢɜɨɝɨ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɫɭɳɟɫɬɜɨɜɚɧɢɹ, ɡɧɚɱɢɬɟɥɶɧɨ ɪɚɡɥɢɱɚɸɳɢɟɫɹ ɩɨ ɷɧɟɪɝɨɫɨɞɟɪɠɚɧɢɸ. ɉɪɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦ ɢɡɦɟɧɟɧɢɢ ɪɟɠɢɦɚ ɢɫɬɨɱɧɢɤɚ, ɩɨɞɞɟɪɠɢɜɚɸɳɟɝɨ ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɩɥɚɡɦɵ, ɩɟɪɟɯɨɞ ɦɟɠɞɭ ɷɬɢɦɢ ɫɨɫɬɨɹɧɢɹɦɢ ɦɨɠɟɬ ɛɵɬɶ «ɩɥɚɜɧɵɦ», ɛɟɡ ɤɚɤɢɯ-ɥɢɛɨ ɤɚɬɚɫɬɪɨɮ. ɇɚɩɪɢɦɟɪ, ɡɜɟɡɞɚ, ɥɢɲɟɧɧɚɹ ɹɞɟɪɧɨɝɨ «ɝɨɪɸɱɟɝɨ», ɦɨɠɟɬ ɢɡɥɭɱɢɬɶ ɢɡɛɵɬɨɤ ɬɟɩɥɨɜɨɣ ɷɧɟɪɝɢɢ ɢ ɩɪɨɫɬɨ ɩɨɬɭɯɧɭɬɶ, ɧɨ ɜɨɡɦɨɠɧɵ ɢ ɤɚɬɚɫɬɪɨɮɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ ɬɢɩɚ ɜɫɩɵɲɟɤ ɋɜɟɪɯɧɨɜɵɯ, ɤɨɝɞɚ ɩɟɪɟɯɨɞ ɡɜɟɡɞɵ ɜ ɧɨɜɭɸ ɭɫɬɨɣɱɢɜɭɸ ɮɚɡɭ ɟɟ ɫɭɳɟɫɬɜɨɜɚɧɢɹ ɧɨɫɢɬ ɧɟɭɫɬɨɣɱɢɜɵɣ ɯɚɪɚɤɬɟɪ ɢ ɫɨɩɪɨɜɨɠɞɚɟɬɫɹ ɜɡɪɵɜɨɦ. ɂɡɜɟɫɬɧɨ ɦɧɨɝɨ ɩɪɢɦɟɪɨɜ ɧɟɭɫɬɨɣɱɢɜɨɝɨ ɩɨɜɟɞɟɧɢɹ ɢ ɭ ɩɥɚɡɦɵ ɝɚɡɨɜɵɯ ɪɚɡɪɹɞɨɜ: ɜɨɡɧɢɤɧɨɜɟɧɢɟ ɫɬɪɚɬ, ɮɢɥɚɦɟɧɬɚɰɢɹ (ɲɧɭɪɨɜɚɧɢɟ), «ɲɢɩɹɳɢɟ» ɞɭɝɢ ɢ ɩɪɨɱɟɟ. Ɉɫɨɛɭɸ ɪɨɥɶ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɩɥɚɡɦɵ ɩɪɢɨɛɪɟɬɚɸɬ ɜ ɩɪɨɛɥɟɦɟ ɫɨɡɞɚɧɢɢ ɢ ɭɞɟɪɠɚɧɢɢ ɩɥɚɡɦɵ ɜ ɭɫɬɚɧɨɜɤɚɯ ɩɨ ɭɩɪɚɜɥɹɟɦɨɦɭ ɬɟɪɦɨɹɞɟɪɧɨɦɭ ɫɢɧɬɟɡɭ. ȿɫɬɟɫɬɜɟɧɧɨ, ɭɫɥɨɜɢɹ ɭɫɬɨɣɱɢɜɨɝɨ ɭɞɟɪɠɚɧɢɹ ɩɥɚɡɦɵ «ɡɜɟɡɞɧɵɯ» ɬɟɦɩɟɪɚɬɭɪ ɜ ɥɚɛɨɪɚɬɨɪɧɵɯ ɭɫɥɨɜɢɹɯ ɧɟ ɛɵɥɢ ɢɡɜɟɫɬɧɵ ɢɡɧɚɱɚɥɶɧɨ, ɤɨɝɞɚ ɬɟɪɦɨɹɞɟɪɧɚɹ ɩɪɨɝɪɚɦɦɚ ɬɨɥɶɤɨ ɧɚɱɢɧɚɥɚɫɶ. ɉɨɷɬɨɦɭ ɢɫɬɨɪɢɸ ɬɟɪɦɨɹɞɟɪɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɣ, ɜ ɨɩɪɟɞɟɥɟɧɧɨɦ ɫɦɵɫɥɟ, ɦɨɠɧɨ ɬɪɚɤɬɨɜɚɬɶ ɤɚɤ ɢɫɬɨɪɢɸ ɨɬɤɪɵɬɢɹ ɧɨɜɵɯ ɧɟɭɫɬɨɣɱɢɜɨɫɬɟɣ ɩɥɚɡɦɵ, ɪɚɡɪɚɛɨɬɤɢ ɢ ɫɨɜɟɪɲɟɧɫɬɜɨɜɚɧɢɹ ɦɟɬɨɞɨɜ ɢɯ ɩɨɞɚɜɥɟɧɢɹ. ɉɪɢɧɹɬɨ ɪɚɡɥɢɱɚɬɶ [12] ɦɚɝɧɢɬɨɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢɟ (ɆȽȾ) ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɩɥɚɡɦɵ, ɫɪɚɜɧɢɬɟɥɶɧɨ ɦɟɞɥɟɧɧɵɟ, ɧɨ ɩɪɢɜɨɞɹɳɢɟ ɤ ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɢɦ ɩɨɫɥɟɞɫɬɜɢɹɦ – ɤ ɤɚɬɚɫɬɪɨɮɢɱɟɫɤɨɦɭ ɧɚɪɭɲɟɧɢɸ ɮɨɪɦɵ
ɩɥɚɡɦɟɧɧɨɝɨ ɫɝɭɫɬɤɚ, ɜɵɛɪɨɫɚɦ ɛɨɥɶɲɢɯ ɫɝɭɫɬɤɨɜ ɩɥɚɡɦɵ ɧɚ ɩɟɪɢɮɟɪɢɸ, ɢ ɬ.ɩ., ɚ ɬɚɤɠɟ ɦɢɤɪɨɧɟɭɫɬɨɣɱɢɜɨɫɬɢ, ɢɥɢ ɤɢɧɟɬɢɱɟɫɤɢɟ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ, ɨɛɹɡɚɧɧɵɟ ɫɜɨɢɦ ɩɪɨɢɫɯɨɠɞɟɧɢɟɦ ɨɫɨɛɟɧɧɨɫɬɹɦ ɧɟɪɚɜɧɨɜɟɫɧɨɣ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɩɨ ɫɤɨɪɨɫɬɹɦ. ȼ ɤɨɧɟɱɧɨɦ ɢɬɨɝɟ, ɷɬɢ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɩɪɢɜɨɞɹɬ ɤ ɝɟɧɟɪɚɰɢɢ ɜ ɩɥɚɡɦɟ ɭɫɤɨɪɹɸɳɢɯ ɩɨɥɟɣ ɢ ɲɭɦɨɜ, ɜɵɡɵɜɚɸɳɢɯ ɚɧɨɦɚɥɶɧɨ ɛɨɥɶɲɢɟ ɩɨɬɨɤɢ ɬɟɩɥɚ ɢ ɱɚɫɬɢɰ. ȿɫɬɟɫɬɜɟɧɧɨ, ɥɸɛɨɟ ɤɨɧɤɪɟɬɧɨɟ ɭɫɬɪɨɣɫɬɜɨ ɩɨ ɭɞɟɪɠɚɧɢɸ ɩɥɚɡɦɵ ɞɨɥɠɧɨ ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ɭɞɨɜɥɟɬɜɨɪɹɬɶ ɭɫɥɨɜɢɹɦ ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɨɣ ɭɫɬɨɣɱɢɜɨɫɬɢ ɪɚɜɧɨɜɟɫɢɹ ɩɥɚɡɦɵ, ɢ, ɤɨɝɞɚ ɬɚɤɢɟ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɩɨɞɚɜɥɟɧɵ, ɧɚ ɩɟɪɜɵɣ ɩɥɚɧ ɜɵɫɬɭɩɚɸɬ ɤɢɧɟɬɢɱɟɫɤɢɟ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɢ ɭɠɟ ɨɧɢ ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɨɝɪɚɧɢɱɢɜɚɸɬ ɜɪɟɦɹ ɠɢɡɧɢ ɱɚɫɬɢɰ ɜ ɩɥɚɡɦɟ ɢ ɜɪɟɦɹ ɭɞɟɪɠɚɧɢɹ ɷɧɟɪɝɢɢ ɩɥɚɡɦɵ. ɆȽȾ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ •
ɇɟɭɫɬɨɣɱɢɜɨɫɬɶ Ɋɟɥɟɹ - Ɍɟɣɥɨɪɚ ɗɬɨ ɨɞɧɚ ɢɡ ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɯ ɧɟɭɫɬɨɣɱɢɜɨɫɬɟɣ, ɤɨɬɨɪɚɹ ɢɦɟɟɬ ɦɧɨɝɨɱɢɫɥɟɧɧɵɟ ɩɪɨɹɜɥɟɧɢɹ ɜ ɉɪɢɪɨɞɟ. ɉɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɩɥɚɡɦɟ ɟɟ ɪɚɡɧɨɜɢɞɧɨɫɬɶɸ ɹɜɥɹɟɬɫɹ ɠɟɥɨɛɤɨɜɚɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ (ɫɦ. § 19), ɧɚɡɵɜɚɟɦɚɹ ɬɚɤɠɟ ɤɨɧɜɟɤɬɢɜɧɨɣ ɢɥɢ ɩɟɪɟɫɬɚɧɨɜɨɱɧɨɣ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶɸ [22]. ɉɪɢɪɨɞɭ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɨɛɵɱɧɨ ɩɨɹɫɧɹɸɬ ɧɚ ɫɥɟɞɭɸɳɟɦ ɩɪɨɫɬɨɦ ɩɪɢɦɟɪɟ. ɉɭɫɬɶ ɜ ɫɬɚɤɚɧ ɧɚɥɢɬɵ ɞɜɚ ɫɥɨɹ ɧɟɫɦɟɲɢɜɚɸɳɢɯɫɹ ɠɢɞɤɨɫɬɟɣ ɫ ɪɚɡɧɵɦɢ ɩɥɨɬɧɨɫɬɹɦɢ (ɪɢɫ. 4.15). Ɋɚɜɧɨɜɟɫɢɸ ɜ ɩɨɥɟ ɫɢɥ ɬɹɠɟɫɬɢ ɡɞɟɫɶ, ɨɱɟɜɢɞɧɨ, ɨɬɜɟɱɚɟɬ ɝɨɪɢɡɨɧɬɚɥɶɧɨɫɬɶ ɝɪɚɧɢɰɵ ɪɚɡɞɟɥɚ ɦɟɠɞɭ ɠɢɞɤɨɫɬɹɦɢ. ȿɫɥɢ ɜɟɪɯɧɹɹ ɢɡ ɠɢɞɤɨɫɬɟɣ ɢɦɟɟɬ ɦɟɧɶɲɭɸ ɩɥɨɬɧɨɫɬɶ, ɬɨ ɷɬɚ ɫɢɬɭɚɰɢɹ ɛɭɞɟɬ ɭɫɬɨɣɱɢɜɨɣ ɢ ɦɚɥɵɟ ɜɨɡɦɭɳɟɧɢɹ ɧɟ ɪɚɡɪɭɲɚɬ ɧɚɱɚɥɶɧɨɟ ɪɚɜɧɨɜɟɫɢɟ. Ɋɢɫ. 4.15. Ʉ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ȿɫɥɢ ɠɟ ɜɟɪɯɧɹɹ ɠɢɞɤɨɫɬɶ ɢɦɟɟɬ ɛɨɥɶɲɭɸ Ɋɟɥɟɹ – Ɍɟɣɥɨɪɚ: ρ - ɩɥɨɬɧɨɫɬɶ ɩɥɨɬɧɨɫɬɶ, ɬɨ ɪɚɜɧɨɜɟɫɢɟ ɧɟɭɫɬɨɣɱɢɜɨ ɢ ɦɚɥɵɟ ɠɢɞɤɨɫɬɢ ɜɨɡɦɭɳɟɧɢɹ ɟɝɨ ɪɚɡɪɭɲɚɬ. ȼ ɤɨɧɰɟ ɤɨɧɰɨɜ, ɬɹɠɟɥɚɹ ɠɢɞɤɨɫɬɶ «ɩɪɨɬɟɱɟɬ» ɜɧɢɡ, ɠɢɞɤɨɫɬɢ ɩɨɦɟɧɹɸɬɫɹ ɦɟɫɬɚɦɢ, ɢ ɫɢɫɬɟɦɚ ɩɪɢɞɟɬ ɤ ɭɫɬɨɣɱɢɜɨɦɭ ɪɚɜɧɨɜɟɫɢɸ. ɋɯɨɞɧɚɹ ɫɢɬɭɚɰɢɹ ɢɦɟɟɬ ɦɟɫɬɨ ɧɚ ɝɪɚɧɢɰɟ ɦɟɠɞɭ ɩɥɚɡɦɨɣ ɢ ɨɞɧɨɪɨɞɧɵɦ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ. Ɋɨɥɶ «ɥɟɝɤɨɣ ɠɢɞɤɨɫɬɢ» ɡɞɟɫɶ ɢɝɪɚɟɬ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɢ, ɟɫɥɢ ɧɚɩɪɚɜɥɟɧɢɟ ɭɫɤɨɪɟɧɢɹ ɨɤɚɠɟɬɫɹ ɧɟɛɥɚɝɨɩɪɢɹɬɧɵɦ, ɬɨ ɧɚɪɚɫɬɚɸɬ ɠɟɥɨɛɤɢ, ɤɚɤ ɷɬɨ ɤɚɱɟɫɬɜɟɧɧɨ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 4.16. Ⱦɥɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɭɞɟɪɠɚɧɢɹ ɩɥɚɡɦɵ ɜ ɧɟɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɨɛɵɱɧɨ ɜɜɨɞɹɬ ɩɚɪɚɦɟɬɪ β = 8 πp B 2 , ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɣ ɨɬɧɨɲɟɧɢɟ ɞɚɜɥɟɧɢɹ ɩɥɚɡɦɵ ɤ ɞɚɜɥɟɧɢɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ (ɫɦ. § 23). ȿɫɥɢ β<1, ɬɨ ɝɨɜɨɪɹɬ ɨ ɩɥɚɡɦɟ ɧɢɡɤɨɝɨ Ɋɢɫ. 4.16. ɀɟɥɨɛɤɢ ɧɚ ɝɪɚɧɢɰɟ ɩɥɚɡɦɚ – ɞɚɜɥɟɧɢɹ, ɟɫɥɢ β>1, ɬɨ – ɜɵɫɨɤɨɝɨ. ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ. Ʉɪɭɠɤɢ ɫ ɬɨɱɤɚɦɢ ɭɫɥɨɜɧɨ ȿɫɥɢ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ ɭɞɟɪɠɢɜɚɟɬɫɹ ɢɡɨɛɪɚɠɚɸɬ ɫɢɥɨɜɵɟ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɩɥɚɡɦɚ ɫ β~1, ɬɨ ɫɭɞɶɛɚ ɜɨɡɧɢɤɚɸɳɟɝɨ ɧɚ ɝɪɚɧɢɰɟ ɩɥɚɡɦɚ –
ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɩɥɚɡɦɟɧɧɨɝɨ «ɹɡɵɤɚ», ɪɚɡɞɜɢɝɚɸɳɟɝɨ ɫɢɥɨɜɵɟ ɥɢɧɢɢ, ɡɚɜɢɫɢɬ ɨɬ ɬɨɝɨ, ɧɚɪɚɫɬɚɟɬ ɢɥɢ ɭɛɵɜɚɟɬ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɩɪɢ ɭɞɚɥɟɧɢɢ ɨɬ ɩɥɚɡɦɵ. ȿɫɥɢ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɨɬ ɝɪɚɧɢɰɵ ɧɚɪɭɠɭ ɭɛɵɜɚɟɬ, ɬɨ ɩɨɫɤɨɥɶɤɭ ɡɞɟɫɶ ɛɭɞɟɬ ɪ>B2/8π, ɬɨ ɥɨɤɚɥɶɧɨɟ ɜɨɡɦɭɳɟɧɢɟ ɫɬɪɟɦɢɬɫɹ ɪɚɫɬɢ. ɇɚɨɛɨɪɨɬ, ɟɫɥɢ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɪɚɫɬɟɬ ɧɚɪɭɠɭ ɨɬ ɝɪɚɧɢɰɵ, ɬɨ ɪɨɫɬ ɜɨɡɦɭɳɟɧɢɹ ɧɟɜɨɡɦɨɠɟɧ. ȼ ɛɨɥɶɲɢɧɫɬɜɟ ɩɪɟɞɥɨɠɟɧɧɵɯ ɦɚɝɧɢɬɧɵɯ ɥɨɜɭɲɟɤ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɭɛɵɜɚɟɬ ɧɚɪɭɠɭ, ɩɨɷɬɨɦɭ ɩɪɨɝɧɨɡ ɩɨ ɭɫɬɨɣɱɢɜɨɫɬɢ ɩɥɚɡɦɵ ɜɵɫɨɤɨɝɨ ɞɚɜɥɟɧɢɹ ɜɵɝɥɹɞɢɬ ɧɟɭɬɟɲɢɬɟɥɶɧɨ (ɛɟɡ ɤɚɤɢɯ-ɥɢɛɨ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɭɫɢɥɢɣ). Ʉ ɫɱɚɫɬɶɸ, ɨɞɧɚɤɨ, ɜɨ ɦɧɨɝɢɯ ɭɫɬɪɨɣɫɬɜɚɯ ɩɥɚɡɦɚ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɞɨɥɠɧɚ ɛɵɬɶ ɧɢɡɤɨɝɨ ɞɚɜɥɟɧɢɹ β<<1. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɦɨɠɧɨ ɨɛɟɫɩɟɱɢɬɶ ɭɫɬɨɣɱɢɜɨɫɬɶ ɜ ɫɪɟɞɧɟɦ, ɟɫɥɢ ɞɥɹ ɥɸɛɨɣ ɜɵɞɟɥɟɧɧɨɣ ɩɥɚɡɦɟɧɧɨɣ ɬɪɭɛɤɢ ɛɭɞɟɬ ɜɵɩɨɥɧɟɧ ɩɪɢɧɰɢɩ «ɦɢɧɢɦɭɦɚ – ȼ»: δ ³ dl B < 0 , ɤɨɬɨɪɵɣ ɩɨɞɪɨɛɧɨ ɨɛɫɭɠɞɚɥɫɹ ɜ § 19. ȼɯɨɞɹɳɢɣ ɜ ɷɬɭ ɮɨɪɦɭɥɭ ɢɧɬɟɝɪɚɥ ɜɞɨɥɶ ɫɢɥɨɜɨɣ ɥɢɧɢɢ (ɜɞɨɥɶ ɤɨɬɨɪɨɣ ɨɪɢɟɧɬɢɪɨɜɚɧɚ ɜɵɞɟɥɟɧɧɚɹ ɧɚɦɢ ɬɪɭɛɤɚ) ɤɚɤ ɪɚɡ ɢ ɨɛɟɫɩɟɱɢɜɚɟɬ «ɜɡɜɟɲɢɜɚɧɢɟ» ɜɤɥɚɞɚ ɛɥɚɝɨɩɪɢɹɬɧɵɯ ɢ ɧɟɛɥɚɝɨɩɪɢɹɬɧɵɯ ɭɱɚɫɬɤɨɜ. ȼɵɞɟɥɟɧɧɚɹ ɩɥɚɡɦɟɧɧɚɹ ɬɪɭɛɤɚ ɭɞɟɪɠɢɜɚɟɬɫɹ ɭɫɬɨɣɱɢɜɨ, ɟɫɥɢ ɡɚɧɢɦɚɟɦɵɣ ɟɸ ɨɛɴɟɦ ɛɭɞɟɬ ɦɚɤɫɢɦɚɥɟɧ ɜ ɩɨɥɨɠɟɧɢɢ ɪɚɜɧɨɜɟɫɢɹ, ɱɬɨ ɢ ɨɬɪɚɠɟɧɨ ɜ ɧɚɩɢɫɚɧɧɨɦ ɤɪɢɬɟɪɢɢ. •
ɇɟɭɫɬɨɣɱɢɜɨɫɬɶ Ʉɟɥɶɜɢɧɚ – Ƚɟɥɶɦɝɨɥɶɰɚ. ɗɬɨ ɟɳɟ ɨɞɢɧ ɩɪɢɦɟɪ ɤɥɚɫɫɢɱɟɫɤɨɣ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ, ɫɩɨɫɨɛɧɨɣ ɪɚɡɜɢɜɚɬɶɫɹ ɩɪɢ ɧɚɥɢɱɢɢ ɧɟɨɞɧɨɪɨɞɧɨɫɬɢ ɫɤɨɪɨɫɬɢ ɩɨɬɨɤɚ ɠɢɞɤɨɫɬɢ ɢɥɢ ɩɥɚɡɦɵ. ȼ ɩɪɨɫɬɟɣɲɟɦ ɫɥɭɱɚɟ ɜ ɤɚɱɟɫɬɜɟ ɧɟɨɞɧɨɪɨɞɧɨɝɨ ɩɨɬɨɤɚ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɫɟɛɟ ɞɜɚ ɧɟɫɦɟɲɢɜɚɸɳɢɯɫɹ ɩɨɬɨɤɚ ɠɢɞɤɨɫɬɢ, ɬɟɤɭɳɢɯ ɫ ɪɚɡɧɵɦɢ ɫɤɨɪɨɫɬɹɦɢ ɜɵɲɟ ɢ ɧɢɠɟ ɝɪɚɧɢɰɵ ɪɚɡɞɟɥɚ – ɬɚɧɝɟɧɰɢɚɥɶɧɨɝɨ ɪɚɡɪɵɜɚ (ɪɢɫ. 4.17,ɚ). ȿɫɥɢ ɝɪɚɧɢɰɚ ɩɨɬɨɤɨɜ ɜɨɡɦɭɳɚɟɬɫɹ, ɧɚɩɪɢɦɟɪ, ɩɨɹɜɥɹɟɬɫɹ ɝɨɪɛ, ɤɚɤ ɷɬɨ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 4.17,ɛ, ɬɨ ɫɤɨɪɨɫɬɶ ɩɨɬɨɤɚ ɫɜɟɪɯɭ ɭɜɟɥɢɱɢɜɚɟɬɫɹ, ɚ ɫɧɢɡɭ ɭɦɟɧɶɲɚɟɬɫɹ. ɉɨ ɬɟɨɪɟɦɟ Ȼɟɪɧɭɥɥɢ ɞɚɜɥɟɧɢɟ ɠɢɞɤɨɫɬɢ ɦɟɧɹɟɬɫɹ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ, ɫɧɢɡɭ «ɝɨɪɛɚ» ɨɧɨ ɫɬɚɧɨɜɢɬɫɹ ɛɨɥɶɲɟ ɢ Ɋɢɫ. 4.17. ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɵɟ ɩɟɪɜɨɧɚɱɚɥɶɧɨɦɭ ɜɨɡɦɭɳɟɧɢɸ ɜɵɝɨɞɧɨ ɪɚɫɬɢ. ɫɬɚɞɢɢ ɪɚɡɜɢɬɢɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ȼ ɪɟɡɭɥɶɬɚɬɟ ɫɥɨɣ ɪɚɡɛɢɜɚɟɬɫɹ ɧɚ ɫɢɫɬɟɦɭ ɫɤɚɱɤɚ ɫɤɨɪɨɫɬɢ ɩɨɬɨɤɨɜ. ɢɡɨɥɢɪɨɜɚɧɧɵɯ ɜɢɯɪɟɣ, ɢɡ-ɡɚ ɯɚɪɚɤɬɟɪɧɨɣ ɮɨɪɦɵ ɥɢɧɢɣ ɬɨɤɚ (ɪɢɫ. 4.17,ɜ) ɢɯ ɧɚɡɵɜɚɸɬ «ɤɨɲɚɱɶɢɦɢ ɝɥɚɡɚɦɢ» Ʉɟɥɶɜɢɧɚ, ɨɬɤɪɵɜɲɟɝɨ ɷɬɭ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ ɟɳɟ ɜ ɩɨɡɚɩɪɨɲɥɨɦ ɜɟɤɟ. •
Ɋɚɡɪɵɜɧɚɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ. ɉɟɪɟɡɚɦɵɤɚɧɢɟ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ȼɧɟɲɧɟ ɩɨɞɨɛɧɨ ɜɵɝɥɹɞɢɬ ɤɚɪɬɢɧɚ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɩɥɨɫɤɨɫɬɢ ɫɤɚɱɤɚ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ – ɬɚɤ ɧɚɡɵɜɚɟɦɨɝɨ ɧɟɣɬɪɚɥɶɧɨɝɨ ɬɨɤɨɜɨɝɨ ɫɥɨɹ (ɪɢɫ. 4.18). ɉɪɢɪɨɞɚ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɡɞɟɫɶ ɢɧɚɹ. ɍɩɪɨɳɟɧɧɨ ɟɟ ɦɨɠɧɨ ɬɪɚɤɬɨɜɚɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. Ɋɚɜɧɨɦɟɪɧɨ ɪɚɫɩɪɟɞɟɥɟɧɧɵɣ ɩɨ ɩɥɨɫɤɨɫɬɢ ɫɤɚɱɤɚ ɩɨɥɹ ɬɨɤɨɜɵɣ ɫɥɨɣ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɛɟɫɤɨɧɟɱɧɭɸ ɫɨɜɨɤɭɩɧɨɫɬɶ ɨɞɢɧɚɤɨɜɵɯ ɷɤɜɢɞɢɫɬɚɧɬɧɵɯ ɷɥɟɦɟɧɬɚɪɧɵɯ ɬɨɤɨɜ. ɉɨɥɨɠɟɧɢɟ ɤɚɠɞɨɝɨ ɢɡ ɧɢɯ ɹɜɥɹɟɬɫɹ
ɪɚɜɧɨɜɟɫɧɵɦ, ɬɚɤ ɤɚɤ ɩɪɢɬɹɠɟɧɢɟ ɫɨɫɟɞɟɣ ɫɩɪɚɜɚ ɜ ɬɨɱɧɨɫɬɢ ɤɨɦɩɟɧɫɢɪɭɟɬɫɹ
Ɋɢɫ. 4.18. Ɋɚɡɪɵɜɧɚɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ ɬɨɤɨɜɨɝɨ ɫɥɨɹ. Ʉɪɟɫɬɢɤɨɦ ɩɨɦɟɱɟɧɨ ɧɚɩɪɚɜɥɟɧɢɟ ɬɨɤɚ ɜ ɫɥɨɟ (ɚ). Ɉɧɨ ɫɨɯɪɚɧɹɟɬɫɹ ɢ ɜ ɫɢɫɬɟɦɟ ɮɢɥɚɦɟɧɬɨɜ, ɧɚ ɤɨɬɨɪɭɸ ɪɚɫɩɚɞɚɟɬɫɹ ɫɥɨɣ (ɛ)
Ɋɢɫ. 4.19. Ʉ ɦɟɯɚɧɢɡɦɭ ɩɟɪɟɡɚɦɵɤɚɧɢɹ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ
ɩɪɢɬɹɠɟɧɢɟɦ ɫɨɫɟɞɟɣ ɫɥɟɜɚ. ɇɨ ɫɬɨɢɬ ɧɚɦ ɧɚɪɭɲɢɬɶ ɪɚɜɧɨɦɟɪɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ, ɫɛɥɢɡɢɜ ɝɪɭɩɩɭ ɢɡ ɧɟɫɤɨɥɶɤɢɯ ɬɨɤɨɜ, ɤɚɤ ɦɵ ɨɛɧɚɪɭɠɢɦ, ɱɬɨ ɢɯ ɜɡɚɢɦɧɨɟ ɩɪɢɬɹɠɟɧɢɟ ɛɭɞɟɬ ɫɢɥɶɧɟɟ ɩɪɢɬɹɠɟɧɢɹ ɫɨɫɟɞɟɣ, ɨɧɢ ɧɚɱɧɭɬ ɫɬɹɝɢɜɚɬɶɫɹ ɜ ɟɞɢɧɭɸ ɢɡɨɥɢɪɨɜɚɧɧɭɸ ɬɨɤɨɜɭɸ ɧɢɬɶ – ɮɢɥɚɦɟɧɬ. Ɋɟɡɭɥɶɬɚɬɨɦ ɪɚɡɜɢɬɢɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɛɭɞɟɬ ɪɚɡɪɵɜ ɬɨɤɨɜɨɝɨ ɫɥɨɹ ɢ ɪɚɡɛɢɟɧɢɟ ɟɝɨ ɧɚ ɫɨɜɨɤɭɩɧɨɫɬɶ ɮɢɥɚɦɟɧɬɨɜ. ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ ɱɚɫɬɨ ɧɚɡɵɜɚɸɬ ɪɚɡɪɵɜɧɨɣ, ɢɥɢ ɬɢɪɢɧɝ-ɧɟɭɫɬɨɣɱɢɜɨɫɬɶɸ (ɨɬ ɚɧɝɥɢɣɫɤɨɝɨ: tearing instability). Ɏɢɡɢɱɟɫɤɨɣ ɤɚɪɬɢɧɟ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɦɨɠɧɨ ɩɪɢɞɚɬɶ ɢɧɭɸ ɬɪɚɤɬɨɜɤɭ, ɟɫɥɢ ɜɫɩɨɦɧɢɬɶ, ɱɬɨ ɫɢɥɨɜɵɟ ɥɢɧɢɢ «ɨɛɥɚɞɚɸɬ ɧɚɬɹɠɟɧɢɟɦ», ɚ ɩɨɬɨɦɭ ɫɬɪɟɦɹɬɫɹ ɫɨɤɪɚɬɢɬɶɫɹ (ɫɦ. § 23). ɋ ɷɬɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ «ɪɚɫɬɹɧɭɬɵɟ» ɫɢɥɨɜɵɟ ɥɢɧɢɢ ɤɨɧɮɢɝɭɪɚɰɢɢ ɧɚ ɪɢɫ. 4.18,ɚ ɧɟ ɜɵɝɨɞɧɵ, ɫɢɥɨɜɵɦ ɥɢɧɢɹɦ ɜɵɝɨɞɧɨ «ɩɟɪɟɡɚɦɤɧɭɬɶɫɹ» ɱɟɪɟɡ ɫɥɨɣ, ɫɨɤɪɚɬɢɜ ɫɜɨɸ ɞɥɢɧɭ (ɪɢɫ. 4.19). ɗɬɨ ɢ ɩɪɨɢɫɯɨɞɢɬ, ɤɚɤ ɦɵ ɜɢɞɟɥɢ ɜɵɲɟ. Ɍɟɪɦɢɧ ɩɟɪɟɡɚɦɵɤɚɧɢɟ ɩɪɨɱɧɨ ɜɨɲɟɥ ɜ ɫɨɜɪɟɦɟɧɧɭɸ ɩɥɚɡɦɟɧɧɭɸ ɧɚɭɤɭ. •
ɇɟɭɫɬɨɣɱɢɜɨɫɬɢ ɬɨɤɨɜɵɯ ɫɢɫɬɟɦ (Z – ɩɢɧɱɟɣ) Z – ɩɢɧɱ – ɷɬɨ ɫɚɦɨɫɠɚɬɵɣ ɫɬɨɥɛ ɩɥɚɡɦɵ ɫ ɩɪɨɞɨɥɶɧɵɦ (ɜɞɨɥɶ ɨɫɢ z) ɬɨɤɨɦ, ɨɤɪɭɠɟɧɧɵɣ ɫɨɡɞɚɜɚɟɦɵɦ ɷɬɢɦ ɬɨɤɨɦ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ. Ɋɚɜɧɨɜɟɫɢɟ ɡɞɟɫɶ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɛɚɥɚɧɫɨɦ ɦɚɝɧɢɬɧɨɝɨ ɞɚɜɥɟɧɢɹ ɢ ɞɚɜɥɟɧɢɹ ɩɥɚɡɦɵ, ɤɚɤ ɷɬɨ ɛɵɥɨ ɩɨɤɚɡɚɧɨ ɜ § 24. Ⱦɢɧɚɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ, ɫɨɩɪɨɜɨɠɞɚɸɳɢɟ ɜɨɡɧɢɤɧɨɜɟɧɢɟ ɬɚɤɨɝɨ ɩɢɧɱɚ ɨɛɫɭɠɞɚɥɢɫɶ ɜ § 25. Ɂɞɟɫɶ ɨɛɫɭɞɢɦ ɭɫɬɨɣɱɢɜɨɫɬɶ ɩɨɞɨɛɧɨɝɨ ɪɚɜɧɨɜɟɫɢɹ, ɩɨɥɚɝɚɹ ɞɥɹ ɩɪɨɫɬɨɬɵ, ɱɬɨ ɬɨɤ ɩɥɚɡɦɵ ɩɨɥɧɨɫɬɶɸ ɫɤɢɧɢɪɨɜɚɧ - ɫɨɫɪɟɞɨɬɨɱɟɧ ɜ ɨɫɧɨɜɧɨɦ ɜ ɩɪɢɩɨɜɟɪɯɧɨɫɬɧɨɦ ɫɥɨɟ. Ɍɨɝɞɚ ɜɧɭɬɪɢ ɩɥɚɡɦɵ ɩɢɧɱɚ ɧɟɬ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɢ ɪɚɜɧɨɜɟɫɢɟ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɛɚɥɚɧɫɨɦ ɞɚɜɥɟɧɢɣ ɩɥɚɡɦɵ ɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɚ ɝɪɚɧɢɰɟ (ɫɦ. ɪɢɫ. 4.20): Bϕ2 2I pɩɥɚɡ = p ɦɚɝ , p ɦɚɝ = , Bϕ = . (4.87) 8π ca Ɂɞɟɫɶ ɚ – ɪɚɞɢɭɫ ɩɥɚɡɦɟɧɧɨɝɨ ɫɬɨɥɛɚ, I – ɩɨɥɧɵɣ ɬɨɤ, ɢ ɦɵ ɭɱɥɢ, ɱɬɨ ɜɧɟ ɩɥɚɡɦɵ ɞɥɹ ɩɪɹɦɨɝɨ ɫɬɨɥɛɚ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɫɨɜɩɚɞɚɟɬ ɫ ɩɨɥɟɦ ɩɪɹɦɨɝɨ ɩɪɨɜɨɞɚ.
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ɉɟɪɟɬɹɠɤɢ Ɇɚɝɧɢɬɧɨɟ ɞɚɜɥɟɧɢɟ ɜɧɟ ɩɢɧɱɚ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɫ ɭɦɟɧɶɲɟɧɢɟɦ ɪɚɞɢɭɫɚ, ɤɚɤ ɷɬɨ ɨɱɟɜɢɞɧɨ ɢɡ ɮɨɪɦɭɥɵ (4.87). ɉɪɢ ɦɟɫɬɧɨɦ ɫɭɠɟɧɢɢ ɬɨɤɨɜɨɝɨ ɤɚɧɚɥɚ ɩɥɚɡɦɚ ɜɵɞɚɜɥɢɜɚɟɬɫɹ ɢɡ ɦɟɫɬɚ ɫɭɠɟɧɢɹ (ɩɨɞɨɛɧɨ ɩɚɫɬɟ, ɜɵɞɚɜɥɢɜɚɟɦɨɣ ɢɡ ɬɸɛɢɤɚ, ɪɢɫ. 4.20ɛ), ɩɨɷɬɨɦɭ ɞɚɜɥɟɧɢɟ ɟɟ ɧɟ ɦɨɠɟɬ ɩɪɨɬɢɜɨɞɟɣɫɬɜɨɜɚɬɶ ɧɚɪɚɫɬɚɸɳɟɦɭ ɞɚɜɥɟɧɢɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɢ ɩɟɪɟɬɹɠɤɟ ɜɵɝɨɞɧɨ ɧɚɪɚɫɬɚɬɶ. Ɋɢɫ. 4.20. ɇɟɭɫɬɨɣɱɢɜɨɫɬɢ ɩɥɚɡɦɵ ɫ ɬɨɤɨɦ: ɚ − ɫɤɢɧɢɪɨɜɚɧɧɵɣ ɩɢɧɱ; ɛ − ɩɟɪɟɬɹɠɤɚ; ɜ − ɫɬɚɛɢɥɢɡɚɰɢɹ ɩɟɪɟɬɹɠɤɢ ɩɪɨɞɨɥɶɧɵɦ ɩɨɥɟɦ: ɜ ɨɛɥɚɫɬɢ ɩɟɪɟɠɚɬɢɹ ɫɢɥɨɜɵɟ ɥɢɧɢɢ ɫɝɭɳɚɸɬɫɹ, ɞɚɜɥɟɧɢɟ ɜɧɭɬɪɟɧɧɟɝɨ ɩɨɥɹ ɧɚɪɚɫɬɚɟɬ; ɝ − ɢɡɝɢɛ «ɡɦɟɣɤɚ»; ɞ − ɫɬɚɛɢɥɢɡɚɰɢɹ ɢɡɝɢɛɚ ɩɪɨɜɨɞɹɳɢɦ ɤɨɠɭɯɨɦ
Ɋɚɡɜɢɬɢɟ ɩɟɪɟɬɹɠɟɤ ɦɨɠɧɨ ɩɪɟɞɨɬɜɪɚɬɢɬɶ, ɟɫɥɢ ɜ ɩɥɚɡɦɭ ɩɢɧɱɚ «ɜɦɨɪɨɡɢɬɶ» ɩɪɨɞɨɥɶɧɨɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ (ɪɢɫ. 4.20,ɜ). ɉɨɬɨɤ ɩɪɨɞɨɥɶɧɨɝɨ ɩɨɥɹ ɫɨɯɪɚɧɹɟɬɫɹ Φ = πa 2 Bz = const , Bz ~ a −2 ,
pz ɦɚɝ ~ a −4 ,
(4.88)
ɚ ɩɨɷɬɨɦɭ ɷɬɚ ɤɨɦɩɨɧɟɧɬɚ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɩɪɢ ɫɠɚɬɢɢ ɭɜɟɥɢɱɢɜɚɟɬɫɹ, ɢ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɟɦɭ ɞɚɜɥɟɧɢɟ ɜɧɭɬɪɟɧɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ɉɪɢɱɟɦ ɨɧɨ ɧɚɪɚɫɬɚɟɬ, ɤɚɤ ɷɬɨ ɜɢɞɧɨ ɢɡ ɫɪɚɜɧɟɧɢɹ (4.87) ɢ (4.88), ɛɵɫɬɪɟɟ ɞɚɜɥɟɧɢɹ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ɗɬɨ ɢ ɩɪɢɜɨɞɢɬ ɤ ɜɨɡɦɨɠɧɨɫɬɢ ɫɬɚɛɢɥɢɡɚɰɢɢ ɩɟɪɟɬɹɠɟɤ. Ɇɨɠɧɨ ɩɨɤɚɡɚɬɶ, ɱɬɨ ɩɟɪɟɬɹɠɤɢ ɧɟ ɛɭɞɭɬ ɪɚɡɜɢɜɚɬɶɫɹ, ɟɫɥɢ ɜɦɨɪɨɠɟɧɧɨɟ ɩɪɨɞɨɥɶɧɨɝɨ ɩɨɥɹ ɛɭɞɟɬ ɞɨɫɬɚɬɨɱɧɨ ɜɟɥɢɤɨ: Bϕ Bz > , 2 ɝɞɟ ȼϕ - ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɬɨɤɚ ɧɚ ɝɪɚɧɢɰɟ ɩɢɧɱɚ. ȼɨɡɦɨɠɧɨɫɬɶ ɫɬɚɛɢɥɢɡɚɰɢɢ ɩɟɪɟɬɹɠɟɤ ɜɦɨɪɨɠɟɧɧɵɦ ɩɨɥɟɦ ɛɵɥɚ ɩɨɞɬɜɟɪɠɞɟɧɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ.
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«Ɂɦɟɣɤɚ» «Ɂɦɟɣɤɚ» – ɷɬɨ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ ɬɨɤɨɜɨɝɨ ɤɚɧɚɥɚ ɤ ɢɡɝɢɛɭ (ɪɢɫ. 4.20,ɝ). ɇɚɝɥɹɞɧɨ ɩɪɢɱɢɧɭ ɪɚɡɜɢɬɢɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɦɨɠɧɨ ɩɨɹɫɧɢɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: ɩɪɢ ɢɡɝɢɛɟ, ɤɚɤ ɷɬɨ ɤɚɱɟɫɬɜɟɧɧɨ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 4.20,ɝ, ɫɢɥɨɜɵɟ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɫɧɚɪɭɠɢ ɦɟɫɬɚ ɢɡɝɢɛɚ ɪɚɡɪɟɠɚɸɬɫɹ, ɚ ɜɧɭɬɪɢ – ɫɝɭɳɚɸɬɫɹ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɹɜɥɹɟɬɫɹ ɫɢɥɚ, ɭɫɢɥɢɜɚɸɳɚɹ ɩɟɪɜɨɧɚɱɚɥɶɧɨɟ ɜɨɡɦɭɳɟɧɢɟ, ɬɚɤ ɱɬɨ ɢɡɝɢɛɭ ɜɵɝɨɞɧɨ ɪɚɫɬɢ. ɇɚɪɚɫɬɚɧɢɟ ɢɡɝɢɛɨɜ ɤɚɧɚɥɚ ɪɚɡɪɹɞɚ ɧɟɨɞɧɨɤɪɚɬɧɨ ɧɚɛɥɸɞɚɥɨɫɶ ɜ ɷɤɫɩɟɪɢɦɟɧɬɚɯ ɧɚ Z-ɩɢɧɱɚɯ. «Ɂɦɟɣɤɢ» ɦɨɠɧɨ ɫɬɚɛɢɥɢɡɢɪɨɜɚɬɶ, ɟɫɥɢ ɨɤɪɭɠɢɬɶ ɩɥɚɡɦɭ ɯɨɪɨɲɨ ɩɪɨɜɨɞɹɳɢɦ ɤɨɠɭɯɨɦ (ɪɟɚɥɶɧɨ ɢɦɟɧɧɨ ɬɚɤ ɢ ɞɟɥɚɸɬ, ɩɥɚɡɦɟɧɧɵɣ ɲɧɭɪ ɨɤɪɭɠɚɸɬ ɦɚɫɫɢɜɧɵɦ ɦɟɞɧɵɦ ɤɨɠɭɯɨɦ). ɉɪɢ ɛɵɫɬɪɨɦ ɢɡɝɢɛɟ ɬɨɤɨɜɨɝɨ ɤɚɧɚɥɚ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɡɚ ɫɱɟɬ ɫɤɢɧ-ɷɮɮɟɤɬɚ ɧɟ ɭɫɩɟɜɚɟɬ ɩɪɨɧɢɤɧɭɬɶ ɜ ɩɪɨɜɨɞɹɳɢɣ ɤɨɠɭɯ, ɢ ɫɢɥɨɜɵɟ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɬɨɤɚ ɨɤɚɡɵɜɚɸɬɫɹ «ɡɚɠɚɬɵ» ɦɟɠɞɭ ɫɬɟɧɤɨɣ ɢ ɩɥɚɡɦɨɣ (ɫɦ. ɪɢɫ. 4.20,ɞ.). ȼɜɢɞɭ ɫɨɯɪɚɧɟɧɢɹ ɩɨɬɨɤɚ, ɜ ɷɬɨɣ ɨɛɥɚɫɬɢ
ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɫɬɚɧɟɬ ɛɨɥɶɲɟ, ɱɟɦ ɧɚ ɞɢɚɦɟɬɪɚɥɶɧɨ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɣ ɫɬɨɪɨɧɟ ɬɨɤɨɜɨɝɨ ɤɚɧɚɥɚ, ɢ ɜɨɡɧɢɤɚɟɬ ɫɢɥɚ, ɫɬɪɟɦɹɳɚɹɫɹ ɜɨɫɫɬɚɧɨɜɢɬɶ ɪɚɜɧɨɜɟɫɢɟ. ɉɨɫɤɨɥɶɤɭ ɦɟɯɚɧɢɡɦ ɫɬɚɛɢɥɢɡɚɰɢɢ ɫɭɳɟɫɬɜɟɧɧɨ ɫɜɹɡɚɧ ɫɨ ɜɪɟɦɟɧɟɦ ɫɤɢɧɢɪɨɜɚɧɢɹ, ɦɟɞɥɟɧɧɵɣ ɢɡɝɢɛ, ɨɱɟɜɢɞɧɨ, ɫɬɚɛɢɥɢɡɢɪɨɜɚɬɶɫɹ ɧɟ ɦɨɠɟɬ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɛɨɥɟɟ ɷɮɮɟɤɬɢɜɧɨ ɭɩɪɚɜɥɹɬɶ ɩɨɥɨɠɟɧɢɟɦ ɬɨɤɨɜɨɝɨ ɲɧɭɪɚ ɫ ɩɨɦɨɳɶɸ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɩɪɨɜɨɞɧɢɤɨɜ ɫ ɬɨɤɨɦ, ɪɚɫɩɨɥɚɝɚɟɦɵɯ ɧɚ ɩɟɪɢɮɟɪɢɢ ɩɥɚɡɦɵ.
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ȼɢɧɬɨɜɚɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ. Ʉɪɢɬɟɪɢɣ ɒɚɮɪɚɧɨɜɚ - Ʉɪɭɫɤɚɥɚ ȼɨɡɧɢɤɧɨɜɟɧɢɹ ɡɦɟɟɤ ɦɨɠɧɨ ɛɵɥɨ ɛɵ ɢɡɛɟɠɚɬɶ, ɟɫɥɢ ɫɧɚɪɭɠɢ ɨɤɪɭɠɢɬɶ ɩɢɧɱ ɩɪɨɞɨɥɶɧɵɦ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ. ɇɨ ɫɢɬɭɚɰɢɹ ɡɞɟɫɶ ɧɟ ɬɚɤɚɹ ɨɞɧɨɡɧɚɱɧɚɹ, ɤɚɤ ɦɨɠɟɬ ɩɨɤɚɡɚɬɶɫɹ ɧɚ ɩɟɪɜɵɣ ɜɡɝɥɹɞ. ȼɧɟɲɧɟɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɫɤɥɚɞɵɜɚɟɬɫɹ ɫ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ ɬɨɤɚ ɩɢɧɱɚ, ɢ ɨɛɪɚɡɭɟɬɫɹ ɤɨɧɮɢɝɭɪɚɰɢɹ ɫ ɜɢɧɬɨɜɵɦɢ ɫɢɥɨɜɵɦɢ ɥɢɧɢɹɦɢ (ɪɢɫ. 4.21,ɚ). ɉɪɢ ɢɡɝɢɛɟ ɬɨɤɨɜɨɝɨ ɤɚɧɚɥɚ ɞɟɣɫɬɜɭɸɳɢɟ ɧɚ ɪɚɡɧɵɟ ɟɝɨ ɭɱɚɫɬɤɢ ɫɢɥɵ Ⱥɦɩɟɪɚ ɫɨ ɫɬɨɪɨɧɵ ɜɧɟɲɧɟɝɨ ɩɨɥɹ «ɫɤɪɭɱɢɜɚɸɬ» ɩɥɚɡɦɟɧɧɵɣ ɲɧɭɪ, ɤɚɤ ɷɬɨ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 4.21,ɛ, ɢ ɲɧɭɪ ɫɬɪɟɦɢɬɫɹ ɡɚɜɢɬɶɫɹ ɜ ɜɢɧɬ. ɗɬɨ ɢ ɨɩɪɟɞɟɥɢɥɨ ɧɚɡɜɚɧɢɟ ɨɛɫɭɠɞɚɟɦɨɣ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ. ɋɢɥɚ Ⱥɦɩɟɪɚ, ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɬɨɤ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ, ɢɫɱɟɡɚɟɬ, ɤɨɝɞɚ ɬɨɤ ɩɚɪɚɥɥɟɥɟɧ ɫɢɥɨɜɨɣ ɥɢɧɢɢ. ɂɦɟɧɧɨ ɬɚɤɨɟ ɩɨɥɨɠɟɧɢɟ ɢ ɫɬɪɟɦɢɬɫɹ ɡɚɧɹɬɶ ɬɨɤɨɜɵɣ ɲɧɭɪ, ɡɚɜɢɜɚɹɫɶ ɜ ɜɢɧɬ. ɇɟɬɪɭɞɧɨ ɩɨɞɫɱɢɬɚɬɶ ɲɚɝ ɜɢɧɬɨɜɨɣ ɫɢɥɨɜɨɣ ɥɢɧɢɢ. Ɍɚɤ ɤɚɤ ɞɥɢɧɚ ɨɤɪɭɠɧɨɫɬɢ ɜ ɫɟɱɟɧɢɢ ɲɧɭɪɚ ɪɚɞɢɭɫɚ ɚ ɫɨɫɬɚɜɥɹɟɬ 2πɚ, ɚ ɩɪɢ ɨɞɧɨɤɪɚɬɧɨɦ ɨɛɯɨɞɟ ɜɨɤɪɭɝ ɲɧɭɪɚ ɫɦɟɳɟɧɢɟ ɪɚɜɧɨ ɲɚɝɭ ɫɢɥɨɜɨɣ ɥɢɧɢɢ h, ɬɨ, ɭɦɧɨɠɢɜ ɞɥɢɧɭ ɨɤɪɭɠɧɨɫɬɢ ɧɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɭɝɥɨɜɨɣ ɤɨɷɮɮɢɰɢɟɧɬ, ɩɨɥɭɱɚɟɦ B h = 2πa z . (4.89) Bϕ ȿɫɥɢ ɭɱɟɫɬɶ, ɱɬɨ ɤɨɧɰɵ ɲɧɭɪɚ «ɜɦɨɪɨɠɟɧɵ» ɜ ɯɨɪɨɲɨ ɩɪɨɜɨɞɹɳɢɟ ɷɥɟɤɬɪɨɞɵ, ɤɚɤ ɷɬɨ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 4.21,ɛ, ɬɨ ɜ ɩɪɨɦɟɠɭɬɤɟ ɞɥɢɧɵ L ɧɟ ɭɥɨɠɢɬɫɹ ɧɢ ɨɞɧɨɝɨ ɲɚɝɚ ɜɢɧɬɚ, ɚ, ɡɧɚɱɢɬ, ɜɢɧɬɨɜɚɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ ɪɚɡɜɢɜɚɬɶɫɹ ɧɟ ɫɦɨɠɟɬ, ɟɫɥɢ ɜɵɩɨɥɧɟɧɨ ɭɫɥɨɜɢɟ B h = 2πa z > L . (4.90) Bϕ ɗɬɨ ɢ ɟɫɬɶ ɤɪɢɬɟɪɢɣ ɭɫɬɨɣɱɢɜɨɫɬɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɪɚɡɜɢɬɢɹ ɜɢɧɬɨɜɵɯ ɜɨɡɦɭɳɟɧɢɣ. Ɇɵ ɜɢɞɢɦ, ɱɬɨ ɞɥɹ ɩɨɞɚɜɥɟɧɢɹ ɜɢɧɬɨɜɨɣ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɩɪɨɞɨɥɶɧɨɟ ɩɨɥɟ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɷɬɢɦ ɤɪɢɬɟɪɢɟɦ ɞɨɥɠɧɨ ɛɵɬɶ ɞɨɫɬɚɬɨɱɧɨ ɫɢɥɶɧɵɦ. ɋɥɚɛɨɟ ɩɪɨɞɨɥɶɧɨɟ ɩɨɥɟ ɬɨɥɶɤɨ ɭɯɭɞɲɚɟɬ ɫɢɬɭɚɰɢɸ ɜ ɩɥɚɧɟ ɭɫɬɨɣɱɢɜɨɫɬɢ, ɬɚɤ ɤɚɤ ɭɫɥɨɜɢɟ (4.90) ɦɨɠɟɬ ɧɚɪɭɲɚɬɶɫɹ. Ⱦɥɹ ɫɢɫɬɟɦ ɫ ɡɚɦɤɧɭɬɵɦ ɩɥɚɡɦɟɧɧɵɦ ɲɧɭɪɨɦ, ɤɚɤ ɷɬɨ ɢɦɟɟɬ Ɋɢɫ. 4.21. ȼɢɧɬɨɜɚɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ ɦɟɫɬɨ ɜ ɬɨɪɨɢɞɚɥɶɧɨɣ ɦɚɝɧɢɬɧɨɣ ɥɨɜɭɲɤɟ, ɧɚɩɪɢɦɟɪ ɜ ɬɨɤɚɦɚɤɟ (ɫɦ. § 17), ɪɨɥɶ ɞɥɢɧɵ ɫɢɫɬɟɦɵ ɜɵɩɨɥɧɹɟɬ ɞɥɢɧɚ ɫɚɦɨɝɨ ɡɚɦɤɧɭɬɨɝɨ ɲɧɭɪɚ. ȿɫɥɢ ɟɝɨ ɛɨɥɶɲɨɣ ɪɚɞɢɭɫ ɪɚɜɟɧ R (ɫɦ. ɪɢɫ. 2.6), ɬɨ, ɩɨɞɫɬɚɜɢɜ ɜ (4.90) ɜ ɤɚɱɟɫɬɜɟ ɞɥɢɧɵ L ɞɥɢɧɭ ɨɤɪɭɠɧɨɫɬɢ ɛɨɥɶɲɨɝɨ ɪɚɞɢɭɫɚ 2πR, ɩɨɥɭɱɢɦ ɤɪɢɬɟɪɢɣ ɭɫɬɨɣɱɢɜɨɫɬɢ ɒɚɮɪɚɧɨɜɚ – Ʉɪɭɫɤɚɥɚ [23]:
h a Bz = > 1. (4.91) 2πR R Bϕ ɝɞɟ q – ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɡɚɩɚɫɚ ɭɫɬɨɣɱɢɜɨɫɬɢ ɉɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɬɨɤɚɦɚɤɚɦ, ɩɪɨɞɨɥɶɧɨɟ ɩɨɥɟ Bz ɩɪɢɧɹɬɨ ɧɚɡɵɜɚɬɶ ɬɨɪɨɢɞɚɥɶɧɵɦ, ɚ ɩɨɥɟ ɬɨɤɚ Bϕ − ɩɨɥɨɢɞɚɥɶɧɵɦ. ɋɨɝɥɚɫɧɨ ɤɪɢɬɟɪɢɸ ɒɚɮɪɚɧɨɜɚ – Ʉɪɭɫɤɚɥɚ ɬɨɪɨɢɞɚɥɶɧɨɟ ɩɨɥɟ ɞɨɥɠɧɨ ɛɵɬɶ ɨɱɟɧɶ ɛɨɥɶɲɢɦ, ɟɫɥɢ ɞɢɚɦɟɬɪ ɫɟɱɟɧɢɹ ɲɧɭɪɚ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɟ ɟɝɨ ɞɥɢɧɵ ɩɨ ɛɨɥɶɲɨɦɭ ɪɚɞɢɭɫɭ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ, ɨɰɟɧɢɜɚɹ ɜɟɥɢɱɢɧɭ ɩɨɥɨɢɞɚɥɶɧɨɝɨ ɩɨɥɹ ɬɨɤɚ ɩɥɚɡɦɟɧɧɨɝɨ ɲɧɭɪɚ ɤɚɤ 2I Bϕ = , ca ɦɨɠɟɦ ɡɚɩɢɫɚɬɶ ɤɪɢɬɟɪɢɣ ɭɫɬɨɣɱɢɜɨɫɬɢ ɤɚɤ ɭɫɥɨɜɢɟ, ɨɝɪɚɧɢɱɢɜɚɸɳɟɟ ɞɨɩɭɫɬɢɦɵɣ ɬɨɤ ɜ ɬɨɤɚɦɚɤɟ: a2 I < I max = c B . (4.92) R z ɗɬɨ ɭɫɥɨɜɢɟ ɨɩɪɟɞɟɥɹɟɬ ɨɞɧɭ ɢɡ ɝɪɚɧɢɰ ɪɚɛɨɱɟɣ ɨɛɥɚɫɬɢ ɞɥɹ ɬɚɤɨɣ ɫɢɫɬɟɦɵ (ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ ɩɪɟɞɟɥ ɩɨ ɬɨɤɭ). ɉɨɞɱɟɪɤɧɟɦ ɜ ɡɚɤɥɸɱɟɧɢɟ, ɱɬɨ ɤɪɢɬɟɪɢɣ ɒɚɮɪɚɧɨɜɚ – Ʉɪɭɫɤɚɥɚ ɹɜɥɹɟɬɫɹ ɤɪɢɬɟɪɢɟɦ ɝɥɨɛɚɥɶɧɨɣ ɭɫɬɨɣɱɢɜɨɫɬɢ, ɬ.ɟ. ɭɫɬɨɣɱɢɜɨɫɬɢ ɩɥɚɡɦɟɧɧɨɝɨ ɲɧɭɪɚ ɜ ɰɟɥɨɦ, ɢ ɧɟ ɝɚɪɚɧɬɢɪɭɟɬ ɥɨɤɚɥɶɧɨɣ ɭɫɬɨɣɱɢɜɨɫɬɢ. ɇɚɩɪɢɦɟɪ, ɨɞɢɧ ɢɡ ɤɪɢɬɟɪɢɟɜ ɥɨɤɚɥɶɧɨɣ ɭɫɬɨɣɱɢɜɨɫɬɢ (ɤɪɢɬɟɪɢɣ ɋɚɣɞɟɦɚ) ɡɚɩɢɫɵɜɚɟɬɫɹ ɜ ɜɢɞɟ 8πp ′( r ) 1 dp d ( 1 − q 2 ) + s 2 > 0 , p ′( r ) = , s= ln q . (4.93) 2 4 B dr dr Ɂɞɟɫɶ ɩɨɫɥɟɞɧɟɟ ɫɥɚɝɚɟɦɨɟ – ɲɢɪ (ɢɥɢ ɩɟɪɟɤɪɟɳɟɧɧɨɫɬɶ) ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɜɫɟɝɞɚ ɨɤɚɡɵɜɚɟɬ ɫɬɚɛɢɥɢɡɢɪɭɸɳɟɟ ɞɟɣɫɬɜɢɟ. Ɍɚɤ ɤɚɤ ɜ ɩɨɩɟɪɟɱɧɨɦ ɫɟɱɟɧɢɢ ɲɧɭɪɚ ɞɚɜɥɟɧɢɟ ɩɥɚɡɦɵ p(r) ɩɨ ɦɟɪɟ ɭɞɚɥɟɧɢɹ ɨɬ ɰɟɧɬɪɚ ɭɛɵɜɚɟɬ, ɬɨ ɞɥɹ ɭɫɬɨɣɱɢɜɨɫɬɢ, ɩɪɢ ɦɚɥɨɦ ɲɢɪɟ, ɞɨɥɠɧɨ ɛɵɬɶ q>1 ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɤɪɢɬɟɪɢɟɦ ɒɚɮɪɚɧɨɜɚ – Ʉɪɭɫɤɚɥɚ. ȿɫɥɢ ɨɤɚɠɟɬɫɹ ɬɚɤ, ɱɬɨ ɧɚ ɩɟɪɢɮɟɪɢɢ ɩɥɚɡɦɟɧɧɨɝɨ ɲɧɭɪɚ ɛɭɞɟɬ q(a)>1, ɬɨ ɝɥɨɛɚɥɶɧɨ ɲɧɭɪ ɛɭɞɟɬ ɭɫɬɨɣɱɢɜ. ɇɨ ɟɫɥɢ ɩɪɢ ɷɬɨɦ ɜ ɰɟɧɬɪɟ ɲɧɭɪɚ ɨɤɚɠɟɬɫɹ q(0)<1, ɬɨ ɜɨɡɦɨɠɧɨ ɪɚɡɜɢɬɢɟ ɜɧɭɬɪɟɧɧɟɣ ɜɢɧɬɨɜɨɣ ɦɨɞɵ, ɜɵɡɵɜɚɸɳɟɣ «ɜɵɜɨɪɚɱɢɜɚɧɢɟ» ɲɧɭɪɚ «ɧɚɢɡɧɚɧɤɭ» ɢ ɩɨɹɜɥɟɧɢɟ ɩɢɥɨɨɛɪɚɡɧɵɯ ɤɨɥɟɛɚɧɢɣ ɟɝɨ ɬɟɦɩɟɪɚɬɭɪɵ, ɜɫɥɟɞɫɬɜɢɟ ɩɟɪɟɦɟɲɢɜɚɧɢɹ ɝɨɪɹɱɟɣ ɰɟɧɬɪɚɥɶɧɨɣ ɢ ɯɨɥɨɞɧɨɣ ɩɟɪɢɮɟɪɢɣɧɨɣ ɩɥɚɡɦɵ ɲɧɭɪɚ. q=
§ 37. Ʉɢɧɟɬɢɱɟɫɤɢɟ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɩɥɚɡɦɵ. •
Ɇɟɯɚɧɢɡɦ ɨɛɪɚɬɧɨɝɨ ɩɨɝɥɨɳɟɧɢɹ Ʌɚɧɞɚɭ. Ʉɢɧɟɬɢɱɟɫɤɢɟ ɷɮɮɟɤɬɵ ɫɬɚɧɨɜɹɬɫɹ ɫɭɳɟɫɬɜɟɧɧɵɦɢ, ɤɨɝɞɚ ɮɚɡɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɨɥɧ ɨɤɚɡɵɜɚɟɬɫɹ ɩɨɪɹɞɤɚ ɯɚɪɚɤɬɟɪɧɨɣ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰ ɩɥɚɡɦɵ. Ɉɞɧɨ ɢɡ ɩɪɨɹɜɥɟɧɢɣ ɷɬɢɯ ɷɮɮɟɤɬɨɜ – ɛɟɫɫɬɨɥɤɧɨɜɢɬɟɥɶɧɨɟ ɡɚɬɭɯɚɧɢɟ Ʌɚɧɞɚɭ, ɩɪɢɜɨɞɹɳɟɟ ɤ ɡɚɬɭɯɚɧɢɸ ɜɨɥɧ ɜ ɦɚɤɫɜɟɥɥɨɜɫɤɨɣ ɩɥɚɡɦɟ. ɇɚɥɢɱɢɟ (ɢɥɢ ɨɬɫɭɬɫɬɜɢɟ) ɛɟɫɫɬɨɥɤɧɨɜɢɬɟɥɶɧɨɝɨ ɡɚɬɭɯɚɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɡɧɚɤɨɦ ɩɪɨɢɡɜɨɞɧɨɣ ɩɨ ɫɤɨɪɨɫɬɢ ɨɬ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜ ɪɟɡɨɧɚɧɫɧɨɣ ɬɨɱɤɟ, ɡɚɞɚɜɚɟɦɨɣ ɭɫɥɨɜɢɟɦ ɱɟɪɟɧɤɨɜɫɤɨɝɨ ɪɟɡɨɧɚɧɫɚ & ω − kv& = 0 , ɢɥɢ, ɞɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɡɚɬɭɯɚɧɢɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ ɤɨɥɢɱɟɫɬɜɚ ɱɚɫɬɢɰ, ɫɤɨɪɨɫɬɶ ɤɨɬɨɪɵɯ ɜɵɲɟ ɢɥɢ ɧɢɠɟ ɮɚɡɨɜɨɣ ɫɤɨɪɨɫɬɢ ɜɨɥɧɵ. ȿɫɥɢ
Ɋɢɫ. 4.22. Ɋɟɡɨɧɚɧɫɧɨɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɜɨɥɧ ɢ ɱɚɫɬɢɰ ɜ ɩɥɚɡɦɟ
Ɋɢɫ. 4.23. ɇɟɪɚɜɧɨɜɟɫɧɚɹ ɮɭɧɤɰɢɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɱɚɫɬɢɰ ɜ ɚɞɢɚɛɚɬɢɱɟɫɤɨɣ ɥɨɜɭɲɤɟ
ɩɨɫɥɟɞɧɢɯ ɛɨɥɶɲɟ, ɬɨ ɷɧɟɪɝɢɹ ɜɨɥɧɵ ɩɨɝɥɨɳɚɟɬɫɹ (§ 33). ɉɪɢ ɧɚɥɢɱɢɢ ɜ ɩɥɚɡɦɟ ɢɧɬɟɧɫɢɜɧɨɝɨ ɩɭɱɤɚ ɱɚɫɬɢɰ (ɫɦ. ɪɢɫ. 4.22, «ɝɨɪɛ» ɧɚ ɷɬɨɦ ɪɢɫɭɧɤɟ ɨɬɜɟɱɚɟɬ ɩɪɟɜɵɲɟɧɢɸ ɱɢɫɥɚ ɱɚɫɬɢɰ ɫ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɫɤɨɪɨɫɬɶɸ ɜ ɩɭɱɤɟ ɧɚɞ ɱɢɫɥɨɦ ɱɚɫɬɢɰ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɦɚɤɫɜɟɥɥɨɜɫɤɨɦɭ ɪɚɫɩɪɟɞɟɥɟɧɢɸ), ɡɚɬɭɯɚɧɢɟ ɪɟɡɨɧɚɧɫɧɨɣ ɜɨɥɧɵ ɦɨɠɟɬ ɫɦɟɧɢɬɶɫɹ ɪɚɫɤɚɱɤɨɣ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɝɨɜɨɪɹɬ ɨɛ ɨɛɪɚɬɧɨɦ ɦɟɯɚɧɢɡɦɟ ɩɨɝɥɨɳɟɧɢɹ Ʌɚɧɞɚɭ. ȿɫɥɢ ɫɤɨɪɨɫɬɶ ɱɚɫɬɢɰ ɩɭɱɤɚ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɚɹ, ɬɨ ɱɚɫɬɨɬɵ ɪɟɡɨɧɚɧɫɧɵɯ ɜɨɥɧ ɛɭɞɭɬ ɜɟɥɢɤɢ, ɚ ɞɥɢɧɵ ɜɨɥɧ – ɦɚɥɵ. ȼ ɷɬɨɦ ɨɬɧɨɲɟɧɢɢ ɬɚɤɢɟ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ, ɜ ɨɬɥɢɱɢɟ ɨɬ ɆȽȾɧɟɭɫɬɨɣɱɢɜɨɫɬɟɣ, ɩɪɟɢɦɭɳɟɫɬɜɟɧɧɨ ɦɟɥɤɨɦɚɫɲɬɚɛɧɵɟ ɢ, ɤɚɡɚɥɨɫɶ ɛɵ, ɧɟ ɦɨɝɭɬ ɩɪɢɜɨɞɢɬɶ ɤ ɝɥɨɛɚɥɶɧɵɦ ɩɨɫɥɟɞɫɬɜɢɹɦ. Ɇɵ ɭɠɟ ɡɧɚɟɦ, ɨɞɧɚɤɨ, ɱɬɨ ɧɚɥɢɱɢɟ ɢɧɬɟɧɫɢɜɧɵɯ ɲɭɦɨɜ ɜ ɩɥɚɡɦɟ ɦɨɠɟɬ ɩɪɢɜɨɞɢɬɶ ɤ ɷɮɮɟɤɬɢɜɧɨɦɭ ɭɜɟɥɢɱɟɧɢɸ ɱɚɫɬɨɬɵ ɫɬɨɥɤɧɨɜɟɧɢɣ ɱɚɫɬɢɰ (ɪɚɫɫɟɹɧɢɟ ɧɚ ɜɨɥɧɚɯ), ɜɵɡɵɜɚɸɳɟɦɭ ɚɧɨɦɚɥɶɧɵɟ ɷɮɮɟɤɬɵ ɜ ɩɪɨɰɟɫɫɚɯ ɩɟɪɟɧɨɫɚ: ɚɧɨɦɚɥɶɧɨ ɜɵɫɨɤɚɹ ɫɤɨɪɨɫɬɶ ɞɢɮɮɭɡɢɢ ɢ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ, ɚɧɨɦɚɥɶɧɨ ɛɨɥɶɲɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɩɥɚɡɦɵ ɢ ɬ.ɩ. ɂɬɚɤ, ɤɢɧɟɬɢɱɟɫɤɢɟ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɟɫɬɶ ɫɥɟɞɫɬɜɢɟ ɨɬɫɬɭɩɥɟɧɢɹ ɨɬ ɪɚɜɧɨɜɟɫɧɨɣ, ɦɚɤɫɜɟɥɥɨɜɫɤɨɣ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ. ɇɟɪɚɜɧɨɜɟɫɧɵɟ ɭɫɥɨɜɢɹ ɦɨɝɭɬ ɪɟɚɥɢɡɨɜɚɬɶɫɹ ɧɟ ɬɨɥɶɤɨ ɩɪɢ ɧɚɥɢɱɢɢ ɩɭɱɤɚ. ɇɚɩɪɢɦɟɪ, ɜ ɚɞɢɚɛɚɬɢɱɟɫɤɨɣ ɥɨɜɭɲɤɟ (§ 33) ɮɭɧɤɰɢɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ «ɨɛɟɞɧɹɟɬɫɹ» ɡɚ ɫɱɟɬ ɭɯɨɞɚ ɦɟɞɥɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɨɩɚɫɧɵɣ ɤɨɧɭɫ ɩɨɬɟɪɶ (ɪɢɫ. 4.23). ɗɬɨ ɫɨɡɞɚɟɬ ɛɥɚɝɨɩɪɢɹɬɧɵɟ ɭɫɥɨɜɢɹ
ɞɥɹ ɪɚɫɤɚɱɤɢ ɪɚɡɧɨɜɢɞɧɨɫɬɟɣ «ɤɨɧɭɫɧɵɯ» ɧɟɭɫɬɨɣɱɢɜɨɫɬɟɣ (ɧɚɩɪɢɦɟɪ, ɨɞɧɚ ɢɡ ɧɚɢɛɨɥɟɟ ɨɩɚɫɧɵɯ – ɞɪɟɣɮɨɜɨ–ɤɨɧɭɫɧɚɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ [12]), ɨɝɪɚɧɢɱɢɜɚɸɳɢɯ ɜɪɟɦɹ ɠɢɡɧɢ ɩɥɚɡɦɵ ɜ ɥɨɜɭɲɤɟ. ɉɪɢɱɢɧɨɣ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɦɨɠɟɬ ɛɵɬɶ ɢ ɧɚɥɢɱɢɟ ɩɨɬɨɤɨɜ ɩɥɚɡɦɵ, ɟɫɥɢ ɧɚɣɞɟɬɫɹ ɩɨɞɯɨɞɹɳɚɹ ɜɨɥɧɚ ɫ ɮɚɡɨɜɨɣ ɫɤɨɪɨɫɬɶɸ, ɛɥɢɡɤɨɣ ɤ ɫɤɨɪɨɫɬɢ ɩɨɬɨɤɚ. ɂɦɟɧɧɨ ɬɚɤɨɜɚ ɦɨɠɟɬ ɛɵɬɶ ɫɢɬɭɚɰɢɹ ɩɪɢ ɧɚɥɢɱɢɢ ɫɢɫɬɟɦɚɬɢɱɟɫɤɢɯ ɞɪɟɣɮɨɜɵɯ ɩɨɬɨɤɨɜ ɩɥɚɡɦɵ (§ 17). ɇɚɩɪɢɦɟɪ, ɫɤɨɪɨɫɬɶ ɥɚɪɦɨɪɨɜɫɤɨɝɨ ɞɪɟɣɮɚ, ɨɛɹɡɚɧɧɨɝɨ ɫɜɨɢɦ ɩɪɨɢɫɯɨɠɞɟɧɢɟɦ ɧɟɨɞɧɨɪɨɞɧɨɫɬɢ ɩɥɨɬɧɨɫɬɢ ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɵ, ɩɨ ɩɨɪɹɞɤɭ ɜɟɥɢɱɢɧɵ ɫɨɫɬɚɜɥɹɟɬ v ɞ ɪ ~ vT ρB L , ɝɞɟ L – ɯɚɪɚɤɬɟɪɧɵɣ ɪɚɡɦɟɪ ɧɟɨɞɧɨɪɨɞɧɨɫɬɢ. ɋ ɷɬɨɣ ɫɤɨɪɨɫɬɶɸ ɦɨɠɧɨ ɫɜɹɡɚɬɶ ɱɚɫɬɨɬɭ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɞɪɟɣɮɨɜɨɣ ɜɨɥɧɵ. ȿɫɥɢ, ɧɚɩɪɢɦɟɪ, B||z, ∇n||x, ɬɨ ɜɨɥɧɚ ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɨɫɢ y: ω = k y vɞ ɪ .
•
ɉɭɱɤɨɜɚɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ Ɉɞɧɢɦ ɢɯ ɩɪɨɫɬɟɣɲɢɯ ɩɪɢɦɟɪɨɜ ɤɢɧɟɬɢɱɟɫɤɨɣ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɹɜɥɹɟɬɫɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ ɩɭɱɤɚ ɷɥɟɤɬɪɨɧɨɜ, ɩɪɨɧɢɡɵɜɚɸɳɟɝɨ ɩɥɚɡɦɭ. Ɋɚɫɫɦɨɬɪɢɦ ɧɚɢɛɨɥɟɟ ɩɪɨɫɬɨɣ ɫɥɭɱɚɣ ɪɚɫɤɚɱɤɢ ɩɪɨɞɨɥɶɧɵɯ ɜɨɥɧ, ɤɨɝɞɚ ɱɟɪɟɡ ɯɨɥɨɞɧɭɸ ɩɥɚɡɦɭ (Te→0, Ti→0) noi=noe=no, ɩɪɨɯɨɞɢɬ ɯɨɥɨɞɧɵɣ ɩɭɱɨɤ ɷɥɟɤɬɪɨɧɨɜ (vno≠0, nno≠0) ɦɚɥɨɣ ɩɥɨɬɧɨɫɬɢ. Ⱦɢɫɩɟɪɫɢɨɧɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɷɬɨɝɨ ɫɥɭɱɚɹ ɡɚɩɢɫɵɜɚɟɬɫɹ ɜ ɜɢɞɟ: ω2 +ω2 ωn2 ε = 1 − Le 2 Li − =0. (4.94) ω ( ω − kv no )2 ɉɟɪɜɵɟ ɞɜɚ ɫɥɚɝɚɟɦɵɯ ɡɞɟɫɶ ɨɬɜɟɱɚɸɬ ɯɨɥɨɞɧɨɣ ɩɥɚɡɦɟ (ɫɦ. § 29), ɚ ɩɨɫɥɟɞɧɟɟ ɨɩɢɫɵɜɚɟɬ ɜɤɥɚɞ ɯɨɥɨɞɧɨɝɨ ɩɭɱɤɚ ɷɥɟɤɬɪɨɧɨɜ. Ɂɞɟɫɶ ωLe, ωLi ɢ ωɩ – ɥɟɧɝɦɸɪɨɜɫɤɢɟ ɱɚɫɬɨɬɵ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɩɥɚɡɦɵ, ɢɨɧɨɜ ɩɥɚɡɦɵ ɢ ɷɥɟɤɬɪɨɧɨɜ ɩɭɱɤɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, vɩ – ɫɤɨɪɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ɩɭɱɤɚ.
ɗɬɨ ɩɨɥɧɨɟ ɭɪɚɜɧɟɧɢɟ 4-ɣ ɫɬɟɩɟɧɢ, ɩɪɢɜɨɞɢɦɨɟ ɤ ɤɚɧɨɧɢɱɟɫɤɨɣ ɮɨɪɦɟ. ɉɪɢɛɥɢɠɟɧɧɨɟ ɪɟɲɟɧɢɟ ɟɝɨ ɛɵɥɨ ɩɪɟɞɥɨɠɟɧɨ ə.Ɏɟɣɧɛɟɪɝɨɦ ɢɡ ɞɨɜɨɥɶɧɨ ɧɚɝɥɹɞɧɵɯ ɮɢɡɢɱɟɫɤɢɯ ɫɨɨɛɪɚɠɟɧɢɣ. ɂɡɜɟɫɬɧɨ, ɱɬɨ ɩɪɢ ɩɪɨɯɨɠɞɟɧɢɢ ɩɭɱɤɚ ɱɟɪɟɡ ɩɥɚɡɦɭ ɜɨɡɧɢɤɚɸɬ (ɬɨɱɧɟɟ, ɦɨɝɭɬ ɜɨɡɧɢɤɚɬɶ ɩɪɢ ɨɩɪɟɞɟɥɟɧɧɵɯ ɭɫɥɨɜɢɹɯ) ɤɨɥɟɛɚɧɢɹ ɫ ɧɚɪɚɫɬɚɸɳɟɣ ɜɨ ɜɪɟɦɟɧɢ ɚɦɩɥɢɬɭɞɨɣ. Ɋɚɡɜɢɜɚɟɬɫɹ ɬɚɤ ɧɚɡɵɜɚɟɦɚɹ ɩɭɱɤɨɜɚɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ. Ɉɧɚ ɹɜɥɹɟɬɫɹ ɱɚɫɬɧɵɦ ɫɥɭɱɚɟɦ ɧɟɭɫɬɨɣɱɢɜɨɫɬɟɣ, ɨɛɭɫɥɨɜɥɟɧɧɵɯ ɧɚɥɢɱɢɟɦ ɭɱɚɫɬɤɨɜ ɫ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɩɪɨɢɡɜɨɞɧɨɣ ɱɚɫɬɢ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ. ɂɡ ɪɢɫ. 4.22 ɜɢɞɧɨ, ɱɬɨ ɫ ɜɨɥɧɨɣ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ ɱɚɫɬɢɰɵ ɩɥɚɡɦɵ, ɫɤɨɪɨɫɬɶ ɤɨɬɨɪɵɯ ɛɥɢɡɤɚ ɤ ɫɤɨɪɨɫɬɢ ɜɨɥɧɵ vɮ2. Ʉɚɠɟɬɫɹ, ɜɨɡɧɢɤɚɟɬ ɩɪɨɬɢɜɨɪɟɱɢɟ: ɫɧɚɱɚɥɚ ɩɪɢɧɹɥɢ Ɍe→0, ɚ ɬɟɩɟɪɶ ɞɨɥɠɧɵ ɩɪɢɧɹɬɶ, ɱɬɨ ɱɚɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ɩɥɚɡɦɵ ɢɦɟɸɬ ɬɟɩɥɨɜɭɸ ɫɤɨɪɨɫɬɶ, ɛɥɢɡɤɭɸ ɤ ɮɚɡɨɜɨɣ ɫɤɨɪɨɫɬɢ ɜɨɥɧɵ. ɇɨ ɭɫɥɨɜɢɟ Ɍe→0 ɟɳɟ ɧɟ ɡɧɚɱɢɬ, ɱɬɨ ɬɟɦɩɟɪɚɬɭɪɚ ɬɨɠɞɟɫɬɜɟɧɧɨ ɪɚɜɧɚ ɧɭɥɸ (ɬɚɤɨɝɨ ɧɟ ɛɵɜɚɟɬ), ɚ ɨɛɨɡɧɚɱɚɟɬ ɬɨɥɶɤɨ, ɱɬɨ ɫɤɨɪɨɫɬɢ, ɩɪɢɨɛɪɟɬɚɟɦɵɟ ɜ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɨɥɹɯ, ɦɧɨɝɨ ɛɨɥɶɲɟ ɬɟɩɥɨɜɵɯ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɪɨɬɢɜɨɪɟɱɢɹ ɧɟɬ. Ɉɞɧɚɤɨ ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ ɩɪɟɧɟɛɪɟɠɟɦ ɜɤɥɚɞɨɦ ω Li << ω Le , ɢ ɛɭɞɟɦ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɩɪɟɞɩɨɥɨɠɟɧɢɸ, ɩɥɨɬɧɨɫɬɶ ɩɭɱɤɚ ɦɚɥɚ, nn<<no, ɬɨ ɩɪɢɦɟɦ ω ≅ ω Le + δω ≅ kv no + δω , |δω| << ω Le . 2
2
ω → ωɩ → kv no .
ɉɨɞɫɬɚɜɥɹɹ ɷɬɨ ɜ (4.94) ɢ ɪɚɡɥɚɝɚɹ ɜ ɪɹɞ ɩɨ ɦɚɥɨɣ ɜɟɥɢɱɢɧɟ, ɩɨɥɭɱɢɦ 1 − 2
Ɍɚɤ ɤɚɤ, ɩɨ (4.95)
δω ω n2 + =1, ω Le δω 2
ɬ.ɟ. ɤɭɛɢɱɟɫɤɨɟ ɭɪɚɜɧɟɧɢɟ
2δω 3 − ω n2ω Le = 0 .
(4.96) ɗɬɨ ɭɪɚɜɧɟɧɢɟ ɜɫɟɝɞɚ ɢɦɟɟɬ ɪɟɲɟɧɢɟ ɫ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɦɧɢɦɨɣ ɱɚɫɬɶɸ, ɱɬɨ ɢ ɞɚɟɬ ɜɟɥɢɱɢɧɭ ɢɧɤɪɟɦɟɧɬɚ (ɫɤɨɪɨɫɬɢ ɪɨɫɬɚ) ɜɨɡɦɭɳɟɧɢɣ:
§1 · δω = iγ , γ ≅ ¨ ω n2ω Le ¸ ©2 ¹
1/ 3
§n · = ω Le ¨ no ¸ © no ¹
1/ 3
.
&
(4.97)
&
&
ɉɨɫɤɨɥɶɤɭ ɜɨɡɦɭɳɟɧɢɹ ɜɫɟɯ ɜɟɥɢɱɢɧ ( ne , v e , nn , v n , E ) ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵ
&&
e − iωt +ikr , ɬɨ
γt
ɨɧɢ ɛɭɞɭɬ ɭɜɟɥɢɱɢɜɚɬɶɫɹ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ e . ȼɟɥɢɱɢɧɚ γ ɧɚɡɵɜɚɟɬɫɹ ɢɧɤɪɟɦɟɧɬɨɦ ɢ ɨɩɪɟɞɟɥɹɟɬ ɫɤɨɪɨɫɬɶ ɧɚɪɚɫɬɚɧɢɹ ɚɦɩɥɢɬɭɞɵ ɜɨɥɧɵ ɜɨ ɜɪɟɦɟɧɢ. Ɂɚɦɟɬɢɦ ɬɚɤɠɟ, ɱɬɨ ɜɨɡɦɭɳɟɧɢɹ ɞɥɹ ɷɬɨɣ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɹɜɥɹɸɬɫɹ ɫɧɨɫɨɜɵɦɢ (ɭɜɥɟɤɚɸɬɫɹ ɩɭɱɤɨɦ), ɬɚɤ ɤɚɤ ɪɟɲɟɧɢɟ ɢɦɟɟɬ ɧɟɧɭɥɟɜɭɸ ɞɟɣɫɬɜɢɬɟɥɶɧɭɸ ɱɚɫɬɶ ɱɚɫɬɨɬɵ. ȼɚɠɧɨ ɨɬɦɟɬɢɬɶ ɬɚɤɠɟ, ɱɬɨ ɢɡɥɨɠɟɧɧɨɟ ɩɪɢɛɥɢɠɟɧɧɨɟ ɪɟɲɟɧɢɟ ɩɨɡɜɨɥɹɟɬ ɨɰɟɧɢɬɶ ɥɢɲɶ ɜɟɥɢɱɢɧɭ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɢɧɤɪɟɦɟɧɬɚ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ. Ɇɟɠɞɭ ɬɟɦ, ɭɠɟ ɢɡ ɫɚɦɨɝɨ ɭɪɚɜɧɟɧɢɹ (4.94) ɨɱɟɜɢɞɧɨ, ɱɬɨ ɤɨɪɨɬɤɢɟ ɜɨɥɧɵ, ɞɥɹ ɤɨɬɨɪɵɯ | k| >> ω Le v no , ɪɚɫɤɚɱɢɜɚɬɶɫɹ ɧɟ ɦɨɝɭɬ. Ⱦɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ ɢɦɟɟɬ ɤɨɪɨɬɤɨɜɨɥɧɨɜɵɣ ɩɨɪɨɝ, ɤɚɤ ɦɨɠɧɨ ɩɨɤɚɡɚɬɶ, ɪɚɜɧɵɣ
[
| k ɩɨ ɪ ɨɝ | = 2( ω Le v no ) 1 + ( nn n0 )
]
23 32
≅ 2( ω Le v no ) .
(4.98)
ɉɨɪɨɝ, ɤɚɤ ɦɵ ɜɢɞɢɦ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɟɥɢɱɢɧɨɣ ɮɨɪɦɚɥɶɧɨ ɩɨɯɨɠɟɣ ɧɚ ɞɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ, ɨɞɧɚɤɨ ɜɦɟɫɬɨ ɬɟɩɥɨɜɨɣ ɫɤɨɪɨɫɬɢ, ɤɨɬɨɪɚɹ ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ ɪɚɜɧɚ ɧɭɥɸ, ɜɯɨɞɢɬ ɫɤɨɪɨɫɬɶ ɱɚɫɬɢɰ ɩɭɱɤɚ.
Ⱦɥɹ ɞɪɭɝɢɯ ɩɭɱɤɨɜɵɯ ɧɟɭɫɬɨɣɱɢɜɨɫɬɟɣ ɢɧɤɪɟɦɟɧɬɵ ɛɭɞɭɬ ɞɪɭɝɢɦɢ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɛɭɧɟɦɚɧɨɜɫɤɨɣ (ɬɨɤɨɜɨɣ) ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ, ɨɩɢɫɵɜɚɟɦɨɣ ɫɯɨɞɧɵɦ ɫ (4.94) ɭɪɚɜɧɟɧɢɟɦ
ω Le2
ω Li2 ε = 1− − = 0, ( ω − kv eo )2 ω 2
(4.99)
ɦɚɤɫɢɦɚɥɶɧɵɣ ɢɧɤɪɟɦɟɧɬ, ɤɚɤ ɦɨɠɧɨ ɩɨɤɚɡɚɬɶ, ɛɭɞɟɬ ɡɚɜɢɫɟɬɶ ɨɬ ɨɬɧɨɲɟɧɢɹ ɦɚɫɫ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ 1/ 3
§m · γ ≈ ω Le ¨ e ¸ . (4.100) © mi ¹ ɗɬɚ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ ɬɚɤɠɟ ɩɨɪɨɝɨɜɚɹ, ɨɞɧɚɤɨ, ɜ ɨɬɥɢɱɢɟ ɨɬ ɩɪɟɞɵɞɭɳɟɝɨ ɫɥɭɱɚɹ, ɫɧɨɫɚ ɧɟɬ ɢ ɮɚɤɬɢɱɟɫɤɢ ɷɬɨ ɫɬɨɹɱɢɟ ɚɩɟɪɢɨɞɢɱɟɫɤɢ ɧɚɪɚɫɬɚɸɳɢɟ ɜɨɡɦɭɳɟɧɢɹ. ɉɪɢ ɧɚɥɢɱɢɢ ɩɭɱɤɨɜ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɜɫɟɝɞɚ ɢɦɟɸɬ ɜɨɡɦɨɠɧɨɫɬɶ ɪɚɡɜɢɜɚɬɶɫɹ, ɟɫɬɟɫɬɜɟɧɧɨ, ɩɪɢ ɭɫɥɨɜɢɢ ɩɪɟɨɞɨɥɟɧɢɹ ɩɨɪɨɝɚ, ɟɫɥɢ ɜ ɫɩɟɤɬɪɟ ɲɭɦɨɜ ɩɥɚɡɦɵ ɧɚɣɞɟɬɫɹ ɜɨɡɦɭɳɟɧɢɟ ɫ ɩɨɞɯɨɞɹɳɟɣ ɞɥɢɧɨɣ ɜɨɥɧɵ.
ȽɅȺȼȺ 5 ɗɅȿɄɌɊɈɇɇȺə ɂ ɂɈɇɇȺə ɈɉɌɂɄȺ §38. Ⱥɧɚɥɨɝɢɹ ɫɜɟɬɨɜɨɣ ɢ ɷɥɟɤɬɪɨɧɧɨɣ ɨɩɬɢɤɢ Ɏɢɡɢɱɟɫɤɢɦ ɨɛɨɫɧɨɜɚɧɢɟɦ ɜɨɡɦɨɠɧɨɫɬɢ ɩɨɫɬɪɨɟɧɢɹ ɚɧɚɥɨɝɢɢ ɩɪɨɯɨɠɞɟɧɢɹ ɷɥɟɤɬɪɨɧɧɨɝɨ ɥɭɱɚ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ ɫ ɩɨɫɬɟɩɟɧɧɨ ɢɡɦɟɧɹɸɳɢɦɫɹ ɩɨɬɟɧɰɢɚɥɨɦ ɢ ɩɪɨɯɨɠɞɟɧɢɹ ɫɜɟɬɨɜɨɝɨ ɥɭɱɚ ɱɟɪɟɡ ɫɪɟɞɭ ɫ ɢɡɦɟɧɹɸɳɢɦɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɩɪɟɥɨɦɥɟɧɢɹ (ɨɩɬɢɤɨ-ɦɟɯɚɧɢɱɟɫɤɚɹ ɚɧɚɥɨɝɢɹ) ɹɜɥɹɟɬɫɹ ɨɛɳɟɟ ɫɯɨɞɫɬɜɨ ɦɟɠɞɭ ɨɛɵɱɧɨɣ ɦɟɯɚɧɢɤɨɣ ɢ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɨɩɬɢɤɨɣ. ɂ ɞɥɹ ɞɜɢɠɟɧɢɹ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ ɢ ɞɥɹ ɫɜɟɬɨɜɨɝɨ ɥɭɱɚ ɢɡɜɟɫɬɟɧ ɜɚɪɢɚɰɢɨɧɧɵɣ t1
ɩɪɢɧɰɢɩ Ƚɚɦɢɥɶɬɨɧɚ: δ ³ Ldt = 0 , ɝɞɟ t0 ɢ t1 ɜɪɟɦɹ ɜ ɧɚɱɚɥɶɧɨɣ ɢ ɤɨɧɟɱɧɨɣ t0
ɬɨɱɤɚɯ ɬɪɚɟɤɬɨɪɢɢ, L(q, q ,t) – ɮɭɧɤɰɢɹ Ʌɚɝɪɚɧɠɚ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɨɛɨɛɳɟɧɧɵɯ ɤɨɨɪɞɢɧɚɬ, ɫɤɨɪɨɫɬɟɣ ɢ ɜɪɟɦɟɧɢ. Ɋɚɜɟɧɫɬɜɨ ɧɭɥɸ ɜɚɪɢɚɰɢɢ ɢɧɬɟɝɪɚɥɚ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɷɬɨɬ ɢɧɬɟɝɪɚɥ, ɜɡɹɬɵɣ ɜɞɨɥɶ ɞɟɣɫɬɜɢɬɟɥɶɧɨɣ ɬɪɚɟɤɬɨɪɢɢ, ɢɦɟɟɬ ɷɤɫɬɪɟɦɭɦ (ɦɢɧɢɦɭɦ) ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɞɪɭɝɢɦɢ ɜɨɡɦɨɠɧɵɦɢ ɜɢɪɬɭɚɥɶɧɵɦɢ ɬɪɚɟɤɬɨɪɢɹɦɢ (ɪɢɫ. 5.1). Ɏɭɧɤɰɢɹ Ʌɚɝɪɚɧɠɚ ɞɥɹ ɦɚɬɟɪɢɚɥɶɧɨɣ ɱɚɫɬɢɰɵ ɪɚɜɧɚ ɪɚɡɧɨɫɬɢ ɦɟɠɞɭ ɤɢɧɟɬɢɱɟɫɤɨɣ ɢ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɟɣ L = T – U, ɞɥɹ ɷɥɟɤɬɪɨɧɚ, ɞɜɢɠɭɳɟɝɨɫɹ ɜ ɱɢɫɬɨ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɦ ɩɨɥɟ L = mv2/2 – (-eϕ). ȼ Ɋɢɫ. 5.1. Ⱦɟɣɫɬɜɢɬɟɥɶɧɚɹ ɢ & ɩɪɢɫɭɬɫɬɜɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ B ɮɭɧɤɰɢɹ ɜɢɪɬɭɚɥɶɧɚɹ ɬɪɚɟɤɬɨɪɢɹ && & ɱɚɫɬɢɰɵ Ʌɚɝɪɚɧɠɚ L = mv2/2 – (-eϕ) + (-e Av /c), ɝɞɟ A & & ɜɟɤɬɨɪɧɵɣ ɩɨɬɟɧɰɢɚɥ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ: B = rot A . ȿɫɥɢ ɜɜɟɫɬɢ ɨɛɨɛɳɟɧɧɵɣ & & & e & ɢɦɩɭɥɶɫ P = p − Al , ɝɞɟ l - ɟɞɢɧɢɱɧɵɣ ɜɟɤɬɨɪ, ɧɚɩɪɚɜɥɟɧɧɵɣ ɩɨ ɤɚɫɚɬɟɥɶɧɨɣ c ɤ ɬɪɚɟɤɬɨɪɢɢ, ɬɨ ɜɚɪɢɚɰɢɨɧɧɵɣ ɩɪɢɧɰɢɩ Ƚɚɦɢɥɶɬɨɧɚ δS = 0, ɧɚɡɵɜɚɟɦɵɣ ɩɪɢɧɰɢɩɨɦ ɧɚɢɦɟɧɶɲɟɝɨ ɞɟɣɫɬɜɢɹ ɢɥɢ ɩɪɢɧɰɢɩɨɦ Ɇɨɩɟɪɬɸɢ (ɢɧɬɟɝɪɚɥ t1
S = ³ Ldt ɧɚɡɵɜɚɟɬɫɹ ɢɧɬɟɝɪɚɥɨɦ ɞɟɣɫɬɜɢɟɦ, ɢɥɢ ɩɪɨɫɬɨ ɞɟɣɫɬɜɢɟɦ) ɦɨɠɧɨ t0
B
& & ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ: δ ³ Pdl = 0 . ɗɬɨɬ ɩɪɢɧɰɢɩ ɚɧɚɥɨɝɢɱɟɧ ɩɪɢɧɰɢɩɭ Ɏɟɪɦɚ A
B
ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ
ɨɩɬɢɤɢ:
δ ³ ndl = 0 ,
ɤɨɬɨɪɵɣ
ɨɡɧɚɱɚɟɬ
ɦɢɧɢɦɚɥɶɧɨɫɬɶ
A
B
ɨɩɬɢɱɟɫɤɨɣ ɞɥɢɧɵ ɧɚ ɪɟɚɥɶɧɨɦ ɩɭɬɢ ɫɜɟɬɚ. Ɍɨ ɟɫɬɶ ɨɩɬɢɱɟɫɤɢɣ ɩɭɬɶ
³ ndl ɞɥɹ A
ɫɜɟɬɨɜɨɝɨ ɥɭɱɚ – ɫɚɦɵɣ ɤɨɪɨɬɤɢɣ, ɝɞɟ n – ɩɨɤɚɡɚɬɟɥɶ ɩɪɟɥɨɦɥɟɧɢɹ ɫɪɟɞɵ, dl – ɷɥɟɦɟɧɬ ɬɪɚɟɤɬɨɪɢɢ ɥɭɱɚ. ȿɫɥɢ n = const, ɬɨ ɩɪɟɥɨɦɥɟɧɢɟ ɥɭɱɚ ɨɬɫɭɬɫɬɜɭɟɬ ɢ ɫɜɟɬ ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ ɩɪɹɦɨɥɢɧɟɣɧɨ. ɂɡ ɩɪɢɧɰɢɩɚ Ɏɟɪɦɚ ɜɵɬɟɤɚɟɬ ɢɡɜɟɫɬɧɵɣ ɡɚɤɨɧ ɩɪɟɥɨɦɥɟɧɢɹ ɋɧɟɥɥɢɭɫɚ, ɤɨɬɨɪɵɣ ɡɚɞɚɟɬ ɫɨɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ ɭɝɥɨɦ
ɩɚɞɟɧɢɹ α ɢ ɭɝɥɨɦ ɩɪɟɥɨɦɥɟɧɢɹ β (ɭɝɥɵ ɦɟɠɞɭ ɥɭɱɨɦ ɢ ɧɨɪɦɚɥɶɸ ɤ ɝɪɚɧɢɰɟ sin α n2 ɪɚɡɞɟɥɚ): , ɝɞɟ n1 ɢ n2 – ɤɨɷɮɮɢɰɢɟɧɬɵ ɩɪɟɥɨɦɥɟɧɢɹ ɫɪɟɞ [27]. = sin β n1 ȼ ɫɥɭɱɚɟ ɷɥɟɤɬɪɨɧɨɜ ɢɯ ɤɨɦɩɨɧɟɧɬɚ ɫɤɨɪɨɫɬɢ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɚɹ ɷɥɟɤɬɪɢɱɟɫɤɨɦɭ ɩɨɥɸ, ɧɟ ɦɟɧɹɟɬɫɹ, ɚ ɦɨɞɭɥɶ ɫɤɨɪɨɫɬɢ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ U , ɝɞɟ U – ɩɨɬɟɧɰɢɚɥ ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɨɱɤɢ, ɜ ɤɨɬɨɪɨɣ ɫɤɨɪɨɫɬɶ ɷɥɟɤɬɪɨɧɚ ɪɚɜɧɚ ɧɭɥɸ. ɉɨɷɬɨɦɭ ɜ ɷɥɟɤɬɪɨɧɧɨɣ ɨɩɬɢɤɟ U ɢɝɪɚɟɬ ɪɨɥɶ ɩɨɤɚɡɚɬɟɥɹ ɩɪɟɥɨɦɥɟɧɢɹ ɫɪɟɞɵ, ɚ ɡɚɤɨɧ ɩɪɟɥɨɦɥɟɧɢɹ ɢɦɟɟɬ ɜɢɞ: U2 sin α , (5.1) = sin β U1 ɟɫɥɢ ɫɱɢɬɚɬɶ, ɱɬɨ ɧɚ ɝɪɚɧɢɰɟ ɪɚɡɞɟɥɚ ɩɨɬɟɧɰɢɚɥ ɫɤɚɱɤɨɦ ɦɟɧɹɟɬɫɹ ɨɬ U1 ɞɨ U2. Ɋɟɡɤɢɣ ɫɤɚɱɨɤ ɩɨɬɟɧɰɢɚɥɚ ɧɚ ɩɭɬɢ ɷɥɟɤɬɪɨɧɧɨɝɨ ɩɭɱɤɚ ɦɨɠɧɨ ɫɨɡɞɚɬɶ ɦɟɠɞɭ ɞɜɭɯ ɦɟɬɚɥɥɢɱɟɫɤɢɯ ɫɟɬɨɤ ɫ ɦɟɥɤɢɦɢ ɹɱɟɣɤɚɦɢ ɧɚ ɛɥɢɡɤɨɦ ɪɚɫɫɬɨɹɧɢɢ ɞɪɭɝ ɨɬ ɞɪɭɝɚ, ɧɚ ɤɨɬɨɪɵɟ ɩɨɞɚɧɵ ɧɚɩɪɹɠɟɧɢɹ U1 ɢ U2 (ɪɢɫ. 5.2). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɩɨ ɚɧɚɥɨɝɢɢ ɫɨ ɫɜɟɬɨɜɨɣ ɨɩɬɢɤɨɣ ɦɨɠɧɨ ɝɨɜɨɪɢɬɶ ɨɛ ɷɥɟɤɬɪɨɧɧɵɯ ɥɭɱɚɯ, ɚ ɬɚɤɠɟ Ɋɢɫ. 5.2. ɉɪɟɥɨɦɥɟɧɢɟ ɩɭɱɤɚ ɡɚɪɹɠɟɧɧɵɯ ɨɩɪɟɞɟɥɢɬɶ ɭɫɥɨɜɢɟ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɱɚɫɬɢɰ ɧɚ ɝɪɚɧɢɰɟ ɩɨɬɟɧɰɢɚɥɨɜ (a) ɢ ɫɜɟɬɚ ɨɩɬɢɤɢ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ: ɞɥɢɧɚ ɜɨɥɧɵ ɧɚ ɝɪɚɧɢɰɟ ɞɜɭɯ ɫɪɟɞ (ɛ) 12.25 h ɷɥɟɤɬɪɨɧɚ λ[ A ] = ɦɚɥɚ ≈ mv U [ ɷȼ] ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɯɚɪɚɤɬɟɪɧɵɦ ɪɚɡɦɟɪɨɦ ɧɟɨɞɧɨɪɨɞɧɨɫɬɟɣ ɫɢɫɬɟɦɵ, ɬ. ɟ. ɷɥɟɤɬɪɨɧ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɱɚɫɬɢɰɭ. ɇɨ ɭ ɷɥɟɤɬɪɨɧɧɨɣ ɨɩɬɢɤɢ ɟɫɬɶ ɢ ɫɭɳɟɫɬɜɟɧɧɵɟ ɨɬɥɢɱɢɹ ɨɬ ɫɜɟɬɨɜɨɣ, ɨɧɢ ɜ ɨɫɧɨɜɧɨɦ ɫɨɫɬɨɹɬ ɜ ɫɥɟɞɭɸɳɟɦ: 1. Ɉɬɞɟɥɶɧɵɟ ɥɭɱɢ ɜ ɫɜɟɬɨɜɨɣ ɨɩɬɢɤɟ ɧɟɡɚɜɢɫɢɦɵ – ɷɥɟɤɬɪɨɧɧɵɟ ɥɭɱɢ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ ɞɪɭɝ ɫ ɞɪɭɝɨɦ. 2. ɉɨɤɚɡɚɬɟɥɶ ɩɪɟɥɨɦɥɟɧɢɹ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɜɫɟɝɞɚ ɧɟɩɪɟɪɵɜɟɧ, ɞɥɹ ɫɜɟɬɚ ɨɧ, ɤɚɤ ɩɪɚɜɢɥɨ, ɦɟɧɹɟɬɫɹ ɫɤɚɱɤɨɦ. 3. Ⱦɢɚɩɚɡɨɧ ɢɡɦɟɧɟɧɢɹ ɩɨɤɚɡɚɬɟɥɹ ɩɪɟɥɨɦɥɟɧɢɹ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɧɟ ɨɝɪɚɧɢɱɟɧ, ɜ ɨɩɬɢɤɟ n ≤ 2.5. 4. ɋɤɨɪɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ɬɟɦ ɛɨɥɶɲɟ, ɱɟɦ ɛɨɥɶɲɟ ɩɨɤɚɡɚɬɟɥɶ ɩɪɟɥɨɦɥɟɧɢɹ, ɚ ɫɤɨɪɨɫɬɶ ɫɜɟɬɚ ɧɚɨɛɨɪɨɬ. 5. ɉɪɟɥɨɦɥɹɸɳɢɟ ɩɨɜɟɪɯɧɨɫɬɢ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ, ɜ ɨɬɥɢɱɢɟ ɨɬ ɫɜɟɬɨɜɵɯ ɥɭɱɟɣ, ɧɟ ɦɨɝɭɬ ɛɵɬɶ ɩɪɨɢɡɜɨɥɶɧɵɦɢ – ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɨɜ ɜɫɟɝɞɚ ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɪɚɜɧɟɧɢɸ Ʌɚɩɥɚɫɚ (ɥɢɧɟɣɧɚɹ ɷɥɟɤɬɪɨɧɧɚɹ ɨɩɬɢɤɚ) ɢɥɢ ɉɭɚɫɫɨɧɚ (ɧɟɥɢɧɟɣɧɚɹ ɷɥɟɤɬɪɨɧɧɚɹ ɨɩɬɢɤɚ). §39. ɗɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɢɟ ɥɢɧɡɵ
Ⱦɜɢɠɟɧɢɟ ɷɥɟɤɬɪɨɧɨɜ, ɡɚɜɢɫɹɳɟɟ ɨɬ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ, ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɜɨɡɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɥɢɲɶ ɱɢɫɥɟɧɧɵɦɢ ɦɟɬɨɞɚɦɢ. Ɉɞɧɚɤɨ ɜ ɨɬɞɟɥɶɧɵɯ ɫɥɭɱɚɹɯ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨɬɟɧɰɢɚɥɚ ɜɨɡɦɨɠɧɨ ɚɧɚɥɢɬɢɱɟɫɤɨɟ ɪɟɲɟɧɢɟ, ɧɚɩɪɢɦɟɪ, ɜ ɫɥɭɱɚɟ ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɨɝɨ
ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨɬɟɧɰɢɚɥ U(z,r) ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɚɡɢɦɭɬɚɥɶɧɨɝɨ ɭɝɥɚ θ. Ɍɚɤ ɤɚɤ U(z,-r) = U(z,r), ɬɨ ɜ ɪɚɡɥɨɠɟɧɢɢ U ɩɨ ɫɬɟɩɟɧɹɦ r ɛɭɞɭɬ ɬɨɥɶɤɨ ɱɟɬɧɵɟ ɫɬɟɩɟɧɢ: U(z,r) = b0(z) + b2(z)r2 + b4(z)r4 + … + b2k(z)r2k + …
(5.2)
ɉɨɞɫɬɚɜɥɹɹ ɷɬɨ ɜɵɪɚɠɟɧɢɟ ɜ ɭɪɚɜɧɟɧɢɟ Ʌɚɩɥɚɫɚ (ɧɟɬ ɡɚɪɹɞɨɜ ɜ ɩɪɨɦɟɠɭɬɤɟ) ɜ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ: ∂ 2U 1 ∂U ∂ 2U + + 2 =0 ∂r 2 r ∂r ∂z
(5.3)
∂ 2U = 0 ), ɦɨɠɧɨ ɧɚɣɬɢ ɤɨɷɮɮɢɰɢɟɧɬɵ ∂θ 2 ɪɚɡɥɨɠɟɧɢɹ, ɩɨɥɭɱɢɜ ɜ ɢɬɨɝɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɜ ɜɢɞɟ:
(ɭɪɚɜɧɟɧɢɟ ɭɩɪɨɳɟɧɨ ɫ ɭɱɟɬɨɦ
r U (2k ) ( z) 1 r + ... , U ( z , r ) = U ( z ) − ( ) 2 U '' ( z ) + 2 ( ) 4 U IV ( z ) + ... + (−1) k 2 ( k !) 2 2 2 k 2 2
(5.4)
ɤɨɬɨɪɨɟ ɩɨɥɧɨɫɬɶɸ ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ ɩɨɬɟɧɰɢɚɥɚ ɧɚ ɨɫɢ ɫɢɫɬɟɦɵ U(z) = U(0,z). ɗɬɨ ɫɢɥɶɧɨ ɭɩɪɨɳɚɟɬ ɪɚɫɱɟɬ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ. Ⱦɥɹ ɩɪɢɨɫɟɜɵɯ ɷɥɟɤɬɪɨɧɨɜ (r2/L2ɯɚɪ<< r/Lɯɚɪ, ɝɞɟ Lɯɚɪ – ɯɚɪɚɤɬɟɪɧɚɹ ɞɥɢɧɚ ɫɢɫɬɟɦɵ), ɤɨɬɨɪɵɟ ɟɳɟ ɧɚɡɵɜɚɸɬ ɩɚɪɚɤɫɢɚɥɶɧɵɦɢ, ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɭɪɚɜɧɟɧɢɟ ɬɪɚɟɤɬɨɪɢɢ. Ⱦɥɹ ɷɬɨɝɨ ɜ ɪɚɫɩɪɟɞɟɥɟɧɢɢ ɩɨɬɟɧɰɢɚɥɚ ɩɪɟɧɟɛɪɟɝɚɟɦ ɫɥɚɝɚɟɦɵɦɢ ɫɨ ɫɬɟɩɟɧɹɦɢ r, ɬɨɝɞɚ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɧɚ: m z = -eEz = eU´(z) ɢ m r = -eEr = -erU´´(z).
(5.5)
ɉɨɫɥɟɞɧɟɟ ɭɪɚɜɧɟɧɢɟ ɡɚɦɟɱɚɬɟɥɶɧɨ ɬɟɦ, ɱɬɨ ɜ ɩɨɥɹɯ ɫ ɚɤɫɢɚɥɶɧɨɣ ɫɢɦɦɟɬɪɢɟɣ ɪɚɞɢɚɥɶɧɚɹ ɮɨɤɭɫɢɪɭɸɳɚɹ ɢɥɢ ɪɚɫɮɨɤɭɫɢɪɭɸɳɚɹ ɫɢɥɚ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɭɞɚɥɟɧɢɸ ɱɚɫɬɢɰɵ ɨɬ ɨɫɢ. ɍɱɢɬɵɜɚɹ, ɱɬɨ ɥɟɜɵɟ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ ɫɨɞɟɪɠɚɬ ɩɪɨɢɡɜɨɞɧɵɟ ɩɨ ɜɪɟɦɟɧɢ, ɚ ɩɪɚɜɵɟ ɩɪɨɢɡɜɨɞɧɵɟ ɩɨ z, ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ d 2 z 1 d dz 2 = ( ) . Ɍɨɝɞɚ, ɢɧɬɟɝɪɢɪɭɹ ɩɟɪɟɯɨɞ ɤ ɩɪɨɢɡɜɨɞɧɨɣ ɩɨ ɩɟɪɟɦɟɧɧɨɣ z: dt 2 2 dz dt ɩɟɪɜɨɟ ɭɪɚɜɧɟɧɢɟ ɫ ɭɱɟɬɨɦ ɝɪɚɧɢɱɧɨɝɨ ɭɫɥɨɜɢɹ ɩɪɢ z = 0 U(z) = 0 ɢ dz/dt0 = 0 (ɩɪɟɧɟɛɪɟɝɚɟɦ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɶɸ ɱɚɫɬɢɰ), ɩɨɥɭɱɢɦ dz/dt = 2eU ( z ) / m . ɂɫɩɨɥɶɡɭɹ ɷɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɞɥɹ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɜɬɨɪɨɝɨ ɭɪɚɜɧɟɧɢɹ ɢ ɩɟɪɟɯɨɞɹ d 2 r dz d dr dz = ɤ ɩɪɨɢɡɜɨɞɧɨɣ ɩɨ z: ( ) , ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɟ ɬɪɚɟɤɬɨɪɢɢ r(z) dt 2 dt dz dz dt ɩɚɪɚɤɫɢɚɥɶɧɨɝɨ ɩɭɱɤɚ: 2 ' '' d r U ( z ) dr U ( z ) + + r=0 (5.6), dz 2 2U ( z ) dz 4U ( z ) ɤɨɬɨɪɨɟ ɧɚɡɵɜɚɟɬɫɹ ɨɫɧɨɜɧɵɦ ɭɪɚɜɧɟɧɢɟɦ ɷɥɟɤɬɪɨɧɧɨɣ ɨɩɬɢɤɢ. ɉɨɥɭɱɟɧɧɨɟ ɥɢɧɟɣɧɨɟ ɨɞɧɨɪɨɞɧɨɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ 2-ɝɨ ɩɨɪɹɞɤɚ ɨɬɧɨɫɢɬɟɥɶɧɨ U(z) ɢ r(z) ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɜɨɡɦɨɠɧɨ Ɋɢɫ. 5.3. ɂɡɨɛɪɚɠɟɧɢɟ ɬɨɱɤɢ ɜ ɥɢɧɡɟ. ɦɚɫɲɬɚɛɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ, ɬ. ɟ. ɟɫɥɢ
ɩɨɬɟɧɰɢɚɥ ɜɨ ɜɫɟɯ ɬɨɱɤɚɯ ɩɪɨɫɬɪɚɧɫɬɜɚ ɭɜɟɥɢɱɢɬɶ ɜ k ɪɚɡ (ɭɜɟɥɢɱɢɬɶ ɩɨɬɟɧɰɢɚɥ ɧɚ ɜɫɟɯ ɷɥɟɤɬɪɨɞɚɯ ɫɢɫɬɟɦɵ ɜ ɨɞɢɧɚɤɨɜɨɟ ɱɢɫɥɨ ɪɚɡ), ɬɨ ɭɪɚɜɧɟɧɢɟ, ɚ ɫɥɟɞɨɜɚɬɟɥɶɧɨ ɢ ɬɪɚɟɤɬɨɪɢɹ ɷɥɟɤɬɪɨɧɚ ɧɟ ɢɡɦɟɧɢɬɫɹ. Ʉɪɨɦɟ ɬɨɝɨ, ɭɪɚɜɧɟɧɢɟ ɧɟ ɫɨɞɟɪɠɢɬ ɨɬɧɨɲɟɧɢɹ e/m, ɩɨɷɬɨɦɭ ɬɪɚɟɤɬɨɪɢɢ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ ɧɟ ɨɬɥɢɱɚɸɬɫɹ. ȿɫɥɢ ɩɪɟɞɦɟɬɧɚɹ ɩɥɨɫɤɨɫɬɶ ɧɚɯɨɞɢɬɫɹ ɩɪɢ z = a, ɚ ɩɥɨɫɤɨɫɬɶ ɢɡɨɛɪɚɠɟɧɢɹ ɩɪɢ z = b (ɪɢɫ. 5.3), ɬɨ Ɋɢɫ. 5.4. ɍɝɥɵ, ɨɛɪɚɡɭɟɦɵɟ ɬɪɚɟɤɬɨɪɢɟɣ ɫ ɥɢɧɟɣɧɨɟ ɭɜɟɥɢɱɟɧɢɟ ɥɢɧɡɵ: ɨɫɶɸ ɜ ɩɪɟɞɦɟɬɧɨɣ ɩɥɨɫɤɨɫɬɢ ɢ ɬɨɱɤɟ r (b) M = , ɝɞɟ r(a) ɢ r(b) ɪɚɫɫɬɨɹɧɢɟ ɞɨ ɬɪɚɟɤɬɨɪɢɢ ɨɬ ɨɫɢ ɫɢɫɬɟɦɵ. ɍɝɥɨɜɨɟ r (a) ɭɜɟɥɢɱɟɧɢɟ ɥɢɧɡɵ, ɨɩɪɟɞɟɥɹɟɦɨɟ ɤɚɤ ɨɬɧɨɲɟɧɢɟ ɬɚɧɝɟɧɫɨɜ ɭɝɥɨɜ ɧɚɤɥɨɧɚ tgγ 2 r ' (b) ɬɪɚɟɤɬɨɪɢɢ ɤ ɨɫɢ G = (ɪɢɫ. 5.4). ɂɡ ɨɫɧɨɜɧɨɝɨ ɭɪɚɜɧɟɧɢɹ = tgγ 1 r ' (a) ɷɥɟɤɬɪɨɧɧɨɣ ɨɩɬɢɤɢ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɫɨɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ ɥɢɧɟɣɧɵɦ ɢ ɭɝɥɨɜɵɦ ɭɜɟɥɢɱɟɧɢɟɦ ɥɢɧɡɵ[28]: U (a) , (5.7) M ⋅G = U (b ) ɤɨɬɨɪɨɟ ɹɜɥɹɟɬɫɹ ɚɧɚɥɨɝɨɦ ɬɟɨɪɟɦɵ Ʌɚɝɪɚɧɠɚ-Ƚɟɥɶɦɝɨɥɶɰɚ ɞɥɹ ɫɜɟɬɨɜɨɣ n M ⋅G = 1 . ɨɩɬɢɤɢ: n2 Ɏɨɤɭɫɧɵɟ ɪɚɫɫɬɨɹɧɢɹ ɫɥɟɜɚ f1 ɢ ɫɩɪɚɜɚ f2 ɨɬ ɝɥɚɜɧɵɯ ɩɥɨɫɤɨɫɬɟɣ h1 ɢ h2 ɷɥɟɤɬɪɨɧɧɨɣ ɥɢɧɡɵ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɱɟɪɟɡ ɬɪɚɟɤɬɨɪɢɢ, ɩɪɨɯɨɞɹɳɢɟ ɱɟɪɟɡ ɮɨɤɭɫ ɥɢɧɡɵ r1 ɢ Ɋɢɫ. 5.5. ɏɨɞ ɝɥɚɜɧɵɯ ɥɭɱɟɣ ɜ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɣ ɩɚɪɚɥɥɟɥɶɧɨ ɨɫɢ r2 ɥɢɧɡɟ ɫɢɫɬɟɦɵ (ɪɢɫ. 5.5): r1 (b) r2 (a ) , f2 = ' . f1 = ' r1 (a ) r2 (b) Ɍɨɧɤɢɟ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɢɟ ɥɢɧɡɵ
Ɋɚɫɫɦɨɬɪɢɦ ɬɨɧɤɢɟ ɥɢɧɡɵ, ɝɥɚɜɧɵɟ ɩɥɨɫɤɨɫɬɢ ɤɨɬɨɪɵɯ ɧɚɯɨɞɹɬɫɹ ɩɪɢ z = a ɢ ɩɪɢ z = b. Ⱦɥɹ ɬɨɧɤɢɯ ɥɢɧɡ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɝɥɚɜɧɵɦɢ ɩɥɨɫɤɨɫɬɹɦɢ ɦɧɨɝɨ ɦɟɧɶɲɟ ɮɨɤɭɫɧɵɯ ɪɚɫɫɬɨɹɧɢɣ (b - a) << f1, f2 , ɬ. ɟ. ɝɥɚɜɧɵɟ ɩɥɨɫɤɨɫɬɢ ɫɥɢɜɚɸɬɫɹ, ɮɨɤɭɫɧɵɟ ɪɚɫɫɬɨɹɧɢɹ ɫɥɟɜɚ ɢ ɫɩɪɚɜɚ ɨɩɪɟɞɟɥɹɸɬɫɹ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɫɨɨɬɧɨɲɟɧɢɹɦɢ: b b 1 1 U '' ( z ) 1 1 U '' ( z ) ɢ (5.8) = dz = dz . f 1 4 U (a ) ³a U ( z ) f 2 4 U (b) ³a U ( z )
Ɉɬɧɨɲɟɧɢɟ ɮɨɤɭɫɧɵɯ ɪɚɫɫɬɨɹɧɢɣ:
U (a ) f1 . =− f2 U (b)
Ɉɩɬɢɱɟɫɤɚɹ ɫɢɥɚ: b 1 1 U ' (b) U ' (a ) 1 (U ' ( z )) 2 ( = − )+ dz . D= f 2 4 U (b) U (b) U (a ) 8 U (b) ³a U 3 / 2 ( z )
(5.9)
ȿɫɥɢ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɫɩɪɚɜɚ ɢ ɫɥɟɜɚ ɨɬ ɥɢɧɡɵ ɪɚɜɧɨ, ɬɨ D > 0, ɬ. ɟ. ɥɢɧɡɚ ɜɫɟɝɞɚ ɫɨɛɢɪɚɸɳɚɹ. Ⱦɥɹ ɨɞɢɧɨɱɧɨɣ ɞɢɚɮɪɚɝɦɵ ɫ ɤɪɭɝɥɵɦ ɨɬɜɟɪɫɬɢɟɦ: D=
E − E2 1 = 1 , fd 4U d
(5.10)
ɝɞɟ E1 ɢ E2 – ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɨɥɟɣ ɫɥɟɜɚ ɢ ɫɩɪɚɜɚ ɨɬ ɞɢɚɮɪɚɝɦɵ, Ud – ɩɨɬɟɧɰɢɚɥ ɞɢɚɮɪɚɝɦɵ. Ⱦɥɹ ɫɢɫɬɟɦɵ ɢɡ ɞɜɭɯ ɥɢɧɡ – ɞɢɚɮɪɚɝɦ ɫ ɮɨɤɭɫɚɦɢ f1 ɢ f2 ɢ ɪɚɫɫɬɨɹɧɢɟɦ ɦɟɠɞɭ ɥɢɧɡɚɦɢ l ɨɩɬɢɱɟɫɤɚɹ ɫɢɥɚ ɡɚɞɚɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ:
l 1 1 1 = + + . f f1 f 2 f1 f 2
(5.11)
ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɨɝɨ ɩɨɥɹ ɬɪɚɟɤɬɨɪɢɹ ɷɥɟɤɬɪɨɧɚ ɨɩɢɫɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢɹɦɢ:
er '' ⋅⋅ °m r = −eEr ≈ − 2 U ( z ) , ® ° ⋅⋅ ' ¯m z = −eEz ≈ eU ( z )
(5.12)
ɬ.ɟ. ɮɨɤɭɫɢɪɭɸɳɚɹ ɫɢɥɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɡɧɚɤɨɦ ɜɬɨɪɨɣ ɩɪɨɢɡɜɨɞɧɨɣ ɨɬ ɩɨɬɟɧɰɢɚɥɚ ɧɚ ɨɫɢ ɫɢɫɬɟɦɵ. ȿɫɥɢ U′′(z) > 0, ɬɨ ɫɢɫɬɟɦɚ ɮɨɤɭɫɢɪɭɸɳɚɹ, ɟɫɥɢ U′′(z) < 0, ɬɨ ɪɚɫɮɨɤɭɫɢɪɭɸɳɚɹ. §40. Ɇɚɝɧɢɬɧɵɟ ɥɢɧɡɵ
Ɏɨɤɭɫɢɪɨɜɤɭ ɩɭɱɤɨɜ ɜ ɚɤɫɢɚɥɶɧɨɫɢɦɦɟɬɪɢɱɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɩɪɨɳɟ ɜɫɟɝɨ ɩɪɨɞɟɦɨɧɫɬɪɢɪɨɜɚɬɶ ɧɚ ɩɪɢɦɟɪɟ ɩɚɪɚɤɫɢɚɥɶɧɨɝɨ ɩɭɱɤɚ ɷɥɟɤɬɪɨɧɨɜ, ɫɤɨɪɨɫɬɶ ɤɨɬɨɪɵɯ ɜɞɨɥɶ ɨɫɢ ɫɢɫɬɟɦɵ ɦɧɨɝɨ ɛɨɥɶɲɟ ɫɤɨɪɨɫɬɢ ɜ ɪɚɞɢɚɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ vz >> vr. ɇɚ ɷɥɟɤɬɪɨɧ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ Ʌɨɪɟɧɰɚ & e& & F = − v × B . Ɋɚɞɢɚɥɶɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ c ɷɬɨɣ ɫɢɥɵ ɹɜɥɹɟɬɫɹ ɮɨɤɭɫɢɪɭɸɳɟɣ: Fr = (e/c)vϕBz (ɪɢɫ.5.6). Ⱥɡɢɦɭɬɚɥɶɧɚɹ
Ɋɢɫ. 5.6. Ɏɨɤɭɫɢɪɨɜɤɚ ɜ ɚɤɫɢɚɥɶɧɨɫɢɦɦɟɬɪɢɱɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ
ɫɨɫɬɚɜɥɹɸɳɚɹ ɫɤɨɪɨɫɬɢ ɷɥɟɤɬɪɨɧɚ ɩɨɹɜɥɹɟɬɫɹ ɡɚ ɫɱɟɬ ɚɡɢɦɭɬɚɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɫɢɥɵ Ʌɨɪɟɧɰɚ: Fϕ = -(e/c)(vzBr + vrBz) ≈ -(e/c)vzBr , ɬɚɤ ɤɚɤ vz >> vr. ɋɨɫɬɚɜɥɹɸɳɚɹ ɫɤɨɪɨɫɬɢ vz ɧɟ ɦɟɧɹɟɬ ɡɧɚɤɚ, ɪɚɞɢɚɥɶɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ Br ɦɨɠɟɬ ɦɟɧɹɬɶ ɡɧɚɤ, ɩɪɢ ɷɬɨɦ ɚɡɢɦɭɬɚɥɶɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɫɤɨɪɨɫɬɢ ɷɥɟɤɬɪɨɧɚ vϕ ɛɭɞɟɬ ɭɦɟɧɶɲɚɬɶɫɹ (ɜɪɚɳɟɧɢɟ ɡɚɦɟɞɥɹɬɶɫɹ), ɧɨ ɧɚɩɪɚɜɥɟɧɢɟ ɜɪɚɳɟɧɢɟ ɧɢɤɨɝɞɚ ɧɟ ɦɟɧɹɟɬɫɹ, ɩɨɷɬɨɦɭ ɮɨɤɭɫɢɪɭɸɳɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɫɢɥɵ Ʌɨɪɟɧɰɚ Fr ɜɫɟɝɞɚ ɫɨɯɪɚɧɹɟɬ ɡɧɚɤ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɦɚɝɧɢɬɧɚɹ ɥɢɧɡɚ ɜɫɟɝɞɚ ɫɨɛɢɪɚɸɳɚɹ. ɋ ɭɱɟɬɨɦ ɬɟɨɪɟɦɵ Ƚɚɭɫɫɚ, ɞɚɸɳɟɣ ɫɨɨɬɧɨɲɟɧɢɹ ɦɟɠɞɭ ɩɪɨɞɨɥɶɧɨɣ Bz ɢ ɪɚɞɢɚɥɶɧɨɣ ɤɨɦɩɨɧɟɧɬɚɦɢ Br ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ & B (Bz,Br) Br = -(r/2)(dBz/dz), ɞɜɢɠɟɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɜɞɨɥɶ ɨɫɢ ɨɩɢɫɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ: dB d 2z e2 (5.13) r 2 B z 2z . = − 2 2 2 dt 4m c dz
Ⱥɡɢɦɭɬɚɥɶɧɨɟ ɞɜɢɠɟɧɢɟ (ɩɨɜɨɪɨɬ) ɨɩɢɫɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ: dϕ eB z = dt 2mc
(5.14)
(ɥɚɪɦɨɪɨɜɫɤɨɟ ɜɪɚɳɟɧɢɟ), ɬ. ɟ. ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɫɟɯ ɷɥɟɤɬɪɨɧɨɜ ɨɞɢɧɚɤɨɜɚ ɢ ɢɡɨɛɪɚɠɟɧɢɟ ɜɪɚɳɚɟɬɫɹ ɤɚɤ ɰɟɥɨɟ, ɩɪɢɱɟɦ, ɧɚɩɪɚɜɥɟɧɢɟ ɜɪɚɳɟɧɢɹ ɡɚɜɢɫɢɬ ɨɬ ɧɚɩɪɚɜɥɟɧɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ȿɫɥɢ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɫɥɨɜɢɸ: b
³B
z
( z )dz = 0, ɬɨ ɜɪɚɳɟɧɢɟ ɢɡɨɛɪɚɠɟɧɢɹ ɛɭɞɟɬ ɨɬɫɭɬɫɬɜɨɜɚɬɶ. ɍɱɢɬɵɜɚɹ, ɱɬɨ ɞɥɹ
a
ɩɚɪɚɤɫɢɚɥɶɧɵɯ ɩɭɱɤɨɜ vz>>vr (ɜ ɩɪɢɛɥɢɠɟɧɢɢ
mv 2 ≈ U 0 ), ɞɜɢɠɟɧɢɟ ɩɨ ɪɚɞɢɭɫɭ 2
ɡɚɞɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ: eB z2 d 2r =− r, 8mc 2U 0 dz 2
(5.15)
ɝɞɟ U0 – ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɨɜ. Ⱦɚɧɧɨɟ ɭɪɚɜɧɟɧɢɟ ɨɩɢɫɵɜɚɟɬ ɬɪɚɟɤɬɨɪɢɸ ɜ ɩɥɨɫɤɨɫɬɢ, ɤɨɬɨɪɚɹ ɜɪɚɳɚɟɬɫɹ ɫ ɥɚɪɦɨɪɨɜɫɤɨɣ ɱɚɫɬɨɬɨɣ. Ʉɚɤ ɜɢɞɧɨ ɢɡ ɭɪɚɜɧɟɧɢɣ ɞɜɢɠɟɧɢɹ, ɬɪɚɟɤɬɨɪɢɹ ɷɥɟɤɬɪɨɧɚ ɩɨɥɧɨɫɬɶɸ ɨɩɪɟɞɟɥɹɟɬɫɹ ɡɧɚɱɟɧɢɟɦ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɚ ɨɫɢ Bz. ȼ ɭɪɚɜɧɟɧɢɹ ɜɯɨɞɹɬ ɡɚɪɹɞ ɢ ɦɚɫɫɚ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɪɚɡɧɵɟ ɱɚɫɬɢɰɵ ɞɜɢɠɭɬɫɹ ɩɨ ɪɚɡɧɵɦ ɬɪɚɟɤɬɨɪɢɹɦ. ɍɪɚɜɧɟɧɢɹ ɥɢɧɟɣɧɵ ɢ ɨɞɧɨɪɨɞɧɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɪɚɫɫɬɨɹɧɢɹ ɨɬ ɨɫɢ r, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɥɸɛɨɟ ɚɤɫɢɚɥɶɧɨɫɢɦɦɟɬɪɢɱɧɨɟ ɩɨɥɟ ɫɩɨɫɨɛɧɨ ɫɨɡɞɚɬɶ ɢɡɨɛɪɚɠɟɧɢɟ ɢ ɹɜɥɹɟɬɫɹ ɥɢɧɡɨɣ. Ⱦɥɹ ɬɨɧɤɨɣ ɦɚɝɧɢɬɧɨɣ ɥɢɧɡɵ (ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɧɚ ɨɫɢ ɛɵɫɬɪɨ ɩɚɞɚɟɬ ɩɨ ɦɟɪɟ ɭɞɚɥɟɧɢɹ ɨɬ ɥɢɧɡɵ) ɨɩɬɢɱɟɫɤɚɹ ɫɢɥɚ: b
b
1 e 1 1 0.022 = B z2 dz ɢɥɢ [ ] = B z2 [ Ƚɫ]dz . ³ ³ 2 f ɫɦ U 0 [ ɷȼ ] a f 8mc U 0 a ɍɝɨɥ ɩɨɜɨɪɨɬɚ ɜ ɦɚɝɧɢɬɧɨɣ ɥɢɧɡɟ
(5.16)
ϕ ( z) =
1 e c 8mU 0
b
b
³ B z dz ɢɥɢ ϕ[ ɪɚɞ] = a
0.15 B z [ Ƚɫ]dz . U 0 [ ɷȼ] ³a
(5.17)
Bm , z 2 3/ 2 (1 + 2 ) R ɝɞɟ Bm – ɩɨɥɟ ɜ ɰɟɧɬɪɟ ɜɢɬɤɚ (ɮɨɪɦɭɥɚ Ȼɢɨ-ɋɚɜɚɪɚ). ɂɧɬɟɝɪɢɪɭɹ (5.16), ɦɨɠɧɨ ɧɚɣɬɢ ɮɨɤɭɫɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɞɥɹ ɨɞɧɨɝɨ ɬɨɤɨɜɨɝɨ ɜɢɬɤɚ:
Ⱦɥɹ ɦɚɝɧɢɬɧɨɝɨ ɜɢɬɤɚ ɫ ɬɨɤɨɦ I ɪɚɞɢɭɫɚ R ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ Bz=
U 0 [ ɷȼ ]R[ɫɦ] . I 2 [ A] Ⱦɥɹ ɤɚɬɭɲɤɢ ɢɡ N ɜɢɬɤɨɜ: f [ɫɦ] ≈ 96.8
f [ɫɦ] ≈ 96.8
(5.18ɚ)
U 0 [ ɷȼ ]R[ɫɦ] . ( NI [ A]) 2
(5.18ɛ)
NI [ A] . U 0 [ ɷȼ]
(5.19)
ɍɝɨɥ ɩɨɜɨɪɨɬɚ:
ϕ [ ɪɚɞ] ≈ 10.7
Ⱦɥɹ ɷɤɪɚɧɢɪɨɜɚɧɧɨɣ ɥɢɧɡɵ fɷ = kf, ɝɞɟ k – ɩɨɩɪɚɜɨɱɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ, k = 0.5÷0.7. §41. Ɉɬɤɥɨɧɹɸɳɢɟ ɢ ɮɨɤɭɫɢɪɭɸɳɢɟ ɷɥɟɤɬɪɨɧɧɨ-ɨɩɬɢɱɟɫɤɢɟ ɫɢɫɬɟɦɵ
Ɉɬɤɥɨɧɟɧɢɟ ɢ ɮɨɤɭɫɢɪɨɜɤɚ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɢ ɦɚɝɧɢɬɧɨɦ ɩɨɥɹɯ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ ɫɨɡɞɚɧɢɹ ɢ ɞɢɚɝɧɨɫɬɢɤɢ ɩɥɚɡɦɵ, ɚ ɬɚɤɠɟ ɞɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ ɩɪɨɰɟɫɫɨɜ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɩɥɚɡɦɵ ɫ ɬɜɟɪɞɵɦ ɬɟɥɨɦ. Ɋɚɫɫɦɨɬɪɢɦ ɧɟɤɨɬɨɪɵɟ ɢɡ ɬɚɤɢɯ ɫɢɫɬɟɦ. ɗɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɢɟ ɷɧɟɪɝɨɚɧɚɥɢɡɚɬɨɪɵ
ɇɚɢɛɨɥɟɟ ɩɪɨɫɬɨɣ ɹɜɥɹɟɬɫɹ ɫɢɫɬɟɦɚ ɜ ɜɢɞɟ ɩɥɨɫɤɨɝɨ ɤɨɧɞɟɧɫɚɬɨɪɚ. ȿɫɥɢ ɩɭɱɨɤ ɱɚɫɬɢɰ ɡɚɩɭɫɤɚɟɬɫɹ ɩɚɪɚɥɥɟɥɶɧɨ ɩɥɚɫɬɢɧɚɦ (ɪɢɫ. 5.7 ), ɬɨ ɭɝɨɥ ɨɬɤɥɨɧɟɧɢɹ ɩɭɱɤɚ α ɡɚɜɢɫɢɬ ɨɬ ɷɧɟɪɝɢɢ ɱɚɫɬɢɰ U0: α(U0) = ∆UlE/(2U0d),
(5.20)
ɝɞɟ ∆U - ɪɚɡɧɨɫɬɶ ɩɨɬɟɧɰɢɚɥɨɜ, ɩɪɢɥɨɠɟɧɧɚɹ ɤ ɩɥɚɫɬɢɧɚɦ, lE - ɞɥɢɧɚ ɩɥɚɫɬɢɧ ɜɞɨɥɶ ɞɜɢɠɟɧɢɹ ɩɭɱɤɚ, d ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɩɥɚɫɬɢɧɚɦɢ. Ȼɥɚɝɨɞɚɪɹ ɪɚɡɥɢɱɧɵɦ ɡɧɚɱɟɧɢɹɦ ɩɨɬɟɧɰɢɚɥɚ ɧɚ Ɋɢɫ. 5.7. Ɏɨɤɭɫɢɪɨɜɤɚ ɜ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɦ ɩɨɥɟ ɩɥɨɫɤɨɝɨ ɤɨɧɞɟɧɫɚɬɨɪɚ ɜɟɪɯɧɟɣ ɢ ɧɢɠɧɟɣ ɝɪɚɧɢɰɟ ɩɭɱɤɚ, ɚ ɡɧɚɱɢɬ ɢ ɪɚɡɥɢɱɧɵɦ ɫɤɨɪɨɫɬɹɦ ɱɚɫɬɢɰ, ɩɪɨɢɫɯɨɞɢɬ ɮɨɤɭɫɢɪɨɜɤɚ ɩɭɱɤɚ. ɏɨɪɨɲɭɸ ɮɨɤɭɫɢɪɨɜɤɭ ɩɨɡɜɨɥɹɟɬ ɩɨɥɭɱɢɬɶ ɰɢɥɢɧɞɪɢɱɟɫɤɢɣ ɤɨɧɞɟɧɫɚɬɨɪ (ɪɢɫ. 5.8). ɗɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɤɨɧɞɟɧɫɚɬɨɪɚ ɨɛɪɚɬɧɨ
ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɪɚɞɢɭɫɭ E(r) = a/r, ɢɧɬɟɝɪɢɪɭɹ ɭɪɚɜɧɟɧɢɟ dU(r)/dr = a/r, ɦɨɠɧɨ ɧɚɣɬɢ ɤɨɷɮɮɢɰɢɟɧɬ a = (U2 – U1)/ln(R2/R1), ɚ ɡɧɚɱɢɬ E(r) == (U2 – U1)/(rln(R2/R1)), ɝɞɟ U1, U2, R1, R2 – ɩɨɬɟɧɰɢɚɥɵ ɢ ɪɚɞɢɭɫɵ ɜɧɭɬɪɟɧɧɟɝɨ ɢ ɜɧɟɲɧɟɝɨ ɰɢɥɢɧɞɪɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ɑɟɪɟɡ ɭɡɤɭɸ ɜɵɯɨɞɧɭɸ ɳɟɥɶ ɛɭɞɭɬ «ɭɫɩɟɲɧɨ» ɩɪɨɯɨɞɢɬɶ ɬɨɥɶɤɨ ɱɚɫɬɢɰɵ, ɢɦɟɸɳɢɟ ɤɪɭɝɨɜɵɟ ɬɪɚɟɤɬɨɪɢɢ ɢ ɫɤɨɪɨɫɬɢ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɭɫɥɨɜɢɸ: mv2/r = qE (ɨɫɬɚɥɶɧɵɟ ɩɨɩɚɞɭɬ ɧɚ ɫɬɟɧɤɢ ɰɢɥɢɧɞɪɚ), ɬ. ɟ. ɱɚɫɬɢɰɵ, ɢɦɟɸɳɢɟ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ: U0[ɷȼ]= q(U2 – U1)/(2ln(R2/R1)).
(5.21)
Ⱦɥɹ ɪɟɲɟɧɢɹ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɞɥɹ ɧɟɤɪɭɝɨɜɵɯ ɬɪɚɟɤɬɨɪɢɣ ɜ ɩɨɥɹɪɧɵɯ qa , ɫ ɭɱɟɬɨɦ ɤɨɨɪɞɢɧɚɬɚɯ: r − rϕ 2 = − mr ɩɨɫɬɨɹɧɫɬɜɚ ɫɟɤɬɨɪɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ 2 r ϕ = const , ɭɞɨɛɧɨ ɪɚɫɫɦɨɬɪɟɬɶ ɨɬɤɥɨɧɟɧɢɟ u ɬɪɚɟɤɬɨɪɢɢ ɨɬ ɤɪɭɝɨɜɨɣ: r = r0+u (u << r), ɝɞɟ r0 - ɪɚɞɢɭɫ, ɧɚ ɤɨɬɨɪɨɦ ɩɭɱɨɤ ɱɚɫɬɢɰ ɜɥɟɬɚɟɬ ɜ ɤɨɧɞɟɧɫɚɬɨɪ. Ɍɨɝɞɚ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ: u + 2ω 02 u = 0 , ɝɞɟ ω02 = (qa)/(mr02), ɪɟɲɟɧɢɟ ɤɨɬɨɪɨɝɨ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɤɨɥɟɛɚɧɢɹ ɨɤɨɥɨ ɤɪɭɝɨɜɨɣ ɬɪɚɟɤɬɨɪɢɢ ɫ ɩɟɪɢɨɞɨɦ 2π/ 2 , ɬɨ ɟɫɬɶ ɩɨɫɥɟ ɩɨɜɨɪɨɬɚ Ɋɢɫ. 5.8. Ɏɨɤɭɫɬɪɨɜɤɚ ɜ ɰɢɥɢɧɞɪɢɱɟɫɤɨɦ ɤɨɧɞɟɧɫɚɬɨɪɟ ɧɚ ɭɝɨɥ π/ 2 =127.3ɨ ɩɭɱɨɤ ɮɨɤɭɫɢɪɭɟɬɫɹ ɧɚ ɤɪɭɝɨɜɨɣ ɬɪɚɟɤɬɨɪɢɢ (ɮɨɤɭɫɢɪɨɜɤɚ ɩɨ ɘɡɭ ɢ Ɋɨɠɚɧɫɤɨɦɭ). Ɇɚɝɧɢɬɧɵɟ ɦɚɫɫ-ɫɟɩɚɪɚɬɨɪɵ ɢ ɷɧɟɪɝɨɚɧɚɥɢɡɚɬɨɪɵ
Ȼɥɚɝɨɞɚɪɹ ɡɚɜɢɫɢɦɨɫɬɢ ɪɚɞɢɭɫɚ ɜɪɚɳɟɧɢɹ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ rɥ = vmc (ɥɚɪɦɨɪɨɜɫɤɨɝɨ ɪɚɞɢɭɫɚ) ɨɬ ɫɤɨɪɨɫɬɢ eB v ɢ ɦɚɫɫɵ m ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ, ɜɨɡɦɨɠɧɨ ɢɯ ɪɚɡɞɟɥɟɧɢɟ (ɫɟɩɚɪɚɰɢɹ) ɩɨ ɷɧɟɪɝɢɹɦ ɢ ɦɚɫɫɚɦ, ɚ ɬɚɤɠɟ ɮɨɤɭɫɢɪɨɜɤɚ ɤɚɤ ɜ ɩɨɩɟɪɟɱɧɨɦ, ɬɚɤ ɢ ɜ ɩɪɨɞɨɥɶɧɨɦ ɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ. ȼ ɩɨɩɟɪɟɱɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɧɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɨɣ ɹɜɥɹɟɬɫɹ ɫɯɟɦɚ ɫ ɩɨɥɭɤɪɭɝɨɜɨɣ ɮɨɤɭɫɢɪɨɜɤɨɣ (ɪɢɫ. 5.9). ȼɵɯɨɞɹɳɢɣ ɢɡ ɬɨɱɟɱɧɨɝɨ ɢɫɬɨɱɧɢɤɚ Ⱥ Ɋɢɫ. 5.9. Ɏɨɤɭɫɢɪɨɜɤɚ ɜ ɨɞɧɨɪɨɞɧɨɦ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɫɢɥɨɜɵɦ ɥɢɧɢɹɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɩɭɱɨɤ ɦɨɧɨɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɱɚɫɬɢɰ ɛɭɞɟɬ ɮɨɤɭɫɢɪɨɜɚɬɶɫɹ ɩɨɫɥɟ ɩɨɥɭɨɛɨɪɨɬɚ ɧɚ ɪɚɫɫɬɨɹɧɢɢ 2rɥ. Ɏɨɤɭɫɢɪɨɜɤɚ ɱɚɫɬɢɰ, ɜɵɥɟɬɟɜɲɢɯ ɩɨɞ ɨɞɢɧɚɤɨɜɵɦ ɭɝɥɨɦ α ɤ ɰɟɧɬɪɚɥɶɧɨɣ ɬɪɚɟɤɬɨɪɢɢ ɩɭɱɤɚ, ɩɪɨɢɫɯɨɞɢɬ ɛɥɚɝɨɞɚɪɹ ɬɨɦɭ, ɱɬɨ ɤɪɭɝɨɜɵɟ ɬɪɚɟɤɬɨɪɢɢ ɱɚɫɬɢɰ ɢɦɟɸɬ ɨɞɢɧɚɤɨɜɵɟ ɪɚɞɢɭɫɵ, ɢ ɢɯ ɬɪɚɟɤɬɨɪɢɢ ɨɩɢɪɚɸɬɫɹ ɧɚ ɞɢɚɦɟɬɪɵ, ɪɚɫɩɨɥɨɠɟɧɧɵɟ ɩɨɞ ɬɟɦ ɠɟ ɭɝɥɨɦ 2α, ɱɬɨ ɢ ɤɚɫɚɬɟɥɶɧɵɟ ɤ ɬɪɚɟɤɬɨɪɢɹɦ ɜ ɧɚɱɚɥɶɧɨɣ ɬɨɱɤɟ.
ɒɢɪɢɧɚ ɳɟɥɢ δ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɩɪɨɯɨɠɞɟɧɢɹ ɜɫɟɝɨ ɩɭɱɤɚ, ɡɚɜɢɫɢɬ ɨɬ ɪɚɫɯɨɞɢɦɨɫɬɢ 2α ɜɯɨɞɹɳɟɝɨ ɩɭɱɤɚ: δ =2rɥ(1-cosα). ȼ ɫɟɤɬɨɪɧɵɯ ɦɚɫɫ-ɫɩɟɤɬɪɨɦɟɬɪɚɯ ɫ ɨɞɧɨɪɨɞɧɵɦ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ (ɪɢɫ. 5.10) ɮɨɤɭɫɢɪɨɜɤɚ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɡɚ ɫɱɟɬ ɬɨɝɨ, ɱɬɨ ɞɥɢɧɚ ɬɪɚɟɤɬɨɪɢɢ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɞɥɹ ɱɚɫɬɢɰ, ɧɚɯɨɞɹɳɢɯɫɹ ɧɚ ɪɚɡɧɨɦ ɪɚɫɫɬɨɹɧɢɢ ɨɬ ɰɟɧɬɪɚ ɫɟɤɬɨɪɚ, ɪɚɡɥɢɱɧɚ. Ɏɨɤɭɫɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɬɚɤɨɣ ɫɢɫɬɟɦɵ ɡɚɜɢɫɢɬ ɨɬ ɭɝɥɚ ɫɟɤɬɨɪɚ ϕ ɢ Ɋɢɫ. 5.10. ɋɟɤɬɨɪɧɵɣ ɦɚɝɧɢɬɧɵɣ ɪɚɫɫɬɨɹɧɢɹ ɨɬ ɢɫɬɨɱɧɢɤɚ ɞɨ ɦɚɫɫ-ɫɟɩɚɪɚɬɨɪ ɝɪɚɧɢɰɵ ɩɨɥɹ. ȿɫɥɢ ɬɪɚɟɤɬɨɪɢɹ ɨɫɟɜɵɯ ɱɚɫɬɢɰ ɩɭɱɤɚ ɧɚ ɜɯɨɞɟ ɢ ɜɵɯɨɞɟ ɢɡ ɫɟɤɬɨɪɚ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɚ ɟɝɨ ɝɪɚɧɢɰɟ (ɰɟɧɬɪ ɜɪɚɳɟɧɢɹ ɨɫɟɜɵɯ ɱɚɫɬɢɰ ɫɨɜɩɚɞɚɟɬ ɫ ɰɟɧɬɪɨɦ ɫɟɤɬɨɪɚ), ɬɨ ɪɚɫɱɟɬɵ ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ ɮɨɤɭɫɢɪɨɜɤɚ ɩɪɨɢɫɯɨɞɢɬ ɧɚ ɝɪɚɧɢɰɟ ɜɥɟɬɚ ɩɭɱɤɚ ɜ ɫɢɫɬɟɦɭ, ɬ. ɟ. ε1 + ϕ + ε2 = 180ɨ (ɪɢɫ. 5.10). ȼ ɩɪɨɞɨɥɶɧɨɦ ɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɮɨɤɭɫɢɪɨɜɤɚ ɩɪɨɢɫɯɨɞɢɬ ɜ ɫɢɥɭ ɬɨɝɨ, ɱɬɨ ɜɵɲɟɞɲɢɟ ɢɡ ɨɞɧɨɣ ɬɨɱɤɢ ɱɚɫɬɢɰɵ ɩɨɫɥɟ ɫɨɜɟɪɲɟɧɢɹ ɨɞɧɨɝɨ ɨɛɨɪɨɬɚ Ɋɢɫ. 5.11. Ɏɨɤɭɫɢɪɨɜɤɚ ɜ ɨɞɧɨɪɨɞɧɨɦ ɩɪɨɞɨɥɶɧɨɦ ɩɨ ɥɚɪɦɨɪɨɜɫɤɨɣ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɨɤɪɭɠɧɨɫɬɢ ɜɨɡɜɪɚɳɚɸɬɫɹ ɧɚ ɢɫɯɨɞɧɭɸ ɫɢɥɨɜɭɸ ɥɢɧɢɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ (ɪɢɫ. 5.11). ɉɪɨɟɤɰɢɹ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɧɚ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɭɸ ɤ ɫɢɥɨɜɵɦ ɥɢɧɢɹɦ ɩɥɨɫɤɨɫɬɶ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɭɱɨɤ ɨɤɪɭɠɧɨɫɬɟɣ, ɢɦɟɸɳɢɯ ɨɛɳɭɸ ɬɨɱɤɭ. ȿɫɥɢ ɭɝɨɥ ɪɚɫɯɨɞɢɦɨɫɬɢ ɩɭɱɤɚ α ɧɟɜɟɥɢɤ, ɬɨ ɮɨɤɭɫɢɪɨɜɤɚ ɦɨɧɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɩɭɱɤɚ ɩɪɨɢɡɨɣɞɟɬ ɱɟɪɟɡ ɨɞɢɧ ɨɛɨɪɨɬ ɧɚ ɪɚɫɫɬɨɹɧɢɢ l = τɥvcosα ≈ 2πmvc/(eB), ɝɞɟ τɥ = 2πmc/(eB) – ɩɟɪɢɨɞ ɜɪɚɳɟɧɢɹ ɩɨ ɥɚɪɦɨɪɨɜɫɤɨɣ ɨɤɪɭɠɧɨɫɬɢ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɚɫɫɬɨɹɧɢɟ ɞɨ ɦɟɫɬɚ ɮɨɤɭɫɢɪɨɜɤɢ ɩɭɱɤɚ ɡɚɜɢɫɢɬ ɨɬ ɫɤɨɪɨɫɬɢ ɢ ɦɚɫɫɵ ɱɚɫɬɢɰ, ɢ ɩɪɨɞɨɥɶɧɨɟ ɨɞɧɨɪɨɞɧɨɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɦɨɠɟɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɨ ɞɥɹ ɷɧɟɪɝɨ- ɢ ɦɚɫɫɫɟɩɚɪɚɰɢɢ ɱɚɫɬɢɰ. ɗɥɟɤɬɪɨɧɧɵɟ ɢ ɢɨɧɧɵɟ ɩɭɲɤɢ
ȼ ɛɨɥɶɲɢɧɫɬɜɟ ɷɥɟɤɬɪɨɧɧɵɯ ɩɭɲɟɤ ɢɫɬɨɱɧɢɤɨɦ ɷɥɟɤɬɪɨɧɨɜ ɫɥɭɠɢɬ ɬɟɪɦɨɤɚɬɨɞ (ɜɨɥɶɮɪɚɦɨɜɵɣ, ɨɤɫɢɞɧɵɣ ɢ ɬ.ɩ.) (ɪɢɫ. 5.12).
Ɋɢɫ. 5.12. ɗɥɟɤɬɪɨɧɧɚɹ ɩɭɲɤɚ: 1 – ɧɢɬɶ ɧɚɤɚɥɚ, 2 – ɤɚɬɨɞ, ɩɨɞɨɝɪɟɜɚɟɦɵɣ ɧɢɬɶɸ ɧɚɤɚɥɚ, 3 – ɭɩɪɚɜɥɹɸɳɢɣ ɷɥɟɤɬɪɨɞ ɫ ɫɟɬɤɨɣ, 4 – ɚɧɨɞ ɫ ɫɟɬɤɨɣ.
Ɏɨɤɭɫɢɪɨɜɤɚ ɩɭɱɤɚ ɢ ɭɩɪɚɜɥɟɧɢɟ ɟɝɨ ɢɧɬɟɧɫɢɜɧɨɫɬɶɸ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɭɩɪɚɜɥɹɸɳɢɦ (ɢɥɢ ɮɨɤɭɫɢɪɭɸɳɢɦ) ɷɥɟɤɬɪɨɞɨɦ. Ⱥɧɨɞɨɦ ɹɜɥɹɟɬɫɹ ɞɢɚɮɪɚɝɦɚ, ɦɟɠɞɭ ɤɨɬɨɪɨɣ ɢ ɤɚɬɨɞɨɦ ɦɨɠɟɬ ɩɪɢɤɥɚɞɵɜɚɬɶɫɹ ɧɚɩɪɹɠɟɧɢɟ ɨɬ ɟɞɢɧɢɰ ɞɨ ɫɨɬɟɧ ɤɢɥɨɜɨɥɶɬ. ɇɚ ɭɩɪɚɜɥɹɸɳɢɣ ɷɥɟɤɬɪɨɞ ɩɨɞɚɟɬɫɹ ɨɬɪɢɰɚɬɟɥɶɧɨɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɤɚɬɨɞɚ ɧɚɩɪɹɠɟɧɢɟ ɞɨ 500 ȼ. ɍɩɪɚɜɥɟɧɢɟ ɭɠɟ ɫɮɨɪɦɢɪɨɜɚɧɧɨɝɨ ɷɥɟɤɬɪɨɧɧɨɝɨ ɩɭɱɤɚ ɦɨɠɟɬ ɨɫɭɳɟɫɬɜɥɹɬɶɫɹ ɫ ɩɨɦɨɳɶɸ ɨɬɤɥɨɧɹɸɳɟɣ ɫɢɫɬɟɦɵ, ɤɚɤ ɷɬɨ ɩɪɨɢɫɯɨɞɢɬ ɜ ɷɥɟɤɬɪɨɧɧɨ-ɥɭɱɟɜɵɯ ɬɪɭɛɤɚɯ ɬɟɥɟɜɢɡɨɪɨɜ ɢ ɦɨɧɢɬɨɪɨɜ. ɉɪɢɧɰɢɩ ɪɚɛɨɬɵ ɢɨɧɧɨɣ ɩɭɲɤɢ ɩɨɞɨɛɟɧ ɷɥɟɤɬɪɨɧɧɨɣ. ɋɭɳɟɫɬɜɭɟɬ ɛɨɥɶɲɨɟ ɦɧɨɠɟɫɬɜɨ ɪɚɡɧɨɨɛɪɚɡɧɵɯ ɤɨɧɫɬɪɭɤɰɢɣ ɢɨɧɧɵɯ ɩɭɲɟɤ (ɢɨɧɧɵɯ ɢɫɬɨɱɧɢɤɨɜ). ȼ ɧɢɯ ɢɫɩɨɥɶɡɭɸɬɫɹ ɪɚɡɥɢɱɧɵɟ ɫɩɨɫɨɛɵ ɫɨɡɞɚɧɢɹ ɢɨɧɨɜ, ɧɚɩɪɢɦɟɪ, ɬɟɪɦɨɢɨɧɧɚɹ ɷɦɢɫɫɢɹ, ɢɨɧɢɡɚɰɢɹ ɝɚɡɚ ɢɥɢ ɩɚɪɨɜ ɜɟɳɟɫɬɜɚ ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ. ɇɚɢɛɨɥɟɟ ɷɮɮɟɤɬɢɜɧɵɦɢ ɢɫɬɨɱɧɢɤɚɦɢ ɢɨɧɨɜ ɹɜɥɹɸɬɫɹ ɩɥɚɡɦɟɧɧɵɟ, ɜ ɤɨɬɨɪɵɯ ɫɨɡɞɚɟɬɫɹ ɝɚɡɨɪɚɡɪɹɞɧɚɹ ɩɥɚɡɦɚ, ɚ ɢɨɧɵ ɜɵɬɹɝɢɜɚɸɬɫɹ ɷɥɟɤɬɪɢɱɟɫɤɢɦ ɩɨɥɟɦ ɫ ɟɟ ɝɪɚɧɢɰɵ. ɉɪɢɦɟɪɨɦ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɜɟɫɶɦɚ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɣ ɢɫɬɨɱɧɢɤ ɢɨɧɨɜ ɬɢɩɚ ɞɭɨɩɥɚɡɦɚɬɪɨɧ (ɪɢɫ. 5.13), ɜ ɤɨɬɨɪɨɦ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɪɚɡɪɹɞ ɮɨɪɦɢɪɭɟɬɫɹ ɦɟɠɞɭ ɤɚɬɨɞɨɦ ɢ ɩɪɨɦɟɠɭɬɨɱɧɵɦ ɚɧɨɞɨɦ. Ʉɨɧɢɱɟɫɤɚɹ ɮɨɪɦɚ ɩɪɨɦɟɠɭɬɨɱɧɨɝɨ ɚɧɨɞɚ ɩɪɢɜɨɞɢɬ ɤ ɫɠɚɬɢɸ ɩɥɚɡɦɵ ɜ ɪɚɣɨɧɟ ɜɵɯɨɞɧɨɝɨ ɨɬɜɟɪɫɬɢɹ. ɇɟɨɞɧɨɪɨɞɧɨɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɫɨɡɞɚɜɚɟɦɨɟ ɤɚɬɭɲɤɨɣ ɦɟɠɞɭ ɩɪɨɦɟɠɭɬɨɱɧɵɦ ɚɧɨɞɨɦ ɢ ɚɧɨɞɨɦ, ɩɪɢɜɨɞɢɬ ɤ ɞɨɩɨɥɧɢɬɟɥɶɧɨɦɭ ɫɠɚɬɢɸ ɩɥɚɡɦɟɧɧɨɣ ɫɬɪɭɢ. Ⱦɢɚɮɪɚɝɦɚ ɜ ɦɟɫɬɟ ɧɚɢɛɨɥɶɲɟɝɨ ɫɠɚɬɢɹ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ ɩɨɜɵɲɟɧɢɹ ɝɚɡɨɜɨɣ ɷɤɨɧɨɦɢɱɧɨɫɬɢ ɢɫɬɨɱɧɢɤɚ ɡɚ ɫɱɟɬ ɨɝɪɚɧɢɱɟɧɢɹ ɩɨɬɨɤɚ ɧɟɢɨɧɢɡɨɜɚɧɧɨɣ Ɋɢɫ. 5. 13. ɂɫɬɨɱɧɢɤ ɢɨɧɨɜ ɬɢɩɚ ɞɭɨɩɥɚɡɦɚɬɪɨɧ: 1 – ɤɨɦɩɨɧɟɧɬɵ ɪɚɛɨɱɟɝɨ ɜɟɳɟɫɬɜɚ. ɤɚɬɨɞ ɫ ɧɚɤɚɥɢɜɚɟɦɨɣ ɧɢɬɶɸ, 2 – ɩɪɨɦɟɠɭɬɨɱɧɵɣ ɷɥɟɤɬɪɨɞ, 3 – ɤɚɬɭɲɤɚ ɞɥɹ ɫɨɡɞɚɧɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɂɨɧɵ ɜɵɬɹɝɢɜɚɸɬɫɹ ɢɡ ɩɥɚɡɦɵ 4 – ɚɧɨɞ, 5 - ɚɧɨɞɧɚɹ ɜɫɬɚɜɤɚ, 6 – ɜɵɬɹɝɢɜɚɸɳɢɣ ɷɥɟɤɬɪɨɞɨɦ, ɤɨɬɨɪɵɣ ɫɬɨɢɬ ɫɪɚɡɭ ɷɥɟɤɬɪɨɞ, 7 – ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɚɹ ɥɢɧɡɚ, 8 – ɩɨɫɥɟ ɚɧɨɞɚ ɢ ɧɚ ɤɨɬɨɪɵɣ ɢɡɨɥɹɬɨɪ, 9 – ɮɥɚɧɟɰ ɜɚɤɭɭɦɧɨɣ ɤɚɦɟɪɵ, 10 – ɬɪɭɛɤɚ ɩɨɞɚɟɬɫɹ ɨɬɪɢɰɚɬɟɥɶɧɵɣ ɞɥɹ ɧɚɬɟɤɚɧɢɹ ɝɚɡɚ, 11 – ɞɢɚɮɪɚɝɦɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɚɧɨɞɚ ɩɨɬɟɧɰɢɚɥ. Ⱦɢɚɮɪɚɝɦɚ ɜɵɬɹɝɢɜɚɸɳɟɝɨ ɷɥɟɤɬɪɨɞɚ ɹɜɥɹɟɬɫɹ ɮɨɤɭɫɢɪɭɸɳɟɣ ɫɢɫɬɟɦɨɣ. Ʉɪɨɦɟ ɬɨɝɨ, ɝɪɚɧɢɰɚ ɩɥɚɡɦɵ, ɢɡ ɤɨɬɨɪɨɣ ɜɵɬɹɝɢɜɚɸɬɫɹ ɢɨɧɵ, ɹɜɥɹɟɬɫɹ ɬɚɤɠɟ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɣ ɥɢɧɡɨɣ. Ɏɨɪɦɚ ɝɪɚɧɢɰɵ ɩɥɚɡɦɵ ɫɭɳɟɫɬɜɟɧɧɨ ɜɥɢɹɟɬ ɧɚ ɪɚɫɯɨɞɢɦɨɫɬɶ ɮɨɪɦɢɪɭɟɦɨɝɨ ɜ ɢɨɧɧɨɨɩɬɢɱɟɫɤɢɣ ɫɢɫɬɟɦɟ ɢɨɧɧɨɝɨ ɩɭɱɤɚ. Ɇɟɧɹɹ ɤɨɧɰɟɧɬɪɚɰɢɸ ɩɥɚɡɦɵ (ɧɚɩɪɢɦɟɪ, ɦɟɧɹɹ ɬɨɤ ɪɚɡɪɹɞɚ) ɩɪɢ ɮɢɤɫɢɪɨɜɚɧɧɨɦ ɭɫɤɨɪɹɸɳɟɦ ɧɚɩɪɹɠɟɧɢɢ, ɦɨɠɧɨ ɭɩɪɚɜɥɹɬɶ ɮɨɪɦɨɣ ɩɥɚɡɦɟɧɧɨɣ ɝɪɚɧɢɰɵ. ɉɪɢ ɛɨɥɶɲɨɣ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɥɚɡɦɵ ɝɪɚɧɢɰɚ ɜɵɩɭɤɥɚɹ – ɩɭɱɨɤ ɫɢɥɶɧɨ ɪɚɫɯɨɞɢɬɫɹ. ɋɧɢɠɚɹ ɤɨɧɰɟɧɬɪɚɰɢɸ ɩɥɚɡɦɵ, ɦɨɠɧɨ ɫɨɡɞɚɬɶ ɩɥɨɫɤɭɸ ɟɟ ɝɪɚɧɢɰɭ, ɬɨɝɞɚ ɪɚɫɯɨɞɢɦɨɫɬɶ ɦɨɠɟɬ ɛɵɬɶ ɦɢɧɢɦɚɥɶɧɨɣ, ɚ ɜɵɬɹɝɢɜɚɟɦɵɣ ɢɡ ɢɫɬɨɱɧɢɤɚ ɬɨɤ ɩɨɞɱɢɧɹɟɬɫɹ ɡɚɤɨɧɭ «3/2» (ɫɦ. § 42). ɉɪɢ ɞɚɥɶɧɟɣɲɟɦ ɭɦɟɧɶɲɟɧɢɢ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɥɚɡɦɵ ɝɪɚɧɢɰɚ ɫɬɚɧɨɜɢɬɫɹ ɜɨɝɧɭɬɨɣ, ɢ ɪɚɫɯɨɞɢɦɨɫɬɶ ɩɭɱɤɚ ɜɧɨɜɶ ɜɨɡɪɚɫɬɚɟɬ. Ɋɚɫɱɟɬ ɩɚɪɚɦɟɬɪɨɜ ɮɨɤɭɫɢɪɨɜɤɢ ɩɭɱɤɚ ɫ ɭɱɟɬɨɦ ɝɪɚɧɢɰɵ ɩɥɚɡɦɵ ɹɜɥɹɟɬɫɹ ɞɨɫɬɚɬɨɱɧɨ ɫɥɨɠɧɨɣ ɡɚɞɚɱɟɣ ɢ ɜɨɡɦɨɠɟɧ ɥɢɲɶ ɱɢɫɥɟɧɧɵɦɢ ɦɟɬɨɞɚɦɢ.
ɗɥɟɤɬɪɨɧɧɵɟ ɦɢɤɪɨɫɤɨɩɵ
ɉɪɟɢɦɭɳɟɫɬɜɨ ɷɥɟɤɬɪɨɧɧɨɝɨ ɦɢɤɪɨɫɤɨɩɚ ɩɟɪɟɞ ɨɩɬɢɱɟɫɤɢɦ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɟɝɨ ɝɨɪɚɡɞɨ ɛɨɥɶɲɟɣ ɪɚɡɪɟɲɚɸɳɟɣ ɫɩɨɫɨɛɧɨɫɬɢ. Ɋɚɡɪɟɲɚɸɳɚɹ ɫɩɨɫɨɛɧɨɫɬɶ ɨɩɬɢɱɟɫɤɨɝɨ ɦɢɤɪɨɫɤɨɩɚ ɨɝɪɚɧɢɱɟɧɚ ɧɟɜɨɡɦɨɠɧɨɫɬɶɸ ɫɧɢɠɟɧɢɹ ɞɢɮɮɪɚɤɰɢɢ ɥɭɱɟɣ ɩɭɬɟɦ ɭɦɟɧɶɲɟɧɢɹ ɞɥɢɧɵ ɜɨɥɧɵ ɢɡ-ɡɚ ɨɝɪɚɧɢɱɟɧɧɨɝɨ ɞɢɚɩɚɡɨɧɚ ɞɥɢɧ ɜɨɥɧ ɜɢɞɢɦɨɝɨ ɫɜɟɬɚ. ȼ ɷɥɟɤɬɪɨɧɧɵɯ ɦɢɤɪɨɫɤɨɩɚɯ ɜɨɡɦɨɠɧɨ ɚ) ɭɦɟɧɶɲɚɬɶ ɞɥɢɧɭ ɜɨɥɧɵ ɛ) ɜ) ɞɟ Ȼɪɨɣɥɹ λ = h/(mv) ɞɨ ɧɟɫɤɨɥɶɤɢɯ ɚɧɝɫɬɪɟɦ Ɋɢɫ. 5.14. ɋɯɟɦɵ ɨɩɬɢɱɟɫɤɨɝɨ (ɚ), ɦɚɝɧɢɬɧɨɝɨ (ɛ) ɢ ɩɭɬɟɦ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ (ɜ) ɷɥɟɤɬɪɨɧɧɨɝɨ ɦɢɤɪɨɫɤɨɩɚ: Ʉ – ɢɫɬɨɱɧɢɤ ɷɥɟɤɬɪɨɧɨɜ, Ɉ – ɨɛɴɟɤɬ, D –ɞɢɚɮɪɚɝɦɚ, L1, L2, L3 – ɭɫɤɨɪɹɸɳɢɯ ɷɥɟɤɬɪɨɧɵ ɥɢɧɡɵ, I1, I2 – ɩɟɪɜɢɱɧɨɟ ɢ ɜɬɨɪɢɱɧɨɟ ɢɡɨɛɪɚɠɟɧɢɟ, S – ɷɤɪɚɧ. ɜɵɫɨɤɢɯ ɧɚɩɪɹɠɟɧɢɣ (ɞɨ ɧɟɫɤɨɥɶɤɢɯ ɞɟɫɹɬɤɨɜ ɢ ɞɚɠɟ ɫɨɬɟɧ ɤɷȼ). ɋɯɟɦɵ ɷɥɟɤɬɪɨɧɧɵɯ ɦɢɤɪɨɫɤɨɩɨɜ ɫ ɦɚɝɧɢɬɧɨɣ ɢ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɣ ɮɨɤɭɫɢɪɨɜɤɨɣ ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɚ ɪɢɫ. 5.14. ɂɫɫɥɟɞɭɟɦɵɣ ɨɛɴɟɤɬ ɩɪɨɫɜɟɱɢɜɚɟɬɫɹ ɩɭɱɤɨɦ ɦɨɧɨɯɪɨɦɚɬɢɱɟɫɤɢɯ ɷɥɟɤɬɪɨɧɨɜ. ɉɟɪɜɢɱɧɨɟ ɢɡɨɛɪɚɠɟɧɢɟ ɨɛɴɟɤɬɚ ɩɨɩɚɞɚɟɬ ɜ ɮɨɤɚɥɶɧɭɸ ɩɥɨɫɤɨɫɬɶ ɩɪɨɟɤɰɢɨɧɧɨɣ ɥɢɧɡɵ, ɤɨɬɨɪɚɹ ɞɚɟɬ ɭɜɟɥɢɱɟɧɧɨɟ ɢɡɨɛɪɚɠɟɧɢɟ ɨɛɴɟɤɬɚ ɧɚ ɷɤɪɚɧɟ. Ɉɞɧɢɦ ɢɡ ɫɭɳɟɫɬɜɟɧɧɵɯ ɬɪɟɛɨɜɚɧɢɣ ɤ ɷɥɟɤɬɪɨɧɧɨɦɭ ɦɢɤɪɨɫɤɨɩɭ ɹɜɥɹɟɬɫɹ ɩɨɞɞɟɪɠɚɧɢɟ ɜ ɨɛɥɚɫɬɢ ɥɢɧɡ ɜɵɫɨɤɨɝɨ ɜɚɤɭɭɦɚ (ɩɨɪɹɞɤɚ 10-4÷10-5 ɦɦ ɪɬ. ɫɬ.), ɬɚɤ ɤɚɤ ɩɪɢ ɬɚɤɢɯ ɜɵɫɨɤɢɯ ɧɚɩɪɹɠɟɧɢɹɯ ɜɨɡɦɨɠɧɨ ɜɨɡɧɢɤɧɨɜɟɧɢɟ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɪɚɡɪɹɞɚ, ɧɚɪɭɲɚɸɳɟɝɨ ɧɟɨɛɯɨɞɢɦɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ. Ɋɚɡɪɟɲɚɸɳɚɹ ɫɩɨɫɨɛɧɨɫɬɶ ɷɥɟɤɬɪɨɧɧɨɝɨ ɦɢɤɪɨɫɤɨɩɚ ɨɝɪɚɧɢɱɢɜɚɟɬɫɹ ɩɪɟɠɞɟ ɜɫɟɝɨ ɯɪɨɦɚɬɢɱɟɫɤɨɣ ɢ ɫɮɟɪɢɱɟɫɤɨɣ ɚɛɟɪɪɚɰɢɹɦɢ. Ɇɨɧɨɯɪɨɦɚɬɢɱɧɨɫɬɶ ɷɥɟɤɬɪɨɧɧɨɝɨ ɩɭɱɤɚ ɧɚɪɭɲɚɟɬɫɹ ɢɡ-ɡɚ ɤɨɥɟɛɚɧɢɣ ɭɫɤɨɪɹɸɳɟɝɨ ɧɚɩɪɹɠɟɧɢɹ ɢ ɪɚɡɛɪɨɫɚ ɷɧɟɪɝɢɣ ɷɥɟɤɬɪɨɧɨɜ, ɢɡɥɭɱɚɟɦɵɯ ɧɚɤɚɥɟɧɧɵɦ ɤɚɬɨɞɨɦ. ȼ ɦɚɝɧɢɬɧɨɦ ɷɥɟɤɬɪɨɧɧɨɦ ɦɢɤɪɨɫɤɨɩɟ ɤɨɥɟɛɚɧɢɟ ɫɢɥɵ ɬɨɤɚ ɜ ɨɛɦɨɬɤɟ ɥɢɧɡ ɩɪɢɜɨɞɢɬ ɤ ɞɨɩɨɥɧɢɬɟɥɶɧɨɦɭ ɪɚɡɦɵɬɢɸ ɢɡɨɛɪɚɠɟɧɢɹ. Ʉɪɨɦɟ ɩɪɨɫɜɟɱɢɜɚɸɳɢɯ ɷɥɟɤɬɪɨɧɧɵɯ ɦɢɤɪɨɫɤɨɩɨɜ ɲɢɪɨɤɨɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɩɨɥɭɱɢɥɢ ɫɤɚɧɢɪɭɸɳɢɟ ɷɥɟɤɬɪɨɧɧɵɟ ɦɨɤɪɨɫɤɨɩɵ, ɜ ɤɨɬɨɪɵɯ ɢɡɨɛɪɚɠɟɧɢɟ ɮɨɪɦɢɪɭɟɬɫɹ ɨɬɪɚɠɟɧɧɵɦɢ ɨɬ ɢɫɫɥɟɞɭɟɦɨɝɨ ɨɛɪɚɡɰɚ ɢɥɢ ɜɬɨɪɢɱɧɵɦɢ ɷɥɟɤɬɪɨɧɚɦɢ.
ȽɅȺȼȺ 6 ȼɅɂəɇɂȿ ɉɊɈɋɌɊȺɇɋɌȼȿɇɇɈȽɈ ɁȺɊəȾȺ ɗɅȿɄɌɊɈɇɇɕɏ ɂ ɂɈɇɇɕɏ ɉɍɑɄɈȼ §42. Ɉɝɪɚɧɢɱɟɧɢɟ ɬɨɤɚ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɦ ɡɚɪɹɞɨɦ ɜ ɞɢɨɞɟ ȼ ɩɪɨɦɟɠɭɬɤɟ ɞɥɢɧɨɣ d ɦɟɠɞɭ ɩɥɨɫɤɢɦɢ ɤɚɬɨɞɨɦ ɢ ɚɧɨɞɨɦ ɪɚɫɩɪɟɞɟɥɟɧɢɟ x ɩɨɬɟɧɰɢɚɥɚ ɜ ɜɚɤɭɭɦɟ ɥɢɧɟɣɧɨ: U(x)=U(a) (ɷɬɨ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɹɜɥɹɟɬɫɹ d ɪɟɲɟɧɢɟɦ ɭɪɚɜɧɟɧɢɹ Ʌɚɩɥɚɫɚ ∆U = 0). ɉɨ ɦɟɪɟ ɭɜɟɥɢɱɟɧɢɹ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ ɨɛɴɟɦɧɵɣ ɡɚɪɹɞ ρ(x) ɜ ɩɪɨɦɟɠɭɬɤɟ ɪɚɫɬɟɬ, ɢɡɦɟɧɹɹ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɢ ɩɪɢɜɨɞɹ ɤ ɜɨɡɧɢɤɧɨɜɟɧɢɸ ɜɛɥɢɡɢ ɩɨɜɟɪɯɧɨɫɬɢ ɤɚɬɨɞɚ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ «ɜɢɪɬɭɚɥɶɧɨɝɨ ɤɚɬɨɞɚ», ɨɬ ɤɨɬɨɪɨɝɨ ɷɥɟɤɬɪɨɧɵ ɨɬɪɚɠɚɸɬɫɹ ɨɛɪɚɬɧɨ ɧɚ ɤɚɬɨɞ (ɪɢɫ. 6.1). Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɨɦɟɠɭɬɤɟ ɧɟɨɛɯɨɞɢɦɨ ɪɟɲɚɬɶ ɭɪɚɜɧɟɧɢɟ ɉɭɚɫɫɨɧɚ ∆U= -4πρ(x) ɫ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ ɜ ɩɪɨɦɟɠɭɬɤɟ j = - ρv. ȿɫɥɢ ɫɱɢɬɚɬɶ, ɱɬɨ ɷɥɟɤɬɪɨɧɵ ɷɦɢɬɢɪɭɸɬɫɹ ɫ ɤɚɬɨɞɚ ɫ ɧɭɥɟɜɨɣ ɫɤɨɪɨɫɬɶɸ (ɬɟɩɥɨɜɚɹ ɷɧɟɪɝɢɹ ɷɦɢɫɫɢɨɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɦɧɨɝɨ ɦɟɧɶɲɟ ɷɧɟɪɝɢɢ, ɩɪɢɨɛɪɟɬɚɟɦɨɣ ɜ ɩɪɨɦɟɠɭɬɤɟ), ɬɨ ɭɫɬɨɣɱɢɜɵɦ ɹɜɥɹɟɬɫɹ ɪɟɠɢɦ, ɤɨɝɞɚ «ɜɢɪɬɭɚɥɶɧɵɣ ɤɚɬɨɞ» ɧɟ Ɋɢɫ. 6.1. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɥɨɫɤɨɦ ɞɢɨɞɟ ɨɛɪɚɡɭɟɬɫɹ, ɚ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɛɟɡ ɜɥɢɹɧɢɹ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɝɨ ɡɚɪɹɞɚ (I), ɜ ɪɟɠɢɦɟ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɤɚɬɨɞɚ ɪɚɜɧɨ ɨɝɪɚɧɢɱɟɧɢɹ ɬɨɤɚ ɨɛɴɟɦɧɵɦ ɡɚɪɹɞɨɦ (II) ɢ ɜ ɪɟɠɢɦɟ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɜɢɪɬɭɚɥɶɧɨɝɨ ɤɚɬɨɞɚ (III) dU ɧɭɥɸ: E = x = 0 = 0 . ɉɪɢ ɬɚɤɨɦ dx ɝɪɚɧɢɱɧɨɦ ɭɫɥɨɜɢɢ ɜ ɪɟɠɢɦɟ ɨɝɪɚɧɢɱɟɧɢɹ ɬɨɤɚ ɨɛɴɟɦɧɵɦ ɡɚɪɹɞɨɦ ɪɟɲɟɧɢɟɦ ɭɪɚɜɧɟɧɢɹ ɉɭɚɫɫɨɧɚ 4πj d 2U 1 = 2 dx 2e / m U
(6.1)
(ɡɞɟɫɶ ɭɱɬɟɧɨ, ɱɬɨ ɩɪɢ ɧɚɱɚɥɶɧɨɣ ɧɭɥɟɜɨɣ ɫɤɨɪɨɫɬɢ ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɨɜ mv2/2 = eU) ɹɜɥɹɟɬɫɹ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɨɦɟɠɭɬɤɟ ɜ ɜɢɞɟ: x U ( x) = U (a)( ) 4 / 3 . d
(6.2)
ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɩɥɨɬɧɨɫɬɶ ɷɥɟɤɬɪɨɧɧɨɝɨ ɬɨɤɚ, ɤɨɬɨɪɵɣ ɦɨɠɧɨ ɩɪɨɩɭɫɬɢɬɶ ɱɟɪɟɡ ɩɪɨɦɟɠɭɬɨɤ ɨɝɪɚɧɢɱɟɧɚ ɜɟɥɢɱɢɧɨɣ, ɡɚɜɢɫɹɳɟɣ ɨɬ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɚɧɨɞɟ Ua ɢ ɨɬ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɤɚɬɨɞɚɦ ɢ ɚɧɨɞɨɦ d:
2
j 3 / 2 [ Ⱥ / ɫɦ ] =
2 9π
3/ 2 e U a3 / 2 −6 U a [ ȼ] = 2.33 ⋅ 10 . me d 2 d 2 [ɫɦ]
(6.3)
ɗɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɩɨɥɭɱɢɥɨ ɧɚɡɜɚɧɢɟ ɡɚɤɨɧɚ ɑɚɣɥɶɞɚ-Ʌɟɧɝɦɸɪɚ, ɢɥɢ ɡɚɤɨɧɚ «3/2». Ⱦɥɹ ɢɨɧɧɨɝɨ ɬɨɤɚ: ji [ Ⱥ / ɫɦ] =
2 9π
U a3 / 2 [ ȼ] e U a3 / 2 = 5.46 . Mi d 2 M i [ɚ.ɟ. ɦ.]d 2 [ɫɦ]
(6.4)
ȿɫɥɢ ɭɱɢɬɵɜɚɬɶ ɧɚɱɚɥɶɧɭɸ ɫɤɨɪɨɫɬɶ ɷɦɢɬɢɪɨɜɚɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ v0, ɬɨ ɭɪɚɜɧɟɧɢɟ ɉɭɚɫɫɨɧɚ ɩɪɢɦɟɬ ɜɢɞ: 4πj d 2U , = 2 dx v 0 1 + 2eU /(mv 02 )
(6.5)
ɪɟɲɟɧɢɟɦ ɤɨɬɨɪɨɝɨ ɹɜɥɹɟɬɫɹ ɡɚɜɢɫɢɦɨɫɬɶ U(x) = (mv02/2e)((±(x/xm-1))4/3-1),
(6.6)
(ɡɞɟɫɶ “+” ɩɪɢ x > xm, “-“ ɩɪɢ x < xm). Ɉɤɨɥɨ ɤɚɬɨɞɚ ɜɨɡɧɢɤɚɟɬ «ɜɢɪɬɭɚɥɶɧɵɣ ɤɚɬɨɞ» (ɩɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ) ɝɥɭɛɢɧɨɣ eUm=mv02/2 ɧɚ ɪɚɫɫɬɨɹɧɢɢ mv03 ɨɬ ɤɚɬɨɞɚ (ɪɢɫ.6.1). 18πej Ⱦɥɹ ɰɢɥɢɧɞɪɢɱɟɫɤɢɯ ɞɢɨɞɨɜ ɩɪɟɞɟɥɶɧɚɹ ɩɥɨɬɧɨɫɬɶ ɷɥɟɤɬɪɨɧɧɨɝɨ ɬɨɤɚ ɬɚɤ ɠɟ ɡɚɜɢɫɢɬ ɨɬ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɚɧɨɞɟ, ɤɚɤ ɫɬɟɩɟɧɶ «3/2», ɧɨ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɤɚɬɨɞɨɦ ɢ ɚɧɨɞɨɦ ɧɨɫɢɬ ɛɨɥɟɟ ɫɥɨɠɧɵɣ ɯɚɪɚɤɬɟɪ (ɤɚɤ ɪɟɡɭɥɶɬɚɬ ɪɟɲɟɧɢɹ ɭɪɚɜɧɟɧɢɹ ɉɭɚɫɫɨɧɚ ɜ ɰɢɥɢɧɞɪɢɱɟɫɤɢɯ ɤɨɨɪɞɢɧɚɬɚɯ) ɢ r ɨɩɢɫɵɜɚɟɬɫɹ ɫɩɟɰɢɚɥɶɧɨɣ ɮɭɧɤɰɢɟɣ Ȼɨɝɭɫɥɚɜɫɤɨɝɨ β ( a ) , ɝɞɟ ra ɢ rk – ɪɚɞɢɭɫɵ rk ɚɧɨɞɚ ɢ ɤɚɬɨɞɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ: xm =
U a3 / 2 . (6.7) 2 ra ra β ( ) rk Ⱦɥɹ ɩɨɥɧɨɝɨ ɬɨɤɚ, ɩɪɢɯɨɞɹɳɟɝɨ ɧɚ ɚɧɨɞ, I3/2=J3/2Sa (Sa=2πrala – ɩɥɨɳɚɞɶ ɚɧɨɞɚ.): J3/ 2 =
2 9π
J 3 / 2 [ Ⱥ] =
2e me
1 9π
U 3 / 2 [ ȼ]S a [ɫɦ 2 ] 2e U a3 / 2 S a = 2.33 ⋅ 10 −6 a r me 2 2 ra ra β ( ) ra2 [ɫɦ]β 2 ( a ) rk rk
(6.8)
- ɮɨɪɦɭɥɚ Ʌɟɧɝɦɸɪɚ-Ȼɨɝɭɫɥɚɜɫɤɨɝɨ. Ɂɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ Ȼɨɝɭɫɥɚɜɫɤɨɝɨ ɞɥɹ ɲɢɪɨɤɨɝɨ ɞɢɚɩɚɡɨɧɚ ra/rk ɦɨɠɧɨ ɧɚɣɬɢ ɜ ɬɚɛɥɢɰɚɯ [29]. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɨɦɟɠɭɬɤɟ ɨɩɢɫɵɜɚɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ:
β 2 (r / rk ) 2 / 3 r U (r ) = U a ( ) 3 / 2 ( 2 ) . ra β (ra / rk )
(6.9)
Ⱦɥɹ ɫɮɟɪɢɱɟɫɤɨɝɨ ɞɢɨɞɚ ɩɨɥɧɵɣ ɬɨɤ ɧɚ ɚɧɨɞ Ia: 3/ 2 4 2e U a3 / 2 −6 U a [ ȼ] I a [ Ⱥ] = = 29.3 ⋅ 10 , (6.10) 9 m e 2 rk 2 rk α ( ) α ( ) ra ra ɝɞɟ α(ra/rk) – ɬɚɛɭɥɢɪɨɜɚɧɧɚɹ ɮɭɧɤɰɢɹ Ʌɟɧɝɦɸɪɚ [30]. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɦɟɠɞɭ ɤɚɬɨɞɨɦ ɢ ɚɧɨɞɨɦ:
U (r ) = U (a )(
α (rk / r ) 2 ) . α (rk / ra )
(6.11)
§43. ɉɪɟɞɟɥɶɧɚɹ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ ɩɭɱɤɚ ɱɚɫɬɢɰ ɜ ɩɪɨɥɟɬɧɨɦ ɩɪɨɦɟɠɭɬɤɟ ɜ ɜɚɤɭɭɦɟ
ɉɥɨɬɧɨɫɬɶ ɬɨɤɚ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɩɪɨɥɟɬɧɨɦ ɩɪɨɦɟɠɭɬɤɟ ɦɟɠɞɭ ɷɥɟɤɬɪɨɞɚɦɢ ɫ ɨɞɢɧɚɤɨɜɵɦ ɩɨɬɟɧɰɢɚɥɨɦ ɬɚɤɠɟ ɨɝɪɚɧɢɱɟɧɚ ɢɡ-ɡɚ ɫɨɛɫɬɜɟɧɧɨɝɨ ɨɛɴɟɦɧɨɝɨ ɡɚɪɹɞɚ ɢ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɩɨɬɟɧɰɢɚɥɚ ɩɭɱɤɚ. Ɋɚɫɫɦɨɬɪɢɦ ɷɬɭ ɡɚɞɚɱɭ (ɡɚɞɚɱɭ Ȼɭɪɫɢɚɧɚ) ɧɚ ɩɪɢɦɟɪɟ ɩɨɬɨɤɚ ɜ ɩɪɨɥɟɬɧɨɦ ɩɪɨɦɟɠɭɬɤɟ ɞɥɢɧɵ d ɢɨɧɨɜ ɦɚɫɫɵ M, ɭɫɤɨɪɟɧɧɵɯ ɞɨ ɷɬɨɝɨ ɜ ɩɥɨɫɤɨɦ ɞɢɨɞɟ ɩɨɬɟɧɰɢɚɥɨɦ U0 (ɪɢɫ. 6.2). Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɨɦɟɠɭɬɤɟ ɡɚɞɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ ɉɭɚɫɫɨɧɚ: 4πj M / 2e d 2U =− . 2 dx U0 −U
(6.12)
ɍɫɬɨɣɱɢɜɨɟ ɪɟɲɟɧɢɟ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɩɪɢ ɝɪɚɧɢɱɧɵɯ ɭɫɥɨɜɢɹɯ U(0) = U(d) = 0 ɫɭɳɟɫɬɜɭɟɬ ɬɨɥɶɤɨ ɩɪɢ ɞɨɩɨɥɧɢɬɟɥɶɧɨɦ ɝɪɚɧɢɱɧɨɦ ɭɫɥɨɜɢɢ ɧɚ ɩɨɥɟ [31]:
Ε0 = dψ/dξ0 < 2 , ψ
ɝɞɟ
=
U/U0,
(6.13)
ξ
=
x/rd,
2
rd = Mv 0 /(4πne 2 ) - ɞɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ
ɩɭɱɤɚ. ɗɬɨ ɭɫɥɨɜɢɟ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɭɫɥɨɜɢɸ ɧɚ ɦɚɤɫɢɦɚɥɶɧɭɸ ɞɥɢɧɭ ɩɪɨɥɟɬɧɨɝɨ ɩɪɨɦɟɠɭɬɤɚ: d < (4 2 /3)rd = dm
Ɋɢɫ. 6.2. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɨɥɟɬɧɨɦ ɩɪɨɦɟɠɭɬɤɟ
(6.14).
ɗɤɫɬɪɟɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ dm ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɤɪɢɬɢɱɟɫɤɨɦɭ ɡɧɚɱɟɧɢɸ ɦɚɤɫɢɦɭɦɚ ɩɨɬɟɧɰɢɚɥɚ: (6.15) Um = (3/4)U0.
ɉɪɢ ɜɨɡɪɚɫɬɚɧɢɢ ɩɥɨɬɧɨɫɬɢ ɢɨɧɧɨɝɨ ɬɨɤɚ ɩɨɬɟɧɰɢɚɥ ɜ ɩɪɨɥɟɬɧɨɦ ɩɪɨɦɟɠɭɬɤɟ ɛɭɞɟɬ ɜɨɡɪɚɫɬɚɬɶ ɞɨ Um, ɡɚɬɟɦ ɫɤɚɱɤɨɦ ɜɨɡɧɢɤɚɟɬ «ɜɢɪɬɭɚɥɶɧɵɣ ɚɧɨɞ» ɫ Um = U0, ɨɬ ɤɨɬɨɪɨɝɨ ɩɪɨɢɡɨɣɞɟɬ ɨɬɪɚɠɟɧɢɟ ɱɚɫɬɢ ɢɨɧɨɜ ɨɛɪɚɬɧɨ ɜ ɫɬɨɪɨɧɭ ɢɫɬɨɱɧɢɤɚ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɱɟɝɨ ɬɨɤ ɧɚ ɤɨɥɥɟɤɬɨɪ ɭɦɟɧɶɲɢɬɫɹ ɜ 4.5 ɪɚɡɚ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɬɨɤ ɜ ɩɪɨɥɟɬɧɨɦ ɩɪɨɦɟɠɭɬɤɟ ɨɝɪɚɧɢɱɟɧ ɬɨɤɨɦ Ȼɭɪɫɢɚɧɚ: 8 jȻ = 9π
2e U 03 / 2 = 8 j3 / 2 . M d2
(6.16)
Ɇɟɯɚɧɢɡɦ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ Ȼɭɪɫɢɚɧɚ ɫɜɹɡɚɧ ɫ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɨɛɪɚɬɧɨɣ ɫɜɹɡɶɸ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ ɩɭɱɤɚ ɢ ɜɧɟɲɧɟɣ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɰɟɩɶɸ, ɤɨɝɞɚ ɩɨɜɵɲɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɩɭɱɤɚ ɧɚ ɦɚɥɭɸ ɜɟɥɢɱɢɧɭ ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɜɵɡɵɜɚɟɬ ɞɚɥɶɧɟɣɲɟɟ ɟɝɨ ɩɨɜɵɲɟɧɢɟ. ɗɬɚ ɫɜɹɡɶ ɜɨɡɧɢɤɚɟɬ, ɤɨɝɞɚ ɞɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ ɩɭɱɤɚ ɫɬɚɧɨɜɢɬɫɹ ɦɟɧɶɲɟ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɷɥɟɤɬɪɨɞɚɦɢ. Ɍɨɱɧɨ ɬɚɤɨɟ ɠɟ ɨɝɪɚɧɢɱɟɧɢɟ ɫɭɳɟɫɬɜɭɟɬ ɢ ɞɥɹ ɩɨɬɨɤɚ ɷɥɟɤɬɪɨɧɨɜ ɜ ɜɚɤɭɭɦɟ. Ⱦɚɠɟ ɜ ɫɥɭɱɚɟ ɫɤɨɦɩɟɧɫɢɪɨɜɚɧɧɨɝɨ ɩɭɱɤɚ ɷɥɟɤɬɪɨɧɨɜ, ɤɨɝɞɚ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɣ ɡɚɪɹɞ ɷɥɟɤɬɪɨɧɨɜ ɜ ɩɪɨɥɟɬɧɨɦ ɩɪɨɦɟɠɭɬɤɟ ɫɤɨɦɩɟɧɫɢɪɨɜɚɧ ɢɨɧɚɦɢ (ɡɚɞɚɱɚ ɉɢɪɫɚ), ɜɨɡɧɢɤɚɟɬ ɨɝɪɚɧɢɱɟɧɢɟ ɧɚ ɦɚɤɫɢɦɚɥɶɧɨ ɜɨɡɦɨɠɧɭɸ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ ɢɡ-ɡɚ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ, ɬɚɤɠɟ ɩɪɢɜɨɞɹɳɟɣ ɤ ɨɛɪɚɡɨɜɚɧɢɸ ɜɢɪɬɭɚɥɶɧɨɝɨ ɤɚɬɨɞɚ ɢ ɡɚɩɢɪɚɧɢɸ ɩɭɱɤɚ. Ɏɢɡɢɱɟɫɤɚɹ ɩɪɢɱɢɧɚ ɩɢɪɫɨɜɫɤɨɣ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɬɚ ɠɟ, ɱɬɨ ɢ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ Ȼɭɪɫɢɚɧɚ, – ɩɨɥɨɠɢɬɟɥɶɧɚɹ ɨɛɪɚɬɧɚɹ ɫɜɹɡɶ ɷɥɟɤɬɪɨɧɨɜ ɩɭɱɤɚ ɫ ɷɥɟɤɬɪɨɧɚɦɢ ɜɧɟɲɧɟɣ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɰɟɩɢ, ɤɨɬɨɪɚɹ ɜɨɡɧɢɤɚɟɬ, ɟɫɥɢ ɞɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ ɩɭɱɤɚ ɫɬɚɧɨɜɢɬɫɹ ɦɟɧɶɲɟ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɷɥɟɤɬɪɨɞɚɦɢ. Ʉɚɱɟɫɬɜɟɧɧɨ ɷɬɢ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɫɪɨɞɧɢ ɩɭɱɤɨɜɨɣ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ, ɩɪɢ ɤɨɬɨɪɨɣ ɷɧɟɪɝɢɹ ɧɚɩɪɚɜɥɟɧɧɨɝɨ ɞɜɢɠɟɧɢɹ ɩɟɪɟɞɚɟɬɫɹ ɜ ɷɧɟɪɝɢɸ ɩɥɚɡɦɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ (ɫɦ. §37). ɍɫɥɨɜɢɟɦ ɭɫɬɨɣɱɢɜɨɫɬɢ ɧɚ ɞɥɢɧɭ ɩɪɨɥɟɬɧɨɝɨ ɩɪɨɦɟɠɭɬɤɚ ɜ ɫɥɭɱɚɟ ɫɤɨɦɩɟɧɫɢɪɨɜɚɧɧɨɝɨ ɩɨɬɨɤɚ ɹɜɥɹɟɬɫɹ d < πrd, ɚ ɩɪɟɞɟɥɶɧɚɹ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ (ɬɨɤ ɉɢɪɫɚ) ɪɚɜɧɚ:
jɉ =
2e U 03 / 2 9π 2 ≈ j3 / 2 . 4 4(1 + (m / M ) 1 / 3 ) m d 2
π
(6.17)
Ɋɚɫɯɨɠɞɟɧɢɟ ɩɭɱɤɨɜ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɨɛɫɬɜɟɧɧɨɝɨ ɨɛɴɟɦɧɨɝɨ ɡɚɪɹɞɚ
Ɉɫɧɨɜɧɨɣ ɩɪɨɛɥɟɦɨɣ ɬɪɚɧɫɩɨɪɬɢɪɨɜɤɢ ɢɧɬɟɧɫɢɜɧɵɯ ɩɭɱɤɨɜ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɹɜɥɹɟɬɫɹ ɢɯ ɪɚɫɯɨɠɞɟɧɢɟ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɨɛɫɬɜɟɧɧɨɝɨ ɨɛɴɟɦɧɨɝɨ ɡɚɪɹɞɚ. Ⱦɥɹ ɨɬɵɫɤɚɧɢɹ ɮɨɪɦɵ ɩɭɱɤɚ ɧɟɨɛɯɨɞɢɦɨ ɪɟɲɚɬɶ ɭɪɚɜɧɟɧɢɟ ɉɭɚɫɫɨɧɚ (ɞɥɹ ɥɟɧɬɨɱɧɨɝɨ ɩɭɱɤɚ ɞɜɭɦɟɪɧɨɟ): d 2U d 2U + = −4πρ ( x, y ) , (6.18) dx 2 dy 2 ɚ ɬɚɤɠɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɞɥɹ ɝɪɚɧɢɱɧɨɣ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ. ȼ ɫɥɭɱɚɟ ɛɟɫɤɨɧɟɱɧɨɝɨ ɥɟɧɬɨɱɧɨɝɨ ɩɭɱɤɚ (ɪɢɫ.6.3), ɭ ɤɨɬɨɪɨɝɨ ɲɢɪɢɧɚ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ ɬɨɥɳɢɧɵ 2X, ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɧɚ ɝɪɚɧɢɰɟ ɜɦɟɫɬɨ ɭɪɚɜɧɟɧɢɹ ɉɭɚɫɫɨɧɚ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɟɨɪɟɦɭ Ƚɚɭɫɫɚ ɨ ɪɚɜɟɧɫɬɜɟ ɩɨɬɨɤɚ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɱɟɪɟɡ ɩɨɜɟɪɯɧɨɫɬɶ ɢ ɡɚɪɹɞɚ, ɡɚɤɥɸɱɟɧɧɨɝɨ ɜ ɨɛɴɟɦɟ,
ɨɝɪɚɧɢɱɟɧɧɨɦ ɷɬɨɣ ɩɨɜɟɪɯɧɨɫɬɶɸ. Ɍɨɝɞɚ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɧɚ ɝɪɚɧɢɰɟ: Ex = J/(2ε0v)=J(/2ε0 2eU 0 / m ),
(6.19)
ɝɞɟ J – ɥɢɧɟɣɧɚɹ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ (ɬɨɤ ɧɚ ɟɞɢɧɢɰɭ ɲɢɪɢɧɵ ɛɟɫɤɨɧɟɱɧɨɝɨ ɥɟɧɬɨɱɧɨɝɨ ɩɭɱɤɚ), U0 – ɩɨɬɟɧɰɢɚɥ, ɤɨɬɨɪɵɦ ɛɵɥ ɭɫɤɨɪɟɧ ɩɭɱɨɤ ɞɨ ɜɯɨɞɚ ɜ ɩɪɨɥɟɬɧɵɣ ɩɪɨɦɟɠɭɬɨɤ. Ɋɟɲɚɹ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ mx = eE x , ɩɨɥɭɱɢɦ ɩɪɨɮɢɥɶ ɝɪɚɧɢɰɵ ɩɭɱɤɚ, ɤɨɬɨɪɚɹ ɨɩɢɫɵɜɚɟɬɫɹ ɡɚɜɢɫɢɦɨɫɬɶɸ x(z): x = x0 + tgγ⋅z + pz2/2 ,
(6.20)
Ɋɢɫ. 6.3. ɉɥɨɫɤɢɣ ɷɥɟɤɬɪɨɧɧɵɣ ɥɟɧɬɨɱɧɵɣ ɩɭɱɨɤ
J
, ɝɞɟ γ - ɭɝɨɥ 2e 3 / 2 4ε 0 U0 m ɫɯɨɞɢɦɨɫɬɢ ɩɭɱɤɚ ɧɚ ɜɯɨɞɟ, ɬ. ɟ. ɭɝɨɥ ɦɟɠɞɭ ɧɚɩɪɚɜɥɟɧɢɟɦ ɫɤɨɪɨɫɬɢ ɝɪɚɧɢɱɧɨɝɨ ɷɥɟɤɬɪɨɧɚ ɢ ɧɚɩɪɚɜɥɟɧɢɟɦ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɩɭɱɤɚ ɩɨ ɨɫɢ z. Ɇɟɫɬɨɩɨɥɨɠɟɧɢɟ ɫɚɦɨɝɨ ɭɡɤɨɝɨ ɜ ɩɨɩɟɪɟɱɧɨɦ ɪɚɡɦɟɪɟ ɭɱɚɫɬɤɚ ɩɭɱɤɚ, ɬɚɤ ɧɚɡɵɜɚɟɦɨɝɨ «ɤɪɨɫɫɨɜɟɪɚ» xɤɪ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɭɫɥɨɜɢɹ: ɝɞɟ
p=
dx/dz = 0, ɬ.ɟ. zɤɪ= tgγ/p.
(6.21)
Ⱦɥɹ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɩɭɱɤɚ, ɜɥɟɬɚɸɳɟɝɨ ɜ ɩɪɨɥɟɬɧɵɣ ɭɱɚɫɬɨɤ ɩɚɪɚɥɥɟɥɶɧɨ ɨɫɢ z ɫ ɧɚɱɚɥɶɧɵɦ ɪɚɞɢɭɫɨɦ r0, ɡɚɜɢɫɢɦɨɫɬɶ ɪɚɞɢɭɫɚ ɩɭɱɤɚ r(z) ɡɚɞɚɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ: z 4 e U 03 / 4 = 2m I 1 / 2 r0
R
³ 1
Ɋɢɫ. 6.4. Ɋɚɫɯɨɞɢɦɨɫɬɶ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɷɥɟɤɬɪɨɧɧɨɝɨ ɩɭɱɤɚ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɨɛɫɬɜɟɧɧɨɝɨ ɨɛɴɟɦɧɨɝɨ ɡɚɪɹɞɚ
U 03 / 4 [ɤȼ] R dς = 32.3 1 / 2 , I [ ɦȺ] ³1 ln ς ln ς
dς
(6.22)
ɝɞɟ I – ɩɨɥɧɵɣ ɬɨɤ ɩɭɱɤɚ, ɭɫɤɨɪɟɧɧɨɝɨ ɩɨɬɟɧɰɢɚɥɨɦ U0, R=r/r0 (ɱɢɫɥɨɜɨɣ ɤɨɷɮɮɢɰɢɟɧɬ ɞɚɧ ɞɥɹ ɷɥɟɤɬɪɨɧɧɨɝɨ ɩɭɱɤɚ). Ⱦɥɹ ɫɯɨɞɹɳɟɝɨɫɹ ɩɭɱɤɚ, ɜɯɨɞɹɳɟɝɨ ɜ ɩɪɨɥɟɬɧɵɣ ɩɪɨɦɟɠɭɬɨɤ ɩɨɞ ɭɝɥɨɦ γ ɤ ɨɫɢ z (ɪɢɫ. 6.4): R
z 2e U0 ³ = r0 m 1
dς 8e 2e I ln ς + U 0 ⋅ tg 2 γ mU 0 m
.
(6.23)
Ɋɚɞɢɭɫ ɩɭɱɤɚ ɜ ɧɚɢɛɨɥɟɟ ɭɡɤɨɦ ɦɟɫɬɟ (ɜ ɤɪɨɫɫɨɜɟɪɟ) ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ r U 3/ 2 e 2 U 3 / 2 [ɤȼ] 2 ɫɨɨɬɧɨɲɟɧɢɹ: ln 0 = 0 tg γ ≈ 1.04 ⋅ 10 3 0 tg γ , (6.24) rmin I 2m I [ ɦȺ] ɝɞɟ ɱɢɫɥɟɧɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɞɚɧ ɞɥɹ ɷɥɟɤɬɪɨɧɧɨɝɨ ɩɭɱɤɚ. ɉɪɢ ɷɬɨɦ ɧɟ ɛɵɥɚ ɭɱɬɟɧɚ ɫɢɥɚ Ʌɨɪɟɧɰɚ, ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɞɜɢɠɭɳɭɸɫɹ ɡɚɪɹɠɟɧɧɭɸ ɱɚɫɬɢɰɭ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ. ȼ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɷɬɚ ɮɨɤɭɫɢɪɭɸɳɚɹ ɫɢɥɚ ɜ ɫɨɛɫɬɜɟɧɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɬɨɤɚ ɩɭɱɤɚ ɛɭɞɟɬ ɫɭɳɟɫɬɜɟɧɧɚ ɬɨɥɶɤɨ ɩɪɢ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɢɯ ɫɤɨɪɨɫɬɹɯ ɱɚɫɬɢɰ. Ɋɚɫɯɨɠɞɟɧɢɟ ɩɭɱɤɨɜ ɨɝɪɚɧɢɱɟɧɧɵɯ ɩɨɩɟɪɟɱɧɵɯ ɪɚɡɦɟɪɨɜ ɫɥɟɞɭɟɬ ɭɱɢɬɵɜɚɬɶ ɧɟ ɬɨɥɶɤɨ ɜ ɩɪɨɥɟɬɧɵɯ ɩɪɨɦɟɠɭɬɤɚɯ, ɧɨ ɢ ɜ ɷɥɟɤɬɪɨɧɧɵɯ ɢɥɢ ɢɨɧɧɵɯ ɩɭɲɤɚɯ. ɉɢɪɫɨɦ ɛɵɥɨ ɩɨɤɚɡɚɧɨ, ɱɬɨ ɦɨɠɧɨ ɩɨɞɨɛɪɚɬɶ ɮɨɪɦɭ ɨɤɚɣɦɥɹɸɳɢɯ ɩɭɱɨɤ ɩɪɨɦɟɠɭɬɨɱɧɵɯ ɷɥɟɤɬɪɨɞɨɜ ɬɚɤ, ɱɬɨɛɵ ɤɨɦɩɟɧɫɢɪɨɜɚɬɶ ɪɚɫɬɚɥɤɢɜɚɸɳɟɟ ɞɟɣɫɬɜɢɟ ɨɛɴɟɦɧɨɝɨ ɡɚɪɹɞɚ ɩɭɱɤɚ ɢ ɫɨɯɪɚɧɢɬɶ ɩɪɹɦɨɥɢɧɟɣɧɨɫɬɶ ɟɝɨ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ (ɩɭɲɤɢ ɉɢɪɫɚ). Ⱦɥɹ ɷɬɨɝɨ ɧɟɨɛɯɨɞɢɦɨ, ɱɬɨɛɵ ɞɥɹ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɜɧɟ ɩɭɱɤɚ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɟɝɨ ɜ ɫɥɭɱɚɟ ɩɥɨɫɤɨɣ ɝɟɨɦɟɬɪɢɢ ɭɪɚɜɧɟɧɢɸ d 2U d 2U Ɋɢɫ. 6.5. Ƚɟɨɦɟɬɪɢɹ ɷɤɜɢɩɨɬɟɧɰɢɚɥɟɣ ɜ ɩɭɲɤɟ Ʌɚɩɥɚɫɚ: ɧɚ + = 0, 2 2 ɉɢɪɫɚ, ɮɨɪɦɢɪɭɸɳɟɣ ɩɚɪɚɥɥɟɥɶɧɵɣ ɩɭɱɨɤ dx dy ɝɪɚɧɢɰɟ ɩɭɱɤɚ ɜɵɩɨɥɧɹɥɨɫɶ ɭɫɥɨɜɢɟ dU/dy = 0. Ɋɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɟ Ʌɚɩɥɚɫɚ ɫ x ɭɱɟɬɨɦ ɷɬɨɝɨ ɭɫɥɨɜɢɹ ɢ ɡɚɜɢɫɢɦɨɫɬɢ ɩɨɬɟɧɰɢɚɥɚ ɧɚ ɨɫɢ U ( x) = U (a)( ) 4 / 3 d ɩɨɡɜɨɥɹɟɬ ɨɩɪɟɞɟɥɢɬɶ ɬɪɟɛɭɟɦɭɸ ɝɟɨɦɟɬɪɢɸ ɷɥɟɤɬɪɨɞɨɜ, ɤɨɬɨɪɚɹ ɞɥɹ ɩɥɨɫɤɨɝɨ ɫɥɭɱɚɹ ɡɚɞɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ: 4 ( x 2 + y 2 ) 2 / 3 cos( arctg ( y / x)) = U . 3
(6.25)
ɍɝɨɥ ɧɚɤɥɨɧɚ ɩɥɨɫɤɨɫɬɢ ɤɚɬɨɞɚ (U = 0) ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɩɭɱɤɚ arctg(y/x) = 3π/8 = 67.5ɨ. ȼ ɫɥɭɱɚɟ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɝɟɨɦɟɬɪɢɢ ɱɢɫɥɟɧɧɵɣ ɪɚɫɱɟɬ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɭɝɨɥ ɧɚɤɥɨɧɚ ɷɥɟɤɬɪɨɞɚ, ɩɪɢɥɟɝɚɸɳɟɝɨ ɤ ɤɚɬɨɞɭ, ɬɚɤɠɟ ɫɨɫɬɚɜɥɹɟɬ 67.5ɨ (ɪɢɫ .6.5).
ȽɅȺȼȺ 7 ɗɆɂɋɋɂɈɇɇȺə ɗɅȿɄɌɊɈɇɂɄȺ §44. Ɍɟɪɦɨɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɂɫɩɭɫɤɚɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɧɚɝɪɟɬɵɦɢ ɩɪɨɜɨɞɹɳɢɦɢ ɦɚɬɟɪɢɚɥɚɦɢ ɧɚɡɵɜɚɟɬɫɹ ɬɟɪɦɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɟɣ. ɗɬɨ ɹɜɥɟɧɢɟ ɛɵɥɨ ɨɛɧɚɪɭɠɟɧɨ ɜ 1883 ɝ. ɗɞɢɫɨɧɨɦ. Ⱥɧɚɥɢɬɢɱɟɫɤɢɣ ɪɚɫɱɟɬ ɩɥɨɬɧɨɫɬɢ ɬɟɪɦɨɷɦɢɫɫɢɨɧɧɨɝɨ ɬɨɤɚ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɢɫɯɨɞɹ ɢɡ ɦɨɞɟɥɢ Ɂɨɦɦɟɪɮɟɥɶɞɚ ɨ ɧɚɯɨɠɞɟɧɢɢ ɷɥɟɤɬɪɨɧɨɜ ɜ ɦɟɬɚɥɥɟ ɤɚɤ ɜ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɹɦɟ. ɗɥɟɤɬɪɨɧɵ ɜ ɦɟɬɚɥɥɟ, ɤɚɠɞɵɣ ɢɡ ɤɨɬɨɪɵɯ ɦɨɠɧɨ ɨɩɢɫɚɬɶ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɟɣ:
ψk( r& ) =
&& 1 exp( i k r), L3 / 2
(7.1)
ɝɞɟ L3 = V – ɨɛɴɟɦ ɦɟɬɚɥɥɚ, ɜɨɥɧɨɜɨɣ ɜɟɤɬɨɪ k = 2π/L, ɩɨɞɱɢɧɹɸɬɫɹ ɪɚɫɩɪɟɞɟɥɟɧɢɸ Ɏɟɪɦɢ-Ⱦɢɪɚɤɚ, ɬ. ɟ. ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɱɚɫɬɢɰ ɜ ɨɞɧɨɦ ɫɨɫɬɨɹɧɢɢ f(E) =
1 . E − EF 1 + exp( ) k BT
(7.2)
ɉɪɢ Ɍ = 0 ɜɫɟ ɷɥɟɤɬɪɨɧɵ ɧɚɯɨɞɹɬɫɹ ɜɧɭɬɪɢ ɫɮɟɪɵ Ɏɟɪɦɢ. ɋ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ «ɩɥɨɬɧɨɫɬɶ» ɷɥɟɤɬɪɨɧɨɜ ɪɚɜɧɚ 1/h3, ɚ ɬɚɤɠɟ ɩɪɢɧɰɢɩɚ ɉɚɭɥɢ ɨ ɞɜɭɯ ɜɨɡɦɨɠɧɵɯ ɨɪɢɟɧɬɚɰɢɹɯ ɫɩɢɧɚ, ɱɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ, «ɧɚɯɨɞɹɳɢɯɫɹ» ɜ ɩɪɟɞɟɥɚɯ ɫɮɟɪɵ Ɏɟɪɦɢ ɫ ɪɚɞɢɭɫɨɦ kF: N = 2(1/h3)(4/3)πpF3V. ɂɦɩɭɥɶɫ, ɤɨɬɨɪɵɣ ɢɦɟɸɬ ɷɥɟɤɬɪɨɧɵ ɧɚ ɫɮɟɪɟ Ɏɟɪɦɢ: pF = h(3n/8π)1/3, ɝɞɟ n = N/V – ɱɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ ɜ 1 ɫɦ3. ɗɧɟɪɝɢɹ Ɏɟɪɦɢ EF = pF2/(2m) =
!2 (3π 2 n) 2 / 3 . 2m
(7.3)
Ʉɨɥɢɱɟɫɬɜɨ ɱɚɫɬɢɰ ɫ ɷɧɟɪɝɢɟɣ ɦɟɧɶɲɟ E: n(E) =
1 3π
2
(
2mE 3 / 2 ) , !2
(7.4)
ɬɨɝɞɚ ɩɥɨɬɧɨɫɬɶ ɱɚɫɬɢɰ (ɱɢɫɥɨ ɱɚɫɬɢɰ, ɢɦɟɸɳɢɯ ɷɧɟɪɝɢɸ ɨɬ E ɞɨ E + dE)
ρ(E) = dn =
1 2π
2
(
2m 3 / 2 1 / 2 ) E dE . !2
ɋ ɭɱɟɬɨɦ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ɏɟɪɦɢ-Ⱦɢɪɚɤɚ:
Ɋɢɫ. 7.1. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɜ ɦɟɬɚɥɥɟ ɩɨ ɷɧɟɪɝɢɹɦ
ρ(E) =
1 2π 2
(
2m 3 / 2 ) !2
E 1 / 2 dE . E − EF 1 + exp( ) k BT
(7.5)
ɉɪɢ ɚɛɫɨɥɸɬɧɨɦ ɧɭɥɟ ɬɟɦɩɟɪɚɬɭɪɵ ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɨɜ ɦɟɬɚɥɥɚ ɧɟ ɦɨɠɟɬ ɛɵɬɶ ɛɨɥɶɲɟ ɷɧɟɪɝɢɢ Ɏɟɪɦɢ, ɩɨɷɬɨɦɭ ɧɢ ɨɞɢɧ ɷɥɟɤɬɪɨɧ ɧɟ ɦɨɠɟɬ ɜɵɣɬɢ ɢɡ ɦɟɬɚɥɥɚ, ɚ ɮɭɧɤɰɢɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɨɛɪɵɜɚɟɬɫɹ ɩɪɢ EF (ɪɢɫ. 7.1). ɉɪɢ Ɍ > 0 ɨɛɪɵɜ ɫɝɥɚɠɢɜɚɟɬɫɹ, ɩɨɹɜɥɹɟɬɫɹ «ɯɜɨɫɬ» ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɫ ɷɧɟɪɝɢɹɦɢ ɛɨɥɶɲɟ EF, ɢɦɟɧɧɨ ɭ ɷɬɢɯ ɷɥɟɤɬɪɨɧɨɜ, ɤɨɥɢɱɟɫɬɜɨ ɤɨɬɨɪɵɯ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨ ɪɚɫɬɟɬ ɫ ɪɨɫɬɨɦ ɬɟɦɩɟɪɚɬɭɪɵ ɩɨɜɟɪɯɧɨɫɬɢ, ɩɨɹɜɥɹɟɬɫɹ ɧɟɧɭɥɟɜɚɹ ɜɟɪɨɹɬɧɨɫɬɶ ɩɪɟɨɞɨɥɟɧɢɹ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ ɧɚ ɝɪɚɧɢɰɟ ɦɟɬɚɥɥɚ. ɉɨɷɬɨɦɭ ɬɟɪɦɨɷɦɢɫɫɢɨɧɧɵɣ ɬɨɤ ɡɚɦɟɬɟɧ ɬɨɥɶɤɨ ɞɥɹ ɧɚɝɪɟɬɵɯ ɬɟɥ. ȿɝɨ ɜɟɥɢɱɢɧɚ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟɦ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨ ɧɨɪɦɚɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɷɧɟɪɝɢɢ Wx ɜ ɩɪɟɞɟɥɚɯ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɨɬ Wa ɞɨ ∞ , ɝɞɟ Wa - ɜɵɫɨɬɚ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ. ɋ ɭɱɟɬɨɦ ɜɟɪɨɹɬɧɨɫɬɢ ɩɪɟɨɞɨɥɟɧɢɹ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ, ɚ ɬɚɤɠɟ ɫ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ ɞɥɹ ɬɟɪɦɨɷɥɟɤɬɪɨɧɨɜ Wx - EF >> kBT , ɩɥɨɬɧɨɫɬɶ ɬɟɪɦɨɷɦɢɫɫɢɨɧɧɨɝɨ ɬɨɤɚ ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɚ ɮɨɪɦɭɥɨɣ Ɋɢɱɚɪɞɫɨɧɚ-Ⱦɷɲɦɚɧɚ: j t = AT 2 exp( −
eϕ a ), kT
(7.6)
ɝɞɟ ϕa = Wa - EF – ɪɚɛɨɬɚ ɜɵɯɨɞɚ ɷɥɟɤɬɪɨɧɚ ɢɡ ɦɚɬɟɪɢɚɥɚ ɤɚɬɨɞɚ, ɪɚɜɧɚɹ ɧɚɢɦɟɧɶɲɟɣ ɷɧɟɪɝɢɢ, ɤɨɬɨɪɭɸ ɧɭɠɧɨ ɫɨɨɛɳɢɬɶ ɷɥɟɤɬɪɨɧɚɦ ɞɥɹ ɢɯ ɷɦɢɫɫɢɢ, kB – ɩɨɫɬɨɹɧɧɚɹ Ȼɨɥɶɰɦɚɧɚ. ȼɟɥɢɱɢɧɭ A = A0D , ɭɱɢɬɵɜɚɸɳɭɸ ɩɪɨɡɪɚɱɧɨɫɬɶ ɛɚɪɶɟɪɚ ɦɟɠɞɭ ɦɟɬɚɥɥɨɦ ɢ ɜɚɤɭɭɦɨɦ D = (1 - r ), r – ɤɨɷɮɮɢɰɢɟɧɬ ɨɬɪɚɠɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɨɬ ɛɚɪɶɟɪɚ, ɭɫɪɟɞɧɟɧɧɵɣ ɩɨ ɷɧɟɪɝɢɹɦ ɷɥɟɤɬɪɨɧɨɜ, ɢɧɨɝɞɚ ɧɚɡɵɜɚɸɬ «ɩɨɫɬɨɹɧɧɨɣ Ɋɢɱɚɪɞɫɨɧɚ», ɝɞɟ 2
A0 [
4π mek B Ⱥ ]= = 120 .4 2 2 h3 ɫɦ Ʉ
(7.7)
- ɭɧɢɜɟɪɫɚɥɶɧɚɹ ɩɨɫɬɨɹɧɧɚɹ. ɋɥɟɞɭɟɬ ɭɱɟɫɬɶ, ɱɬɨ ɪɚɛɨɬɚ ɜɵɯɨɞɚ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ (ɜɫɥɟɞɫɬɜɢɟ ɬɟɩɥɨɜɨɝɨ ɪɚɫɲɢɪɟɧɢɹ), ɨɛɵɱɧɨ ɷɬɚ ɡɚɜɢɫɢɦɨɫɬɶ ɥɢɧɟɣɧɚɹ:
ϕa = ϕ0 + α(T-T0),
(7.8)
α = dϕ/dT|T=To = 10-5 ÷ 10-4 ɷȼ/ɝɪɚɞ – ɬɟɦɩɟɪɚɬɭɪɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ, ɤɨɬɨɪɵɣ ɦɨɠɟɬ ɛɵɬɶ ɤɚɤ ɩɨɥɨɠɢɬɟɥɶɧɵɦ, ɬɚɤ ɢ ɨɬɪɢɰɚɬɟɥɶɧɵɦ. Ɂɧɚɱɟɧɢɟ ɩɨɫɬɨɹɧɧɨɣ Ɋɢɱɚɪɞɫɨɧɚ Ⱥ ɞɥɹ ɪɚɡɧɵɯ ɦɟɬɚɥɥɨɜ ɢɡɦɟɧɹɸɬɫɹ ɨɬ 15 ɞɨ 350 Ⱥ/(ɫɦ2⋅Ʉ2). ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɟ ɨɩɪɟɞɟɥɟɧɢɟ ɪɚɛɨɬɵ ɜɵɯɨɞɚ ϕa ɢ «ɩɨɫɬɨɹɧɧɨɣ» Ɋɢɱɚɪɞɫɨɧɚ Ⱥ ɦɨɠɧɨ ɩɪɨɜɟɫɬɢ ɩɨ ɦɟɬɨɞɭ «ɩɪɹɦɨɣ Ɋɢɱɚɪɞɫɨɧɚ», ɫɬɪɨɹ ɩɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɞɚɧɧɵɦ ɡɚɜɢɫɢɦɨɫɬɶ ln(jT/T2) ɨɬ 1/T. ɉɨ ɬɚɧɝɟɧɫɭ ɭɝɥɚ ɧɚɤɥɨɧɚ ɩɨɥɭɱɟɧɧɨɣ ɩɪɹɦɨɣ ɨɩɪɟɞɟɥɹɸɬ ɪɚɛɨɬɭ ɜɵɯɨɞɚ ϕa, ɚ ɬɨɱɤɚ ɩɟɪɟɫɟɱɟɧɢɹ ɩɪɹɦɨɣ ɫ ɨɫɶɸ ɨɪɞɢɧɚɬ ɞɚɟɬ ɡɧɚɱɟɧɢɟ ln(A) .
Ɂɚɜɢɫɢɦɨɫɬɶ ɩɥɨɬɧɨɫɬɢ ɬɟɪɦɨɷɦɢɫɫɢɨɧɧɨɝɨ ɬɨɤɚ (7.6) ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɢɡ ɭɫɥɨɜɢɹ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ, ɟɫɥɢ ɪɚɫɫɱɢɬɚɬɶ ɩɨɬɨɤ ɷɥɟɤɬɪɨɧɨɜ ɜ ɜɚɤɭɭɦ: jɌ = enevɫɪ/4, ɝɞɟ
n e = 2(
me k B T 3 / 2 eϕ ) exp(− a ) k BT 2π!
(7.9) (7.10)
8kTe - ɫɪɟɞɧɹɹ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɚɹ ɫɤɨɪɨɫɬɶ. πm e ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ (ɢɥɢ ɩɪɟɧɟɛɪɟɠɢɦɨ ɦɚɥɨɣ ɧɚɩɪɹɠɟɧɧɨɫɬɢ) ɭɫɤɨɪɹɸɳɟɝɨ ɷɥɟɤɬɪɨɧɵ ɜɧɟɲɧɟɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɷɦɢɬɢɪɨɜɚɧɧɵɟ ɷɥɟɤɬɪɨɧɵ ɫɨɡɞɚɸɬ ɨɤɨɥɨ ɩɨɜɟɪɯɧɨɫɬɢ ɨɬɪɢɰɚɬɟɥɶɧɵɣ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɣ ɡɚɪɹɞ, ɨɝɪɚɧɢɱɢɜɚɸɳɢɣ ɬɨɤ ɬɟɪɦɨɷɦɢɫɫɢɢ. ɉɨɷɬɨɦɭ, ɜ ɫɥɭɱɚɟ ɦɚɥɵɯ ɧɚɩɪɹɠɟɧɢɣ ɦɟɠɞɭ ɤɚɬɨɞɨɦ ɢ ɚɧɨɞɨɦ ɬɟɪɦɨɷɦɢɫɫɢɨɧɧɵɣ ɬɨɤ ɦɨɠɧɨ ɩɪɢɪɚɜɧɹɬɶ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ j3/2, 3/2 ɡɚɜɢɫɢɦɨɫɬɶ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ jɌ ɨɬ ɧɚɩɪɹɠɟɧɢɹ jɌ ∼ Ua . ɉɪɢ ɞɚɥɶɧɟɣɲɟɦ ɭɜɟɥɢɱɟɧɢɢ Ua ɨɛɴɟɦɧɵɣ ɡɚɪɹɞ ɭ ɤɚɬɨɞɚ ɢɫɱɟɡɚɟɬ ɢ, ɤɚɡɚɥɨɫɶ ɛɵ, ɬɨɤ ɞɨɥɠɟɧ ɜɵɣɬɢ ɧɚ ɧɚɫɵɳɟɧɢɟ, ɤɨɝɞɚ ɜɫɟ ɷɦɢɬɢɪɨɜɚɧɧɵɟ ɷɥɟɤɬɪɨɧɵ ɭɯɨɞɹɬ ɧɚ ɚɧɨɞ, ɢ ɧɟ ɡɚɜɢɫɟɬɶ ɨɬ Ua. Ɉɞɧɚɤɨ, ɤɚɤ ɩɨɤɚɡɚɥɢ ɷɤɫɩɟɪɢɦɟɧɬɵ, ɩɪɢ ɞɚɥɶɧɟɣɲɟɦ ɭɜɟɥɢɱɟɧɢɢ Ua ɬɨɤ ɷɦɢɫɫɢɢ ɩɪɨɞɨɥɠɚɟɬ ɦɟɞɥɟɧɧɨ ɪɚɫɬɢ. Ɋɨɫɬ ɷɥɟɤɬɪɨɧɧɨɝɨ ɬɨɤɚ ɷɦɢɫɫɢɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɜɧɟɲɧɟɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜɫɥɟɞɫɬɜɢɟ ɫɧɢɠɟɧɢɹ ɪɚɛɨɬɵ ɜɵɯɨɞɚ ɷɥɟɤɬɪɨɧɚ ɢɡ ɬɜɟɪɞɨɝɨ ɬɟɥɚ (ɩɨɧɢɠɟɧɢɹ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ)
- ɩɥɨɬɧɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ, v ɫɪ =
ϕȿ = ϕa - ∆ϕɲ
(7.11)
ɧɚɡɵɜɚɟɬɫɹ ɷɮɮɟɤɬɨɦ ɒɨɬɬɤɢ (ɪɢɫ. 7.2). ɉɨɬɟɧɰɢɚɥ ɩɨɥɹ ɧɚ ɪɚɫɫɬɨɹɧɢɢ x ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ ɦɟɬɚɥɥɚ ɫ ɭɱɟɬɨɦ ɫɢɥ ɡɟɪɤɚɥɶɧɨɝɨ ɨɬɨɛɪɚɠɟɧɢɹ ɡɚɪɹɞɚ ɢ ɜɧɟɲɧɟɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ E ɦɨɠɧɨ ɨɩɢɫɚɬɶ ɜ ɜɢɞɟ: U(x) = EF + ϕa - e2/4x – eEx.
(7.12)
ɋɧɢɠɟɧɢɟ ɪɚɛɨɬɵ ɜɵɯɨɞɚ ɦɨɠɧɨ ɨɰɟɧɢɬɶ ɢɡ ɫɨɨɬɧɨɲɟɧɢɹ, ɩɪɢɪɚɜɧɢɜɚɹ ɧɚ ɜɟɪɲɢɧɟ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɯɨɥɦɚ ɫɢɥɵ ɬɨɪɦɨɠɟɧɢɹ ɜɧɭɬɪɶ ɦɟɬɚɥɥɚ ɢ ɫɢɥɵ ɭɫɤɨɪɟɧɢɹ ɜɨ ɜɧɟ: eE = e2/4x2m, ɬɨɝɞɚ ɩɨɥɨɠɟɧɢɟ ɦɚɤɫɢɦɭɦɚ xm= e / 4 E ,
(7.13)
ɚ ɩɨɬɟɧɰɢɚɥ ɜ ɦɚɤɫɢɦɭɦɟ Um = EF + ϕa - e3/2E1/2.
(7.14)
ɋɧɢɠɟɧɢɟ ɪɚɛɨɬɵ ɜɵɯɨɞɚ: e∆ϕɲ[ɷȼ] = e3/2E1/2 = 3.79⋅E1/2 [ȼ/ɫɦ]. ɉɥɨɬɧɨɫɬɶ ɬɟɪɦɨɷɦɢɫɫɢɨɧɧɨɝɨ ɬɨɤɚ ɫ ɭɱɟɬɨɦ ɷɮɮɟɤɬɚ ɒɨɬɬɤɢ:
(7.15)
jɌɒ = jTexp(e3/2E1/2/kBT) = jTexp(4.39E1/2[ȼ/ɫɦ]/T[K]).
(7.16)
§45. Ⱥɜɬɨɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ
ȼ ɩɪɢɫɭɬɫɬɜɢɢ ɜɧɟɲɧɟɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜɵɫɨɤɨɣ ɧɚɩɪɹɠɟɧɧɨɫɬɢ E (106÷107 ȼ/ɫɦ), ɩɨɦɢɦɨ ɭɜɟɥɢɱɟɧɢɹ ɬɨɤɚ ɷɦɢɫɫɢɢ ɡɚ ɫɱɟɬ ɫɧɢɠɟɧɢɹ ɪɚɛɨɬɵ ɜɵɯɨɞɚ (ɷɮɮɟɤɬɚ ɒɨɬɬɤɢ), ɢɡ-ɡɚ ɨɝɪɚɧɢɱɟɧɧɨɫɬɢ ɬɨɥɳɢɧɵ ɛɚɪɶɟɪɚ ɩɨɹɜɥɹɟɬɫɹ ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɞɛɚɪɶɟɪɧɨɝɨ ɩɟɪɟɯɨɞɚ – «ɬɭɧɟɥɶɧɨɝɨ» ɷɮɮɟɤɬɚ. ɂɫɩɭɫɤɚɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɜɧɟɲɧɟɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɨɛɭɫɥɨɜɥɟɧɨɟ ɜɟɪɨɹɬɧɨɫɬɶɸ ɩɨɞɛɚɪɶɟɪɧɨɝɨ ɩɟɪɟɯɨɞɚ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ, ɢɦɟɸɳɟɝɨ ɜɨ ɜɧɟɲɧɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ ɨɝɪɚɧɢɱɟɧɧɭɸ ɲɢɪɢɧɭ, ɧɚɡɵɜɚɟɬɫɹ ɚɜɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɟɣ. Ʉɨɷɮɮɢɰɢɟɧɬ ɩɪɨɯɨɠɞɟɧɢɹ (ɩɪɨɡɪɚɱɧɨɫɬɢ) ɛɚɪɶɟɪɚ ɡɚɜɢɫɢɬ ɨɬ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɚ Wx, ɜɵɫɨɬɵ Ɋɢɫ. 7.2 ɉɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ ɧɚ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ Wa, ɢ ɞɥɹ ɝɪɚɧɢɰɟ ɦɟɬɚɥɥ – ɜɚɤɭɭɦ ɩɪɹɦɨɭɝɨɥɶɧɨɝɨ ɛɚɪɶɟɪɚ ɲɢɪɢɧɵ h ɜɵɪɚɠɚɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ: D(W x ) = exp(−4π 2m e (Wa − W x ) / h) .
(7.17)
Ⱦɥɹ ɜɵɱɢɫɥɟɧɢɹ ɩɪɨɡɪɚɱɧɨɫɬɢ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ ɧɟɩɪɹɦɨɭɝɨɥɶɧɨɣ ɮɨɪɦɵ ɦɨɠɧɨ ɟɝɨ ɪɚɡɞɟɥɢɬɶ ɧɚ ɪɹɞ ɩɪɹɦɨɭɝɨɥɶɧɵɯ ɛɚɪɶɟɪɨɜ ɲɢɪɢɧɵ dx, ɢ ɩɪɨɢɧɬɟɝɪɢɪɨɜɚɬɶ ɩɨ ɲɢɪɢɧɟ ɛɚɪɶɟɪɚ. ȼ ɢɬɨɝɟ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɚ ɜɵɪɚɠɚɟɬɫɹ ɮɨɪɦɭɥɨɣ: D(W x ) = exp[−
8π 2m e 3he
⋅(
Wa − W x 3 / 2 ) ⋅ θ (ζ )] , E
(7.18)
ɝɞɟ θ(ζ) – ɮɭɧɤɰɢɹ ɇɨɪɞɝɟɣɦɚ, ɜɵɪɚɠɚɸɳɚɹɫɹ ɱɟɪɟɡ ɷɥɥɢɩɬɢɱɟɫɤɢɟ ɢɧɬɟɝɪɚɥɵ, ∆ϕ ɲ ∆ϕ ɲ e3 / 2 E1/ 2 . ɇɟɤɨɬɨɪɵɟ ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ ɇɨɪɞɝɟɣɦɚ = = ɝɞɟ ζ = ϕ a (W x ) Wa − W x Wa − W x ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɬɚɛɥɢɰɟ 7.1. Ɍɚɛɥɢɰɚ 7.1. 0 ∆ϕɲ/ ϕa 1 θ
0.1 0.98
0.2 0.94
0.3 0.87
0.4 0.79
0.5 0.69
0.6 0.58
0.7 0.45
0.8 0.31
0.9 0.16
1.0 0
Ⱦɥɹ 0 < ζ < 1 θ(ζ) ≈ 0.955 – 1.03ζ 2. ɉɥɨɬɧɨɫɬɶ ɬɨɤɚ ɚɜɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɦɨɠɧɨ ɨɩɢɫɚɬɶ ɮɨɪɦɭɥɨɣ Ɏɚɭɥɟɪɚ-ɇɨɪɞɝɟɣɦɚ:
j Ⱥɗ [
(eϕ a ) 3 / 2 θ (∆ϕ ɲ / ϕ a ) Ⱥ E2 = ⋅ ⋅ − )= ] exp( B 0 eϕ a E / E0 ɫɦ 2
= 6.2 ⋅ 10
−6
⋅
E F / eϕ a E 2 [ ȼ / ɫɦ] E F + eϕ a
6.85 ⋅ 10 7 ⋅ (eϕ a ) 3 / 2 θ (∆ϕ ɲ / ϕ a ) ⋅ exp(− ), E[ ȼ / ɫɦ]
(7.19)
ɝɞɟ EF – ɷɧɟɪɝɢɹ Ɏɟɪɦɢ, B0=e2/(8πh), E0=8π 2me /(3he). ȼɥɢɹɧɢɟ ɦɧɨɠɢɬɟɥɹ E2, ɩɨɞɨɛɧɨ ɜɥɢɹɧɢɸ ɦɧɨɠɢɬɟɥɹ T2 ɜ ɮɨɪɦɭɥɟ Ɋɢɱɚɪɞɫɨɧɚ-Ⱦɷɲɦɚɧɚ, ɧɟɡɧɚɱɢɬɟɥɶɧɨ. Ȼɨɥɟɟ ɫɭɳɟɫɬɜɟɧɧɨ ɜɥɢɹɧɢɟ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɪɚɛɨɬɵ ɜɵɯɨɞɚ ɷɥɟɤɬɪɨɧɚ eϕa. Ⱥɜɬɨɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɫ ɦɢɤɪɨɫɤɨɩɢɱɟɫɤɢɯ ɨɫɬɪɢɣ ɱɚɳɟ ɜɫɟɝɨ ɹɜɥɹɟɬɫɹ ɩɪɢɱɢɧɨɣ ɩɪɨɛɨɹ ɜɚɤɭɭɦɧɵɯ ɩɪɨɦɟɠɭɬɤɨɜ. Ⱥɜɬɨɷɥɟɤɬɪɨɧɧɵɟ ɤɚɬɨɞɵ ɢɡɝɨɬɨɜɥɹɸɬɫɹ ɜ ɜɢɞɟ ɢɝɥ (ɨɫɬɪɢɣ) ɫ ɛɨɥɶɲɨɣ ɤɪɢɜɢɡɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɨɤɨɥɨ ɤɨɬɨɪɵɯ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɟ ɩɨɥɟ ɞɨɫɬɢɝɚɟɬ ɛɨɥɟɟ 106 ȼ/ɫɦ. §46. ɂɡɦɟɧɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɷɦɢɬɬɟɪɚ ɩɪɢ ɬɟɪɦɨ- ɢ ɚɜɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ
ɋɪɟɞɧɹɹ ɷɧɟɪɝɢɹ, ɭɧɨɫɢɦɚɹ ɷɥɟɤɬɪɨɧɨɦ ɫ ɩɨɜɟɪɯɧɨɫɬɢ ɩɪɢ ɬɟɪɦɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ, ɦɨɠɟɬ ɛɵɬɶ ɜɵɱɢɫɥɟɧɚ ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ ɦɚɤɫɜɟɥɥɨɜɫɤɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɩɨ ɷɧɟɪɝɢɹɦ, ɫ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ ɷɧɟɪɝɢɹ ɜɵɲɟɞɲɢɯ ɢɡ ɦɟɬɚɥɥɚ ɷɥɟɤɬɪɨɧɨɜ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɫɨɨɬɧɨɲɟɧɢɣ ɦɟɠɞɭ ɤɨɦɩɨɧɟɧɬɚɦɢ ɫɤɨɪɨɫɬɢ ɷɥɟɤɬɪɨɧɚ ɜ ɦɟɬɚɥɥɟ v ɢ ɜ ɜɚɤɭɭɦɟ u : mu x 2 / 2 = mv x 2 − Wa ° , (7.20) ®u y = v y ° ¯u z = v z ɝɞɟ ɨɫɶ x ɧɚɩɪɚɜɥɟɧɚ ɩɨ ɧɨɪɦɚɥɢ ɤ ɩɨɜɟɪɯɧɨɫɬɢ. ɑɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɩɨ ɧɨɪɦɚɥɢ ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɦɟɬɚɥɥɚ ɫɨ ɫɤɨɪɨɫɬɹɦɢ ɜ ɩɪɟɞɟɥɚɯ ɨɬ ux ɞɨ ux + dux ɡɚɞɚɟɬɫɹ ɦɨɞɢɮɢɰɢɪɨɜɚɧɧɵɦ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ Ɇɚɤɫɜɟɥɥɚ : 2
2mWa + m 2 u x 4πm 2 dN = exp( / ) exp( )u x du x = − k T E k T B F B 2mk B T h3 2
2
mu x mu x mN 4πm 2 k B T exp(−eϕ a / k B T ) exp(− exp(− )u x du x = )u x du x = 3 k BT 2k B T 2k B T h W N exp(− x )dW x , (7.21) = k BT k BT
=
ɝɞɟ N = jT/e – ɱɢɫɥɨ ɬɟɪɦɨɷɥɟɤɬɪɨɧɨɜ ɫ ɟɞɢɧɢɰɵ ɩɥɨɳɚɞɢ ɜ ɫɟɤɭɧɞɭ. ɋɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɩɨ ɧɨɪɦɚɥɢ ɤ ɩɨɜɟɪɯɧɨɫɬɢ: u x =∞
Wx =
³
u x =0
∞
Wx
dN = k B T ³ ε exp(−ε )dε =k B T , N 0
(7.22)
ɝɞɟ ε = Wx/kBT. Ⱦɥɹ ɞɜɭɯ ɞɪɭɝɢɯ ɧɚɩɪɚɜɥɟɧɢɣ ɫɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɤɚɤ ɞɥɹ ɨɛɵɱɧɨɝɨ 1 1 ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ɇɚɤɫɜɟɥɥɚ: W y = k B T ɢ W z = k B T . ȼ ɢɬɨɝɟ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ 2 2 ɩɨɥɧɨɣ ɷɧɟɪɝɢɢ ɜɵɥɟɬɚɸɳɟɝɨ ɫ ɩɨɜɟɪɯɧɨɫɬɢ ɷɦɢɬɬɟɪɚ ɬɟɦɩɟɪɚɬɭɪɵ Ɍs: W = W x + W y + W z = 2 k B TS . (7.23)
ȿɫɥɢ ɦɟɠɞɭ ɤɚɬɨɞɨɦ ɢ ɚɧɨɞɨɦ ɩɨɞɚɬɶ ɬɨɪɦɨɡɹɳɭɸ ɪɚɡɧɨɫɬɶ ɩɨɬɟɧɰɢɚɥɨɜ, ɬɨ ɭɫɥɨɜɢɟ ɩɨɩɚɞɚɧɢɹ ɷɥɟɤɬɪɨɧɚ ɧɚ ɤɚɬɨɞ: mev2/2 ≥ -eUa, ɝɞɟ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɚɧɨɞɟ Ua < 0. Ɍɨɤ ɧɚ ɚɧɨɞ: ∞
Ia = Sa
³
−
2 eU a me
ux Ne
eU me mu x2 exp(− )du x = I ɷ exp( a ) , k BT 2k B T k BT
(7.24)
ɝɞɟ Iɷ – ɬɨɤ ɫ ɷɦɢɬɬɟɪɚ. Ɇɟɧɹɹ Ua, ɦɨɠɧɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɨɩɪɟɞɟɥɹɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɩɨ ɷɧɟɪɝɢɹɦ. ɗɤɫɩɟɪɢɦɟɧɬɵ ɩɨɞɬɜɟɪɠɞɚɸɬ ɬɨ, ɱɬɨ ɷɦɢɬɢɪɨɜɚɧɧɵɟ ɷɥɟɤɬɪɨɧɵ ɢɦɟɸɬ ɪɚɫɩɪɟɞɟɥɟɧɢɟ Ɇɚɤɫɜɟɥɥɚ, ɩɪɢɱɟɦ ɬɟɦɩɟɪɚɬɭɪɚ ɷɥɟɤɬɪɨɧɨɜ ɩɨ ɦɚɤɫɜɟɥɥɨɜɫɤɨɦɭ ɪɚɫɩɪɟɞɟɥɟɧɢɸ ɪɚɜɧɚ ɬɟɦɩɟɪɚɬɭɪɟ ɷɦɢɬɬɟɪɚ. ɉɨɷɬɨɦɭ ɧɚɱɚɥɶɧɵɟ ɷɧɟɪɝɢɢ ɷɦɢɬɬɢɪɨɜɚɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ (ɫ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ 1 ɷȼ ≈ 11600 Ʉ) ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɧɭɥɟɜɵɦɢ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɷɧɟɪɝɢɹɦɢ, ɩɪɢɨɛɪɟɬɚɟɦɵɦɢ ɜ ɭɫɤɨɪɹɸɳɟɣ ɪɚɡɧɨɫɬɢ ɩɨɬɟɧɰɢɚɥɨɜ ɭɠɟ ɜ ɧɟɫɤɨɥɶɤɨ ɜɨɥɶɬ. Ɉɞɧɚɤɨ ɞɥɹ ɨɯɥɚɠɞɟɧɢɹ ɩɨɜɟɪɯɧɨɫɬɢ ɷɦɢɬɬɟɪɚ ɷɬɚ ɷɧɟɪɝɢɹ ɫɭɳɟɫɬɜɟɧɧɚ, ɤ ɬɨɦɭ ɠɟ ɤɚɠɞɵɣ ɷɥɟɤɬɪɨɧ ɩɨɦɢɦɨ ɬɟɩɥɨɜɨɣ ɷɧɟɪɝɢɢ ɭɧɨɫɢɬ ɢɡ ɦɟɬɚɥɥɚ ɷɧɟɪɝɢɸ, ɪɚɜɧɭɸ ɪɚɛɨɬɟ ɜɵɯɨɞɚ. Ɇɨɳɧɨɫɬɶ ɩɨɜɟɪɯɧɨɫɬɧɨɝɨ ɨɯɥɚɠɞɟɧɢɹ w = (jT/e)(2kBTS+eϕa). ɉɪɢ ɚɜɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɡɚ ɫɱɟɬ «ɬɭɧɧɟɥɶɧɨɝɨ» ɷɮɮɟɤɬɚ ɷɦɢɬɢɪɭɸɬɫɹ ɷɥɟɤɬɪɨɧɵ, ɨɛɥɚɞɚɸɳɢɟ ɷɧɟɪɝɢɟɣ, ɦɟɧɶɲɟɣ ɷɧɟɪɝɢɢ Ɏɟɪɦɢ: E < EF. ɋɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɷɦɢɬɢɪɨɜɚɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɜ ɷɬɨɦ ɫɥɭɱɚɟ W = - ϕa – (EF-E), ɦɨɳɧɨɫɬɶ ɩɨɜɟɪɯɧɨɫɬɧɨɝɨ ɧɚɝɪɟɜɚ ɩɨɜɟɪɯɧɨɫɬɢ ɡɚ ɫɱɟɬ ɩɪɢɯɨɞɚ ɛɨɥɟɟ ɜɵɫɨɤɨɷɧɟɪɝɟɬɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɢɡ ɨɛɴɟɦɚ ɦɟɬɚɥɥɚ: w = (jT/e)( EF-E). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɬɟɪɦɨɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɫɨɩɪɨɜɨɠɞɚɟɬɫɹ ɨɯɥɚɠɞɟɧɢɟɦ ɩɨɜɟɪɯɧɨɫɬɢ, ɚ ɚɜɬɨɷɥɟɤɬɪɨɧɧɚɹ – ɧɚɝɪɟɜɨɦ (ɷɮɮɟɤɬ ɇɨɬɬɢɧɝɟɦɚ). §47. Ɏɨɬɨɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ
ɂɫɩɭɫɤɚɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɩɚɞɚɸɳɟɝɨ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɢɡɥɭɱɟɧɢɹ ɧɚɡɵɜɚɟɬɫɹ ɮɨɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɟɣ (Ɏɗɗ). ɉɨɬɨɤ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɢɡɥɭɱɟɧɢɹ ɱɚɫɬɶɸ ɨɬɪɚɠɚɟɬɫɹ, ɚ ɱɚɫɬɶɸ ɩɪɨɧɢɤɚɟɬ ɜɧɭɬɪɶ ɬɟɥɚ ɢ ɬɚɦ ɩɨɝɥɨɳɚɟɬɫɹ, ɨɬɞɚɜɚɹ ɷɧɟɪɝɢɸ ɷɥɟɤɬɪɨɧɚɦ ɩɪɨɜɨɞɢɦɨɫɬɢ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɩɪɟɨɞɨɥɟɬɶ ɩɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ ɢ ɜɵɣɬɢ ɢɡ ɬɟɥɚ. Ɏɗɗ ɛɵɥɚ ɨɛɧɚɪɭɠɟɧɚ Ƚɟɪɰɟɦ 1887 ɝ. Ɉɫɧɨɜɧɵɟ ɡɚɤɨɧɵ Ɏɗɗ, ɭɫɬɚɧɨɜɥɟɧɧɵɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɡɚɞɨɥɝɨ ɞɨ ɬɟɨɪɟɬɢɱɟɫɤɨɝɨ ɨɛɨɫɧɨɜɚɧɢɹ, ɫɜɨɞɹɬɫɹ ɤ ɫɥɟɞɭɸɳɟɦɭ: 1. Ɏɨɬɨɷɥɟɤɬɪɨɧɧɵɣ ɬɨɤ ɜ ɪɟɠɢɦɟ ɧɚɫɵɳɟɧɢɹ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɩɚɞɚɸɳɟɦɭ ɧɚ ɷɦɢɬɬɟɪ ɩɥɨɬɧɨɫɬɢ ɩɨɬɨɤɚ ɦɨɳɧɨɫɬɢ (ɢɥɢ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɨɛɥɭɱɟɧɢɹ I [ȼɬ/ɫɦ2])
jɎɗ ∼ I (ɡɚɤɨɧ ɋɬɨɥɟɬɨɜɚ – 1889 ɝ.).
(7.25)
2. Ɍɟɨɪɟɬɢɱɟɫɤɨɟ ɨɛɨɫɧɨɜɚɧɢɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɨɬɤɪɵɬɨɣ Ʌɟɧɚɪɞɨɦ (1899 ɝ.) ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ – ɦɚɤɫɢɦɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɮɨɬɨɷɥɟɤɬɪɨɧɨɜ ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɱɚɫɬɨɬɟ ɩɚɞɚɸɳɟɝɨ ɢɡɥɭɱɟɧɢɹ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɟɝɨ ɢɧɬɟɧɫɢɜɧɨɫɬɢ – ɜɩɟɪɜɵɟ ɞɚɥ ɗɣɧɲɬɟɣɧ, ɜɜɟɞɹ ɜ ɮɢɡɢɤɭ ɩɨɧɹɬɢɟ ɨ ɤɜɚɧɬɚɯ ɫɜɟɬɚ (ɮɨɬɨɧɚɯ): 2 mv max = hν − eϕ a (ɡɚɤɨɧ ɗɣɧɲɬɟɣɧɚ). (7.26) 2 Ɉɬɤɥɨɧɟɧɢɟ ɨɬ ɡɚɤɨɧɚ ɗɣɧɲɬɟɣɧɚ ɜɨɡɧɢɤɚɟɬ ɩɪɢ ɛɨɥɶɲɢɯ ɢɧɬɟɧɫɢɜɧɨɫɬɹɯ ɢɡɥɭɱɟɧɢɹ, ɤɨɝɞɚ ɷɥɟɤɬɪɨɧ ɦɨɠɟɬ ɩɨɝɥɨɳɚɬɶ ɧɟɫɤɨɥɶɤɨ n ɮɨɬɨɧɨɜ: 2 mv max = nhν − eϕ a 2
(7.27)
3. ɋɥɟɞɫɬɜɢɟɦ ɡɚɤɨɧɚ ɗɣɧɲɬɟɣɧɚ ɹɜɥɹɟɬɫɹ ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɞɥɢɧɨɜɨɥɧɨɜɨɣ (ɤɪɚɫɧɨɣ) ɝɪɚɧɢɰɵ λ ɨɛɥɚɫɬɢ ɫɩɟɤɬɪɚ ɩɚɞɚɸɳɟɝɨ ɢɡɥɭɱɟɧɢɹ, ɤɨɬɨɪɨɟ ɦɨɠɟɬ ɜɵɡɵɜɚɬɶ ɮɨɬɨɷɦɢɫɫɢɸ ɷɥɟɤɬɪɨɧɨɜ:
λ < λɝɪ, ɢɥɢ ν > νɝɪ = c/λɝɪ = eϕa/h,
(7.28)
ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɝɪɚɧɢɱɧɚɹ ɞɥɢɧɚ ɜɨɥɧɵ ɜɵɪɚɠɚɟɬɫɹ ɱɟɪɟɡ ɪɚɛɨɬɭ ɜɵɯɨɞɚ:
λɝɪ=12300/( eϕa[ɷȼ]) ɩɪɢ Ɍ = 0 Ʉ. ɉɪɢ Ɍ ≠ 0 Ʉ ɜ ɦɟɬɚɥɥɟ ɢɦɟɸɬɫɹ ɷɥɟɤɬɪɨɧɵ
ɫ ɷɧɟɪɝɢɹɦɢ, ɛɨɥɶɲɢɦɢ EF, ɞɥɹ ɧɢɯ ɝɪɚɧɢɱɧɚɹ ɱɚɫɬɨɬɚ ɫɧɢɠɚɟɬɫɹ. ɇɨ ɜ ɯɨɥɨɞɧɨɦ ɦɟɬɚɥɥɟ ɞɨɥɹ ɬɚɤɢɯ ɷɥɟɤɬɪɨɧɨɜ ɤɪɚɣɧɟ ɦɚɥɚ. Ʉɪɨɦɟ ɬɨɝɨ, ɪɚɛɨɬɚ ɜɵɯɨɞɚ, ɚ ɡɧɚɱɢɬ, ɢ ɝɪɚɧɢɱɧɚɹ ɱɚɫɬɨɬɚ ɡɚɜɢɫɢɬ ɨɬ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ (ɷɮɮɟɤɬ ɒɨɬɬɤɢ).
4. Ɏɨɬɨɷɮɮɟɤɬ ɨɛɥɚɞɚɟɬ ɫɜɨɣɫɬɜɨɦ ɛɟɡɵɧɟɪɰɢɚɥɶɧɨɫɬɢ - ɮɨɬɨɬɨɤ ɩɨɹɜɥɹɟɬɫɹ ɢ ɢɫɱɟɡɚɟɬ ɜɦɟɫɬɟ ɫ ɨɫɜɟɳɟɧɢɟɦ, ɡɚɩɚɡɞɵɜɚɹ ɧɟ ɛɨɥɟɟ ɱɟɦ ɧɚ 10-9 ɫ. Ɏɨɬɨɷɮɮɟɤɬ ɦɨɠɧɨ ɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɥɢɛɨ ɤɜɚɧɬɨɜɵɦ ɜɵɯɨɞɨɦ Y – ɱɢɫɥɨɦ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɨɞɢɧ ɮɨɬɨɧ (Y = 10-3÷10-1), ɥɢɛɨ ɩɥɨɬɧɨɫɬɶɸ ɮɨɬɨɬɨɤɚ jɮ. Ɉɬɧɨɲɟɧɢɟ ɮɨɬɨɬɨɤɚ ɤ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɩɨɬɨɤɚ ɦɨɧɨɯɪɨɦɚɬɢɱɟɫɤɨɝɨ ɢɡɥɭɱɟɧɢɹ ɜɵɪɚɠɚɟɬ ɫɩɟɤɬɪɚɥɶɧɭɸ ɱɭɜɫɬɜɢɬɟɥɶɧɨɫɬɶ ɮɨɬɨɤɚɬɨɞɨɜ, ɚ ɤ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɩɨɬɨɤɚ ɢɡɥɭɱɟɧɢɹ ɫɬɚɧɞɚɪɬɧɨɝɨ ɢɫɬɨɱɧɢɤɚ ɫɜɟɬɚ – ɢɧɬɟɝɪɚɥɶɧɭɸ ɱɭɜɫɬɜɢɬɟɥɶɧɨɫɬɶ. Ƚɥɭɛɢɧɚ ɜɵɯɨɞɚ ɷɥɟɤɬɪɨɧɨɜ ɢɡ ɦɟɬɚɥɥɨɜ ɫɨɫɬɚɜɥɹɟɬ ɧɚɫɤɨɥɶɤɨ ɚɬɨɦɧɵɯ ɫɥɨɟɜ, ɩɨɷɬɨɦɭ, ɬɟɪɹɹ ɧɚ ɫɜɨɟɦ ɩɭɬɢ ɱɚɫɬɶ ɷɧɟɪɝɢɢ, ɮɨɬɨɷɥɟɤɬɪɨɧɵ ɧɚ ɜɵɯɨɞɟ ɢɡ ɦɟɬɚɥɥɨɜ ɢɦɟɸɬ ɧɟɤɨɬɨɪɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨ ɷɧɟɪɝɢɹɦ ɨɬ ɧɭɥɹ ɞɨ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ, ɨɩɪɟɞɟɥɹɟɦɨɝɨ ɩɨ ɡɚɤɨɧɭ ɗɣɧɲɬɟɣɧɚ. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɮɨɬɨɷɥɟɤɬɪɨɧɨɜ ɩɨ ɷɧɟɪɝɢɹɦ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɦɟɬɨɞɨɦ ɡɚɞɟɪɠɢɜɚɸɳɟɝɨ ɩɨɬɟɧɰɢɚɥɚ. Ⱦɥɹ ɫɛɨɪɚ ɧɚ ɚɧɨɞ ɜɫɟɯ ɮɨɬɨɷɥɟɤɬɪɨɧɨɜ ɜ ɨɩɵɬɚɯ Ʌɭɤɢɪɫɤɨɝɨ ɢ ɉɪɟɥɢɠɚɟɜɚ ɢɫɩɨɥɶɡɨɜɚɥɢɫɶ ɤɚɬɨɞ ɜ ɜɢɞɟ ɲɚɪɚ ɢ ɚɧɨɞ ɜ ɜɢɞɟ ɤɨɧɰɟɧɬɪɢɱɟɫɤɨɣ ɤɚɬɨɞɭ ɫɮɟɪɵ, ɱɟɪɟɡ ɭɡɤɨɟ ɨɬɜɟɪɫɬɢɟ ɤɨɬɨɪɨɣ ɧɚ ɤɚɬɨɞ ɩɨɞɚɜɚɥɫɹ ɥɭɱ ɫɜɟɬɚ. Ɋɚɡɧɨɫɬɶ ɡɧɚɱɟɧɢɣ ɬɨɤɚ ɩɪɢ ɞɜɭɯ ɡɚɞɟɪɠɢɜɚɸɳɢɯ ɩɨɬɟɧɰɢɚɥɚɯ -U ɢ -(U + ∆U) ɞɚɟɬ ɱɢɫɥɨ ɮɨɬɨɷɥɟɤɬɪɨɧɨɜ, ɷɧɟɪɝɢɹ ɤɨɬɨɪɵɯ ɩɪɢ ɜɵɥɟɬɟ ɫ ɤɚɬɨɞɚ ɥɟɠɢɬ ɜ ɩɪɟɞɟɥɚɯ ɨɬ eU ɞɨ e(U + ∆U). ɗɬɨɬ ɠɟ ɦɟɬɨɞ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɪɚɫɧɨɣ ɝɪɚɧɢɰɵ
ɮɨɬɨɷɮɮɟɤɬɚ. Ɂɚɞɟɪɠɢɜɚɸɳɢɣ ɩɨɬɟɧɰɢɚɥ, ɩɪɢ ɤɨɬɨɪɨɦ ɮɨɬɨɬɨɤ ɫɬɚɧɨɜɢɬɫɹ ɪɚɜɧɵɦ ɧɭɥɸ, ɨɩɪɟɞɟɥɹɟɬ ɪɚɡɧɨɫɬɶ ɦɟɠɞɭ ɱɚɫɬɨɬɨɣ ɝɚɦɦɚ-ɤɜɚɧɬɚ ν ɢ ɝɪɚɧɢɱɧɨɣ ɱɚɫɬɨɬɨɣ ɮɨɬɨɷɮɮɟɤɬɚ νɝɪ ɞɥɹ ɞɚɧɧɨɝɨ ɦɚɬɟɪɢɚɥɚ: U0 = h(ν - νɝɪ)/e. Ɂɧɚɱɟɧɢɹ U0, ɨɩɪɟɞɟɥɹɟɦɵɟ ɞɥɹ ɪɚɡɧɵɯ ɱɚɫɬɨɬ ɨɛɥɭɱɟɧɢɹ ν, ɥɟɠɚɬ ɧɚ ɩɪɹɦɨɣ, ɬɨɱɤɚ ɩɟɪɟɫɟɱɟɧɢɹ ɤɨɬɨɪɨɣ ɫ ɨɫɶɸ ɚɛɫɰɢɫɫ ɞɚɟɬ ɝɪɚɧɢɱɧɭɸ ɱɚɫɬɨɬɭ νɝɪ. Ɉɫɧɨɜɧɵɟ ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ Ɏɗɗ ɦɟɬɚɥɥɨɜ ɯɨɪɨɲɨ ɨɩɢɫɵɜɚɸɬɫɹ ɬɟɨɪɢɟɣ Ɏɚɭɥɟɪɚ, ɫɨɝɥɚɫɧɨ ɤɨɬɨɪɨɣ ɩɨɫɥɟ ɩɨɝɥɨɳɟɧɢɹ ɜ ɦɟɬɚɥɥɟ ɮɨɬɨɧɚ ɟɝɨ ɷɧɟɪɝɢɹ ɩɟɪɟɯɨɞɢɬ ɷɥɟɤɬɪɨɧɚɦ ɩɪɨɜɨɞɢɦɨɫɬɢ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɱɟɝɨ ɷɥɟɤɬɪɨɧɧɵɣ ɝɚɡ ɜ ɦɟɬɚɥɥɟ ɨɤɨɥɨ ɟɝɨ ɩɨɜɟɪɯɧɨɫɬɢ ɫɨɫɬɨɢɬ ɢɡ ɫɦɟɫɢ ɝɚɡɨɜ ɫ ɧɨɪɦɚɥɶɧɵɦ (ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ Ɏɟɪɦɢ) ɢ ɜɨɡɛɭɠɞɟɧɧɵɦ (ɫɞɜɢɧɭɬɵɦ ɧɚ hν) ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ ɩɨ ɷɧɟɪɝɢɹɦ (ɪɢɫ. 7.3). Ⱦɥɹ ɩɨɞɫɱɟɬɚ ɱɢɫɥɚ ɮɨɬɨɷɥɟɤɬɪɨɧɨɜ ɦɨɠɧɨ ɩɪɨɜɟɫɬɢ ɬɚɤɨɟ ɠɟ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ, ɱɬɨ ɢ ɩɪɢ ɩɨɞɫɱɟɬɟ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ ɬɟɪɦɨɷɦɢɫɫɢɢ, Ɋɢɫ. 7.3. Ɏɨɬɨɷɦɢɫɫɢɨɧɧɵɣ ɬɨɤ ɷɥɟɤɬɪɨɧɨɜ ɢɡ ɢɡɦɟɧɢɜ ɧɢɠɧɢɣ ɩɪɟɞɟɥ «ɯɜɨɫɬɚ» ɜɨɡɦɭɳɟɧɧɨɣ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ, ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɫ Wa ɧɚ Wa - hν, ɩɪɟɨɞɨɥɟɜɚɸɳɢɯ ɩɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ ɬɟɦ ɫɚɦɵɦ ɜɤɥɸɱɢɜ ɜ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɷɥɟɤɬɪɨɧɵ, ɤɨɬɨɪɵɟ ɩɪɢɨɛɪɟɬɚɸɬ ɧɟɞɨɫɬɚɸɳɭɸ ɞɥɹ ɩɪɟɨɞɨɥɟɧɢɹ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ ɷɧɟɪɝɢɸ ɡɚ ɫɱɟɬ ɩɨɝɥɨɳɟɧɧɵɯ ɤɜɚɧɬɨɜ. Ɍɚɤ ɠɟ, ɤɚɤ ɢ ɞɥɹ ɬɟɪɦɨɷɥɟɤɬɪɨɧɨɜ, ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ ɜɟɪɨɹɬɧɨɫɬɶ ɩɪɨɯɨɠɞɟɧɢɹ ɛɚɪɶɟɪɚ, ɬɚɤ ɤɚɤ ɱɚɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ɩɪɢ ɞɜɢɠɟɧɢɢ ɢɡ ɦɟɬɚɥɥɚ ɦɨɠɟɬ ɛɵɬɶ ɨɬɪɚɠɟɧɚ ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ ɪɚɡɞɟɥɚ ɦɟɬɚɥɥ - ɜɚɤɭɭɦ. Ʉɪɨɦɟ ɷɬɨɝɨ, ɧɟɨɛɯɨɞɢɦɨ ɭɱɟɫɬɶ ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɝɥɨɳɟɧɢɹ ɮɨɬɨɧɚ. ɗɬɚ ɜɟɪɨɹɬɧɨɫɬɶ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɡɚɜɢɫɢɬ ɨɬ ɷɧɟɪɝɢɢ ɩɨɝɥɨɳɚɸɳɟɝɨ ɷɥɟɤɬɪɨɧɚ ɢ ɷɧɟɪɝɢɢ ɝɚɦɦɚɤɜɚɧɬɚ. ȼ ɬɟɨɪɢɢ Ɏɚɭɥɟɪɚ ɷɬɚ ɜɟɪɨɹɬɧɨɫɬɶ ɫɱɢɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɨɣ ɜɟɥɢɱɢɧɨɣ, ɱɬɨ, ɤɚɤ Ɋɢɫ. 7.4. Ɉɩɪɟɞɟɥɟɧɢɟ ɤɪɚɫɧɨɣ ɝɪɚɧɢɰɵ ɨɤɚɡɚɥɨɫɶ, ɜ ɢɧɬɟɪɜɚɥɟ ɱɚɫɬɨɬ ɨɬ νɝɪ ɞɨ ɫ ɩɨɦɨɳɶɸ ɮɭɧɤɰɢɢ Ɏɚɭɥɟɪɚ. 1.5νɝɪ ɜɵɩɨɥɧɹɟɬɫɹ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɩɥɨɬɧɨɫɬɶ ɮɨɬɨɬɨɤɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ Ɏɚɭɥɟɪɚ:
hν − hν ɝɪ 2 ),ν ≤ ν ɝɪ = eϕ a / h ° B1T exp( kT ° jɎ = ® , 2 ° B T 2 ( (hν − hν ɝɪ ) + B ),ν > ν 3 ɝɪ °¯ 2 k 2T 2
(7.29)
ɝɞɟ B1, B2, B3 – ɩɨɫɬɨɹɧɧɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵɟ A0. Ɂɚɜɢɫɢɦɨɫɬɶ hγ jɮ( ) ɦɨɠɧɨ ɬɚɤɠɟ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ ɪɹɞɨɜ [32]. ɂɡ ɮɨɪɦɭɥɵ Ɏɚɭɥɟɪɚ ɜɢɞɧɨ, kT ɱɬɨ ɩɪɢ Ɍ ≈0 jɮ → 0 ɢ νɝɪ ɞɟɣɫɬɜɢɬɟɥɶɧɨ ɹɜɥɹɟɬɫɹ ɤɪɚɫɧɨɣ ɝɪɚɧɢɰɟɣ. ɉɪɢ Ɍ ≠ 0 ɧɟ ɫɭɳɟɫɬɜɭɟɬ ɪɟɡɤɨɣ ɝɪɚɧɢɰɵ ɮɨɬɨɷɮɮɟɤɬɚ, ɮɨɬɨɬɨɤ ɩɚɞɚɟɬ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨ ɩɪɢ ν < νɝɪ, ɩɪɢ ν > νɝɪ ɩɥɨɬɧɨɫɬɶ ɮɨɬɨɬɨɤɚ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɤɜɚɞɪɚɬɭ ɱɚɫɬɨɬɵ ɩɚɞɚɸɳɟɝɨ ɢɡɥɭɱɟɧɢɹ jɎ ∼ ν 2. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɩɨɥɨɠɟɧɢɟ νɝɪ ɨɩɪɟɞɟɥɹɸɬ ɩɨ ɢɡɦɟɪɟɧɧɨɣ ɫɩɟɤɬɪɚɥɶɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɮɨɬɨɬɨɤɚ ɩɪɢ ɡɚɞɚɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ Ɍ > 0. ɗɬɚ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬɤɥɚɞɵɜɚɟɬɫɹ ɧɚ ɝɪɚɮɢɤɟ ɜ ɤɨɨɪɞɢɧɚɬɚɯ x = hν/kT ɢ y = ln( jɎ/T2). ɉɨɥɭɱɟɧɧɚɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɚɹ ɤɪɢɜɚɹ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɡɚɜɢɫɢɦɨɫɬɢ: ln( jɎ/T2) = B + F((hν- hνɝɪ)/kT) = B + F(x- hνɝɪ/kT).
(7.30)
Ⱦɚɧɧɚɹ ɤɪɢɜɚɹ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɤɪɢɜɨɣ ɮɭɧɤɰɢɢ Ɏɚɭɥɟɪɚ F = F(hν/kT) ɫɞɜɢɝɨɦ ɩɨ ɨɫɢ y ɧɚ ɤɨɧɫɬɚɧɬɭ B ɢ ɩɨ ɨɫɢ x ɧɚ hνɝɪ/kT (ɪɢɫ. 7.4). ɂɦɟɧɧɨ ɨɩɪɟɞɟɥɟɧɢɟ ɫɞɜɢɝɚ ɩɨ ɨɫɢ x ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɤɪɢɜɨɣ ɞɥɹ ɟɟ ɫɨɜɦɟɳɟɧɢɹ ɫ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɤɪɢɜɨɣ Ɏɚɭɥɟɪɚ ɩɨɡɜɨɥɹɟɬ ɧɚɣɬɢ ɝɪɚɧɢɱɧɭɸ ɱɚɫɬɨɬɭ νɝɪ. §48. ȼɬɨɪɢɱɧɚɹ ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ȼɬɨɪɢɱɧɚɹ ɷɥɟɤɬɪɨɧ-ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ
ɗɦɢɫɫɢɹ ɷɥɟɤɬɪɨɧɨɜ ɫ ɩɨɜɟɪɯɧɨɫɬɢ ɬɜɟɪɞɨɝɨ ɬɟɥɚ, ɛɨɦɛɚɪɞɢɪɭɟɦɨɣ ɩɨɬɨɤɨɦ ɷɥɟɤɬɪɨɧɨɜ, ɧɚɡɵɜɚɟɬɫɹ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɟɣ. ɇɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɚɹ ɫɯɟɦɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ ɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɦɟɬɨɞɨɦ ɡɚɞɟɪɠɢɜɚɸɳɟɝɨ ɩɨɥɹ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɫɮɟɪɢɱɟɫɤɨɝɨ ɤɨɥɥɟɤɬɨɪɚ Ʌɭɤɢɪɫɤɨɝɨ ɢ ɉɪɟɥɢɠɚɟɜɚ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 7.5. Ɂɚɞɟɪɠɢɜɚɸɳɟɟ ɩɨɥɟ ɩɪɢɤɥɚɞɵɜɚɟɬɫɹ ɦɟɠɞɭ Ɋɢɫ. 7.5. ɋɯɟɦɚ ɨɩɵɬɚ ɩɨ ɢɫɫɥɟɞɨɜɚɧɢɸ ɜɬɨɪɢɱɧɨɣ ɦɢɲɟɧɶɸ ɢ ɤɨɥɥɟɤɬɨɪɨɦ. ȿɫɥɢ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɩɨɬɟɧɰɢɚɥ ɤɨɥɥɟɤɬɨɪɚ ɛɭɞɟɬ ɛɨɥɶɲɟ, ɱɟɦ ɧɚ ɦɢɲɟɧɢ, ɬɨ ɧɚ ɤɨɥɥɟɤɬɨɪ ɩɪɢɞɟɬ ɩɨɥɧɵɣ ɬɨɤ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ Is. ȼɬɨɪɢɱɧɚɹ ɷɦɢɫɫɢɢ ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɤɨɥɢɱɟɫɬɜɨɦ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɨɞɧɭ ɩɟɪɜɢɱɧɭɸ ɱɚɫɬɢɰɭ: γe = Ns/Np. ɂɧɬɟɝɪɚɥɶɧɨ ɷɬɨ ɤɨɥɢɱɟɫɬɜɨ ɪɚɜɧɨ ɨɬɧɨɲɟɧɢɸ ɬɨɤɨɜ Ɋɢɫ. 7.6. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɩɨ ɷɧɟɪɝɢɹɦ
ɜɬɨɪɢɱɧɵɯ ɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ Is/Ip. Ȼɨɥɟɟ ɬɨɱɧɵɦ ɦɟɬɨɞɨɦ ɨɩɪɟɞɟɥɟɧɢɹ ɫɤɨɪɨɫɬɟɣ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɹɜɥɹɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɞɢɫɩɟɪɫɢɨɧɧɵɯ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɢɥɢ ɦɚɝɧɢɬɧɨɝɨ ɷɧɟɪɝɨɚɧɚɥɢɡɚɬɨɪɚ ɫ ɩɨɥɭɤɪɭɝɨɜɨɣ ɬɪɚɟɤɬɨɪɢɟɣ, ɨɩɢɫɚɧɧɨɝɨ ɜ ɝɥɚɜɟ 5. ɉɨɥɭɱɟɧɧɨɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɟ ɷɧɟɪɝɟɬɢɱɟɫɤɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ (ɪɢɫ. 7.6) ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɦɚɬɟɪɢɚɥɚ ɢ ɷɧɟɪɝɢɢ Ɋɢɫ. 7.7. Ɂɚɜɢɫɢɦɨɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬɚ ɢɫɬɢɧɧɨɣ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɨɬ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɞɥɹ W, Mo, C, Be ɫɨɞɟɪɠɢɬ ɞɜɚ ɜɵɫɨɤɢɯ ɦɚɤɫɢɦɭɦɚ. ɉɟɪɜɵɣ ɜ ɨɛɥɚɫɬɢ ɦɚɥɵɯ ɷɧɟɪɝɢɣ (< 50 ɷȼ) ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɢɫɬɢɧɧɵɦ ɜɬɨɪɢɱɧɵɦ ɷɥɟɤɬɪɨɧɚɦ, ɤɨɬɨɪɵɟ ɜɵɯɨɞɹɬ ɢɡ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ɡɚ ɫɱɟɬ ɩɨɝɥɨɳɟɧɢɹ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ. Ⱦɚɥɟɤɨ ɧɟ ɜɫɟ ɷɥɟɤɬɪɨɧɵ, ɩɨɥɭɱɢɜɲɢɟ ɞɨɩɨɥɧɢɬɟɥɶɧɭɸ ɷɧɟɪɝɢɸ, ɞɨɛɢɪɚɸɬɫɹ ɞɨ ɩɨɜɟɪɯɧɨɫɬɢ, ɪɚɫɬɪɚɱɢɜɚɹ ɷɧɟɪɝɢɸ ɩɨ ɩɭɬɢ ɧɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɫ ɢɨɧɚɦɢ ɪɟɲɟɬɤɢ ɢ ɞɪɭɝɢɦɢ ɷɥɟɤɬɪɨɧɚɦɢ. ɉɪɟɨɞɨɥɟɜɲɢɟ ɩɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ ɢɫɬɢɧɧɵɟ ɜɬɨɪɢɱɧɵɟ ɷɥɟɤɬɪɨɧɵ ɧɚ ɜɵɯɨɞɟ ɢɦɟɸɬ ɷɧɟɪɝɢɢ, ɧɟ ɡɚɜɢɫɹɳɢɟ ɨɬ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ. Ɋɚɛɨɬɚ ɜɵɯɨɞɚ ɦɚɬɟɪɢɚɥɚ ɬɚɤɠɟ ɧɟ ɨɤɚɡɵɜɚɟɬ ɫɭɳɟɫɬɜɟɧɧɨɝɨ ɜɥɢɹɧɢɹ ɧɚ ɷɦɢɫɫɢɸ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ, ɬɚɤ ɤɚɤ, ɜɨ-ɩɟɪɜɵɯ, ɷɧɟɪɝɢɹ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ, ɤɚɤ ɩɪɚɜɢɥɨ, ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ ɪɚɛɨɬɵ ɜɵɯɨɞɚ, ɜɨ-ɜɬɨɪɵɯ, ɷɦɢɫɫɢɹ ɩɪɨɢɫɯɨɞɢɬ ɧɟ ɢɡ ɩɨɜɟɪɯɧɨɫɬɧɵɯ ɫɥɨɟɜ, ɚ ɢɡ ɝɥɭɛɢɧɵ ɦɟɬɚɥɥɚ, ɩɨɷɬɨɦɭ ɛɨɥɟɟ ɜɚɠɧɵɦ ɹɜɥɹɟɬɫɹ ɩɨɬɟɪɹ ɷɧɟɪɝɢɢ ɩɪɢ ɞɜɢɠɟɧɢɢ ɷɥɟɤɬɪɨɧɚ ɤ ɩɨɜɟɪɯɧɨɫɬɢ. ȼɬɨɪɨɣ, ɝɨɪɚɡɞɨ ɛɨɥɟɟ ɭɡɤɢɣ ɦɚɤɫɢɦɭɦ ɧɚɯɨɞɢɬɫɹ ɜ ɨɛɥɚɫɬɢ ɜɵɫɨɤɢɯ ɷɧɟɪɝɢɣ ɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɭɩɪɭɝɨ ɨɬɪɚɠɟɧɧɵɦ ɩɟɪɜɢɱɧɵɦ ɷɥɟɤɬɪɨɧɚɦ, ɩɪɚɤɬɢɱɟɫɤɢ ɩɨɥɧɨɫɬɶɸ ɫɨɯɪɚɧɢɜɲɢɦ ɫɜɨɸ ɫɤɨɪɨɫɬɶ ɩɨɫɥɟ ɨɬɪɚɠɟɧɢɹ. ɉɨɥɨɠɟɧɢɟ ɷɬɨɝɨ ɦɚɤɫɢɦɭɦɚ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ. Ɉɛɥɚɫɬɶ ɷɧɟɪɝɢɣ ɦɟɠɞɭ ɷɬɢɦɢ ɞɜɭɦɹ ɦɚɤɫɢɦɭɦɚɦɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɟ ɭɩɪɭɝɨ ɨɬɪɚɠɟɧɧɵɦ ɜɬɨɪɢɱɧɵɦ ɷɥɟɤɬɪɨɧɚɦ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɷɧɟɪɝɟɬɢɱɟɫɤɢɣ ɫɩɟɤɬɪ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɫɨɫɬɨɢɬ ɢɡ ɲɢɪɨɤɨɝɨ ɩɢɤɚ ɜ ɨɛɥɚɫɬɢ ɧɢɡɤɢɯ ɷɧɟɪɝɢɣ ɫ ɦɚɤɫɢɦɭɦɨɦ ɩɪɢ Wmax, ɤɨɬɨɪɵɣ ɩɪɢɧɚɞɥɟɠɢɬ ɢɫɬɢɧɧɨɜɬɨɪɢɱɧɵɦ ɷɥɟɤɬɪɨɧɚɦ, ɜɵɯɨɞɹɳɢɦ ɫ ɝɥɭɛɢɧɵ 5 - 100 Α ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ, ɢ ɨɱɟɧɶ ɭɡɤɨɝɨ ɩɢɤɚ ɨɬɪɚɠɟɧɧɵɯ ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ ɜ ɨɛɥɚɫɬɢ ɜɵɫɨɤɢɯ ɷɧɟɪɝɢɣ ɫ ɦɚɤɫɢɦɭɦɨɦ ɩɪɢ ɷɧɟɪɝɢɢ, ɪɚɜɧɨɣ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ. Ⱦɥɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɢɫɬɢɧɧɨɣ ɷɥɟɤɬɪɨɧ-ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɜɜɨɞɹɬ ɤɨɷɮɮɢɰɢɟɧɬ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ δe= Ɋɢɫ. 7.8. Ɂɚɜɢɫɢɦɨɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬɚ Ns/Np , ɝɞɟ Ns – ɱɢɫɥɨ ɢɫɬɢɧɧɨ ɨɬɪɚɠɟɧɢɹ ɨɬ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ, Ns - ɱɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ, ɩɚɞɚɸɳɢɯ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ. Ⱦɥɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɷɦɢɫɫɢɢ ɨɬɪɚɠɟɧɧɵɯ ɨɬ
ɩɨɜɟɪɯɧɨɫɬɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɢɫɩɨɥɶɡɭɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬ ɨɬɪɚɠɟɧɢɹ ηe = (Ne+Nu)/Np, ɝɞɟ Ne ɢ Nu - ɭɩɪɭɝɨ ɢ ɧɟɭɩɪɭɝɨ ɨɬɪɚɠɟɧɧɵɟ ɷɥɟɤɬɪɨɧɵ. ɋɭɦɦɚɪɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ γe = δe + ηe. Ɂɚɜɢɫɢɦɨɫɬɶ δe ɨɬ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ Wp ɡɚɞɚɟɬɫɹ ɷɦɩɢɪɢɱɟɫɤɨɣ ɮɨɪɦɭɥɨɣ (Kollath):
δ e (W p ) Wp Wp = (2.72) 2 exp(−2 ), δ e max Wmax Wmax
(7.31)
ɝɞɟ δemax= 0.35eϕ a , Wmax – ɡɧɚɱɟɧɢɟ ɢ ɩɨɥɨɠɟɧɢɟ ɦɚɤɫɢɦɭɦɚ. ɉɨɥɨɠɟɧɢɟ ɦɚɤɫɢɦɭɦɚ ɡɚɜɢɫɢɦɨɫɬɢ ɤɨɷɮɮɢɰɢɟɧɬɚ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɞɥɹ ɪɚɡɧɵɯ ɦɚɬɟɪɢɚɥɨɜ ɩɪɟɞɫɬɚɜɥɟɧɨ ɜ ɬɚɛɥɢɰɟ 7.2. Ɋɨɫɬ δe ɫ ɷɧɟɪɝɢɟɣ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɫɦɟɧɹɟɬɫɹ ɫɩɚɞɨɦ (ɪɢɫ. 7.7), ɬɚɤ ɤɚɤ ɩɪɢ ɞɚɥɶɧɟɣɲɟɦ ɪɨɫɬɟ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɨɛɪɚɡɨɜɚɧɢɟ ɜɬɨɪɢɱɧɵɯ ɩɪɨɢɫɯɨɞɢɬ ɜɫɟ ɝɥɭɛɠɟ ɢ ɝɥɭɛɠɟ, ɪɚɫɬɭɬ ɩɨɬɟɪɢ ɷɧɟɪɝɢɢ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɜ ɦɟɬɚɥɥɟ ɢ ɢɯ ɜɵɯɨɞ ɫɬɚɧɨɜɢɬɫɹ ɜɫɟ ɛɨɥɟɟ ɡɚɬɪɭɞɧɟɧɧɵɦ. ɗɬɢɦ ɠɟ ɨɛɴɹɫɧɹɟɬɫɹ ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɫɞɜɢɝɚ ɦɚɤɫɢɦɭɦɚ Wmax ɜ ɷɧɟɪɝɟɬɢɱɟɫɤɨɦ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɞɥɹ ɦɚɬɟɪɢɚɥɨɜ ɫ ɜɵɫɨɤɢɦ ɚɬɨɦɧɵɦ ɱɢɫɥɨɦ (ɧɚɩɪɢɦɟɪ, ɞɥɹ ɜɨɥɶɮɪɚɦɚ) ɜ ɫɬɨɪɨɧɭ ɧɢɡɤɢɯ ɷɧɟɪɝɢɣ ɢɡ-ɡɚ ɫɧɢɠɟɧɢɹ ɞɥɢɧɵ ɩɪɨɛɟɝɚ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɜ ɬɜɟɪɞɨɦ ɬɟɥɟ (ɷɥɟɤɬɪɨɧɚɦ, ɩɨɥɭɱɢɜɲɢɦ ɷɧɟɪɝɢɸ ɨɬ ɩɟɪɜɢɱɧɵɯ ɜɛɥɢɡɢ ɩɨɜɟɪɯɧɨɫɬɢ, ɥɟɝɱɟ ɜɵɣɬɢ ɢɡ ɬɜɟɪɞɨɝɨ ɬɟɥɚ). Ɂɚɜɢɫɢɦɨɫɬɶ δe ɨɬ ɭɝɥɚ ɩɚɞɟɧɢɹ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ α (ɭɝɨɥ ɫ ɧɨɪɦɚɥɶɸ ɤ ɩɨɜɟɪɯɧɨɫɬɢ) ɞɥɹ α < 60ɨ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ:
δ e (α ) = δ e (0) / cos β α ,
(7.32)
ɝɞɟ β = 1.3 ÷1.5. ɑɟɦ ɛɨɥɶɲɟ α, ɬɟɦ ɦɟɧɶɲɟ ɝɥɭɛɢɧɚ, ɤɨɬɨɪɭɸ ɧɭɠɧɨ ɩɪɟɨɞɨɥɟɬɶ ɜɬɨɪɢɱɧɨɦɭ ɷɥɟɤɬɪɨɧɭ ɞɥɹ ɜɵɯɨɞɚ. ɗɦɩɢɪɢɱɟɫɤɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬɚ ɨɬɪɚɠɟɧɢɹ ηe ɞɥɹ ɧɨɪɦɚɥɶɧɨɝɨ ɩɚɞɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɨɬ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ Wp (ɪɢɫ.7.8) ɢ ɚɬɨɦɧɨɝɨ ɧɨɦɟɪɚ z:
η e (W p , z ) = W pm ( z ) exp(C ( z )) ,
(7.33)
m(z)=0.1382–0.9211z-0.5, C(z)=0.1904–0.2236lnz+0.1292ln2z–0.01491ln3z ɝɞɟ (Hunger). Ɂɚɜɢɫɢɦɨɫɬɶ ηe ɨɬ ɭɝɥɚ ɩɚɞɟɧɢɹ α:
η e (α ) = 0.891(
η e ( 0) 0.891
) cos α (Darlington).
(7.34)
Ɍɚɛɥɢɰɚ 7.2.
δemax
Wmax[ɷȼ]
Al
Be
1.0 300
0.5 200
C (ɚɥɦɚɡ) 2.8 750
ɋ (ɝɪɚɮɢɬ)
Cu
Fe
Mo
Ni
Ta
Ti
W
1.0 300
1.3 600
1.3 400
1.25 375
1.3 550
1.3 600
0.9 280
1.4 650
ɇɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɦ ɩɪɢɦɟɧɟɧɢɟɦ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɹɜɥɹɸɬɫɹ ɷɥɟɤɬɪɨɧɧɵɟ ɭɦɧɨɠɢɬɟɥɢ, ɩɪɢɧɰɢɩ ɞɟɣɫɬɜɢɹ ɤɨɬɨɪɵɯ ɩɪɟɞɫɬɚɜɥɟɧ
ɫɯɟɦɨɣ ɧɚ ɪɢɫ. 7.9. Ɇɚɤɫɢɦɚɥɶɧɨ ɩɨɥɧɨɟ ɩɨɩɚɞɚɧɢɹ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɫɥɟɞɭɸɳɢɣ ɷɦɢɬɬɟɪ ɦɨɠɟɬ ɨɛɟɫɩɟɱɢɜɚɬɶɫɹ ɦɚɝɧɢɬɧɨɣ ɢɥɢ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɮɨɤɭɫɢɪɨɜɤɨɣ. ȼɬɨɪɢɱɧɚɹ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ
ɉɪɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɢ ɢɨɧɨɜ ɫ ɩɨɜɟɪɯɧɨɫɬɶɸ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ɧɚɛɥɸɞɚɟɬɫɹ ɷɦɢɫɫɢɹ ɷɥɟɤɬɪɨɧɨɜ, ɯɚɪɚɤɬɟɪɢɡɭɟɦɚɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ: γi = ne/ni, ɝɞɟ ne - ɱɢɫɥɨ ɷɦɢɬɢɪɨɜɚɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ, ni ɱɢɫɥɨ ɢɨɧɨɜ, ɭɩɚɜɲɢɯ ɧɚ ɬɭ ɠɟ ɩɨɜɟɪɯɧɨɫɬɶ ɡɚ ɬɨ ɠɟ ɜɪɟɦɹ. Ⱦɥɹ ɨɞɧɨɡɚɪɹɞɧɵɯ ɢɨɧɨɜ γi = ne/ni = je/ji, ɩɪɢ ɷɦɢɫɫɢɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɢɨɧɨɜ ɡɚɪɹɞɨɦ Z γi = Zje/ji. ɗɦɢɫɫɢɹ ɷɥɟɤɬɪɨɧɨɜ ɦɨɠɟɬ Ɋɢɫ. 7.9. ɋɯɟɦɚ ɷɥɟɤɬɪɨɧɧɨɝɨ ɭɦɧɨɠɢɬɟɥɹ ɩɪɨɢɫɯɨɞɢɬɶ ɜ ɪɟɡɭɥɶɬɚɬɟ ɞɜɭɯ ɩɪɨɰɟɫɫɨɜ: ɩɟɪɜɵɣ ɩɪɨɰɟɫɫ, ɫɜɹɡɚɧ ɫ ɜɨɡɛɭɠɞɟɧɢɟɦ ɷɥɟɤɬɪɨɧɨɜ ɬɟɥɚ ɡɚ ɫɱɟɬ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɨɜ ɷɦɢɬɬɟɪɚ ɜ ɩɨɥɟ ɩɪɢɯɨɞɹɳɟɝɨ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ ɬɟɥɚ ɢɨɧɚ – ɬɚɤɭɸ ɷɦɢɫɫɢɸ ɧɚɡɵɜɚɸɬ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɫ γɩ; ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɷɦɢɫɫɢɢ ɜɬɨɪɨɣ ɩɪɨɰɟɫɫ ɫɜɹɡɚɧ ɫ ɜɨɡɛɭɠɞɟɧɢɟɦ ɷɥɟɤɬɪɨɧɧɨɣ ɫɢɫɬɟɦɵ ɬɟɥɚ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɟɣ ɢɨɧɚ – ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɷɦɢɫɫɢɸ ɧɚɡɵɜɚɸɬ ɤɢɧɟɬɢɱɟɫɤɨɣ ɫ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɷɦɢɫɫɢɢ γɤ. ȿɫɥɢ ɩɪɢɫɭɬɫɬɜɭɸɬ ɨɛɚ ɩɪɨɰɟɫɫɚ, ɬɨ γi = γɩ + γɤ. ɉɨɬɟɧɰɢɚɥɶɧɚɹ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɛɵɥɚ ɨɬɤɪɵɬɚ ɉɟɧɧɢɧɝɨɦ ɜ 1928 ɝ. ɉɪɢ ɢɫɫɥɟɞɨɜɚɧɢɢ ɡɚɜɢɫɢɦɨɫɬɢ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɨɬ ɷɧɟɪɝɢɢ ɩɚɞɚɸɳɢɯ ɢɨɧɨɜ ɨɧ ɨɛɧɚɪɭɠɢɥ, ɱɬɨ ɷɦɢɫɫɢɹ ɨɫɬɚɟɬɫɹ ɢ ɩɪɢ ɨɱɟɧɶ ɦɚɥɵɯ, ɩɪɚɤɬɢɱɟɫɤɢ ɧɭɥɟɜɵɯ, ɷɧɟɪɝɢɹɯ ɢɨɧɨɜ. ɂɡ ɷɬɨɝɨ ɦɨɠɧɨ Ɋɢɫ. 7.10. ɋɯɟɦɚ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɢɨɧɧɨɛɵɥɨ ɫɞɟɥɚɬɶ ɜɵɜɨɞ, ɱɬɨ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɢɫɩɭɫɤɚɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɧɟ ɫɜɹɡɚɧɨ ɫ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɟɣ ɢɨɧɨɜ. ȼ ɷɤɫɩɟɪɢɦɟɧɬɚɯ ɛɵɥɨ ɜɵɹɜɥɟɧɨ, ɱɬɨ ɬɚɤɚɹ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɩɪɨɢɫɯɨɞɢɬ ɬɨɥɶɤɨ ɞɥɹ ɢɨɧɨɜ, ɩɨɬɟɧɰɢɚɥ ɢɨɧɢɡɚɰɢɢ ɤɨɬɨɪɵɯ Vi ɜ ɞɜɚ ɪɚɡɚ ɛɨɥɶɲɟ ɪɚɛɨɬɵ ɜɵɯɨɞɚ ɦɚɬɟɪɢɚɥɚ ɷɦɢɬɬɟɪɚ ϕa: Vi >2ϕa.
(7.35)
ɗɬɨ ɧɚɯɨɞɢɬ ɨɛɴɹɫɧɟɧɢɟ ɜ ɦɨɞɟɥɢ ɨɠɟ-ɧɟɣɬɪɚɥɢɡɚɰɢɢ ɢɨɧɚ. ɉɪɢɛɥɢɠɚɹɫɶ ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɦɟɬɚɥɥɚ, ɢɨɧ ɢɡɦɟɧɹɟɬ ɫɜɨɢɦ ɩɨɥɟɦ ɩɨɜɟɪɯɧɨɫɬɧɵɣ ɩɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ, ɩɨɧɢɠɚɹ ɟɝɨ. Ɉɞɢɧ ɷɥɟɤɬɪɨɧ, ɢɦɟɹ ɜ ɦɟɬɚɥɥɟ ɷɧɟɪɝɢɸ E1, ɫɨɜɟɪɲɚɟɬ ɬɭɧɧɟɥɶɧɵɣ ɩɟɪɟɯɨɞ ɢ ɧɟɣɬɪɚɥɢɡɭɟɬ ɢɨɧ (ɪɢɫ. 7.10). ɉɪɢ ɷɬɨɦ
ɜɵɞɟɥɹɟɦɚɹ ɷɧɟɪɝɢɹ Vi – E1 ɦɨɠɟɬ ɛɵɬɶ ɩɟɪɟɞɚɧɚ ɜɬɨɪɨɦɭ ɷɥɟɤɬɪɨɧɭ, ɢɦɟɸɳɟɦɭ ɜ ɦɟɬɚɥɥɟ ɷɧɟɪɝɢɸ E2. Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɜɬɨɪɨɣ ɷɥɟɤɬɪɨɧ ɜɵɲɟɥ ɢɡ ɦɟɬɚɥɥɚ, ɟɝɨ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɞɨɥɠɧɚ ɛɵɬɶ ɛɨɥɶɲɟ ɧɭɥɹ: mv2/2 = Vi – E1 – E2 > 0. ɋ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ ɩɪɢ ɧɢɡɤɢɯ ɬɟɦɩɟɪɚɬɭɪɚɯ E1 ɢ E2 ɦɟɧɶɲɟ ϕa, Vi >2ϕa. Ɉɩɵɬ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɤɨɷɮɮɢɰɢɟɧɬ γɩ ɥɢɧɟɣɧɨ ɪɚɫɬɟɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɪɚɡɧɨɫɬɢ Vi -2ϕa ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɩɚɪ ɦɢɲɟɧɶ – ɢɨɧ. Ⱦɥɹ ɱɢɫɬɵɯ ɩɨɜɟɪɯɧɨɫɬɟɣ ɷɬɭ ɡɚɜɢɫɢɦɨɫɬɶ ɦɨɠɧɨ ɨɩɢɫɚɬɶ ɷɦɩɢɪɢɱɟɫɤɨɣ ɮɨɪɦɭɥɨɣ:
γɩ ≈ 0.016(Vi -2ϕa)[ɷȼ].
(7.36)
Ʉɨɷɮɮɢɰɢɟɧɬ γɩ ɬɟɦ ɛɨɥɶɲɟ, ɱɟɦ ɛɨɥɶɲɟ ɡɚɪɹɞ ɢɨɧɚ (ɤɪɚɬɧɨɫɬɶ ɢɨɧɢɡɚɰɢɢ): γɩ(A+) < γɩ(A++) < γɩ(A+++). Ⱦɥɹ ɦɢɲɟɧɟɣ, ɩɨɜɟɪɯɧɨɫɬɶ ɤɨɬɨɪɵɯ ɞɨɫɬɚɬɨɱɧɨ ɱɢɫɬɚɹ, γɩ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɷɧɟɪɝɢɢ ɩɚɞɚɸɳɢɯ ɢɨɧɨɜ Ep: dγɩ/dEp ≈ 0. ɉɪɢ ɛɨɥɶɲɨɣ ɜɟɥɢɱɢɧɟ ɪɚɡɧɨɫɬɢ Vi -2ϕa >> kBT ɤɨɷɮɮɢɰɢɟɧɬ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɢɨɧɧɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɩɨɜɟɪɯɧɨɫɬɢ ɦɢɲɟɧɢ. ɉɪɢ ɦɚɥɨɣ ɜɟɥɢɱɢɧɟ ɷɬɨɣ ɪɚɡɧɨɫɬɢ: Vi -2ϕa ≈ kBT ɬɟɪɦɢɱɟɫɤɨɟ ɭɜɟɥɢɱɟɧɢɟ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɨɜ ɩɨɜɵɲɚɟɬ ɜɟɪɨɹɬɧɨɫɬɶ ɷɦɢɫɫɢɢ ɢ γɩ ɪɚɫɬɟɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɬɟɦɩɟɪɚɬɭɪɵ, ɩɪɢ ɷɬɨɦ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɦɢɫɫɢɹ ɜɨɡɦɨɠɧɚ ɢ ɩɪɢ Vi < 2ϕa. ɉɪɢ ɜɵɫɨɤɢɯ ɷɧɟɪɝɢɹɯ ɩɚɞɚɸɳɢɯ ɢɨɧɨɜ ɤɢɧɟɬɢɱɟɫɤɚɹ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɩɪɟɨɛɥɚɞɚɟɬ ɧɚɞ ɩɨɬɟɧɰɢɚɥɶɧɨɣ. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɛɵɥɨ ɨɛɧɚɪɭɠɟɧɨ, ɱɬɨ ɫɭɳɟɫɬɜɭɟɬ ɩɨɪɨɝɨɜɨɟ ɡɧɚɱɟɧɢɟ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɢɨɧɨɜ (Ep)ɝɪ ∼1.5 ɤɷȼ, ɦɟɧɶɲɟ ɤɨɬɨɪɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬ ɷɦɢɫɫɢɢ γɤ ≈ 0. ȼ ɩɪɢɩɨɪɨɝɨɜɨɣ ɨɛɥɚɫɬɢ ɷɧɟɪɝɢɣ ɢɨɧɨɜ (Ep < 10 ɤɷȼ) ɤɨɷɮɮɢɰɢɟɧɬ ɷɦɢɫɫɢɢ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɷɧɟɪɝɢɢ: γɤ = ɋ(Ep - (Ep)ɝɪ), ɝɞɟ ɋ = const. Ⱦɥɹ ɱɢɫɬɵɯ ɦɟɬɚɥɥɨɜ ɋ ≤ 0.2⋅10-2 ɷȼ-1. ɉɪɢ ɛɨɥɟɟ ɜɵɫɨɤɢɯ ɷɧɟɪɝɢɹɯ γɤ ∼ Ep1/2 . ɉɪɢ ɨɛɥɭɱɟɧɢɢ ɦɨɧɨɤɪɢɫɬɚɥɥɨɜ ɤɨɷɮɮɢɰɢɟɧɬ γɤ ɡɚɜɢɫɢɬ ɨɬ ɭɝɥɚ ɩɚɞɟɧɢɹ ɢɨɧɨɜ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ, ɩɪɢɱɟɦ ɷɬɚ ɡɚɜɢɫɢɦɨɫɬɶ ɧɨɫɢɬ ɩɟɪɢɨɞɢɱɟɫɤɢɣ ɯɚɪɚɤɬɟɪ: ɩɨɥɨɠɟɧɢɹ ɦɚɤɫɢɦɭɦɨɜ ɫɨɜɩɚɞɚɸɬ ɫ ɧɚɩɪɚɜɥɟɧɢɹɦɢ ɩɚɞɚɸɳɢɯ ɢɨɧɨɜ ɜɞɨɥɶ ɤɪɢɫɬɚɥɥɨɝɪɚɮɢɱɟɫɤɢɯ ɧɚɩɪɚɜɥɟɧɢɣ ɜ ɦɨɧɨɤɪɢɫɬɚɥɥɟ. ɋɨɜɪɟɦɟɧɧɵɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɨ ɤɢɧɟɬɢɱɟɫɤɨɣ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ (ɦɨɞɟɥɶ ɉɚɪɢɥɢɫɚ, ɉɟɬɪɨɜɚ, Ʉɢɲɢɧɟɜɫɤɨɝɨ) ɨɫɧɨɜɵɜɚɸɬɫɹ ɧɚ ɞɜɭɯɷɬɚɩɧɨɫɬɢ ɩɪɨɰɟɫɫɚ. ɇɚ ɩɟɪɜɨɦ ɷɬɚɩɟ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɢɨɧɚ ɩɟɪɟɞɚɟɬɫɹ ɷɥɟɤɬɪɨɧɧɨɣ ɫɢɫɬɟɦɟ ɦɟɬɚɥɥɚ ɫ ɨɛɪɚɡɨɜɚɧɢɟɦ «ɞɵɪɨɤ» (ɩɨɥɭɱɚɹ ɷɧɟɪɝɢɸ, ɷɥɟɤɬɪɨɧɵ ɚɬɨɦɨɜ ɫɨɜɟɪɲɚɸɬ ɦɟɠɡɨɧɧɵɣ ɩɟɪɟɯɨɞ ɜ ɡɨɧɭ ɩɪɨɜɨɞɢɦɨɫɬɢ, ɨɛɪɚɡɭɹ ɞɵɪɤɢ). ɇɚ ɜɬɨɪɨɦ ɷɬɚɩɟ ɩɪɨɢɫɯɨɞɢɬ ɪɟɤɨɦɛɢɧɚɰɢɹ ɞɵɪɤɢ ɢ ɷɥɟɤɬɪɨɧɚ ɩɪɨɜɨɞɢɦɨɫɬɢ ɦɟɬɚɥɥɚ ɫ ɩɟɪɟɞɚɱɟɣ ɜɵɞɟɥɹɸɳɟɣɫɹ ɷɧɟɪɝɢɢ ɡɚ ɫɱɟɬ ɨɠɟ-ɩɪɨɰɟɫɫɚ ɞɪɭɝɨɦɭ ɷɥɟɤɬɪɨɧɭ ɩɪɨɜɨɞɢɦɨɫɬɢ, ɤɨɬɨɪɵɣ ɷɦɢɬɢɪɭɟɬɫɹ ɢɡ ɦɢɲɟɧɢ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜɬɨɪɨɣ ɷɬɚɩ ɤɢɧɟɬɢɱɟɫɤɨɣ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɛɥɢɡɨɤ ɩɨ ɩɪɢɪɨɞɟ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɦɢɫɫɢɢ. ɉɨɜɟɪɯɧɨɫɬɧɚɹ ɢɨɧɢɡɚɰɢɹ
ɂɨɧɧɚɹ ɷɦɢɫɫɢɹ ɜ ɪɟɡɭɥɶɬɚɬɟ ɬɟɪɦɢɱɟɫɤɨɣ ɞɟɫɨɪɛɰɢɢ ɱɚɫɬɢɰ ɫ ɩɨɜɟɪɯɧɨɫɬɢ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ɧɚɡɵɜɚɟɬɫɹ ɩɨɜɟɪɯɧɨɫɬɧɨɣ ɢɨɧɢɡɚɰɢɟɣ. ȼ ɜɢɞɟ ɢɨɧɨɜ ɦɨɝɭɬ ɢɫɩɚɪɹɬɶɫɹ ɤɚɤ ɚɬɨɦɵ ɫɚɦɨɝɨ ɧɚɝɪɟɬɨɝɨ ɬɟɥɚ (ɧɚɩɪɢɦɟɪ, ɦɟɬɚɥɥɚ), ɬɚɤ ɢ ɚɬɨɦɵ ɢ ɦɨɥɟɤɭɥɵ, ɤɨɬɨɪɵɟ ɩɨɩɚɥɢ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ ɢɡ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ. ɑɚɫɬɶ ɢɡ ɧɢɯ ɩɨɫɥɟ ɚɞɫɨɪɛɢɪɨɜɚɧɢɹ ɢɫɩɚɪɹɸɬɫɹ ɨɛɪɚɬɧɨ ɜ ɝɚɡ, ɧɨ ɭɠɟ ɜ ɜɢɞɟ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢɥɢ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɢɨɧɨɜ. ɉɨɜɟɪɯɧɨɫɬɧɚɹ ɢɨɧɢɡɚɰɢɹ ɛɵɥɚ ɨɬɤɪɵɬɚ Ʌɟɧɝɦɸɪɨɦ ɢ Ʉɢɧɝɞɨɧɨɦ (1923 ɝ.), ɤɨɬɨɪɵɟ ɨɛɧɚɪɭɠɢɥɢ ɜ ɰɢɥɢɧɞɪɢɱɟɫɤɨɦ ɞɢɨɞɟ, ɡɚɩɨɥɧɟɧɧɨɦ ɩɚɪɚɦɢ ɰɟɡɢɹ, ɬɨɤ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢɨɧɨɜ. ɋɬɟɩɟɧɶ ɩɨɜɟɪɯɧɨɫɬɧɨɣ
ɢɨɧɢɡɚɰɢɢ α = ni/na, ɝɞɟ ni - ɩɥɨɬɧɨɫɬɶ ɢɨɧɨɜ, ɨɬɥɟɬɚɸɳɢɯ ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ, na ɩɥɨɬɧɨɫɬɶ ɢɫɩɚɪɹɸɳɢɯɫɹ ɚɬɨɦɨɜ, ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɡɚɪɹɞɨɜɨɟ ɪɚɜɧɨɜɟɫɢɟ ɜ ɢɫɩɚɪɹɸɳɟɦɫɹ ɩɨɬɨɤɟ ɱɚɫɬɢɰ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɫɩɨɫɨɛɚ ɩɨɫɬɭɩɥɟɧɢɹ ɱɚɫɬɢɰ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ. Ⱦɪɭɝɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɩɨɜɟɪɯɧɨɫɬɧɨɣ ɢɨɧɢɡɚɰɢɢ ɹɜɥɹɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬ ɩɨɜɟɪɯɧɨɫɬɧɨɣ ɢɨɧɢɡɚɰɢɢ β = ni/n = ni/(ni+na) (β=α/(1+α)). Ʉ ɨɩɢɫɚɧɢɸ ɩɪɨɰɟɫɫɚ ɢɨɧɢɡɚɰɢɢ ɢɫɩɚɪɹɸɳɢɯɫɹ ɚɬɨɦɨɜ Ʌɟɧɝɦɸɪ ɩɪɢɦɟɧɢɥ ɮɨɪɦɭɥɭ ɋɚɯɚ ɞɥɹ ɬɟɪɦɢɱɟɫɤɨɣ ɢɨɧɢɡɚɰɢɢ ɝɚɡɚ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɪɢ ɨɛɪɚɡɨɜɚɧɢɢ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢɨɧɨɜ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢ ɪɚɜɧɨɜɟɫɧɵɣ ɢɨɧɢɡɚɰɢɨɧɧɵɣ ɫɨɫɬɚɜ ɭ ɩɨɜɟɪɯɧɨɫɬɢ ɬɟɥɚ ɦɨɠɧɨ ɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɫɬɟɩɟɧɶɸ ɢɨɧɢɡɚɰɢɢ α, ɤɨɬɨɪɚɹ ɜɵɱɢɫɥɹɟɬɫɹ ɢɡ ɭɪɚɜɧɟɧɢɹ ɋɚɯɚ-Ʌɟɧɝɦɸɪɚ:
α=
gi e(ϕ a − U i ) exp( ), ga kT
(7.37)
ɝɞɟ Ui – ɩɨɬɟɧɰɢɚɥ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ, eϕa – ɪɚɛɨɬɚ ɜɵɯɨɞɚ ɷɥɟɤɬɪɨɧɨɜ ɢɡ ɦɟɬɚɥɥɚ, gi/ga – ɨɬɧɨɲɟɧɢɟ ɫɬɚɬɢɫɬɢɱɟɫɤɢɯ ɜɟɫɨɜ ɢɨɧɧɨɝɨ ɢ ɚɬɨɦɧɨɝɨ ɫɨɫɬɨɹɧɢɣ ɢɨɧɢɡɢɪɭɸɳɢɯɫɹ ɱɚɫɬɢɰ ɪɚɜɧɨ ½ ɞɥɹ ɨɞɧɨɜɚɥɟɧɬɧɨɝɨ ɚɞɫɨɪɛɢɪɭɸɳɟɝɨ ɦɟɬɚɥɥɚ ɢ 2 - ɞɥɹ ɞɜɭɯɜɚɥɟɧɬɧɨɝɨ. ȿɫɥɢ ɷɧɟɪɝɢɹ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ ɩɨɤɪɵɬɢɹ (ɧɚɩɪɢɦɟɪ, Cs, K, Na ɧɚ W) ɦɟɧɶɲɟ ɪɚɛɨɬɵ ɜɵɯɨɞɚ ɷɥɟɤɬɪɨɧɨɜ ɢɡ ɦɟɬɚɥɥɢɱɟɫɤɨɣ ɩɨɞɥɨɠɤɢ, ɬɨ ɩɪɚɤɬɢɱɟɫɤɢ ɜɫɟ ɢɫɩɚɪɹɸɳɢɟɫɹ ɫ ɩɨɤɪɵɬɢɹ ɚɬɨɦɵ ɩɨɤɢɞɚɸɬ ɩɨɜɟɪɯɧɨɫɬɶ ɜ ɜɢɞɟ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢɨɧɨɜ. Ⱥɬɨɦɵ ɧɟɤɨɬɨɪɵɯ ɷɥɟɦɟɧɬɨɜ ɦɨɝɭɬ ɩɨɤɢɞɚɬɶ ɩɨɜɟɪɯɧɨɫɬɶ, ɩɪɢɫɨɟɞɢɧɹɹ ɤ ɫɟɛɟ ɷɥɟɤɬɪɨɧ ɢ ɩɪɟɜɪɚɳɚɹɫɶ ɜ ɨɬɪɢɰɚɬɟɥɶɧɵɣ ɢɨɧ. Ⱦɥɹ ɪɚɡɪɭɲɟɧɢɹ ɨɬɪɢɰɚɬɟɥɶɧɨɝɨ ɢɨɧɚ ɬɪɟɛɭɟɬɫɹ ɫɨɜɟɪɲɢɬɶ ɧɟɤɨɬɨɪɭɸ ɪɚɛɨɬɭ, ɤɨɬɨɪɭɸ ɚɬɨɦɨɜ ɧɚɡɵɜɚɸɬ ɪɚɛɨɬɨɣ ɫɪɨɞɫɬɜɚ eS. ɑɚɫɬɶ ɬɚɤɢɯ ɚɞɫɨɪɛɢɪɨɜɚɧɧɵɯ ɢɫɩɚɪɹɸɬɫɹ ɜ ɜɢɞɟ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɢɨɧɨɜ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɫɬɟɩɟɧɢ ɢɨɧɢɡɚɰɢɢ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɢɨɧɨɜ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɭɪɚɜɧɟɧɢɟ, ɚɧɚɥɨɝɢɱɧɨɟ ɭɪɚɜɧɟɧɢɸ ɋɚɯɚ-Ʌɟɧɝɦɸɪɚ:
α− =
e( S − ϕ a ) g− exp( ). ga kT
(7.38)
ȽɅȺȼȺ 8 ɗɅȿɄɌɊɂɑȿɋɄɂɃ ɌɈɄ ȼ ȽȺɁȺɏ ɂ ȽȺɁɈȼɕɃ ɊȺɁɊəȾ Ƚɚɡɨɜɵɣ ɪɚɡɪɹɞ − ɷɬɨ ɩɪɨɰɟɫɫ ɩɪɨɬɟɤɚɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ ɱɟɪɟɡ ɝɚɡ. Ɋɚɡɥɢɱɚɸɬ ɧɟɫɚɦɨɫɬɨɹɬɟɥɶɧɵɟ ɢ ɫɚɦɨɫɬɨɹɬɟɥɶɧɵɟ ɪɚɡɪɹɞɵ. ɇɟɫɚɦɨɫɬɨɹɬɟɥɶɧɵɣ ɪɚɡɪɹɞ ɜɨɡɦɨɠɟɧ ɩɪɢ ɢɧɠɟɤɰɢɢ ɷɥɟɤɬɪɨɧɨɜ ɜ ɪɚɡɪɹɞɧɵɣ ɩɪɨɦɟɠɭɬɨɤ (ɧɚɩɪɢɦɟɪ, ɬɟɪɦɨɷɦɢɫɫɢɹ ɫ ɤɚɬɨɞɚ) ɢɥɢ ɩɪɢ ɢɨɧɢɡɚɰɢɢ ɝɚɡɚ ɤɚɤɢɦɥɢɛɨ ɜɧɟɲɧɢɦ ɢɫɬɨɱɧɢɤɨɦ. ɇɟɫɚɦɨɫɬɨɹɬɟɥɶɧɵɟ ɪɚɡɪɹɞɵ ɢɫɩɨɥɶɡɭɸɬ ɞɨɜɨɥɶɧɨ ɲɢɪɨɤɨ: ɷɬɨ ɢ ɢɨɧɢɡɚɰɢɨɧɧɵɟ ɤɚɦɟɪɵ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɢ ɞɨɡɢɦɟɬɪɢɱɟɫɤɨɝɨ ɧɚɡɧɚɱɟɧɢɹ ɧɚ ɚɬɨɦɧɵɯ ɪɟɚɤɬɨɪɚɯ, ɝɚɡɨɬɪɨɧɵ ɜ ɜɵɩɪɹɦɢɬɟɥɶɧɵɯ ɭɫɬɚɧɨɜɤɚɯ ɫɟɬɟɣ ɩɢɬɚɧɢɹ ɩɨɫɬɨɹɧɧɵɦ ɬɨɤɨɦ, ɩɥɚɡɦɨɬɪɨɧɵ ɫ ɧɚɤɚɥɢɜɚɟɦɵɦ ɤɚɬɨɞɨɦ ɢ ɬ.ɞ. Ɏɢɡɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ, ɩɪɨɬɟɤɚɸɳɢɟ ɜ ɪɚɡɧɵɯ ɧɟɫɚɦɨɫɬɨɹɬɟɥɶɧɵɯ ɪɚɡɪɹɞɚɯ, ɟɫɬɟɫɬɜɟɧɧɨ, ɪɚɡɥɢɱɚɸɬɫɹ, ɧɨ ɧɟ ɜɫɟ ɨɧɢ ɯɚɪɚɤɬɟɪɧɵ ɞɥɹ ɫɨɛɫɬɜɟɧɧɨ ɝɚɡɨɜɵɯ ɪɚɡɪɹɞɨɜ, ɤɚɤ ɨɛɵɱɧɨ ɩɨɧɢɦɚɸɬ ɷɬɨɬ ɬɟɪɦɢɧ. ȼ ɧɢɯ ɫ ɩɨɦɨɳɶɸ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɩɪɨɫɬɨ ɫɨɛɢɪɚɸɬ ɨɛɪɚɡɭɸɳɢɟɫɹ ɜ ɨɛɴɟɦɟ ɡɚɪɹɞɵ (ɱɬɨ ɜɨɨɛɳɟ-ɬɨ ɧɟ ɫɨɜɫɟɦ "ɩɪɨɫɬɨ"!), ɜ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵɯ ɫɱɟɬɱɢɤɚɯ ɢɫɩɨɥɶɡɭɸɬ ɨɝɪɚɧɢɱɟɧɧɨɟ ɨɛɪɚɡɨɜɚɧɢɟ ɷɥɟɤɬɪɨɧɧɵɯ ɥɚɜɢɧ, ɜ ɝɟɣɝɟɪɨɜɫɤɢɯ ɫɱɟɬɱɢɤɚɯ ɩɪɨɢɫɯɨɞɢɬ ɤɨɪɨɧɧɵɣ ɪɚɡɪɹɞ, ɜ ɝɚɡɨɬɪɨɧɚɯ ɢ ɬɢɪɚɬɪɨɧɚɯ «ɨɛɯɨɞɹɬ» ɡɚɤɨɧ «3/2», ɤɚɤ ɛɵ ɩɪɢɛɥɢɠɚɹ ɚɧɨɞ ɤ ɤɚɬɨɞɭ, ɜ ɞɭɝɨɜɵɯ ɥɚɦɩɚɯ ɞɧɟɜɧɨɝɨ ɫɜɟɬɚ ɬɟɪɦɨɷɦɢɫɫɢɹ ɫ ɩɨɞɨɝɪɟɜɧɵɯ ɤɚɬɨɞɨɜ ɬɨɥɶɤɨ ɨɛɟɫɩɟɱɢɜɚɟɬ ɡɚɠɢɝɚɧɢɟ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɣ ɞɭɝɢ. Ɉɞɧɚɤɨ ɧɚɢɛɨɥɟɟ ɲɢɪɨɤɨ ɩɪɢɦɟɧɹɸɬɫɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɵɟ ɪɚɡɪɹɞɵ, ɨ ɧɢɯ ɢ ɛɭɞɟɬ ɪɟɱɶ. ɋɚɦɨɫɬɨɹɬɟɥɶɧɵɣ ɬɥɟɸɳɢɣ ɪɚɡɪɹɞ ɡɚɠɢɝɚɟɬɫɹ ɬɨɝɞɚ, ɤɨɝɞɚ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɟɝɨ ɚɤɬɢɜɧɵɯ ɭɱɚɫɬɤɚɯ ɞɨɫɬɢɝɚɟɬ "ɧɚɩɪɹɠɟɧɢɹ ɩɪɨɛɨɹ", ɞɥɹ ɞɭɝɨɜɨɝɨ ɪɚɡɪɹɞɚ ɧɟɨɛɯɨɞɢɦɨ ɫɨɡɞɚɬɶ ɭɫɥɨɜɢɹ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɬɟɪɦɨɷɦɢɫɫɢɢ ɫ ɤɚɬɨɞɚ. Ʉɨɪɨɧɧɵɟ ɪɚɡɪɹɞɵ ɜɨɡɧɢɤɚɸɬ ɬɨɥɶɤɨ ɩɪɢ ɧɚɥɢɱɢɢ ɭɱɚɫɬɤɨɜ ɫ ɨɱɟɧɶ ɛɨɥɶɲɨɣ ɧɟɨɞɧɨɪɨɞɧɨɫɬɶɸ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɚ ɢɫɤɪɨɜɵɟ ɪɚɡɪɹɞɵ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɢɦɩɭɥɶɫɧɵɟ. ȼɫɟ ɷɬɨ ɫɩɪɚɜɟɞɥɢɜɨ ɞɥɹ ɩɨɫɬɨɹɧɧɵɯ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɨɥɟɣ, ɭ ɩɨɥɟɣ ȼɑ ɢ ɋȼɑ, ɤɨɬɨɪɵɟ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɸɬɫɹ ɜ ɬɟɯɧɨɥɨɝɢɹɯ, ɟɫɬɶ ɫɜɨɹ ɫɩɟɰɢɮɢɤɚ, ɨɫɨɛɟɧɧɨ ɭ ɩɨɥɟɣ ɥɚɡɟɪɧɨɣ ɢɫɤɪɵ. §49. ɗɥɟɤɬɪɢɱɟɫɤɢɣ ɬɨɤ ɜ ɝɚɡɚɯ ɋɬɨɥɤɧɨɜɟɧɢɹ ɱɚɫɬɢɰ ɦɨɝɭɬ ɢɦɟɬɶ ɭɩɪɭɝɢɣ ɢ ɧɟɭɩɪɭɝɢɣ ɯɚɪɚɤɬɟɪ. ɉɪɢ ɭɩɪɭɝɨɦ ɫɬɨɥɤɧɨɜɟɧɢɢ ɦɟɧɹɟɬɫɹ ɧɚɩɪɚɜɥɟɧɢɟ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ, ɩɪɨɢɫɯɨɞɢɬ ɨɛɦɟɧ ɢɦɩɭɥɶɫɚɦɢ ɢ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɟɣ. ɉɪɢ ɧɟɭɩɪɭɝɨɦ ɫɬɨɥɤɧɨɜɟɧɢɢ ɜɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ ɢ ɫɨɫɬɨɹɧɢɟ ɨɞɧɨɣ ɢɡ ɱɚɫɬɢɰ (ɪɟɞɤɨ ɤɨɝɞɚ ɨɛɨɢɯ) ɢɡɦɟɧɹɟɬɫɹ. ɂɨɧɢɡɚɰɢɹ ɚɬɨɦɚ ɩɪɢ ɭɞɚɪɟ ɷɥɟɤɬɪɨɧɨɦ ɩɪɨɢɫɯɨɞɢɬ ɡɚ ɫɱɟɬ ɩɟɪɟɞɚɱɢ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɚ ɚɬɨɦɭ. Ɂɧɚɱɟɧɢɟ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɚ, ɞɨɫɬɚɬɨɱɧɨɟ ɞɥɹ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚ ɧɚɡɵɜɚɟɬɫɹ ɩɨɬɟɧɰɢɚɥɨɦ ɢɨɧɢɡɚɰɢɢ Ui. ɉɪɢ ɦɧɨɝɨɤɪɚɬɧɨɣ ɢɨɧɢɡɚɰɢɢ ɷɧɟɪɝɢɹ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɨɬɪɵɜɚ ɤɚɠɞɨɝɨ ɫɥɟɞɭɸɳɟɝɨ ɷɥɟɤɬɪɨɧɚ ɜɨɡɪɚɫɬɚɟɬ. ɉɢɨɧɟɪɚɦɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɝɨ ɨɩɪɟɞɟɥɟɧɢɹ ɩɨɬɟɧɰɢɚɥɚ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ ɛɵɥɢ Ɏɪɚɧɤ ɢ Ƚɟɪɰ. Ɇɟɬɨɞ ɨɩɪɟɞɟɥɟɧɢɹ ɨɫɧɨɜɵɜɚɥɫɹ ɧɚ ɬɨɦ, ɱɬɨ ɡɚɜɢɫɢɦɨɫɬɶ ɬɨɤɚ, ɩɪɨɬɟɤɚɸɳɟɝɨ ɱɟɪɟɡ ɞɢɨɞ ɜ ɩɚɪɚɯ ɪɬɭɬɢ, ɨɬ ɭɫɤɨɪɹɸɳɟɝɨ ɷɥɟɤɬɪɨɧɵ ɧɚɩɪɹɠɟɧɢɹ ɧɨɫɢɬ ɧɟ ɦɨɧɨɬɨɧɧɵɣ ɜɨɡɪɚɫɬɚɸɳɢɣ ɯɚɪɚɤɬɟɪ, ɚ ɢɦɟɟɬ ɩɪɨɜɚɥɵ ɢɡ-ɡɚ ɩɨɬɟɪɶ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɜɨɡɛɭɠɞɟɧɢɟ ɢ ɢɨɧɢɡɚɰɢɸ ɚɬɨɦɨɜ ɪɬɭɬɢ. Ɂɚɜɢɫɢɦɨɫɬɶ ɜɟɪɨɹɬɧɨɫɬɢ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ ɥɸɛɨɝɨ ɝɚɡɚ ɨɬ ɷɧɟɪɝɢɢ ɱɚɫɬɢɰ U ɡɚɞɚɟɬɫɹ ɮɭɧɤɰɢɟɣ ɢɨɧɢɡɚɰɢɢ: fi = a(U-Ui)exp(-(U-Ui)/b),
(8.1)
ɝɞɟ a ɢ b − ɷɦɩɢɪɢɱɟɫɤɢɟ ɤɨɧɫɬɚɧɬɵ ɞɥɹ ɤɨɧɤɪɟɬɧɨɝɨ ɝɚɡɚ. ȼɪɟɦɹ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ, ɩɪɢɜɨɞɹɳɢɦɢ ɤ ɢɨɧɢɡɚɰɢɢ, ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɱɚɫɬɨɬɟ ɢɨɧɢɡɚɰɢɢ τi = 1/νi. ɑɢɫɥɨ ɢɨɧɢɡɚɰɢɣ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɩɥɨɬɧɨɫɬɢ ɱɚɫɬɢɰ ɝɚɡɚ n, ɫɤɨɪɨɫɬɢ ɧɚɥɟɬɚɸɳɟɣ ɱɚɫɬɢɰɵ v ɢ ɫɟɱɟɧɢɸ ɢɨɧɢɡɚɰɢɢ σi : νi = nvσi. (8.2) ɂɨɧɢɡɚɰɢɨɧɧɵɣ ɩɪɨɛɟɝ λi (ɞɥɢɧɚ, ɧɚ ɤɨɬɨɪɨɣ ɱɚɫɬɢɰɚ ɦɨɠɟɬ ɢɨɧɢɡɨɜɚɬɶ) ɪɚɜɟɧ λi = vτi = v/νi = 1/(nσi) = 1/Si,
(8.3)
ɝɞɟ Si = nσi ɧɚɡɵɜɚɟɬɫɹ ɫɭɦɦɚɪɧɵɦ ɫɟɱɟɧɢɟɦ ɢɨɧɢɡɚɰɢɢ. ɋɭɦɦɚɪɧɨɟ ɫɟɱɟɧɢɟ ɢɨɧɢɡɚɰɢɢ ɬɚɤ ɠɟ ɯɨɪɨɲɨ ɚɩɩɪɨɤɫɢɦɢɪɭɟɬɫɹ ɩɨɞɨɛɧɨɣ (8.1) ɡɚɜɢɫɢɦɨɫɬɶɸ ɨɬ ɷɧɟɪɝɢɢ ɱɚɫɬɢɰɵ U: Si = a (U - Ui) exp(- b(U - Ui) ) (ɮɨɪɦɭɥɚ Ɇɨɪɝɭɥɢɫɚ),
(8.4)
ɝɞɟ a ɢ b – ɷɦɩɢɪɢɱɟɫɤɢɟ ɤɨɧɫɬɚɧɬɵ ɞɥɹ ɤɨɧɤɪɟɬɧɨɝɨ ɝɚɡɚ. Ɂɚɜɢɫɢɦɨɫɬɶ ɫɭɦɦɚɪɧɨɝɨ ɫɟɱɟɧɢɹ ɜɨɡɛɭɠɞɟɧɢɹ ɢɦɟɟɬ ɩɨɯɨɠɢɣ ɜɢɞ: S r = S max
U −Ur U −Ur exp(1 − ) (ɮɨɪɦɭɥɚ Ɏɚɛɪɢɤɚɧɬɚ), (8.5) U max − U r U max − U r
ɝɞɟ Ur – ɩɨɬɟɧɰɢɚɥ ɜɨɡɛɭɠɞɟɧɧɨɝɨ ɭɪɨɜɧɹ, Umax ɢ Smax – ɷɧɟɪɝɢɹ ɢ ɫɟɱɟɧɢɟ ɜɨɡɛɭɠɞɟɧɢɹ ɜ ɦɚɤɫɢɦɭɦɟ ɮɭɧɤɰɢɢ ɜɨɡɛɭɠɞɟɧɢɹ, ɡɧɚɱɟɧɢɹ ɤɨɬɨɪɵɯ ɦɨɠɧɨ ɧɚɣɬɢ ɜ ɫɩɪɚɜɨɱɧɵɯ ɬɚɛɥɢɰɚɯ ɞɥɹ ɤɨɧɤɪɟɬɧɨɝɨ ɝɚɡɚ. ȼɪɟɦɹ ɩɪɟɛɵɜɚɧɢɹ ɚɬɨɦɚ ɜ ɜɨɡɛɭɠɞɟɧɧɨɦ ɫɨɫɬɨɹɧɢɢ ɦɨɠɧɨ ɫɜɹɡɚɬɶ ɫ ɱɢɫɥɨɦ ɩɟɪɟɯɨɞɨɜ ɜ ɟɞɢɧɢɰɟ ɨɛɴɟɦɚ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ N, ɬɨɝɞɚ ɡɚ ɩɪɨɦɟɠɭɬɨɤ ɜɪɟɦɟɧɢ dt ɱɢɫɥɨ ɩɟɪɟɯɨɞɨɜ: Ndt = wnadt, ɝɞɟ w – ɜɟɪɨɹɬɧɨɫɬɶ ɞɚɧɧɨɝɨ ɩɟɪɟɯɨɞɚ na - ɤɨɧɰɟɧɬɪɚɰɢɹ ɜɨɡɛɭɠɞɟɧɧɵɯ ɚɬɨɦɨɜ. ɑɢɫɥɨ ɚɤɬɨɜ ɢɡɥɭɱɟɧɢɹ ɪɚɜɧɨ ɭɛɵɥɢ ɱɢɫɥɚ ɜɨɡɛɭɠɞɟɧɧɵɯ ɚɬɨɦɨɜ: Ndt = -dna, ɬɨɝɞɚ dna = - wnadt. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɢɫɥɨ ɜɨɡɛɭɠɞɟɧɧɵɯ ɚɬɨɦɨɜ ɢɡɦɟɧɹɟɬɫɹ ɜɨ ɜɪɟɦɟɧɢ ɩɨ ɡɚɤɨɧɭ: na(t) = na0exp(-wt),
(8.6)
ɝɞɟ na0 – ɤɨɧɰɟɧɬɪɚɰɢɹ ɜɨɡɛɭɠɞɟɧɧɵɯ ɚɬɨɦɨɜ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ. Ɂɚ ɜɪɟɦɹ t0 = 1/w ɤɨɧɰɟɧɬɪɚɰɢɹ ɭɦɟɧɶɲɚɟɬɫɹ ɜ «ɟ» ɪɚɡ. ɗɬɨ ɜɪɟɦɹ ɢ ɩɨɥɚɝɚɸɬ ɜɪɟɦɟɧɟɦ ɩɪɟɛɵɜɚɧɢɹ ɚɬɨɦɚ ɜ ɜɨɡɛɭɠɞɟɧɧɨɦ ɫɨɫɬɨɹɧɢɢ. ɇɟɫɦɨɬɪɹ ɧɚ ɦɚɥɨɫɬɶ ɷɬɨɣ ɜɟɥɢɱɢɧɵ t0 ∼ 10-8 ÷ 10-7 ɫ, ɞɚɠɟ ɡɚ ɫɬɨɥɶ ɤɨɪɨɬɤɨɟ ɜɪɟɦɹ ɫɭɳɟɫɬɜɨɜɚɧɢɹ ɜɨɡɛɭɠɞɟɧɧɨɝɨ ɚɬɨɦɚ ɜɨɡɦɨɠɧɨ ɩɨɥɭɱɟɧɢɟ ɧɨɜɨɣ ɩɨɪɰɢɢ ɷɧɟɪɝɢɢ, ɞɨɫɬɚɬɨɱɧɨɣ ɞɥɹ ɩɟɪɟɯɨɞɚ ɚɬɨɦɚ ɧɚ ɫɥɟɞɭɸɳɢɣ ɭɪɨɜɟɧɶ ɜɨɡɛɭɠɞɟɧɢɹ, ɥɢɛɨ ɞɥɹ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚ, ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɝɨɜɨɪɹɬ ɨ ɫɬɭɩɟɧɱɚɬɨɣ ɢɨɧɢɡɚɰɢɢ. ɂɦɟɧɧɨ ɬɚɤɨɣ ɩɪɨɰɟɫɫ ɫɬɭɩɟɧɱɚɬɨɣ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ ɪɬɭɬɢ ɧɚɛɥɸɞɚɥɫɹ ɜ ɨɩɵɬɚɯ Ɏɪɚɧɤɚ ɢ Ƚɟɪɰɚ. ɋɪɟɞɢ ɜɨɡɛɭɠɞɟɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɚɬɨɦɨɜ ɢ ɦɨɥɟɤɭɥ ɫɭɳɟɫɬɜɭɸɬ ɦɟɬɚɫɬɚɛɢɥɶɧɵɟ ɫɨɫɬɨɹɧɢɹ, ɜɪɟɦɟɧɚ ɠɢɡɧɢ ɤɨɬɨɪɵɯ ɨɬ 10-4 ɞɨ ɧɟɫɤɨɥɶɤɢɯ ɫɟɤɭɧɞ. ɋɚɦɵɣ ɧɢɠɧɢɣ ɦɟɬɚɫɬɚɛɢɥɶɧɵɣ ɭɪɨɜɟɧɶ ɧɚɡɵɜɚɟɬɫɹ ɪɟɡɨɧɚɧɫɧɵɦ. Ⱦɥɹ ɪɬɭɬɢ ɪɟɡɨɧɚɧɫɧɵɣ ɭɪɨɜɟɧɶ ɜɨɡɛɭɠɞɟɧɢɹ ɪɚɜɟɧ 4.7 ɷȼ, ɩɪɢ ɩɪɟɜɵɲɟɧɢɢ ɷɧɟɪɝɢɟɣ ɷɥɟɤɬɪɨɧɨɜ ɷɬɨɝɨ ɡɧɚɱɟɧɢɹ ɧɚɛɥɸɞɚɥɫɹ ɩɟɪɜɵɣ ɩɪɨɜɚɥ ɜ ɡɚɜɢɫɢɦɨɫɬɢ
ɬɨɤɚ ɨɬ ɭɫɤɨɪɹɸɳɟɝɨ ɷɥɟɤɬɪɨɧɵ ɩɨɬɟɧɰɢɚɥɚ. Ɇɟɬɚɫɬɚɛɢɥɶɧɚɹ ɱɚɫɬɢɰɚ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɢ ɫ ɷɥɟɤɬɪɨɧɨɦ ɦɨɠɟɬ ɢ ɞɟɡɚɤɬɢɜɢɪɨɜɚɬɶɫɹ, ɬɨ ɟɫɬɶ ɩɟɪɟɣɬɢ ɜ ɨɫɧɨɜɧɨɟ ɫɨɫɬɨɹɧɢɟ, ɷɬɨɬ ɩɪɨɰɟɫɫ ɧɚɡɵɜɚɟɬɫɹ ɧɟɭɩɪɭɝɢɦ ɫɨɭɞɚɪɟɧɢɟɦ ɜɬɨɪɨɝɨ ɪɨɞɚ. Ʉɪɨɦɟ ɨɛɪɚɡɨɜɚɧɢɹ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢɨɧɨɜ ɩɪɢ ɩɪɨɬɟɤɚɧɢɢ ɬɨɤɚ ɜ ɝɚɡɟ ɜɨɡɦɨɠɧɨ ɜɨɡɧɢɤɧɨɜɟɧɢɟ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɢɨɧɨɜ. Ⱦɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɨɬɪɢɰɚɬɟɥɶɧɵɣ ɢɨɧ ɫɭɳɟɫɬɜɨɜɚɥ ɢ ɛɵɥ ɭɫɬɨɣɱɢɜ, ɟɝɨ ɜɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ Ei ɞɨɥɠɧɚ ɛɵɬɶ ɦɟɧɶɲɟ, ɱɟɦ ɷɧɟɪɝɢɹ ɧɨɪɦɚɥɶɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɩɚɪɵ ɚɬɨɦ – ɫɜɨɛɨɞɧɵɣ ɷɥɟɤɬɪɨɧ E0. Ɋɚɡɧɨɫɬɶ A = E0 – Ei ɧɚɡɵɜɚɟɬɫɹ ɫɪɨɞɫɬɜɨɦ ɚɬɨɦɚ ɤ ɷɥɟɤɬɪɨɧɭ. ȼ ɚɬɨɦɚɯ ɫ ɡɚɩɨɥɧɟɧɧɨɣ ɜɧɟɲɧɟɣ ɷɥɟɤɬɪɨɧɧɨɣ ɨɛɨɥɨɱɤɨɣ (ɢɧɟɪɬɧɵɟ ɝɚɡɵ He, Ne, Ar, Xe, Kr,..) ɷɥɟɤɬɪɨɧɧɚɹ ɨɛɨɥɨɱɤɚ ɷɤɪɚɧɢɪɭɟɬ ɹɞɪɨ ɢ ɜɟɪɨɹɬɧɨɫɬɶ ɨɛɪɚɡɨɜɚɧɢɹ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɢɨɧɨɜ ɦɚɥɚ. Ⱥɬɨɦɵ ɫ ɧɟɩɨɥɧɵɦɢ ɜɧɟɲɧɢɦɢ ɨɛɨɥɨɱɤɚɦɢ (F, Cl, K, Na…), ɭ ɤɨɬɨɪɵɯ ɨɛɨɥɨɱɤɢ ɛɥɢɠɟ ɜɫɟɝɨ ɤ ɡɚɩɨɥɧɟɧɢɸ, ɨɛɪɚɡɭɸɬ ɧɚɢɛɨɥɟɟ ɭɫɬɨɣɱɢɜɵɟ ɨɬɪɢɰɚɬɟɥɶɧɵɟ ɢɨɧɵ. ɋɪɨɞɫɬɜɨ ɷɬɢɯ ɚɬɨɦɨɜ ɞɨɫɬɚɬɨɱɧɨ ɜɟɥɢɤɨ: AF − = 3.4 ÷ 3.6 ɷȼ, ACl − = 3.82 ɷȼ. ȿɫɥɢ ɷɥɟɤɬɪɨɧ ɞɨ ɫɬɨɥɤɧɨɜɟɧɢɹ ɢɦɟɥ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ Ek, ɬɨ ɩɪɢ ɟɝɨ ɡɚɯɜɚɬɟ ɞɨɥɠɧɚ ɨɫɜɨɛɨɠɞɚɬɶɫɹ ɷɧɟɪɝɢɹ A + Ek. ɗɬɚ ɷɧɟɪɝɢɹ ɦɨɠɟɬ ɨɫɜɨɛɨɠɞɚɬɶɫɹ ɱɟɪɟɡ ɢɡɥɭɱɟɧɢɟ: e + a → a- + hγ, ɧɨ ɛɨɥɟɟ ɜɟɪɨɹɬɟɧ ɩɪɨɰɟɫɫ ɨɛɪɚɡɨɜɚɧɢɹ ɨɬɪɢɰɚɬɟɥɶɧɨɝɨ ɢɨɧɚ ɜ ɪɟɡɭɥɶɬɚɬɟ ɫɬɨɥɤɧɨɜɟɧɢɹ ɬɪɟɯ ɬɟɥ X + Y + e → X+ + Y- + e ɢɥɢ X + Y → X+ + Y- . Ⱦɥɹ ɨɩɢɫɚɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ ɜ ɝɚɡɚɯ ɧɟɞɨɫɬɚɬɨɱɧɨ ɪɚɫɫɦɨɬɪɟɧɢɹ ɩɪɨɰɟɫɫɨɜ ɢɨɧɢɡɚɰɢɢ ɢ ɪɟɤɨɦɛɢɧɚɰɢɢ. ɇɟɨɛɯɨɞɢɦɨ ɨɩɢɫɚɧɢɟ ɞɜɢɠɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɢ ɦɚɝɧɢɬɧɵɯ ɩɨɥɟɣ, ɩɪɢɱɟɦ ɫɬɚɬɢɫɬɢɱɟɫɤɨɟ, ɬ. ɟ. ɭɫɪɟɞɧɟɧɧɨɟ ɩɨ ɦɧɨɝɨɱɢɫɥɟɧɧɵɦ ɫɬɨɥɤɧɨɜɟɧɢɹɦ. ɉɪɢ ɧɚɥɢɱɢɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɧɚ ɯɚɨɬɢɱɟɫɤɨɟ ɞɜɢɠɟɧɢɟ ɱɚɫɬɢɰ ɧɚɤɥɚɞɵɜɚɟɬɫɹ ɧɚɩɪɚɜɥɟɧɧɨɟ ɞɜɢɠɟɧɢɟ ɜɞɨɥɶ ɩɨɥɹ. Ⱦɥɹ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɩɪɨɰɟɫɫɚ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɬɨɤɚ ɫɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɢ ɫɪɟɞɧɹɹ ɫɤɨɪɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ɞɨɥɠɧɵ ɨɫɬɚɜɚɬɶɫɹ ɩɨɫɬɨɹɧɧɵɦɢ, ɧɟɫɦɨɬɪɹ ɧɚ ɩɪɢɫɭɬɫɬɜɢɟ ɭɫɤɨɪɹɸɳɟɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. ɗɬɨ ɜɨɡɦɨɠɧɨ, ɟɫɥɢ ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɫɢɥɚ ɤɨɦɩɟɧɫɢɪɭɟɬɫɹ ɫɢɥɨɣ ɬɪɟɧɢɹ (ɷɥɟɤɬɪɨɧɵ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɹɯ ɨɬɞɚɸɬ ɱɚɫɬɶ ɫɜɨɟɣ ɷɧɟɪɝɢɢ). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɪɟɞɧɹɹ ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɨɬ ɨɞɧɨɝɨ ɷɥɟɤɬɪɨɞɚ ɤ ɞɪɭɝɨɦɭ, ɤɨɬɨɪɭɸ ɧɚɡɵɜɚɸɬ ɫɤɨɪɨɫɬɶɸ ɞɪɟɣɮɚ ud, ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɨɣ. Ɉɬɧɨɲɟɧɢɟ ɫɤɨɪɨɫɬɢ ɧɚɩɪɚɜɥɟɧɧɨɝɨ ɞɜɢɠɟɧɢɹ (ɫɤɨɪɨɫɬɢ ɞɪɟɣɮɚ) ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɤ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɧɚɡɵɜɚɟɬɫɹ ɩɨɞɜɢɠɧɨɫɬɶɸ:
b[ɫɦ2/(ȼ⋅ɫɦ)] = ud/E.
(8.7)
ɋɤɨɪɨɫɬɶ ɞɪɟɣɮɚ ɦɨɠɧɨ ɨɰɟɧɢɬɶ ɢɡ ɩɪɟɞɩɨɥɨɠɟɧɢɹ, ɱɬɨ ɨɧɚ ɦɧɨɝɨ ɦɟɧɶɲɟ ɬɟɩɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɢ ɜ ɪɟɡɭɥɶɬɚɬɟ ɫɬɨɥɤɧɨɜɟɧɢɹ ɱɚɫɬɢɰɚ ɬɟɪɹɟɬ ɜɫɸ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ. Ɂɚ ɜɪɟɦɹ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ τɫɬ ɡɚɪɹɠɟɧɧɚɹ eE τ ɫɬ , ud = S/τɫɬ, ɬɨɝɞɚ: ɱɚɫɬɢɰɚ ɩɪɨɣɞɟɬ ɩɭɬɶ S = 2me
be =
eλɫɬ , 2mvɌ
(8.8)
ɝɞɟ λ ɫɬ - ɫɪɟɞɧɹɹ ɞɥɢɧɚ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ, vɌ - ɬɟɩɥɨɜɚɹ ɫɤɨɪɨɫɬɶ. Ⱦɥɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ɇɚɤɫɜɟɥɥɥɚ ɭɫɪɟɞɧɟɧɧɚɹ ɩɨ ɫɤɨɪɨɫɬɹɦ ɫɤɨɪɨɫɬɶ ɞɪɟɣɮɚ (ɮɨɪɦɭɥɚ Ʌɚɧɠɟɜɟɧɚ):
u d [ɫɦ / ɫ] =
eλ 2me eE eλ E[ ȼ / ɫɦ] λ ɫɬ = 0.64 ɫɬ E = 0.64 1 ⋅ , πkT 2me mvɌ mvɌ p[ ɦɦ. ɪɬ.ɫɬ.]
(8.9)
ɝɞɟ λ1 = pλɫɬ - ɫɪɟɞɧɢɣ ɩɪɨɛɟɝ ɩɪɢ ɞɚɜɥɟɧɢɢ 1 ɦɦ.ɪɬ.ɫɬ. Ⱦɥɹ ɫɪɟɞɧɟɣ ɫɤɨɪɨɫɬɢ ɞɪɟɣɮɚ ɢɨɧɨɜ ɮɨɪɦɭɥɚ Ʌɚɧɠɟɜɟɧɚ ɢɦɟɟɬ ɜɢɞ:
u d = ai
eλi1 m E 1+ i ⋅ , mi viɌ mµ p
(8.10)
ai – ɤɨɷɮɮɢɰɢɟɧɬ, ɪɚɜɧɵɣ 0.5 ÷1, mµ - ɦɚɫɫɚ ɦɨɥɟɤɭɥɵ ɢɨɧɚ. ɗɥɟɤɬɪɨɧɵ ɧɚ ɫɜɨɟɦ ɩɭɬɢ ɢɨɧɢɡɭɸɬ ɚɬɨɦɵ, «ɢɨɧɢɡɭɸɳɭɸ» ɫɩɨɫɨɛɧɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ɚɧɝɥɢɱɚɧɢɧ Ɍɚɭɧɫɟɧɞ ɩɪɟɞɥɨɠɢɥ ɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɤɨɷɮɮɢɰɢɟɧɬɨɦ α, ɧɚɡɜɚɧɧɵɦ ɜɩɨɫɥɟɞɫɬɜɢɢ ɩɟɪɜɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ Ɍɚɭɧɫɟɧɞɚ, ɪɚɜɧɵɦ ɱɢɫɥɭ ɷɥɟɤɬɪɨɧɨɜ, ɫɨɡɞɚɜɚɟɦɵɯ ɷɥɟɤɬɪɨɧɨɦ ɧɚ ɟɞɢɧɢɰɟ ɞɥɢɧɵ ɩɪɨɛɟɝɚ. ɉɪɢ ɬɚɤɨɦ ɨɩɢɫɚɧɢɢ ɩɪɢɪɨɫɬ ɤɨɥɢɱɟɫɬɜɚ ɷɥɟɤɬɪɨɧɨɜ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ α ɢ ɤɨɥɢɱɟɫɬɜɭ ɚɬɨɦɨɜ n: dn(x) = αndx. Ɍɨɝɞɚ ɱɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɪɚɫɫɬɨɹɧɢɢ x:
ne(x)=n0exp(αx),
(8.11)
ɚ ɩɟɪɜɵɣ ɤɨɷɮɮɢɰɢɟɧɬ Ɍɚɭɧɫɟɧɞɚ:
α = (1/n)(dn/dx).
(8.12)
ɉɪɨɰɟɫɫ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɦɨɠɧɨ ɬɚɤɠɟ ɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɱɚɫɬɨɬɨɣ ɢɨɧɢɡɚɰɢɢ Yi – ɱɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ, ɫɨɡɞɚɜɚɟɦɵɯ ɨɞɧɢɦ ɷɥɟɤɬɪɨɧɨɦ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ:
Yi = (1/n)(dn/dt).
(8.13)
Ɍɨɝɞɚ ɱɚɫɬɨɬɚ ɢɨɧɢɡɚɰɢɢ ɫɜɹɡɚɧɚ ɫ ɩɟɪɜɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ Ɍɚɭɧɫɟɧɞɚ ɱɟɪɟɡ ɫɤɨɪɨɫɬɶ ɞɪɟɣɮɚ:
Yi/α = ud ȼɫɟ ɬɪɢ ɜɟɥɢɱɢɧɵ α, Yi, ud ɡɚɜɢɫɹɬ ɨɬ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ȿ. ɋɪɚɡɭ ɨɬɦɟɬɢɦ, ɱɬɨ α(E), Yi(E), ud(E) ɜɟɫɶɦɚ ɫɥɨɠɧɵɟ ɡɚɜɢɫɢɦɨɫɬɢ, ɦɟɧɹɸɬɫɹ ɫ ɢɡɦɟɧɟɧɢɟɦ ɭɫɥɨɜɢɣ ɪɚɡɪɹɞɚ, ɧɨ ɞɥɹ Yi(E) ɢ α(E) ɜɫɟɝɞɚ ɜɟɫɶɦɚ ɫɢɥɶɧɵɟ (ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɵɟ, ɫɬɟɩɟɧɧɵɟ). §50. Ɍɟɨɪɢɹ ɷɥɟɤɬɪɨɧɧɵɯ ɥɚɜɢɧ
ȼ ɤɨɧɰɟ 80-ɯ ɝ. ɩɪɨɲɥɨɝɨ ɜɟɤɚ ɧɟɦɟɰ Ɏ. ɉɚɲɟɧ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɭɫɬɚɧɨɜɢɥ, ɱɬɨ ɧɚɩɪɹɠɟɧɢɟ ɡɚɠɢɝɚɧɢɹ ɪɚɡɪɹɞɚ Uɡ ɡɚɜɢɫɢɬ ɨɬ ɩɪɨɢɡɜɟɞɟɧɢɹ pd (ɝɞɟ p – ɞɚɜɥɟɧɢɟ ɝɚɡɚ, d – ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɷɥɟɤɬɪɨɞɚɦɢ) ɢ ɢɦɟɟɬ ɧɟɤɨɟ ɦɢɧɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɞɥɹ ɞɚɧɧɨɝɨ ɝɚɡɚ ɢ ɜɟɥɢɱɢɧɵ ɜɬɨɪɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ
Ɍɚɭɧɫɟɧɞɚ γ, (ɤɪɢɜɵɟ ɉɚɲɟɧɚ ɧɚ ɪɢɫ. 8.1). Ⱦɥɹ ɨɛɴɹɫɧɟɧɢɹ ɷɬɨɝɨ ɮɚɤɬɚ ɩɨɬɪɟɛɨɜɚɥɨɫɶ ɤɨɥɢɱɟɫɬɜɟɧɧɨɟ ɨɩɢɫɚɧɢɟ ɩɪɨɰɟɫɫɚ ɪɚɡɦɧɨɠɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɪɚɡɪɹɞɟ. ɉɟɪɜɨɣ ɤɨɥɢɱɟɫɬɜɟɧɧɨɣ ɬɟɨɪɢɟɣ ɝɚɡɨɜɨɝɨ ɪɚɡɪɹɞɚ ɛɵɥɚ ɬɟɨɪɢɹ ɷɥɟɤɬɪɨɧɧɵɯ ɥɚɜɢɧ, ɩɪɟɞɥɨɠɟɧɧɚɹ Ɍɚɭɧɫɟɧɞɨɦ ɜ ɫɚɦɨɦ ɧɚɱɚɥɟ 20-ɝɨ ɜɟɤɚ. Ɋɢɫ 8.1. Ʉɪɢɜɵɟ ɉɚɲɟɧɚ
ȼɨɡɧɢɤɧɨɜɟɧɢɟ, ɪɚɡɜɢɬɢɟ ɢ ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɪɚɡɪɹɞɚ ɜɨ ɜɪɟɦɟɧɢ ɢ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ
1) Ɋɚɡɜɢɬɢɟ ɜɨ ɜɪɟɦɟɧɢ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɪɟɚɥɶɧɨ, ɩɨɦɢɦɨ ɪɨɠɞɟɧɢɹ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ ɧɚ ɨɞɢɧ ɩɟɪɜɢɱɧɵɣ ɷɥɟɤɬɪɨɧ Yi ɷɥɟɤɬɪɨɧɨɜ, ɧɟɤɨɟ ɤɨɥɢɱɟɫɬɜɨ ɷɥɟɤɬɪɨɧɨɜ ɨɞɧɨɜɪɟɦɟɧɧɨ ɝɢɛɧɟɬ: ɚ)ɩɪɢɥɢɩɚɟɬ ɤ ɚɬɨɦɚɦ ɢ ɦɨɥɟɤɭɥɚɦ ɫ ɱɚɫɬɨɬɨɣ Ya, ɛ) ɞɢɮɮɭɧɞɢɪɭɟɬ ɧɚ ɫɬɟɧɤɢ ɭɫɬɚɧɨɜɤɢ ɫ ɱɚɫɬɨɬɨɣ Yd, ɜ) ɪɟɤɨɦɛɢɧɢɪɭɟɬ ɫ ɢɨɧɚɦɢ ɫ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɪɟɤɨɦɛɢɧɚɰɢɢ β. Ɉɛɵɱɧɨ ɪɟɤɨɦɛɢɧɚɰɢɸ ɧɟ ɭɱɢɬɵɜɚɸɬ, ɬɚɤ ɱɬɨ ɭɫɥɨɜɢɟɦ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɢ ɪɚɡɜɢɬɢɹ ɪɚɡɪɹɞɚ:
Yi(E) > Yd + Ya
(8.14)
ɚ ɝɨɪɟɧɢɹ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɪɚɡɪɹɞɚ:
Yi(E) = Yd + Ya
(8.15)
ɗɬɨ ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ "ɫɬɚɰɢɨɧɚɪɧɵɣ ɤɪɢɬɟɪɢɣ ɩɪɨɛɨɹ". ɉɨ ɨɩɪɟɞɟɥɟɧɢɸ, Yd = 1/τd, ɝɞɟ ɜɪɟɦɹ ɞɢɮɮɭɡɢɢ τd ɡɚɜɢɫɢɬ ɨɬ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ D ɢ ɯɚɪɚɤɬɟɪɧɚɹ ɞɢɮɮɭɡɢɨɧɧɚɹ ɞɥɢɧɚ ɩɪɨɛɟɝɚ ɷɥɟɤɬɪɨɧɨɜ ɤ ɫɬɟɧɤɚɦ λd : τd = λd2/D. Ⱦɥɹ ɰɢɥɢɧɞɪɚ 1/λd2 = (2.4/R)2 + (π/L)2 (R ɢ L − ɪɚɞɢɭɫ ɢ ɞɥɢɧɚ ɰɢɥɢɧɞɪɚ); ɞɥɹ ɩɚɪɚɥɥɟɩɢɩɟɞɚ: 1/λd2 = (π/L1)2 + (π/L2)2 + (π/L3)2 (L1, L2, L3 − ɥɢɧɟɣɧɵɟ ɪɚɡɦɟɪɵ ɩɚɪɚɥɥɟɩɢɩɟɞɚ). ɂɡ ɜɵɪɚɠɟɧɢɣ ɞɥɹ ɱɚɫɬɨɬɵ ɢɨɧɢɡɚɰɢɢ (8.13) ɢ ɭɫɥɨɜɢɹ (8.14) ɦɨɠɧɨ ɫɨɫɬɚɜɢɬɶ ɮɟɧɨɦɟɧɨɥɨɝɢɱɟɫɤɨɟ ɫɨɨɬɧɨɲɟɧɢɟ ɛɚɥɚɧɫɚ ɞɥɹ ɩɥɨɬɧɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ:
dne/dt = ne(Yi(E) - Yd - Ya),
(8.16)
ne = ne0exp((Yi(E) - Yd - Ya)t) = ne0exp(t/θ),
(8.17)
ɨɬɤɭɞɚ
ɝɞɟ θ - ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɥɚɜɢɧɵ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɪɚɡɜɢɜɚɬɶɫɹ ɥɚɜɢɧɚ ɦɨɠɟɬ ɬɨɥɶɤɨ, ɟɫɥɢ ɜɵɩɨɥɧɹɟɬɫɹ ɭɫɥɨɜɢɟ (8.14), ɢ ɩɪɢ ɧɟɨɝɪɚɧɢɱɟɧɧɨɦ t ɥɚɜɢɧɚ ɦɨɠɟɬ ɪɚɡɜɢɜɚɬɶɫɹ ɩɪɨɢɡɜɨɥɶɧɨ ɞɨɥɝɨ. ɇɨ ɟɫɬɶ ɫɢɬɭɚɰɢɢ, ɤɨɝɞɚ t ɨɱɟɧɶ ɦɚɥɨ (ɨɫɨɛɟɧɧɨ ɜ ɥɚɡɟɪɧɨɣ ɢɫɤɪɟ), ɬɨɝɞɚ ɧɟɨɛɯɨɞɢɦɨ ɛɨɥɶɲɨɟ ɩɪɟɜɵɲɟɧɢɟ ɪɨɠɞɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɧɚɞ ɝɢɛɟɥɶɸ, ɬ. ɟ. ɛɨɥɶɲɨɟ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ȿ (ɚ ɜ ɥɚɡɟɪɧɨɣ ɢɫɤɪɟ ɩɪɨɫɬɨ ɝɢɝɚɧɬɫɤɨɟ!). ɂɡ ɨɛɨɛɳɟɧɧɨɝɨ ɤɪɢɬɟɪɢɹ ɩɪɨɛɨɹ (8.17):
θ -1(E(t)) = Yi(E) - Yd - Ya = ln(n(t)/n0)/t
(8.18)
ɜɢɞɧɨ, ɱɬɨ ɪɚɡɪɹɞ ɩɪɢɯɨɞɢɬ ɤ ɫɬɚɰɢɨɧɚɪɧɨɦɭ ɩɪɢ t → ∞. ɇɚ ɫɚɦɨɦ ɞɟɥɟ ɷɬɨɬ ɩɟɪɟɯɨɞ ɩɪɨɢɫɯɨɞɢɬ ɪɚɧɶɲɟ. ɇɚɪɚɫɬɚɧɢɟ ɬɨɤɚ ɧɟ ɛɟɡɝɪɚɧɢɱɧɨ, ɤɚɤ ɷɬɨ ɞɨɥɠɧɨ ɛɵɥɨ ɛɵɬɶ ɩɨ ɬɟɨɪɢɢ ɷɥɟɤɬɪɨɧɧɵɯ ɥɚɜɢɧ, ɚ ɨɝɪɚɧɢɱɢɜɚɟɬɫɹ ɨɛɴɟɦɧɵɦ ɡɚɪɹɞɨɦ. Ɍɚɤ ɤɚɤ ɫ ɪɨɫɬɨɦ ɩɨɫɥɟɞɧɟɝɨ ɩɪɢ ɜɨɡɧɢɤɧɨɜɟɧɢɢ ɜɢɪɬɭɚɥɶɧɨɝɨ ɤɚɬɨɞɚ ɷɮɮɟɤɬɢɜɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɞɨ ɚɧɨɞɚ ɫɨɤɪɚɳɚɟɬɫɹ, ɬɨ ɧɚ ɛɨɥɟɟ ɤɨɪɨɬɤɨɣ ɞɥɢɧɟ ɩɪɨɥɟɬɧɨɝɨ ɩɪɨɦɟɠɭɬɤɚ ɭɦɟɧɶɲɚɟɬɫɹ ɜɟɪɨɹɬɧɨɫɬɶ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ ɢ ɦɨɥɟɤɭɥ ɝɚɡɚ ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɪɚɡɪɹɞ ɩɟɪɟɯɨɞɢɬ ɤ ɫɬɚɰɢɨɧɚɪɧɨɦɭ. 2) Ɋɚɡɜɢɬɢɟ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ. ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɢɡ ɤɚɬɨɞɚ ɜɵɥɟɬɟɥ ɨɞɢɧ ɷɥɟɤɬɪɨɧ. ȼ ɫɢɥɶɧɨɦ ɩɨɥɟ ɩɪɢɤɚɬɨɞɧɨɝɨ ɫɥɨɹ ɨɧ ɛɵɫɬɪɨ ɧɚɛɟɪɟɬ ɷɧɟɪɝɢɸ, ɞɨɫɬɚɬɨɱɧɭɸ ɞɥɹ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚ (ɦɨɥɟɤɭɥɵ) ɝɚɡɚ, ɩɨɫɥɟ ɢɨɧɢɡɚɰɢɢ ɛɭɞɟɬ ɞɜɚ ɦɟɞɥɟɧɧɵɯ ɷɥɟɤɬɪɨɧɚ (ɢ ɨɞɢɧ ɢɨɧ). ɗɥɟɤɬɪɨɧɵ ɬɚɤ ɠɟ ɭɫɤɨɪɹɬɫɹ, ɤɚɠɞɵɣ ɩɪɨɢɡɜɟɞɟɬ ɢɨɧɢɡɚɰɢɸ ɫɬɚɧɟɬ ɢɯ ɱɟɬɵɪɟ - ɬɨɠɟ ɭɫɤɨɪɹɬɫɹ, ɢɨɧɢɡɭɸɬ, ɫɬɚɧɟɬ ɜɨɫɟɦɶ ɢ ɬ.ɞ.ɜɨɡɧɢɤɚɟɬ ɥɚɜɢɧɚ, ɢɞɟɬ Ɋɢɫ. 8.2. ɋɯɟɦɵ (ɚ) ɥɚɜɢɧɧɨɝɨ ɪɚɡɦɧɨɠɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɰɟɩɧɨɣ ɩɪɨɰɟɫɫ (ɪɢɫ. 8.2). ɜ ɩɪɨɦɟɠɭɬɤɟ ɦɟɠɞɭ ɤɚɬɨɞɨɦ Ʉ ɢ ɚɧɨɞɨɦ Ⱥ ɢ (ɛ) ɇɚ ɪɚɫɫɬɨɹɧɢɢ x ɩɟɪɜɵɣ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɪɚɫɩɥɵɜɚɧɢɹ ɷɥɟɤɬɪɨɧɧɨɣ ɥɚɜɢɧɵ, ɷɥɟɤɬɪɨɧ ɫɨɡɞɚɫɬ (ɟαx -1) ɤɨɬɨɪɚɹ ɪɨɠɞɚɟɬɫɹ ɨɬ ɷɥɟɤɬɪɨɧɚ, ɜɵɲɟɞɲɟɝɨ ɢɡ ɷɥɟɤɬɪɨɧɧɵɯ ɩɚɪ. ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɦɟɫɬɚ ɤɚɬɨɞɚ ȼɨɡɧɢɤɚɸɳɢɟ ɜ ɩɪɨɦɟɠɭɬɤɟ ɷɥɟɤɬɪɨɧɵ ɞɪɟɣɮɭɸɬ ɤ ɚɧɨɞɭ, ɢɨɧɵ – ɤ ɤɚɬɨɞɭ. ɉɪɢɯɨɞɹɳɢɟ ɧɚ ɤɚɬɨɞ ɢɨɧɵ ɫɩɨɫɨɛɧɵ ɜɵɛɢɜɚɬɶ ɢɡ ɤɚɬɨɞɚ ɜɬɨɪɢɱɧɵɟ ɷɥɟɤɬɪɨɧɵ. Ⱦɥɹ ɨɩɢɫɚɧɢɹ ɩɪɨɰɟɫɫɚ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ Ɍɚɭɧɫɟɧɞɨɦ ɛɵɥ ɩɪɟɞɥɨɠɟɧ ɜɬɨɪɨɣ ɤɨɷɮɮɢɰɢɟɧɬ γ, ɪɚɜɧɵɣ ɱɢɫɥɭ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɨɞɢɧ ɩɪɢɯɨɞɹɳɢɣ ɧɚ ɤɚɬɨɞ ɢɨɧ (ɜɬɨɪɨɣ ɤɨɷɮɮɢɰɢɟɧɬ Ɍɚɭɧɫɟɧɞɚ) ɢ ɡɚɜɢɫɹɳɢɣ ɨɬ ɦɚɬɟɪɢɚɥɚ ɤɚɬɨɞɚ, ɱɢɫɬɨɬɵ ɟɝɨ ɩɨɜɟɪɯɧɨɫɬɢ ɢ ɞɪ., ɨɛɵɱɧɨ γ = 10-4 ÷ 10-2. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɢɨɧɵ ɩɨɣɞɭɬ ɤ ɤɚɬɨɞɭ, ɭɫɤɨɪɹɬɫɹ ɢ ɜɵɛɶɸɬ ɢɡ ɤɚɬɨɞɚ γ(ɟαx -1) ɷɥɟɤɬɪɨɧɨɜ. Ⱦɚɠɟ ɟɫɥɢ ɷɬɨ ɛɭɞɟɬ ɜɫɟɝɨ ɨɞɢɧ ɜɬɨɪɢɱɧɵɣ ɷɥɟɤɬɪɨɧ, ɬɨ ɩɪɨɰɟɫɫ ɩɨɜɬɨɪɢɬɫɹ, ɬɚɤ ɱɬɨ ɭɫɥɨɜɢɟɦ ɝɨɪɟɧɢɹ ɪɚɡɪɹɞɚ ɛɭɞɟɬ:
γ(ɟαx -1) ≥ 1.
(8.19)
Ʉɚɠɞɵɣ ɜɬɨɪɢɱɧɵɣ ɷɥɟɤɬɪɨɧ ɬɚɤɠɟ ɢɨɧɢɡɭɟɬ ɚɬɨɦɵ ɢ ɪɨɠɞɚɟɬ ɷɥɟɤɬɪɨɧɵ (ɟαx 1). ɇɟɬɪɭɞɧɨ ɩɨɤɚɡɚɬɶ, ɟɫɥɢ ɱɢɫɥɨ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ n0, ɞɥɢɧɚ ɩɪɨɦɟɠɭɬɤɚ
ɦɟɠɞɭ ɤɚɬɨɞɨɦ ɢ ɚɧɨɞɨɦ d, ɬɨ ɩɨɫɥɟ ɫɭɦɦɢɪɨɜɚɧɢɹ ɜɫɟɯ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ γ(ɟαx -1) < 1, ɱɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ, ɩɪɢɯɨɞɹɳɢɯ ɧɚ ɚɧɨɞ, ɛɭɞɟɬ ɪɚɜɧɨ:
n = n0 ⋅
exp(αd ) . 1 − γ (exp(αd ) − 1)
(8.20)
ȼɟɥɢɱɢɧɚ
µ = γ(exp(αd)-1)
(8.21)
ɧɚɡɵɜɚɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɢɨɧɢɡɚɰɢɨɧɧɨɝɨ ɧɚɪɚɫɬɚɧɢɹ. ɉɪɢ µ < 1 ɬɨɤ ɛɭɞɟɬ ɡɚɬɭɯɚɬɶ, ɭɫɥɨɜɢɟ µ = 1 ɹɜɥɹɟɬɫɹ ɭɫɥɨɜɢɟɦ ɩɟɪɟɯɨɞɚ ɤ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɦɭ ɪɚɡɪɹɞɭ (ɭɫɥɨɜɢɟ ɡɚɠɢɝɚɧɢɹ ɪɚɡɪɹɞɚ) ɢ ɭɫɥɨɜɢɟɦ ɫɬɚɰɢɨɧɚɪɧɨɫɬɢ ɪɚɡɪɹɞɚ. Ʉɚɪɬɢɧɚ ɭɩɪɨɳɟɧɚ ɢ ɢɞɟɚɥɢɡɢɪɨɜɚɧɚ, ɪɟɚɥɶɧɨ ɷɥɟɤɬɪɨɧɵ ɝɢɛɧɭɬ (ɩɪɢɥɢɩɚɸɬ, ɪɟɤɨɦɛɢɧɢɪɭɸɬ, ɞɢɮɮɭɧɞɢɪɭɸɬ ɤ ɫɬɟɧɤɚɦ), ɧɨ ɢ ɫɨɡɞɚɸɬɫɹ ɧɚ ɤɚɬɨɞɟ ɧɟ ɬɨɥɶɤɨ ɢɨɧɧɨɣ ɛɨɦɛɚɪɞɢɪɨɜɤɨɣ, ɞɚ ɢ α = const ɬɨɥɶɤɨ ɩɪɢ E = const ɧɚ ɜɫɟɣ ɩɪɨɬɹɠɟɧɧɨɫɬɢ d, ɧɨ ɜ ɞɟɣɫɬɜɢɬɟɥɶɧɨɫɬɢ ȿ ɜ ɤɚɬɨɞɧɨɦ ɫɥɨɟ ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɹɟɬɫɹ. ȼ ɤɨɧɰɟ ɩɪɨɲɥɨɝɨ ɫɬɨɥɟɬɢɹ Ɍɚɭɧɞɫɟɧɞ, ɩɪɨɚɧɚɥɢɡɢɪɨɜɚɜ ɨɝɪɨɦɧɨɟ ɱɢɫɥɨ ɨɩɵɬɨɜ, ɭɫɬɚɧɨɜɢɥ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɭɸ ɡɚɜɢɫɢɦɨɫɬɶ:
α/ɪ =Ⱥexp(-Bp/E),
(8.22ɚ)
ɝɞɟ Ⱥ ɢ ȼ ɩɨɫɬɨɹɧɧɵɟ ɞɥɹ ɞɚɧɧɨɝɨ ɝɚɡɚ ɢ ɤɚɬɨɞɚ, ɪ - ɞɚɜɥɟɧɢɟ, ȿ - ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. Ɍɚɤɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɦɨɠɟɬ ɛɵɬɶ ɤɚɱɟɫɬɜɟɧɧɨ ɨɛɴɹɫɧɟɧɚ ɬɟɦ, ɱɬɨ ɜɟɪɨɹɬɧɨɫɬɶ ɩɪɨɣɬɢ ɷɥɟɤɬɪɨɧɭ ɛɟɡ ɫɬɨɥɤɧɨɜɟɧɢɣ ɩɭɬɶ λi, ɧɚ ɤɨɬɨɪɨɦ ɷɥɟɤɬɪɨɧ ɧɚɛɢɪɚɟɬ ɧɟɨɛɯɨɞɢɦɭɸ ɞɥɹ ɢɨɧɢɡɚɰɢɢ ɷɧɟɪɝɢɸ, ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ exp(-λi/ λ ɫɬ ). Ʉɨɷɮɮɢɰɢɟɧɬ Ɍɚɭɧɫɟɧɞɚ α = Nexp(-λi/ λ ɫɬ ),ɝɞɟ N = 1/ λ ɫɬ - ɱɢɫɥɨ ɫɨɭɞɚɪɟɧɢɣ ɧɚ 1 ɫɦ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɟ ɞɚɜɥɟɧɢɸ: N = N0p, N0 – ɱɢɫɥɨ ɫɬɨɥɤɧɨɜɟɧɢɣ ɷɥɟɤɬɪɨɧɚ ɧɚ 1 ɫɦ ɩɭɬɢ ɩɪɢ ɞɚɜɥɟɧɢɢ, ɪɚɜɧɨɦ ɟɞɢɧɢɰɟ. ɋ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ λi = Ui/E ɩɨɥɭɱɢɦ ɫɨɨɬɧɨɲɟɧɢɟ, ɩɨɞɨɛɧɨɟ (8.22ɚ):
α/ɪ =N0exp(-N0Uip/E),
(8.22ɛ)
ɉɨɞɫɬɚɧɨɜɤɚ ɱɢɫɥɟɧɧɵɯ ɡɧɚɱɟɧɢɣ ɞɚɟɬ ɩɪɚɜɢɥɶɧɵɣ ɩɨɪɹɞɨɤ ɜɟɥɢɱɢɧ Ⱥ ɢ ȼ. Ʉɨɷɮɮɢɰɢɟɧɬɵ Ɍɚɭɧɫɟɧɞɚ α ɢ γ ɨɛɥɚɞɚɸɬ ɬɟɦ ɫɜɨɣɫɬɜɨɦ, ɱɬɨ ɨɬɧɨɲɟɧɢɟ α/p ɢ γ ɧɟ ɹɜɥɹɸɬɫɹ ɮɭɧɤɰɢɟɣ ɩɨ ɨɬɞɟɥɶɧɨɫɬɢ ɨɬ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ E ɢ ɞɚɜɥɟɧɢɹ ɝɚɡɚ p, ɚ ɡɚɜɢɫɢɬ ɨɬ ɢɯ ɨɬɧɨɲɟɧɢɹ: α /p=f1(E/p) ɢ γ =f2(E/p). ɍɫɥɨɜɢɟ ɡɚɠɢɝɚɧɢɹ ɪɚɡɪɹɞɚ, ɢɥɢ ɭɫɥɨɜɢɟ, ɩɨɡɜɨɥɹɸɳɟɟ ɨɩɪɟɞɟɥɢɬɶ ɧɚɩɪɹɠɟɧɢɟ ɡɚɠɢɝɚɧɢɹ Uɡ ɢɦɟɟɬ ɜɢɞ: f1 (
Uɡ U )(exp( f 2 ( ɡ )) − 1) = 1 . pd pd
(8.23)
ɂɡ (8.23) ɜɢɞɧɨ, ɱɬɨ ɧɚɩɪɹɠɟɧɢɟ ɡɚɠɢɝɚɧɢɹ Uɡ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɩɪɨɢɡɜɟɞɟɧɢɹ pd, ɢ ɩɪɢ pd = const ɧɚɩɪɹɠɟɧɢɟ ɡɚɠɢɝɚɧɢɹ ɧɟ ɦɟɧɹɟɬɫɹ. ɗɬɚ ɡɚɤɨɧɨɦɟɪɧɨɫɬɶ ɧɨɫɢɬ ɧɚɡɜɚɧɢɟ ɡɚɤɨɧ ɉɚɲɟɧɚ. Ʉɪɢɜɭɸ ɉɚɲɟɧɚ (ɫɦ. ɪɢɫ. 8.1), ɨɬɪɚɠɚɸɳɭɸ
ɡɚɜɢɫɢɦɨɫɬɶ Uɡ ɨɬ pd, ɧɚɡɵɜɚɸɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɡɚɠɢɝɚɧɢɹ ɪɚɡɪɹɞɚ. ȼɵɪɚɠɚɹ α ɢɡ ɭɫɥɨɜɢɹ ɡɚɠɢɝɚɧɢɹ ɪɚɡɪɹɞɚ (µ = 1) ɫ ɭɱɟɬɨɦ (8.21) ɢ ɩɨɞɫɬɚɜɥɹɹ ɜ ɜɵɪɚɠɟɧɢɟ (8.22ɚ), ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ: E/p =B/(C + ln(pd)), ɝɞɟ C = ln(Ⱥ/(ln(1/γ+1))). ɉɪɢɧɹɜ Uɡ = Ed, ɧɚɣɞɟɦ ɡɚɜɢɫɢɦɨɫɬɶ ɧɚɩɪɹɠɟɧɢɟ
ɡɚɠɢɝɚɧɢɹ ɨɬ pd:
Uɡ =Bpd/(C + ln(pd)), ɤɨɬɨɪɚɹ ɢ ɨɩɢɫɵɜɚɟɬɫɹ ɤɪɢɜɵɦɢ ɉɚɲɟɧɚ. ȼɚɠɧɨ, ɱɬɨ ɫɭɳɟɫɬɜɟɧɧɵ ɧɟ p, d, E "ɨɬɞɟɥɶɧɨ", ɚ "ɤɨɦɛɢɧɚɰɢɢ" pd (ɬ.ɤ. p = ngTg, ɝɞɟ ng ɢ Tg - ɩɥɨɬɧɨɫɬɶ ɢ ɬɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ, ɟɫɥɢ Tg = const, ɬɨ pd ɨɩɪɟɞɟɥɹɟɬ ɱɢɫɥɨ ɢɨɧɢɡɭɸɳɢɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɧɚ ɩɪɨɛɟɝɟ d), ɢ, ɨɫɨɛɟɧɧɨ, ȿ/ɪ, ɬ.ɟ. ɤɚɤ ɛɵ "ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɩɨɥɹ ɧɚ ɨɞɧɭ ɱɚɫɬɢɰɭ ɝɚɡɚ". Ɇɢɧɢɦɭɦ Uɡ ɫɨɨɬɜɟɬɫɬɜɭɟɬ (pd)min : (pd)min = ( e /A)ln(1/γ + 1),
(8.24)
ɝɞɟ e ≈ 2.72 - ɧɟ ɡɚɪɹɞ ɷɥɟɤɬɪɨɧɚ, ɚ ɨɫɧɨɜɚɧɢɟ ɧɚɬɭɪɚɥɶɧɨɝɨ ɥɨɝɚɪɢɮɦɚ. ɋɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɦɢɧɢɦɚɥɶɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɡɚɠɢɝɚɧɢɹ Uɡmin = B(1-C) ɡɚɜɢɫɢɬ ɬɨɥɶɤɨ ɨɬ ɫɨɪɬɚ ɝɚɡɚ ɢ ɦɚɬɟɪɢɚɥɚ ɤɚɬɨɞɚ, ɦɢɧɢɦɭɦ ɨɬɧɨɲɟɧɢɹ (ȿ/ɪ)min = ȼ ɡɚɜɢɫɢɬ ɬɨɥɶɤɨ ɨɬ ɫɨɪɬɚ ɝɚɡɚ. ɋɬɨɥɟɬɨɜ, ɢɫɫɥɟɞɭɹ ɮɨɬɨɷɥɟɤɬɪɨɧɧɭɸ ɷɦɢɫɫɢɸ, ɫɬɪɟɦɢɥɫɹ ɩɨɞɨɛɪɚɬɶ ɞɚɜɥɟɧɢɟ ɝɚɡɚ ɞɥɹ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɮɨɬɨɬɨɤɚ. Ɉɧ ɨɛɧɚɪɭɠɢɥ, ɱɬɨ ɟɫɥɢ ɭɦɟɧɶɲɚɬɶ ɞɚɜɥɟɧɢɟ, ɬɨ ɫɢɥɚ ɬɨɤɚ ɫɧɚɱɚɥɚ ɭɜɟɥɢɱɢɜɚɟɬɫɹ, ɚ ɡɚɬɟɦ ɭɦɟɧɶɲɚɟɬɫɹ, ɬ. ɟ. ɫɭɳɟɫɬɜɭɟɬ ɦɚɤɫɢɦɭɦ ɬɨɤɚ ɩɨ ɞɚɜɥɟɧɢɸ. ȿɫɥɢ ɩɪɢ ɷɬɨɦ ɦɟɧɹɬɶ ɨɬ ɨɩɵɬɚ ɤ ɨɩɵɬɭ ɪɚɡɧɨɫɬɶ ɩɨɬɟɧɰɢɚɥɨɜ ɦɟɠɞɭ ɤɚɬɨɞɨɦ ɢ ɚɧɨɞɨɦ, ɬɨ ɦɚɤɫɢɦɭɦ ɬɨɤɚ ɜɫɟɝɞɚ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɨɞɧɨɦɭ ɢ ɬɨɦɭ ɠɟ E/p. ɉɪɨɞɟɥɚɜ ɩɪɢɜɟɞɟɧɧɵɟ ɜɵɲɟ ɪɚɫɫɭɠɞɟɧɢɹ, Ɍɚɭɧɫɟɧɞ ɞɚɥ ɨɛɴɹɫɧɟɧɢɟ ɷɬɨɦɭ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɦɭ ɮɚɤɬɭ ɢ ɧɚɡɜɚɥ ɷɬɨ ɷɮɮɟɤɬɨɦ ɋɬɨɥɟɬɨɜɚ, ɚ ɡɧɚɱɟɧɢɟ (ȿ/ɪ)min ɜɩɨɫɥɟɞɫɬɜɢɢ ɧɚɡɜɚɥɢ ɤɨɧɫɬɚɧɬɨɣ ɋɬɨɥɟɬɨɜɚ. Ɋɚɫɱɟɬɵ ɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɨ ɫɨɜɩɚɞɚɸɬ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɤɪɢɜɵɦɢ ɉɚɲɟɧɚ (ɫɦ. ɪɢɫ.8.1). Ɉɩɢɫɚɬɟɥɶɧɨ ɤɪɢɜɵɟ ɉɚɲɟɧɚ ɦɨɠɧɨ ɩɨɧɹɬɶ ɬɚɤ: ɫ ɭɦɟɧɶɲɟɧɢɟɦ (pd) ɦɟɞɥɟɧɧɨ ɪɚɫɬɟɬ ȿ/ɪ (ɩɪɚɜɚɹ ɜɟɬɜɶ ɧɚ ɪɢɫ.8.1), ɡɧɚɱɢɬ, ɪɚɫɬɟɬ Yi ɢ ɞɥɹ ɩɪɨɛɨɹ ɞɨɫɬɚɬɨɱɧɨ ɦɟɧɶɲɢɯ Uɡ, ɢ ɬɚɤ ɞɨ Uɡmin. Ⱦɚɥɶɧɟɣɲɟɟ ɭɦɟɧɶɲɟɧɢɟ pd (ɥɟɜɚɹ ɜɟɬɜɶ) ɩɪɢɜɨɞɢɬ ɤ ɛɵɫɬɪɨɦɭ ɭɯɨɞɭ ɷɥɟɤɬɪɨɧɨɜ (ɦɚɥɨ ɫɬɨɥɤɧɨɜɟɧɢɣ) ɢ ɞɥɹ ɤɨɦɩɟɧɫɚɰɢɢ ɷɬɨɝɨ ɧɟɨɛɯɨɞɢɦ ɛɵɫɬɪɵɣ ɪɨɫɬ ȿ/ɪ, ɬ.ɟ. ɩɨɬɟɧɰɢɚɥɚ ɩɪɨɛɨɹ Uɡ. Ɇɨɠɧɨ ɞɚɬɶ ɨɩɢɫɚɧɢɟ ɷɬɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɩɪɢ ɮɢɤɫɢɪɨɜɚɧɧɨɦ ɡɧɚɱɟɧɢɢ ɨɞɧɨɣ ɢɡ ɜɟɥɢɱɢɧ p ɢɥɢ d. ɉɭɫɬɶ ɞɚɜɥɟɧɢɟ ɭɦɟɧɶɲɚɟɬɫɹ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ d. Ɍɨɝɞɚ ɫ ɭɦɟɧɶɲɟɧɢɟɦ ɞɚɜɥɟɧɢɹ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɞɥɢɧɚ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ, ɬ.ɟ. ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɧɚɛɢɪɚɟɦɚɹ ɷɥɟɤɬɪɨɧɨɦ ɷɧɟɪɝɢɹ, ɚ ɡɧɚɱɢɬ ɪɚɫɬɟɬ α. Ⱦɚɥɟɟ ɫ ɭɦɟɧɶɲɟɧɢɟɦ p ɪɟɡɤɨ ɫɧɢɠɚɟɬɫɹ ɱɢɫɥɨ ɫɬɨɥɤɧɨɜɟɧɢɣ ɢ α ɭɦɟɧɶɲɚɟɬɫɹ. ɉɪɢ ɩɨɫɬɨɹɧɧɨɦ ɞɚɜɥɟɧɢɢ ɫ ɭɦɟɧɶɲɟɧɢɟɦ ɪɚɫɫɬɨɹɧɢɹ d ɭɜɟɥɢɱɢɜɚɟɬɫɹ α, ɬɚɤ ɤɚɤ ɪɚɫɬɟɬ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ. Ɂɚɬɟɦ ɫ ɭɦɟɧɶɲɟɧɢɟɦ d ɤɨɷɮɮɢɰɢɟɧɬ Ɍɚɭɧɫɟɧɞɚ ɫɧɢɠɚɟɬɫɹ ɢɡ-ɡɚ ɭɦɟɧɶɲɟɧɢɹ ɞɥɢɧɵ ɪɚɡɜɢɬɢɹ ɥɚɜɢɧɵ. Ɍɚɤɠɟ ɨɩɢɫɚɬɟɥɶɧɨ ɦɨɠɧɨ ɩɨɧɹɬɶ ɷɦɩɢɪɢɱɟɫɤɭɸ ɡɚɜɢɫɢɦɨɫɬɶ Ɍɚɭɧɫɟɧɞɚ (8.22) ɢ ɤɪɢɜɵɟ ɉɚɲɟɧɚ (ɪɢɫ.8.1).
Ɍɟɦɧɵɣ (ɬɚɭɧɫɟɧɞɨɜɫɤɢɣ) ɪɚɡɪɹɞ
Ɍɟɦɧɵɣ (ɬɚɭɧɫɟɧɞɨɜɫɤɢɣ) ɪɚɡɪɹɞ – ɷɬɨ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɪɚɡɪɹɞ ɜ ɝɚɡɚɯ ɩɪɢ ɧɢɡɤɨɦ ɞɚɜɥɟɧɢɢ (ɩɨɪɹɞɤɚ ɧɟɫɤɨɥɶɤɢɯ Ɍɨɪɪ) ɢ ɨɱɟɧɶ ɦɚɥɵɯ ɬɨɤɚɯ (ɦɟɧɟɟ 10-5 Ⱥ). ɗɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɜ ɪɚɡɪɹɞɧɨɦ ɩɪɨɦɟɠɭɬɤɟ ɨɞɧɨɪɨɞɧɨ ɢɥɢ ɫɥɚɛɨ ɧɟɨɞɧɨɪɨɞɧɨ, ɢ ɧɟ ɢɫɤɚɠɚɟɬɫɹ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɦ ɡɚɪɹɞɨɦ, ɤɨɬɨɪɵɣ ɩɪɟɧɟɛɪɟɠɢɦɨ ɦɚɥ. ɇɚɡɜɚɧ ɩɨ ɢɦɟɧɢ Ɍɚɭɧɫɟɧɞɚ, ɤɨɬɨɪɵɣ ɜ 1900 ɝ. ɫɨɡɞɚɥ ɬɟɨɪɢɸ ɷɥɟɤɬɪɨɧɧɵɯ ɥɚɜɢɧ, ɩɨ ɤɨɬɨɪɨɣ ɩɪɢ ɭɫɥɨɜɢɢ ɜɵɩɨɥɧɟɧɢɹ ɪɚɡɜɢɬɢɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɚɡɪɹɞɚ (8.19) ɬɨɤ ɪɚɡɪɹɞɚ ɞɨɥɠɟɧ ɧɟɨɝɪɚɧɢɱɟɧɧɨ ɜɨɡɪɚɫɬɚɬɶ ɫɨ ɜɪɟɦɟɧɟɦ. Ɋɟɚɥɶɧɨ ɠɟ ɬɨɤ ɨɝɪɚɧɢɱɟɧ ɩɚɪɚɦɟɬɪɚɦɢ ɰɟɩɢ. Ɉɱɟɧɶ ɦɚɥɵɣ ɬɨɤ ɬɚɭɧɫɟɧɞɨɜɫɤɨɝɨ ɪɚɡɪɹɞɚ ɨɛɭɫɥɨɜɥɟɧ ɛɨɥɶɲɢɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ ɜɧɟɲɧɟɣ ɰɟɩɢ. ȿɫɥɢ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɧɟɲɧɟɣ ɰɟɩɢ ɫɧɢɠɚɬɶ, ɭɜɟɥɢɱɢɜɚɹ ɬɨɤ, ɬɨ ɬɚɭɧɫɟɧɞɨɜɫɤɢɣ ɪɚɡɪɹɞ ɩɟɪɟɯɨɞɢɬ ɜ ɬɥɟɸɳɢɣ. §51. Ɍɥɟɸɳɢɣ ɪɚɡɪɹɞ
Ɍɥɟɸɳɢɣ ɪɚɡɪɹɞ – ɷɬɨ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɪɚɡɪɹɞ ɜ ɝɚɡɟ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɣɫɹ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɣ ɧɟɪɚɜɧɨɜɟɫɧɨɫɬɶɸ ɢ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɶɸ, ɜɨɡɧɢɤɚɸɳɟɣ ɜ ɪɚɡɪɹɞɟ ɩɥɚɡɦɵ. ɗɮɮɟɤɬɢɜɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɷɥɟɤɬɪɨɧɨɜ ɫɭɳɟɫɬɜɟɧɧɨ ɜɵɲɟ ɬɟɦɩɟɪɚɬɭɪɵ ɝɚɡɚ ɢ ɷɥɟɤɬɪɨɞɨɜ. Ɍɟɪɦɨɷɦɢɫɫɢɹ ɩɪɚɤɬɢɱɟɫɤɢ ɨɬɫɭɬɫɬɜɭɟɬ (ɷɥɟɤɬɪɨɞɵ ɯɨɥɨɞɧɵɟ). ɋɜɨɟ ɧɚɡɜɚɧɢɟ ɪɚɡɪɹɞ ɩɨɥɭɱɢɥ ɢɡ-ɡɚ ɧɚɥɢɱɢɹ ɨɤɨɥɨ ɤɚɬɨɞɚ ɬɚɤ ɧɚɡɵɜɚɟɦɨɝɨ ɬɥɟɸɳɟɝɨ ɫɜɟɱɟɧɢɹ. Ȼɥɚɝɨɞɚɪɹ ɫɜɟɱɟɧɢɸ ɝɚɡɚ ɬɥɟɸɳɢɣ ɪɚɡɪɹɞ ɧɚɲɟɥ ɲɢɪɨɤɨɟ ɩɪɢɦɟɧɟɧɢɟ ɜ ɥɚɦɩɚɯ ɞɧɟɜɧɨɝɨ ɫɜɟɬɚ, ɪɚɡɥɢɱɧɵɯ ɨɫɜɟɬɢɬɟɥɶɧɵɯ ɩɪɢɛɨɪɚɯ ɢ ɬ.ɩ. Ʉɥɚɫɫɢɱɟɫɤɚɹ ɫɯɟɦɚ ɭɫɬɚɧɨɜɤɢ ɞɥɹ ɢɡɭɱɟɧɢɹ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ ɢɡɨɛɪɚɠɟɧɚ ɧɚ ɪɢɫ. 8.3, ɝɞɟ 1- ɫɬɟɤɥɹɧɧɵɣ ɛɚɥɥɨɧ, ɞɢɚɦɟɬɪɨɦ 1-3 ɫɦ, ɞɥɢɧɧɨɣ ɞɨ 1 ɦ; 2 - ɤɚɬɨɞ; 3 - ɚɧɨɞ; 4 - ɛɚɥɥɚɫɬɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ (ɨɛɹɡɚɬɟɥɶɧɵɣ ɷɥɟɦɟɧɬ); Ⱥ – ɦɢɤɪɨ-, ɦɢɥɥɢ-, ɢɥɢ ɩɪɨɫɬɨ ɚɦɩɟɪɦɟɬɪ. Ȼɚɥɥɨɧ 1 ɦɨɠɧɨ ɨɬɤɚɱɚɬɶ ɢ ɡɚɬɟɦ Ɋɢɫ. 8.3. Ʉɥɚɫɫɢɱɟɫɤɚɹ ɫɯɟɦɚ ɞɥɹ ɢɡɭɱɟɧɢɹ ɝɚɡɨɜɨɝɨ ɪɚɡɪɹɞɚ ɡɚɩɨɥɧɢɬɶ ɜɵɛɪɚɧɧɵɦ ɝɚɡɨɦ ɞɨ ɡɚɞɚɧɧɨɝɨ ɞɚɜɥɟɧɢɹ. Ɉɛɵɱɧɨ ɜ ɪɚɡɪɹɞɟ ɧɚɛɥɸɞɚɸɬɫɹ ɬɪɢ ɜɢɡɭɚɥɶɧɨ ɪɚɡɥɢɱɢɦɵɟ ɨɛɥɚɫɬɢ: ɚ) ɩɪɢɤɚɬɨɞɧɚɹ ɨɛɥɚɫɬɶ, ɧɚ ɧɟɣ ɩɚɞɚɟɬ ɧɚɩɪɹɠɟɧɢɟ Uk, ɨɛɵɱɧɨ 200 ÷ 700 ȼ; ɛ) ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ - ɜ ɮɢɡɢɤɟ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ ɩɚɫɫɢɜɧɵɣ ɷɥɟɦɟɧɬ: ɫɛɥɢɠɚɹ ɚɧɨɞ ɢ ɤɚɬɨɞ ɦɨɠɧɨ ɥɢɤɜɢɞɢɪɨɜɚɬɶ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ, ɪɚɡɪɹɞ ɛɭɞɟɬ ɝɨɪɟɬɶ; ɨɞɧɚɤɨ ɜ ɬɟɯɧɢɤɟ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ - ɩɨɥɟɡɧɵɣ ɷɥɟɦɟɧɬ: ɨɧ ɫɜɟɬɢɬɫɹ ɜ ɪɟɤɥɚɦɧɵɯ ɬɪɭɛɤɚɯ, ɨɧ ɢ ɟɫɬɶ ɚɤɬɢɜɧɚɹ ɫɪɟɞɚ ɜ ɝɚɡɨɜɵɯ ɥɚɡɟɪɚɯ, ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɧɟɦ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɦɟɧɧɨ ɬɟɯɧɢɱɟɫɤɢɦɢ ɬɪɟɛɨɜɚɧɢɹɦɢ, ɧɚɩɪɢɦɟɪ, ɞɥɢɧɨɣ ɪɟɤɥɚɦɧɵɯ ɬɪɭɛɨɤ; ɜ) ɩɪɢɚɧɨɞɧɵɣ ɫɥɨɣ ɨɛɵɱɧɨ ɨɱɟɧɶ ɬɨɧɤɢɣ, ɫɨɫɬɨɢɬ ɢɡ ɫɜɟɬɹɳɟɣɫɹ "ɩɥɟɧɤɢ", ɢ ɬɨɧɤɨɝɨ ɬɟɦɧɨɝɨ ɭɱɚɫɬɤɚ. Ⱦɨɥɝɨ ɫɱɢɬɚɥɢ, ɱɬɨ ɨɧ ɬɨɠɟ "ɩɚɫɫɢɜɧɵɣ", ɨɞɧɚɤɨ ɬɟɩɟɪɶ ɞɨɤɚɡɚɧɨ, ɱɬɨ ɧɟɤɨɬɨɪɵɟ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɩɪɹɦɨ ɫɜɹɡɚɧɵ ɫ ɧɢɦ. ɉɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ
ɚɧɨɞɧɨɦ ɫɥɨɟ Ua ɧɟɜɟɥɢɤɨ (10 ÷ 20 ȼ) ɢ ɨɛɵɱɧɨ ɛɥɢɡɤɨ ɤ ɩɨɬɟɧɰɢɚɥɭ ɢɨɧɢɡɚɰɢɢ ɝɚɡɚ (ɨɱɟɧɶ ɱɭɜɫɬɜɢɬɟɥɶɧɨ ɤ ɫɨɫɬɨɹɧɢɸ ɩɨɜɟɪɯɧɨɫɬɢ ɚɧɨɞɚ). ɉɪɢɤɚɬɨɞɧɚɹ ɨɛɥɚɫɬɶ
ɉɪɢɤɚɬɨɞɧɚɹ ɨɛɥɚɫɬɶ ɮɢɡɢɱɟɫɤɢ ɧɚɢɛɨɥɟɟ ɜɚɠɧɵɣ ɷɥɟɦɟɧɬ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ: ɢɦɟɧɧɨ ɜ ɧɟɦ ɨɛɪɚɡɭɟɬɫɹ ɷɥɟɤɬɪɨɧɧɚɹ ɥɚɜɢɧɚ. ȼ ɞɚɧɧɨɦ ɝɚɡɟ ɩɪɢ ɞɚɧɧɨɦ ɞɚɜɥɟɧɢɢ ɮɨɪɦɢɪɭɟɬɫɹ ɞɥɢɧɚ ɩɪɢɤɚɬɨɞɧɨɣ ɨɛɥɚɫɬɢ dk, ɪɚɜɧɚɹ ɧɟɫɤɨɥɶɤɢɦ ɞɥɢɧɚɦ ɢɨɧɢɡɚɰɢɢ. ɍɫɬɚɧɨɜɢɜɲɚɹɫɹ ɞɥɢɧɚ dk, ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚɹ ɞɚɜɥɟɧɢɸ p, ɬɚɤɨɜɚ, ɱɬɨɛɵ ɜɟɥɢɱɢɧɚ pdk ɫɨɨɬɜɟɬɫɬɜɨɜɚɥɚ ɦɢɧɢɦɚɥɶɧɨɦɭ ɡɧɚɱɟɧɢɸ Uk (ɩɪɢɪɨɞɚ ɷɤɨɧɨɦɧɚ!). Ɉɫɧɨɜɧɨɣ ɯɚɪɚɤɬɟɪɧɨɣ ɨɫɨɛɟɧɧɨɫɬɶ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ ɹɜɥɹɟɬɫɹ ɛɨɥɶɲɨɟ ɩɚɞɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɢɤɚɬɨɞɧɨɣ ɨɛɥɚɫɬɢ Uk. – ɫɨɬɧɢ ɜɨɥɶɬ. ɂɡ ɤɚɬɨɞɧɨɝɨ ɫɥɨɹ ɜ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ ɭɯɨɞɢɬ ɧɟɤɨɬɨɪɨɟ ɤɨɥɢɱɟɫɬɜɨ ɷɥɟɤɬɪɨɧɨɜ ɫ ɬɚɤɨɣ ɷɧɟɪɝɢɟɣ, ɱɬɨɛɵ ɢɨɧɢɡɨɜɚɬɶ ɜ ɫɬɨɥɛɟ ɞɨɫɬɚɬɨɱɧɨ ɚɬɨɦɨɜ (ɦɨɥɟɤɭɥ) ɞɥɹ ɤɨɦɩɟɧɫɚɰɢɢ ɬɟɪɹɟɦɵɯ ɷɥɟɤɬɪɨɧɨɜ, ɬɨ ɟɫɬɶ Uk ɞɨɥɠɧɨ ɛɵɬɶ ɦɧɨɝɨ ɛɨɥɶɲɟ ɩɨɬɟɧɰɢɚɥɚ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ ɝɚɡɚ. Ʉɚɬɨɞɧɚɹ ɨɛɥɚɫɬɶ ɤɚɤ ɛɵ "ɩɪɢɤɥɟɟɧɚ" ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɤɚɬɨɞɚ: ɟɫɥɢ ɩɪɨɜɨɞɹɳɟɣ ɹɜɥɹɟɬɫɹ ɬɨɥɶɤɨ ɨɞɧɚ ɟɝɨ ɩɨɜɟɪɯɧɨɫɬɶ, ɬɨ ɩɪɢ ɥɸɛɨɦ ɩɨɜɨɪɨɬɟ ɤɚɬɨɞɚ ɪɚɡɪɹɞ ɩɪɢɯɨɞɢɬ ɬɨɥɶɤɨ ɧɚ ɧɟɟ - ɞɚɠɟ ɟɫɥɢ ɟɟ ɩɨɜɟɪɧɭɬɶ ɧɚ 180°, ɤɚɤ ɛɵ ɫɩɢɧɨɣ ɤ ɚɧɨɞɭ. ɋɜɟɱɟɧɢɟ ɤɚɬɨɞɧɨɣ ɨɛɥɚɫɬɢ "ɫɥɨɢɫɬɨɟ" (ɪɢɫ. 8.4). ɍ ɫɚɦɨɝɨ ɤɚɬɨɞɚ ɧɚɯɨɞɢɬɫɹ ɬɟɦɧɨɟ "ɚɫɬɨɧɨɜɨ ɩɪɨɫɬɪɚɧɫɬɜɨ", ɫɜɹɡɚɧɧɨɟ ɫ ɬɟɦ, ɱɬɨ ɷɥɟɤɬɪɨɧɵ, ɜɵɲɟɞɲɢɟ ɫ ɤɚɬɨɞɚ, ɟɳɟ ɧɟ ɧɚɛɪɚɥɢ ɞɨɫɬɚɬɨɱɧɨɣ ɷɧɟɪɝɢɢ ɞɥɹ ɜɨɡɛɭɠɞɟɧɢɹ ɚɬɨɦɨɜ ɢ ɦɨɥɟɤɭɥ ɝɚɡɚ. Ɂɚɬɟɦ ɪɚɫɩɨɥɚɝɚɟɬɫɹ ɨɛɥɚɫɬɶ ɤɚɬɨɞɧɨɝɨ ɫɜɟɱɟɧɢɹ, ɜ ɤɨɬɨɪɨɣ ɩɪɨɢɫɯɨɞɢɬ ɢɧɬɟɧɫɢɜɧɨɟ ɜɨɡɛɭɠɞɟɧɢɟ ɪɚɡɥɢɱɧɵɯ ɭɪɨɜɧɟɣ. Ʉɚɬɨɞɧɨɟ ɬɟɦɧɨɟ ɩɪɨɫɬɪɚɧɫɬɜɨ, ɜɨɡɧɢɤɚɟɬ ɬɚɦ, ɝɞɟ ɷɧɟɪɝɢɹ ɭɫɤɨɪɟɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ «ɩɟɪɟɜɚɥɢɜɚɟɬ» ɱɟɪɟɡ ɡɧɚɱɟɧɢɟ ɜ ɦɚɤɫɢɦɭɦɟ ɮɭɧɤɰɢɢ ɜɨɡɛɭɠɞɟɧɢɹ, ɫɟɱɟɧɢɹ ɜɨɡɛɭɠɞɟɧɢɹ ɭɦɟɧɶɲɚɸɬɫɹ, ɤɨɥɢɱɟɫɬɜɨ ɜɨɡɛɭɠɞɟɧɧɵɯ ɚɬɨɦɨɜ ɩɚɞɚɟɬ. Ⱦɚɥɟɟ ɷɥɟɤɬɪɨɧɵ ɩɪɟɢɦɭɳɟɫɬɜɟɧɧɨ ɢɨɧɢɡɭɸɬ ɚɬɨɦɵ, ɩɪɨɢɫɯɨɞɢɬ ɥɚɜɢɧɨɨɛɪɚɡɧɨɟ ɪɚɡɦɧɨɠɟɧɢɟ ɷɥɟɤɬɪɨɧɨɜ, ɤɨɬɨɪɵɟ ɭɫɤɨɪɹɹɫɶ ɜɧɨɜɶ ɜɵɡɵɜɚɸɬ ɜɨɡɛɭɠɞɟɧɢɟ ɚɬɨɦɨɜ. ɉɨɹɜɥɹɟɬɫɹ «ɬɥɟɸɳɟɟ ɨɬɪɢɰɚɬɟɥɶɧɨɟ ɫɜɟɱɟɧɢɟ», ɛɥɚɝɨɞɚɪɹ ɤɨɬɨɪɨɦɭ ɬɥɟɸɳɢɣ ɪɚɡɪɹɞ ɢ ɩɨɥɭɱɢɥ ɫɜɨɟ ɧɚɡɜɚɧɢɟ. ȼ ɜɨɡɧɢɤɚɸɳɟɣ ɜ ɪɚɡɪɹɞɟ ɩɥɚɡɦɟ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɪɟɡɤɨ ɩɚɞɚɟɬ, ɷɥɟɤɬɪɨɧɵ, ɪɚɫɬɪɚɱɢɜɚɹ ɫɜɨɸ ɷɧɟɪɝɢɸ, ɧɟ ɩɪɢɨɛɪɟɬɚɸɬ ɜ ɫɥɚɛɨɦ ɩɨɥɟ ɞɨɫɬɚɬɨɱɧɨɣ ɞɥɹ ɜɨɡɛɭɠɞɟɧɢɹ ɚɬɨɦɨɜ, ɜɨɡɧɢɤɚɟɬ ɬɟɦɧɨɟ "ɮɚɪɚɞɟɟɜɨ ɩɪɨɫɬɪɚɧɫɬɜɨ". ȼ ɨɛɥɚɫɬɢ ɬɥɟɸɳɟɝɨ ɫɜɟɱɟɧɢɹ (ρ ≈ 0) ɧɚɢɛɨɥɟɟ ɢɞɟɚɥɶɧɚɹ ɩɥɚɡɦɚ. Ɍɚɤ ɤɚɤ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ E ≈ 0 ɷɥɟɤɬɪɨɧɵ ɩɟɪɟɯɨɞɹɬ ɢɡ ɨɛɥɚɫɬɢ ɬɥɟɸɳɟɝɨ ɫɜɟɱɟɧɢɹ ɜ ɮɚɪɚɞɟɟɜɨ ɩɪɨɫɬɪɚɧɫɬɜɨ ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɡɚ ɫɱɟɬ ɞɢɮɮɭɡɢɢ. ɂɨɧɵ ɩɨɩɚɞɚɸɬ ɜ ɩɪɢɤɚɬɨɞɧɭɸ ɨɛɥɚɫɬɶ ɬɚɤɠɟ ɡɚ ɫɱɟɬ ɞɢɮɮɭɡɢɢ. ɍɫɤɨɪɟɧɧɵɟ ɤ ɤɚɬɨɞɭ ɢɨɧɵ ɜɵɛɢɜɚɸɬ ɜɬɨɪɢɱɧɵɟ ɷɥɟɤɬɪɨɧɵ. Ɍɟɦɧɨɟ ɮɚɪɚɞɟɟɜɨ ɩɪɨɫɬɪɚɧɫɬɜɨ – ɷɬɨ ɩɟɪɟɯɨɞɧɚɹ ɨɛɥɚɫɬɶ, ɜ ɤɨɬɨɪɨɣ ɧɟɬ ɢɨɧɢɡɚɰɢɢ ɢ ɜɨɡɛɭɠɞɟɧɢɹ. ɉɨ ɦɟɪɟ ɩɪɢɛɥɢɠɟɧɢɹ ɤ ɩɨɥɨɠɢɬɟɥɶɧɨɦɭ ɫɬɨɥɛɭ ɛɟɫɩɨɪɹɞɨɱɧɨɟ ɬɟɩɥɨɜɨɟ ɞɜɢɠɟɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɜɫɟ ɛɨɥɟɟ ɩɪɟɨɛɥɚɞɚɟɬ ɧɚɞ ɧɚɩɪɚɜɥɟɧɧɵɦ ɞɜɢɠɟɧɢɟɦ. Ɉɩɢɫɚɧɢɟ ɜɫɟɯ ɩɪɨɰɟɫɫɨɜ, ɨɛɴɹɫɧɹɸɳɢɯ ɷɬɭ "ɫɥɨɢɫɬɨɫɬɶ" (ɢ ɧɟɤɨɬɨɪɵɟ ɛɨɥɟɟ ɬɨɧɤɢɟ ɷɮɮɟɤɬɵ) ɢ ɫɟɣɱɚɫ ɹɜɥɹɟɬɫɹ ɞɚɥɟɤɨ ɧɟ ɩɨɥɧɵɦ. ɇɟɩɨɧɹɬɧɨ ɢ ɟɳɟ ɨɞɧɨ ɹɜɥɟɧɢɟ: ɩɥɨɳɚɞɶ ɬɨɤɨɜɨɝɨ ɩɹɬɧɚ Sɩ ɧɚ ɤɚɬɨɞɟ ɜ ɧɨɪɦɚɥɶɧɨɦ ɪɟɠɢɦɟ ɜɫɟɝɞɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɫɨɨɬɧɨɲɟɧɢɹ Sɩ = I/jɩ, ɝɞɟ: I ɩɨɥɧɵɣ ɬɨɤ, ɚ jɩ – ɧɟɤɨɬɨɪɚɹ «ɧɨɪɦɚɥɶɧɚɹ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ», ɩɨɫɬɨɹɧɧɚɹ ɞɥɹ ɞɚɧɧɨɝɨ ɪɚɡɪɹɞɚ. ɗɬɨ ɜɚɠɧɨɟ ɫɜɨɣɫɬɜɨ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ ɧɚɡɵɜɚɟɬɫɹ ɡɚɤɨɧɨɦ ɧɨɪɦɚɥɶɧɨɣ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ. ɉɪɢ ɭɜɟɥɢɱɟɧɢɢ I (ɧɚɩɪɢɦɟɪ, ɩɪɢ ɫɧɢɠɟɧɢɢ ɜɧɟɲɧɟɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R ɢɥɢ ɩɨɜɵɲɟɧɢɢ ɗȾɋ ɢɫɬɨɱɧɢɤɚ
ε)
Sɩ ɪɚɫɬɟɬ
ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɬɨɤɭ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɬɨɤɨɜɨɟ ɩɹɬɧɨ ɧɟ ɡɚɣɦɟɬ ɜɫɸ ɩɪɨɜɨɞɹɳɭɸ ɩɨɜɟɪɯɧɨɫɬɶ ɤɚɬɨɞɚ (ɢ ɩɨɞɜɨɞɹɳɢɯ ɝɨɥɵɯ ɩɪɨɜɨɞɨɜ). ɉɪɢ ɷɬɨɦ ɤɚɬɨɞɧɨɟ ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɟ Uk ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ. Ⱦɚɥɶɧɟɣɲɟɟ ɩɨɜɵɲɟɧɢɟ I ɩɪɢɜɨɞɢɬ ɤ ɪɨɫɬɭ Uk - ɷɬɨ "ɚɧɨɦɚɥɶɧɵɣ ɪɟɠɢɦ" ɫ ɚɧɨɦɚɥɶɧɵɦ ɤɚɬɨɞɧɵɦ ɩɚɞɟɧɢɟɦ ɩɨɬɟɧɰɢɚɥɚ, ɚ ɫɚɦ ɪɚɡɪɹɞ ɩɟɪɟɯɨɞɢɬ ɤ ɚɧɨɦɚɥɶɧɨɦɭ ɬɥɟɸɳɟɦɭ ɪɚɡɪɹɞɭ. ɉɨɱɟɦɭ jɩ = const ɨɫɬɚɟɬɫɹ ɧɟɢɡɜɟɫɬɧɵɦ. ɉɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ
ȿɫɥɢ ɜ ɭɫɬɚɧɨɜɤɟ ɧɚ ɪɢɫ. 8.3 ɩɨɜɵɲɚɬɶ ɬɨɤ, ɬɨ ɜ ɤɚɤɨɣ-ɬɨ ɦɨɦɟɧɬ ɡɚɝɨɪɢɬɫɹ ɪɚɡɪɹɞ, ɩɪɢɱɟɦ ɦɟɠɞɭ ɤɚɬɨɞɧɨɣ ɨɛɥɚɫɬɶɸ ɢ ɚɧɨɞɨɦ ɩɨɹɜɢɬɫɹ ɫɜɟɱɟɧɢɟ ɫ ɞɥɢɧɨɣ ɜɨɥɧɵ, ɯɚɪɚɤɬɟɪɧɨɣ ɞɥɹ ɞɚɧɧɨɝɨ ɝɚɡɚ, ɢ ɡɚɧɢɦɚɸɳɟɟ ɜɫɟ ɫɟɱɟɧɢɟ ɬɪɭɛɤɢ. ɗɬɨ ɢ ɟɫɬɶ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ, ɩɪɢɱɟɦ ɧɚ ɧɟɦ ɛɭɞɟɬ ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ, Uɩɫ =
ε
- IR – Uk - Ua. ɗɬɨ ɟɞɢɧɫɬɜɟɧɧɚɹ ɨɛɥɚɫɬɶ ɪɚɡɪɹɞɚ, ɤɨɬɨɪɚɹ ɦɨɠɟɬ ɛɵɬɶ ɩɪɨɢɡɜɨɥɶɧɨɣ ɞɥɢɧɵ. ɉɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɥɚɡɦɭ ɫ ɤɨɧɰɟɧɬɪɚɰɢɟɣ ɱɚɫɬɢɰ, ɭɛɵɜɚɸɳɢɯ ɨɬ ɨɫɢ ɤ ɫɬɟɧɤɚɦ, ɜ ɧɟɦ ɢɞɟɬ ɢɧɬɟɧɫɢɜɧɵɣ ɩɪɨɰɟɫɫ ɢɨɧɢɡɚɰɢɢ ɢ ɩɨɬɟɪɢ ɱɚɫɬɢɰ ɧɚ ɫɬɟɧɤɢ, ɩɪɢ ɷɬɨɦ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɞɚɟɬ ɢɨɧɨɜ ɜ ɤɚɬɨɞɧɭɸ ɨɛɥɚɫɬɶ. ɍɯɨɞɹɳɢɟ ɧɚ ɫɬɟɧɤɭ ɷɥɟɤɬɪɨɧɵ ɡɚɪɹɠɚɸɬ ɢɯ ɨɬɪɢɰɚɬɟɥɶɧɨ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ, ɢ ɢɨɧɵ ɭɫɤɨɪɹɸɬɫɹ ɧɚ ɫɬɟɧɤɭ, ɬ. ɟ. ɩɪɨɢɫɯɨɞɢɬ ɚɦɛɢɩɨɥɹɪɧɚɹ ɞɢɮɮɭɡɢɹ. ȼ ɢɬɨɝɟ ɷɥɟɤɬɪɨɧɵ ɢ ɢɨɧɵ ɧɚ ɫɬɟɧɤɚɯ ɪɟɤɨɦɛɢɧɢɪɭɸɬ. ɇɚɥɢɱɢɟ ɪɚɞɢɚɥɶɧɨɝɨ ɝɪɚɞɢɟɧɬɚ ɩɪɢɜɨɞɢɬ ɤ ɬɨɦɭ,
Ɋɢɫ. 8.4. Ʉɚɪɬɢɧɚ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ ɜ ɬɪɭɛɤɟ ɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɫɜɟɱɟɧɢɹ J, ɩɨɬɟɧɰɢɚɥɚ U, ɩɪɨɞɨɥɶɧɨɝɨ ɩɨɥɹ ȿ, ɩɥɨɬɧɨɫɬɟɣ ɷɥɟɤɬɪɨɧɧɨɝɨ ɢ ɢɨɧɧɨɝɨ ɬɨɤɨɜ je, j+, ɤɨɧɰɟɧɬɪɚɰɢɣ ne, n+ ɢ ɨɛɴɟɦɧɨɝɨ ɡɚɪɹɞɚ ρ = e(ne - n+)
ɱɬɨ ɷɤɜɢɩɨɬɟɧɰɢɚɥɢ ɢɦɟɸɬ ɜɵɩɭɤɥɭɸ ɮɨɪɦɭ.
Ɉɫɨɛɟɧɧɨ ɨɬɱɟɬɥɢɜɨ ɷɬɨ ɜɢɞɧɨ ɩɪɢ ɜɨɡɧɢɤɧɨɜɟɧɢɢ ɜ ɩɨɥɨɠɢɬɟɥɶɧɨɦ ɫɬɨɥɛɟ ɡɚ ɫɱɟɬ ɤɨɥɟɛɚɬɟɥɶɧɵɯ ɩɪɨɰɟɫɫɨɜ ɫɬɨɹɱɢɯ ɢɥɢ ɛɟɝɭɳɢɯ ɫɬɪɚɬ. ɉɪɨɰɟɫɫ ɨɛɪɚɡɨɜɚɧɢɹ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɫɬɨɥɛɚ ɞɨɜɨɥɶɧɨ ɫɥɨɠɧɵɣ, ɯɨɬɹ ɟɝɨ "ɧɚɡɧɚɱɟɧɢɟ" – ɫɨɟɞɢɧɢɬɶ ɤɚɬɨɞɧɵɣ ɢ ɚɧɨɞɧɵɣ ɫɥɨɢ. ɋɬɨɥɛ ɷɥɟɤɬɪɢɱɟɫɤɢ ɧɟɣɬɪɚɥɟɧ, ɬɚɤ ɱɬɨ ɩɥɨɬɧɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ (ɨɞɧɨɡɚɪɹɞɧɵɯ) ɪɚɜɧɵ, ɚ ɬɨɤɢ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɫɢɥɶɧɨ ɪɚɡɥɢɱɚɸɬɫɹ. Ɍɟɦɩɟɪɚɬɭɪɚ ɨɫɧɨɜɧɨɣ ɦɚɫɫɵ ɷɥɟɤɬɪɨɧɨɜ Ɍe = 1 ÷ 2 ɷȼ, ɚ ɢɨɧɨɜ ɩɪɚɤɬɢɱɟɫɤɢ ɪɚɜɧɚ ɬɟɦɩɟɪɚɬɭɪɟ ɫɬɟɧɨɤ (ɢɨɧɵ ɛɵɫɬɪɨ ɨɛɦɟɧɢɜɚɸɬɫɹ ɩɨɫɬɭɩɚɬɟɥɶɧɨɣ ɷɧɟɪɝɢɟɣ ɫ ɝɚɡɨɦ), ɬɚɤ ɱɬɨ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢ ɫɢɥɶɧɨ ɧɟɪɚɜɧɨɜɟɫɟɧ. Ɉɧ ɨɱɟɧɶ ɧɟɪɚɜɧɨɜɟɫɟɧ ɢ ɜ ɢɨɧɢɡɚɰɢɨɧɧɨɦ ɨɬɧɨɲɟɧɢɢ – ɞɥɹ ɧɟɝɨ ɫɩɪɚɜɟɞɥɢɜɚ ɮɨɪɦɭɥɚ ɗɥɶɜɟɪɬɚ. ɋɛɥɢɠɚɹ ɤɚɬɨɞ ɢ ɚɧɨɞ, ɦɨɠɧɨ ɥɢɤɜɢɞɢɪɨɜɚɬɶ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ, ɧɨ ɪɚɡɪɹɞ ɛɭɞɟɬ ɝɨɪɟɬɶ. Ȼɨɥɟɟ ɬɨɝɨ, ɚɧɨɞɧɵɦ ɫɥɨɟɦ ɦɨɠɧɨ ɩɪɨɣɬɢ ɬɟɦɧɨɟ ɮɚɪɚɞɟɟɜɨ ɩɪɨɫɬɪɚɧɫɬɜɨ, ɧɨ ɤɚɤ ɬɨɥɶɤɨ ɨɧ ɫɨɩɪɢɤɨɫɧɟɬɫɹ ɫ ɬɥɟɸɳɢɦ ɫɥɨɟɦ – ɨɬɪɢɰɚɬɟɥɶɧɨɟ ɬɥɟɸɳɟɟ ɫɜɟɱɟɧɢɟ ɪɚɡɪɹɞɚ ɩɨɝɚɫɧɟɬ. ɋɪɚɜɧɢɬɟɥɶɧɨ ɧɟɞɚɜɧɨ ɛɵɥɨ ɞɨɤɚɡɚɧɨ, ɱɬɨ ɫɜɟɱɟɧɢɟ ɫɬɨɥɛɚ ɩɨɞɞɟɪɠɢɜɚɸɬ ɨɬɧɨɫɢɬɟɥɶɧɨ ɛɵɫɬɪɵɟ ɷɥɟɤɬɪɨɧɵ (20 ÷ 30 ɷȼ), ɭɫɤɨɪɟɧɧɵɟ ɜ ɤɚɬɨɞɧɨɣ ɨɛɥɚɫɬɢ ɢ ɩɨɫɬɭɩɚɸɳɢɟ ɢɡ ɤɚɬɨɞɧɨɝɨ ɫɬɨɥɛɚ ɜ ɤɨɥɢɱɟɫɬɜɟ, ɤɚɤ ɪɚɡ ɞɨɫɬɚɬɨɱɧɨɦ ɞɥɹ ɤɨɦɩɟɧɫɚɰɢɢ ɩɨɬɟɪɶ ɷɥɟɤɬɪɨɧɨɜ ɜ ɧɟɦ ɢ ɨɛɟɫɩɟɱɟɧɢɹ ɜɨɡɛɭɠɞɟɧɢɹ ɝɚɡɚ. ȼ ɪɟɤɥɚɦɧɵɯ ɬɪɭɛɤɚɯ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ ɫɥɟɞɭɟɬ ɡɚ ɜɫɟɦɢ ɢɯ ɢɡɝɢɛɚɦɢ, ɱɬɨ ɨɛɴɹɫɧɹɟɬɫɹ ɨɛɪɚɡɨɜɚɧɢɟɦ ɩɨɜɟɪɯɧɨɫɬɧɵɯ ɡɚɪɹɞɨɜ ɧɚ ɜɧɭɬɪɟɧɧɢɯ ɫɬɟɧɤɚɯ ɬɪɭɛɨɤ ɢ ɩɨɹɜɥɟɧɢɟɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɩɨɩɟɪɟɱɧɵɯ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɨɥɟɣ. ȿɫɥɢ ɭɜɟɥɢɱɢɜɚɬɶ ɞɚɜɥɟɧɢɟ, ɬɨ ɩɪɨɢɫɯɨɞɢɬ ɫɠɚɬɢɟ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɲɧɭɪɚ, ɬɟɦɩɟɪɚɬɭɪɚ ɢ ɩɪɨɜɨɞɢɦɨɫɬɶ ɜɨɡɪɚɫɬɚɸɬ, ɬɨɤ ɪɚɫɬɟɬ, ɜɵɡɵɜɚɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɣ ɪɚɡɨɝɪɟɜ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɪɨɫɬɚ ɬɟɦɩɟɪɚɬɭɪɵ ɦɨɠɟɬ ɧɚɱɚɬɶɫɹ ɬɟɪɦɢɱɟɫɤɚɹ ɢɨɧɢɡɚɰɢɹ ɢ ɬɥɟɸɳɢɣ ɪɚɡɪɹɞ ɦɨɠɟɬ ɩɟɪɟɣɬɢ ɜ ɞɭɝɨɜɨɣ. Ɍɚɤ ɤɚɤ ɷɬɨ ɨɱɟɧɶ ɜɚɠɧɚɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ, ɪɚɫɫɦɨɬɪɢɦ ɟɟ ɦɟɯɚɧɢɡɦ, ɩɪɚɜɞɚ, ɧɟɫɤɨɥɶɤɨ ɭɩɪɨɳɟɧɧɨ. ɇɟɭɫɬɨɣɱɢɜɨɫɬɢ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɫɬɨɥɛɚ
ɑɚɫɬɨ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ "ɫɬɪɚɬɢɮɢɰɢɪɨɜɚɧ" – ɫɨɫɬɨɢɬ ɢɡ ɫɜɟɬɥɵɯ ɢ ɬɟɦɧɵɯ ɩɨɥɨɫ, ɨɛɵɱɧɨ ɛɟɝɭɳɢɯ ɫ ɬɚɤɨɣ ɫɤɨɪɨɫɬɶɸ, ɱɬɨ ɜɢɡɭɚɥɶɧɨ ɫɬɨɥɛ ɜɨɫɩɪɢɧɢɦɚɟɬɫɹ ɫɩɥɨɲɧɵɦ. ɗɬɨ ɨɞɧɚ ɢɡ ɧɟɭɫɬɨɣɱɢɜɨɫɬɟɣ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɫɬɨɥɛɚ, ɧɨ ɧɟ ɫɚɦɚɹ ɧɟɩɪɢɹɬɧɚɹ. ɇɚɢɛɨɥɟɟ ɜɚɠɧɚɹ – ɬɚɤ ɧɚɡɵɜɚɟɦɚɹ "ɤɨɧɬɪɚɤɰɢɹ" ɢɥɢ "ɲɧɭɪɨɜɚɧɢɟ". ɉɪɢ ɧɟɤɨɬɨɪɨɦ ɩɪɟɞɟɥɶɧɨɦ ɡɧɚɱɟɧɢɢ ɬɨɤɚ (ɩɪɟɞɟɥ ɡɚɜɢɫɢɬ ɨɬ ɦɧɨɝɢɯ ɤɨɧɤɪɟɬɧɵɯ ɭɫɥɨɜɢɣ) ɪɚɡɪɹɞ ɜ ɬɪɭɛɤɟ ɫɨɛɢɪɚɟɬɫɹ ɜ ɬɨɧɤɢɣ ɹɪɤɨ ɫɜɟɬɹɳɟɣɫɹ ɲɧɭɪ, ɨɱɟɧɶ ɩɨɯɨɠɢɣ ɧɚ ɲɧɭɪ ɞɭɝɨɜɨɝɨ ɪɚɡɪɹɞɚ (ɜ ɚɧɝɥɨɹɡɵɱɧɨɣ ɥɢɬɟɪɚɬɭɪɟ ɧɚɡɵɜɚɸɬ arcing, "ɞɭɝɨɜɚɧɢɟ"), ɧɨ ɷɬɨ ɟɳɟ ɧɟ ɞɭɝɚ, ɯɨɬɹ ɬɟɦɩɟɪɚɬɭɪɚ ɢɨɧɨɜ Ti ɩɨɞɧɢɦɚɟɬɫɹ ɞɨ ɞɟɫɹɬɵɯ ɞɨɥɟɣ ɷɥɟɤɬɪɨɧ-ɜɨɥɶɬ, ɬɚɤ ɱɬɨ ɨɬɪɵɜ Ɍɟ ɨɬ Ti ɫɭɳɟɫɬɜɟɧɧɨ ɭɦɟɧɶɲɚɟɬɫɹ. ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɮɥɭɤɬɭɚɬɢɜɧɨ ɩɪɨɢɡɨɲɥɨ ɦɟɫɬɧɨɟ ɩɨɜɵɲɟɧɢɟ ɩɥɨɬɧɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ δne↑, ɤɚɤ ɫɥɟɞɫɬɜɢɟ ɜɵɪɚɫɬɚɟɬ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ δj↑ (j = neev), ɩɪɨɜɨɞɢɦɨɫɬɶ δσ↑ (σ = nee2/τ) ɢ ɷɧɟɪɝɨɜɵɞɟɥɟɧɢɟ δw↑ (w = j2/σ). ȼ ɪɟɡɭɥɶɬɚɬɟ ɜɨɡɪɚɫɬɟɬ ɬɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ δɌg↑, ɭɦɟɧɶɲɢɬɫɹ ɟɝɨ ɩɥɨɬɧɨɫɬɶ δng↓ (ɬɚɤ ɤɚɤ ɞɚɜɥɟɧɢɟ pg = ngTg ɜɵɪɚɜɧɢɜɚɟɬɫɹ ɛɵɫɬɪɨ ɢ ɟɝɨ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɩɨɫɬɨɹɧɧɵɦ), ɜɨɡɪɚɫɬɚɟɬ ɨɬɧɨɲɟɧɢɟ δE/ng↑, ɜɵɪɚɫɬɚɟɬ ɱɚɫɬɨɬɚ ɢɨɧɢɡɚɰɢɢ δYi↑, ɜɨɡɪɚɫɬɚɟɬ δne↑ – ɰɟɩɨɱɤɚ ɡɚɦɤɧɭɥɚɫɶ:
δne↑ → δj↑ → δw↑ → δɌg↑ → δng↓ → δE/ng↑ → δYi↑ → δne↑ → …
(8.25)
ɢɞɟɬ ɪɨɫɬ j ɢ Ɍg, ɨɛɪɚɡɭɟɬɫɹ ɲɧɭɪ. ɇɟɭɫɬɨɣɱɢɜɨɫɬɶ ɧɚɡɵɜɚɸɬ "ɢɨɧɢɡɚɰɢɨɧɧɨɩɟɪɟɝɪɟɜɧɨɣ" (ɰɟɩɨɱɤɚ ɦɨɠɟɬ ɧɚɱɚɬɶɫɹ ɢ ɫɨ ɫɥɭɱɚɣɧɨɝɨ ɥɨɤɚɥɶɧɨɝɨ ɜɨɡɪɚɫɬɚɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɝɚɡɚ δTg↑). Ⱥɧɨɞɧɵɣ ɫɥɨɣ
Ⱥɧɨɞɧɵɣ ɫɥɨɣ, ɜɫɟɝɞɚ ɨɱɟɧɶ ɬɨɧɤɢɣ. ɗɥɟɤɬɪɨɧɵ ɭɫɤɨɪɹɸɬɫɹ ɤ ɚɧɨɞɭ ɢ 1 ɢɨɧɢɡɭɸɬ ɝɚɡ. ȿɫɥɢ ɬɨɤ ɧɚ ɚɧɨɞ Ia = ne ev e S ɛɨɥɶɲɟ ɪɚɡɪɹɞɧɨɝɨ ɬɨɤɚ ɜ ɰɟɩɢ (Ia 4 > I), ɬɨ ɚɧɨɞ ɡɚɪɹɠɚɟɬɫɹ ɨɬɪɢɰɚɬɟɥɶɧɨ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɫɬɨɥɛɚ, ɜ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ (Ia < I) ɩɨɥɨɠɢɬɟɥɶɧɨ. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜ ɥɚɡɟɪɧɵɯ ɫɪɟɞɚɯ (ɩɪɢ ɛɨɥɶɲɢɯ p ɢ j) ɩɪɢ ɩɨɜɵɲɟɧɢɢ ɞɚɜɥɟɧɢɹ ɪɚɫɬɟɬ ɚɧɨɞɧɨɟ ɩɚɞɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ, ɧɨ ɫɨɯɪɚɧɹɟɬɫɹ ɧɨɪɦɚɥɶɧɚɹ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ, ɫɪɚɜɧɢɦɚɹ ɫ ɧɨɪɦɚɥɶɧɨɣ ɩɥɨɬɧɨɫɬɶɸ ɬɨɤɚ ɤɚɬɨɞɚ. Ƚɚɡɨɜɵɟ ɥɚɡɟɪɵ ɢ ɬɥɟɸɳɢɣ ɪɚɡɪɹɞ
ɉɨɹɜɥɟɧɢɟ ɝɚɡɨɜɵɯ ɥɚɡɟɪɨɜ, ɭɧɢɜɟɪɫɚɥɶɧɨɫɬɶ ɢɯ ɩɪɢɦɟɧɟɧɢɹ ɢ ɫɬɪɟɦɥɟɧɢɟ ɩɨɜɵɫɢɬɶ ɷɧɟɪɝɨɫɨɞɟɪɠɚɧɢɟ ɥɚɡɟɪɧɨɝɨ ɥɭɱɚ ɩɪɢɜɟɥɢ ɤ ɩɨɫɬɚɧɨɜɤɟ ɢ ɪɚɡɪɟɲɟɧɢɸ ɦɧɨɝɢɯ ɧɨɜɵɯ ɮɢɡɢɤɨ-ɬɟɯɧɢɱɟɫɤɢɯ ɩɪɨɛɥɟɦ. ȿɫɥɢ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ ɜ ɦɚɥɨɦɨɳɧɵɯ ɥɚɡɟɪɚɯ (ɟɫɬɶ ɥɚɡɟɪɵ ɦɨɳɧɨɫɬɢ ɜ ɞɨɥɢ ɦɢɥɥɢɜɚɬɬɚ, ɧɚɩɪɢɦɟɪ, ɞɥɹ ɯɢɪɭɪɝɢɢ ɝɥɚɡɚ ɫ ɰɟɥɶɸ ɩɪɢɜɚɪɢɜɚɧɢɹ ɫɟɬɱɚɬɤɢ) ɩɨɬɪɟɛɨɜɚɥɨ ɥɢɲɶ ɧɟɡɧɚɱɢɬɟɥɶɧɨ ɢɡɦɟɧɢɬɶ ɤɨɧɫɬɪɭɤɰɢɸ ɤɚɬɨɞɚ ɢ ɚɧɨɞɚ (ɨɧɢ ɫɬɚɥɢ ɩɪɨɜɨɞɹɳɢɦɢ ɤɨɥɶɰɚɦɢ ɧɚ ɜɧɭɬɪɟɧɧɢɯ ɤɨɧɰɚɯ ɬɪɭɛɤɢ (ɪɢɫ. 8.5), ɩɨɹɜɢɥɢɫɶ ɡɟɪɤɚɥɚ), ɬɨ ɤɨɧɫɬɪɭɤɰɢɹ ɦɨɳɧɵɯ ɥɚɡɟɪɨɜ ɫɬɚɥɚ Ɋɢɫ. 8.5. ɋɯɟɦɚ ɋ02 - ɥɚɡɟɪɚ ɧɟɛɨɥɶɲɨɣ ɦɨɳɧɨɫɬɢ ɫ ɞɢɮɮɭɡɢɨɧɧɵɦ ɨɯɥɚɠɞɟɧɢɟɦ: 1 – ɪɚɡɪɹɞɧɚɹ ɬɪɭɛɤɚ, 2 – ɫɨɜɟɪɲɟɧɧɨ ɢɧɨɣ. ɉɪɢ ɬɟɦɩɟɪɚɬɭɪɟ ɤɨɥɶɰɟɜɵɟ ɷɥɟɤɬɪɨɞɵ, 3 – ɦɟɞɥɟɧɧɚɹ ɩɪɨɤɚɱɤɚ ɥɚɡɟɪɧɨɣ ɚɤɬɢɜɧɨɣ ɝɚɡɨɜɨɣ ɫɪɟɞɵ ɫɦɟɫɢ, 4 – ɪɚɡɪɹɞɧɚɹ ɩɥɚɡɦɚ, 5 – ɜɧɟɲɧɹɹ ɬɪɭɛɤɚ, 6 – ɨɯɥɚɠɞɚɸɳɚɹ ɩɪɨɬɨɱɧɚɹ ɜɨɞɚ, 7 – ɝɥɭɯɨɟ ɡɟɪɤɚɥɨ, 8 – ɜɵɲɟ ~ 450 ÷ 500Ʉ ɜɵɯɨɞɧɨɟ ɩɨɥɭɩɪɨɡɪɚɱɧɨɟ ɡɟɪɤɚɥɨ, 9 – ɜɵɯɨɞɹɳɟɟ ɢɡɥɭɱɟɧɢɟ ɷɧɟɪɝɢɹ ɤɨɥɟɛɚɬɟɥɶɧɵɯ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɝɟɧɟɪɚɰɢɸ ɤɨɝɟɪɟɧɬɧɨɝɨ ɢɡɥɭɱɟɧɢɹ, ɧɚɱɢɧɚɟɬ ɨɱɟɧɶ ɛɵɫɬɪɨ ɩɟɪɟɯɨɞɢɬɶ ɜ ɩɨɫɬɭɩɚɬɟɥɶɧɵɟ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ, ɬ.ɟ. ɜ ɬɟɩɥɨ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɧɟɞɨɩɭɫɬɢɦ ɧɚɝɪɟɜ ɛɨɥɟɟ ɱɟɦ ɧɚ 300 ɝɪɚɞɭɫɨɜ, ɧɭɠɟɧ ɨɱɟɧɶ ɢɧɬɟɧɫɢɜɧɵɣ ɬɟɩɥɨɨɬɜɨɞ. Ɍɟɩɥɨɨɬɜɨɞ ɢɡ ɛɨɥɶɲɢɯ ɨɛɴɟɦɨɜ ɡɚ ɫɱɟɬ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ ɝɚɡɚ ɨɛɟɫɩɟɱɢɬɶ ɧɟɥɶɡɹ. Ɋɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɩɨɥɭɱɢɥɚ ɢɞɟɹ ɧɟɩɪɟɪɵɜɧɨɣ ɫɦɟɧɵ ɝɚɡɚ, ɩɨɹɜɢɥɢɫɶ ɛɵɫɬɪɨɩɪɨɬɨɱɧɵɟ ɥɚɡɟɪɵ, ɚ ɪɚɛɨɱɢɣ ɨɛɴɟɦ ɜ ɧɢɯ ɫɨɡɞɚɸɬ ɞɜɟ ɩɚɪɚɥɥɟɥɶɧɵɟ ɩɥɚɫɬɢɧɵ, ɞɥɢɧɨɣ ɢ ɲɢɪɢɧɨɣ ɜ ɧɟɫɤɨɥɶɤɨ ɞɟɫɹɬɤɨɜ ɫɚɧɬɢɦɟɬɪɨɜ. Ɋɚɡɪɹɞ ɨɪɝɚɧɢɡɭɸɬ ɢɥɢ ɜɞɨɥɶ ɩɨɬɨɤɚ ɝɚɡɚ, ɢɥɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɟɦɭ (ɪɢɫ. 8.6). Ɍɚɤ ɤɚɤ ɜ ɥɚɡɟɪɧɵɣ ɥɭɱ ɩɟɪɟɯɨɞɢɬ ɧɟ ɛɨɥɟɟ 30% ɜɤɥɚɞɵɜɚɟɦɨɣ ɜ ɪɚɡɪɹɞ ɷɧɟɪɝɢɢ, ɧɟ ɦɟɧɟɟ 70% ɞɨɥɠɟɧ ɭɧɨɫɢɬɶ ɝɚɡ, ɩɨɷɬɨɦɭ ɞɥɹ ɦɨɳɧɵɯ ɥɚɡɟɪɨɜ ɧɭɠɧɵ ɨɱɟɧɶ ɛɨɥɶɲɢɟ ɩɨɬɨɤɢ ɝɚɡɚ. Ɋɚɫɱɟɬɵ (ɢ ɨɩɵɬ) ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ ɜ ɧɚɢɛɨɥɟɟ ɷɮɮɟɤɬɢɜɧɵɯ CO2 ɥɚɡɟɪɚɯ ɧɚ 10 ɤȼɬ ɦɨɳɧɨɫɬɢ
ɢɡɥɭɱɟɧɢɹ ɧɚɞɨ "ɢɡɪɚɫɯɨɞɨɜɚɬɶ" ɛɨɥɟɟ 80 – 100 ɝ/ɫ. əɫɧɨ, ɱɬɨ ɫɢɫɬɟɦɚ ɝɚɡɨɨɬɜɨɞɚ ɞɨɥɠɧɚ ɛɵɬɶ ɡɚɦɤɧɭɬɚɹ ɫ ɨɯɥɚɠɞɟɧɢɟɦ ɝɚɡɚ (ɫɢɫɬɟɦɵ ɩɪɨɤɚɱɤɢ ɢ ɯɨɥɨɞɢɥɶɧɢɤɨɜ): ɧɟɛɨɥɶɲɚɹ ɚɤɬɢɜɧɚɹ ɡɨɧɚ "ɨɛɪɚɫɬɚɟɬ" ɨɝɪɨɦɧɵɦ ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɦ, ɧɨ ɧɟɢɡɛɟɠɧɵɦ ɨɛɨɪɭɞɨɜɚɧɢɟɦ. ȼɬɨɪɚɹ ɨɫɨɛɟɧɧɨɫɬɶ – ɛɨɪɶɛɚ ɫ ɤɨɧɬɪɚɤɰɢɟɣ: ɟɫɥɢ ɜɦɟɫɬɨ ɪɚɜɧɨɦɟɪɧɨ ɫɜɟɬɹɳɟɝɨɫɹ ɩɨɥɧɨɝɨ ɨɛɴɟɦɚ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ "ɫɬɨɥɛɚ" ɨɛɪɚɡɭɟɬɫɹ ɨɞɢɧ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɲɧɭɪɨɜ ɫ ɢɨɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ Ti ɜ ɞɟɫɹɬɵɟ ɞɨɥɢ ɷȼ, ɬɨ ɧɚ ɬɚɤɨɣ ɩɥɚɡɦɟ ɢɧɜɟɪɫɧɨɣ ɡɚɫɟɥɟɧɧɨɫɬɢ ɤɨɥɟɛɚɬɟɥɶɧɵɯ ɭɪɨɜɧɟɣ ɛɵɬɶ ɧɟ ɦɨɠɟɬ. Ɉɞɧɢɦ ɢɡ ɨɫɧɨɜɧɵɯ ɦɟɬɨɞɨɜ, ɩɪɢɦɟɧɹɟɦɵɯ ɩɪɚɤɬɢɱɟɫɤɢ ɜɨ ɜɫɟɯ ɦɨɳɧɵɯ ɥɚɡɟɪɚɯ, ɹɜɥɹɟɬɫɹ ɪɚɡɞɟɥɟɧɢɟ ɤɚɬɨɞɨɜ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɱɟɪɟɡ ɤɚɠɞɵɣ ɲɟɥ ɬɨɤ, ɦɟɧɶɲɢɣ, ɱɟɦ ɧɭɠɧɨ ɞɥɹ ɤɨɧɬɪɚɤɰɢɢ. ɍ ɤɚɠɞɨɝɨ ɤɚɬɨɞɚ ɫɜɨɟ ɛɚɥɥɚɫɬɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ R (ɫɦ. ɪɢɫ. 8.3), ɬɚɤ ɱɬɨ ɟɫɥɢ ɞɚɠɟ ɧɚ ɤɚɤɨɦ-ɥɢɛɨ ɢɡ ɧɢɯ ɢ ɛɭɞɟɬ
Ɋɢɫ.8.6. Ɍɢɩɢɱɧɚɹ ɝɟɨɦɟɬɪɢɹ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ ɜ ɷɥɟɤɬɪɨɪɚɡɪɹɞɧɵɯ ɥɚɡɟɪɚɯ ɧɚ ɋɈ2; ɚ - ɩɨɩɟɪɟɱɧɵɣ ɪɚɡɪɹɞ (ɬɨɤ ɢɞɟɬ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɝɚɡɨɜɨɦɭ ɩɨɬɨɤɭ ɧɚɩɪɚɜɥɟɧɢɹ ɫɤɨɪɨɫɬɢ); ɜɟɪɯɧɹɹ ɩɥɚɬɚ ɭɫɟɹɧɚ ɤɚɬɨɞɧɵɦɢ ɷɥɟɦɟɧɬɚɦɢ Ʉ, ɧɢɠɧɹɹ ɫɥɭɠɢɬ ɚɧɨɞɨɦ Ⱥ; ɛ - ɩɪɨɞɨɥɶɧɵɣ ɪɚɡɪɹɞ, ɤɚɬɨɞɧɵɟ ɷɥɟɦɟɧɬɵ Ʉ ɪɚɫɩɨɥɨɠɟɧɵ ɜɜɟɪɯ ɩɨ ɩɨɬɨɤɭ, ɚɧɨɞɨɦ Ⱥ ɫɥɭɠɢɬ ɬɪɭɛɤɚ
ɤɨɧɬɪɚɤɰɢɹ, ɬɨ ɷɬɨ ɧɟ ɫɭɳɟɫɬɜɟɧɧɨ: ɤɚɬɨɞɨɜ ɬɵɫɹɱɢ. ȿɫɬɶ ɢ ɞɪɭɝɢɟ ɦɟɬɨɞɵ, ɧɚɩɪɢɦɟɪ, ɫɞɟɥɚɬɶ ɢɦɩɭɥɶɫɧɵɣ ɪɚɡɪɹɞ ɧɟɫɚɦɨɫɬɨɹɬɟɥɶɧɵɦ ɢ ɜɨɡɛɭɠɞɚɬɶ ɩɭɱɤɨɦ ɛɵɫɬɪɵɯ (ȿ ~ 100 ɤɷȼ) ɷɥɟɤɬɪɨɧɨɜ, ɤɨɦɛɢɧɢɪɨɜɚɬɶ ɩɨɫɬɨɹɧɧɵɟ ɢ ȼɑ, ɩɨɫɬɨɹɧɧɵɟ ɢ ɢɦɩɭɥɶɫɧɵɟ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɨɥɟɣ. ɉɪɢɦɟɧɟɧɢɟ ȼɑ ɢ, ɨɫɨɛɟɧɧɨ, ɢɦɩɭɥɶɫɧɵɯ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɨɥɟɣ ɛɨɥɶɲɨɣ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɩɨɡɜɨɥɢɥɨ ɪɟɡɤɨ ɭɜɟɥɢɱɢɬɶ ɷɧɟɪɝɨɫɴɟɦ ɫ ɟɞɢɧɢɰɵ ɪɚɛɨɱɟɝɨ ɨɛɴɟɦɚ ɚɤɬɢɜɧɨɣ ɫɪɟɞɵ. §52. Ⱦɭɝɨɜɵɟ ɪɚɡɪɹɞɵ
ɗɥɟɤɬɪɢɱɟɫɤɨɣ ɞɭɝɨɣ ɧɚɡɵɜɚɸɬ ɭɫɬɚɧɨɜɢɜɲɢɣɫɹ (ɢɥɢ ɩɨɱɬɢ ɭɫɬɚɧɨɜɢɜɲɢɣɫɹ) ɪɚɡɪɹɞ, ɤɨɬɨɪɵɣ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɧɢɡɤɢɦ ɤɚɬɨɞɧɵɦ ɩɚɞɟɧɢɟɦ ɩɨɬɟɧɰɢɚɥɚ ɢ ɜɵɫɨɤɨɣ ɩɥɨɬɧɨɫɬɶɸ ɬɨɤɚ ɧɚ ɤɚɬɨɞɟ (jk ≥ 10 ÷ 102 Ⱥ/ɫɦ2). Ɍɚɤɢɟ ɮɨɪɦɵ ɪɚɡɪɹɞɚ ɢɡɜɟɫɬɧɵ ɫ 1802ɝ. (ɉɟɬɪɨɜ ȼ.ȼ.), ɧɨ ɪɹɞ ɨɫɨɛɟɧɧɨɫɬɟɣ ɧɟ ɩɨɧɹɬɟɧ ɢ ɞɨ ɫɢɯ ɩɨɪ. ɇɟ ɭɫɬɚɧɨɜɢɥɚɫɶ ɟɳɟ ɞɚɠɟ ɨɛɳɟɩɪɢɧɹɬɚɹ ɤɥɚɫɫɢɮɢɤɚɰɢɹ ɞɭɝɨɜɵɯ ɪɚɡɪɹɞɨɜ, ɤɨɬɨɪɵɟ ɞɟɥɹɬɫɹ ɩɨ ɬɢɩɭ ɤɚɬɨɞɨɜ ɢ ɩɨ ɞɚɜɥɟɧɢɸ ɪɚɛɨɱɟɝɨ ɜɟɳɟɫɬɜɚ. Ɍɚɤ, ɩɨ ɬɢɩɭ ɤɚɬɨɞɚ ɪɚɡɥɢɱɚɸɬ: ɚ) ɩɨɞɨɝɪɟɜɧɵɟ; ɛ) ɝɨɪɹɱɢɟ; ɜ) ɯɨɥɨɞɧɵɟ; ɝ) ɭɝɨɥɶɧɵɟ; ɩɨ ɞɚɜɥɟɧɢɸ: ɚ) ɧɢɡɤɨɝɨ ɞɚɜɥɟɧɢɹ (p ≤ 10-3 ÷ 1 ɚɬɦ); ɛ) ɜɵɫɨɤɨɝɨ (ɪ ∼ 1 ÷ 5 ɚɬɦ); ɝ) ɫɜɟɪɯɜɵɫɨɤɨɝɨ (ɪ > 10 ɚɬɦ). ȼ ɞɭɝɨɜɨɦ ɪɚɡɪɹɞɟ ɦɨɠɧɨ ɪɚɡɥɢɱɢɬɶ:
1) ɩɪɢɤɚɬɨɞɧɵɣ ɫɥɨɣ – ɬɨɧɤɢɣ, ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɩɨɪɹɞɤɚ ɩɨɬɟɧɰɢɚɥɚ ɢɨɧɢɡɚɰɢɢ (ɛɵɜɚɟɬ ɞɚɠɟ ɦɟɧɶɲɟ) ɚɬɨɦɨɜ ɝɚɡɚ; 2) ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ, ɫɨɫɬɨɹɧɢɟ ɢ ɩɨɜɟɞɟɧɢɟ ɩɥɚɡɦɵ ɜ ɤɨɬɨɪɨɦ ɨɩɪɟɞɟɥɹɟɬɫɹ ɛɚɥɚɧɫɨɦ ɷɧɟɪɝɢɢ; (ɬɟɦɩɟɪɚɬɭɪɵ ɢɨɧɨɜ Ti ɢ ɷɥɟɤɬɪɨɧɨɜ Ɍɟ ɜ ɰɟɧɬɪɚɥɶɧɨɣ ɱɚɫɬɢ ɫɬɨɥɛɚ ɪɚɜɧɵ); ɜ) ɚɧɨɞɧɵɣ, ɬɨɠɟ ɬɨɧɤɢɣ ɫɥɨɣ ɢ ɬɨɠɟ ɫ ɦɚɥɵɦ ɩɚɞɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɧɟɦ. Ⱦɭɝɢ ɫ ɩɨɞɨɝɪɟɜɧɵɦ ɤɚɬɨɞɨɦ
Ⱦɭɝɢ ɫ ɩɨɞɨɝɪɟɜɧɵɦ ɤɚɬɨɞɨɦ ɷɬɨ ɧɟɫɚɦɨɫɬɨɹɬɟɥɶɧɵɟ ɪɚɡɪɹɞɵ, ɢɫɩɨɥɶɡɭɸɬɫɹ ɜ ɨɫɧɨɜɧɨɦ ɤɚɤ ɜɵɩɪɹɦɢɬɟɥɢ, ɭɩɪɚɜɥɹɟɦɵɟ ɜɤɥɸɱɟɧɢɟɦ - ɜɵɤɥɸɱɟɧɢɟɦ ɪɚɡɪɹɞɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ (ɝɚɡɨɬɪɨɧɵ) ɢɥɢ ɢɡɦɟɧɟɧɢɟɦ ɮɚɡɨɜɨɝɨ ɫɞɜɢɝɚ ɧɚɩɪɹɠɟɧɢɣ ɚɧɨɞɚ (ɢɥɢ ɤɚɬɨɞɚ) ɢ ɫɟɬɤɢ (ɬɢɪɚɬɪɨɧɵ). ȼ ɞɭɝɟ ɤɚɬɨɞɧɵɣ ɫɥɨɣ ɬɨɥɶɤɨ ɭɫɤɨɪɹɟɬ ɷɥɟɤɬɪɨɧɵ ɬɟɪɦɨɷɦɢɫɫɢɢ ɧɚɫɬɨɥɶɤɨ, ɱɬɨɛɵ ɨɧɢ ɩɨɞɞɟɪɠɢɜɚɥɢ ɧɭɠɧɭɸ ɢɨɧɢɡɚɰɢɸ ɝɚɡɚ. Ɉɛɪɚɡɭɸɳɚɹɫɹ ɩɥɚɡɦɚ ɤɚɤ ɛɵ "ɩɪɢɛɥɢɠɚɟɬ" ɚɧɨɞ ɤ ɤɚɬɨɞɭ, ɬɚɤ ɱɬɨ ɨɝɪɚɧɢɱɟɧɢɟ ɬɨɤɚ ɨɛɴɟɦɧɵɦ ɡɚɪɹɞɨɦ ("ɡɚɤɨɧ 3/2" ɞɥɹ ɜɚɤɭɭɦɧɨɝɨ ɩɪɨɦɟɠɭɬɤɚ) ɜ ɞɭɝɟ ɧɟɬ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɪɢ ɧɚɩɪɹɠɟɧɢɢ ɦɟɠɞɭ ɚɧɨɞɨɦ ɢ ɤɚɬɨɞɨɦ 10-20 ȼ ɬɨɤ ɧɚ ɩɨɪɹɞɤɢ ɛɨɥɶɲɟ, ɱɟɦ ɛɵɥ ɛɵ ɜ ɜɚɤɭɭɦɟ. Ⱦɭɝɢ ɫ ɝɨɪɹɱɢɦɢ ɤɚɬɨɞɚɦɢ
Ⱦɭɝɢ ɫ ɝɨɪɹɱɢɦɢ ɤɚɬɨɞɚɦɢ ɨɱɟɧɶ ɪɚɫɩɪɨɫɬɪɚɧɟɧɵ. Ɉɧɢ ɛɵɜɚɸɬ ɨɬ ɞɟɫɹɬɤɨɜ ɦɢɥɥɢɚɦɩɟɪ (ɥɚɦɩɵ ɞɧɟɜɧɨɝɨ ɫɜɟɬɚ) ɞɨ ɦɟɝɚɚɦɩɟɪ (ɜ ɷɥɟɤɬɪɨɥɢɬɢɱɟɫɤɢɯ ɜɚɧɧɚɯ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɚɥɸɦɢɧɢɹ ɢ ɦɚɝɧɢɹ). ɉɪɢɤɚɬɨɞɧɚɹ ɨɛɥɚɫɬɶ ɝɨɪɹɱɟɝɨ ɞɭɝɨɜɨɝɨ ɪɚɡɪɹɞɚ ɧɟ ɩɪɨɳɟ ɩɪɢɤɚɬɨɞɧɨɣ ɨɛɥɚɫɬɢ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ, ɞɚ ɢ ɢɡɭɱɟɧɚ ɹɜɧɨ ɯɭɠɟ. ɍɫɤɨɪɟɧɧɵɟ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɜɛɥɢɡɢ ɤɚɬɨɞɚ ɬɟɪɦɨɷɦɢɫɫɢɨɧɧɵɟ ɷɥɟɤɬɪɨɧɵ ɜ ɩɪɢɤɚɬɨɞɧɨɣ ɨɛɥɚɫɬɢ ɫɨɡɞɚɸɬ ɢɨɧ-ɷɥɟɤɬɪɨɧɧɵɟ ɩɚɪɵ. ɂɨɧɵ ɭɫɤɨɪɹɸɬɫɹ ɤ ɤɚɬɨɞɭ, ɧɚ ɤɨɬɨɪɨɦ ɩɪɨɢɡɜɨɞɹɬɫɹ 2 ÷ 9 ɬɟɪɦɨɷɦɢɫɫɢɨɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɨɞɢɧ ɢɨɧ. ɉɪɨɢɡɜɨɞɫɬɜɨ ɷɥɟɤɬɪɨɧɨɜ ɢɨɧɚɦɢ ɧɚ ɤɚɬɨɞɟ ɱɟɪɟɡ ɬɟɩɥɨ (ɬɟɪɦɨɷɦɢɫɫɢɹ) ɷɧɟɪɝɟɬɢɱɟɫɤɢ ɡɧɚɱɢɬɟɥɶɧɨ ɜɵɝɨɞɧɟɟ, ɱɟɦ ɩɪɹɦɚɹ ɢɨɧɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ (ɤɚɤ ɜ ɬɥɟɸɳɟɦ ɪɚɡɪɹɞɟ), ɧɨ ɜɨɡɦɨɠɧɨ ɬɨɥɶɤɨ ɩɪɢ ɛɨɥɶɲɨɣ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ. Ʉɚɬɨɞɨɦ ɨɛɵɱɧɨ ɫɥɭɠɢɬ ɢɥɢ ɜɵɫɨɤɨɬɟɦɩɟɪɚɬɭɪɧɵɣ ɦɟɬɚɥɥ (ɱɚɫɬɨ ɜɨɥɶɮɪɚɦ) ɢɥɢ ɪɚɫɩɥɚɜ ɦɟɬɚɥɥɚ (ɜɚɧɧɵ ɩɪɢ ɩɪɨɢɡɜɨɞɫɬɜɟ Al, Mg). ɇɟɫɦɨɬɪɹ ɧɚ ɧɢɡɤɨɟ ɩɚɞɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ, ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɨɤɨɥɨ ɤɚɬɨɞɚ ɜ ɞɭɝɟ ɛɨɥɶɲɨɟ, ɬɚɤ ɤɚɤ ɩɥɚɡɦɚ ɩɨɞɠɢɦɚɟɬ ɩɪɢɤɚɬɨɞɧɵɣ ɫɥɨɣ ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɤɚɬɨɞɚ. Ɍɚɤ, ɞɥɹ ɩɥɨɬɧɨɫɬɟɣ ɬɨɤɚ j ∼ 103 Ⱥ/ɫɦ2 ɬɨɤ ɬɟɪɦɨɷɦɢɫɫɢɢ ɜɨɡɪɚɫɬɚɟɬ ɡɚ ɫɱɟɬ ɷɮɮɟɤɬɚ ɒɨɬɬɤɢ ɜ ∼ 3 ɪɚɡɚ (Ek ∼ 106 ȼ/ɫɦ). Ɉɞɧɚɤɨ ɬɨɤɢ ɜ 108 Ⱥ/ɫɦ2 ɨɛɴɹɫɧɢɬɶ ɬɟɪɦɨɷɥɟɤɬɪɨɧɧɨɣ ɢ ɚɜɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɟɣ ɤɚɬɨɞɚ ɧɟɜɨɡɦɨɠɧɨ, ɩɪɢɯɨɞɢɬɫɹ ɞɟɥɚɬɶ ɩɪɟɞɩɨɥɨɠɟɧɢɹ ɨ ɜɡɪɵɜɧɨɣ ɷɦɢɫɫɢɢ ɦɢɤɪɨɨɫɬɪɢɣ ɢ ɨ ɪɚɫɩɥɚɜɥɟɧɢɢ ɩɨɜɟɪɯɧɨɫɬɢ ɤɚɬɨɞɚ ɢ ɜɵɛɪɨɫɟ ɪɚɫɩɥɚɜɥɟɧɧɨɝɨ ɦɟɬɚɥɥɚ ɜ ɪɚɡɪɹɞɧɵɣ ɩɪɨɦɟɠɭɬɨɤ ɫ ɩɨɫɥɟɞɭɸɳɟɣ ɟɝɨ ɢɨɧɢɡɚɰɢɟɣ. Ⱦɭɝɢ ɫ ɯɨɥɨɞɧɵɦɢ ɤɚɬɨɞɚɦɢ
Ⱦɭɝɢ ɫ ɯɨɥɨɞɧɵɦɢ ɤɚɬɨɞɚɦɢ − ɷɬɨ ɩɨ ɫɭɳɟɫɬɜɭ ɞɭɝɢ ɫ ɥɨɤɚɥɶɧɵɦɢ ɬɟɪɦɨɷɦɢɬɬɟɪɚɦɢ: ɧɚ ɤɚɬɨɞɟ ɨɛɪɚɡɭɸɬɫɹ ɬɨɤɨɜɵɟ ɩɹɬɧɚ, ɩɪɢ ɱɟɦ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ ɞɨɥɠɧɚ ɛɵɬɶ ɛɨɥɶɲɟ ɤɪɢɬɢɱɟɫɤɨɣ (ɞɥɹ ɞɚɧɧɨɝɨ ɦɟɬɚɥɥɚ), ɢɧɚɱɟ ɞɭɝɚ ɝɚɫɧɟɬ. ɗɬɨ ɨɛɴɹɫɧɹɟɬɫɹ ɧɟɨɛɯɨɞɢɦɨɫɬɶɸ ɤɨɧɰɟɧɬɪɚɰɢɢ ɷɧɟɪɝɢɢ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɫ ɤɚɬɨɞɚ. ɉɥɨɬɧɨɫɬɢ ɬɨɤɚ ɨɱɟɧɶ ɛɨɥɶɲɢɟ (ɭ ɦɟɞɢ ɞɨ 108 Ⱥ/ɫɦ2!), ɞɚɧɧɵɟ ɨɩɵɬɨɜ ɫɢɥɶɧɨ ɪɚɡɥɢɱɚɸɬɫɹ, ɚ ɬɟɨɪɟɬɢɱɟɫɤɨɝɨ ɨɩɢɫɚɧɢɹ ɧɟɬ. ɉɹɬɧɚ ɯɚɨɬɢɱɟɫɤɢ ɛɟɝɚɸɬ ɩɨ ɤɚɬɨɞɭ, ɩɨɩɵɬɤɢ ɭɩɨɪɹɞɨɱɢɬɶ ɢɯ ɞɜɢɠɟɧɢɹ ɩɨɤɚ ɧɟ ɞɚɥɢ ɪɟɡɭɥɶɬɚɬɚ. ɋ 1903ɝ.
ɢɡɜɟɫɬɧɨ, ɱɬɨ ɟɫɥɢ ɩɹɬɧɨ ɩɨɦɟɫɬɢɬɶ ɜ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɇ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɟ ɬɨɤɭ & & j, ɬɨ ɩɹɬɧɨ ɩɨɛɟɠɢɬ ɧɚɜɫɬɪɟɱɭ (!) ɜɟɤɬɨɪɭ j × H ...Ɉɛɴɹɫɧɟɧɢɹ ɞɨ ɫɢɯ ɩɨɪ ɧɟɬ. ɇɟɬ ɩɨɥɧɨɝɨ ɩɨɧɢɦɚɧɢɹ ɢ ɦɟɯɚɧɢɡɦɨɜ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ: ɟɫɥɢ ɞɥɹ ɫɪɟɞɧɢɯ ɡɧɚɱɟɧɢɣ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ (j ∼ 106 Ⱥ/ɫɦ2), ɪɚɫɱɟɬɧɨɟ ɩɨɥɟ ȿ ∼ 107 ȼ/ɫɦ (ɭ ɫɚɦɨɝɨ ɤɚɬɨɞɚ) - ɬɟɨɪɢɹ ɢ ɷɤɫɩɟɪɢɦɟɧɬ ɩɪɢɦɟɪɧɨ ɫɨɜɩɚɞɚɸɬ, ɬɨ ɧɢ ɞɥɹ ɦɚɥɵɯ, ɧɢ ɞɥɹ ɫɚɦɵɯ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɣ j ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɚɜɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɡɧɚɱɟɧɢɹ ȿ ɨɤɚɡɵɜɚɸɬɫɹ ɧɟɩɪɚɜɞɨɩɨɞɨɛɧɨ ɛɨɥɶɲɢɦɢ. ɂɧɨɝɞɚ ɩɹɬɧɚ ɨɫɬɚɧɚɜɥɢɜɚɸɬɫɹ (ɛɵɜɚɟɬ ɧɚɞɨɥɝɨ), ɜ ɬɚɤɨɦ ɦɟɫɬɟ ɢɞɟɬ ɫɢɥɶɧɚɹ ɷɪɨɡɢɹ (ɞɨ ɞɵɪ ɢ ɩɪɟɤɪɚɳɟɧɢɹ ɪɚɡɪɹɞɚ). ɒɢɪɨɤɨ ɩɪɢɦɟɧɹɸɬɫɹ ɤɚɬɨɞɵ ɢɡ ɪɬɭɬɢ ɜ ɜɵɩɪɹɦɢɬɟɥɹɯ - ɢɝɧɢɬɪɨɧɚɯ. ɉɪɢ ɩɚɞɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ ɧɢɠɟ ɩɨɬɟɧɰɢɚɥɚ ɡɚɠɢɝɚɧɢɹ ɪɚɡɪɹɞ ɞɨɥɠɟɧ ɩɨɝɚɫɧɭɬɶ (ɧɟɬ ɬɟɩɥɨɜɨɣ "ɢɧɟɪɰɢɢ" ɝɨɪɹɱɢɯ ɤɚɬɨɞɨɜ), ɟɝɨ ɧɚɞɨ ɩɨɞɠɢɝɚɬɶ. Ⱦɥɹ ɷɬɨɝɨ ɜɜɨɞɹɬ ɫɩɟɰɢɚɥɶɧɵɣ ɞɨɩɨɥɧɢɬɟɥɶɧɵɣ ɚɧɨɞ"ɢɝɧɚɣɬɨɪ", ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɤɨɬɨɪɵɣ ɩɨɞɚɸɬ ɫ ɧɭɠɧɵɦ ɫɞɜɢɝɨɦ ɩɨ ɮɚɡɟ. Ʉɚɠɞɵɣ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɩɨɥɭɩɟɪɢɨɞ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦ ɢɝɧɢɬɪɨɧɟ ɫɨɡɞɚɸɬɫɹ "ɡɚɬɪɚɜɨɱɧɵɟ" ɩɚɪɵ ɪɬɭɬɢ, ɢɧɢɰɢɢɪɭɸɳɢɟ ɪɚɡɪɹɞ. ɉɨ ɬɟɪɦɢɧɨɥɨɝɢɢ [33] ɢɝɧɢɬɪɨɧ, ɩɨɠɚɥɭɣ, ɧɚɞɨ ɨɬɧɟɫɬɢ ɤ "ɜɚɤɭɭɦɧɵɦ ɞɭɝɚɦ" − ɛɟɡ ɩɚɪɨɜ ɦɟɬɚɥɥɚ ɤɚɬɨɞɚ ɪɚɡɪɹɞ ɧɟ ɝɨɪɢɬ. "ȼɚɤɭɭɦɧɵɟ" ɞɭɝɢ ɝɨɪɹɬ ɜɫɟɝɞɚ ɫ ɭɱɚɫɬɢɟɦ ɩɚɪɨɜ ɦɚɬɟɪɢɚɥɚ ɤɚɬɨɞɚ ɢ ɢɦɟɸɬ ɜɨɡɪɚɫɬɚɸɳɭɸ ɜɨɥɶɬ-ɚɦɩɟɪɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ (ȼȺɏ) (ɨɛɵɱɧɨ ȼȺɏ ɩɚɞɚɸɳɚɹ). ɉɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ ɞɭɝɨɜɨɝɨ ɪɚɡɪɹɞɚ
ɉɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ ɞɭɝɨɜɨɝɨ ɪɚɡɪɹɞɚ ɫɢɥɶɧɨ ɡɚɜɢɫɢɬ ɨɬ ɪɨɞɚ ɝɚɡɚ, ɞɚɜɥɟɧɢɹ, ɫɢɥɵ ɬɨɤɚ. ɉɪɢ ɦɚɥɵɯ ɞɚɜɥɟɧɢɹɯ (p ≤ 0.1 ɚɬɦ) ɢ ɫɢɥɟ ɬɨɤɚ (I ∼ 1Ⱥ) ɫɬɨɥɛ ɧɟɪɚɜɧɨɜɟɫɟɧ (Te > Ti) ɢ ɫɢɥɶɧɨ ɧɚɩɨɦɢɧɚɟɬ ɤɨɧɬɪɚɝɢɪɨɜɚɧɧɵɣ ɲɧɭɪ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ. ɉɥɚɡɦɚ ɩɚɪɨɜ ɦɟɬɚɥɥɚ, ɦɨɥɟɤɭɥɹɪɧɵɯ ɝɚɡɨɜ, ɩɪɢ ɞɚɜɥɟɧɢɢ p ≥ 1 ɚɬɦ ɜɫɟɝɞɚ ɪɚɜɧɨɜɟɫɧɚ, ɯɚɪɚɤɬɟɪɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ (ɩɨ ɪɚɞɢɭɫɭ ɫɬɨɥɛɚ) ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɩɪɨɜɨɞɢɦɨɫɬɢ ɩɪɟɞɫɬɚɜɥɟɧɨ ɧɚ ɪɢɫ. 8.7. ɉɪɢ ɨɛɵɱɧɨɦ ɪɚɫɩɪɟɞɟɥɟɧɢɢ ɬɨɤɚ ɬɟɦɩɟɪɚɬɭɪɚ ɛɭɞɟɬ ɢɦɟɬɶ ɤɨɥɨɤɨɨɛɪɚɡɧɭɸ ɮɨɪɦɭ, ɪɚɜɧɨɦɟɪɧɨ ɭɦɟɧɶɲɚɹɫɶ ɨɬ T ~ (10 ÷ 12)⋅103 Ʉ ɜ ɰɟɧɬɪɟ ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ ɫɬɟɧɤɢ. ɉɥɨɬɧɨɫɬɶ Ɋɢɫ. 8.7. ɋɯɟɦɚɬɢɱɟɫɤɢɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ɍ ɢ ɷɥɟɤɬɪɨɧɨɜ ɩɨ ɪɚɞɢɭɫɭ ɫɩɚɞɚɟɬ ɩɪɨɜɨɞɢɦɨɫɬɢ σ ɩɨ ɪɚɞɢɭɫɭ ɫɬɨɥɛɚ ɞɭɝɢ. ɨɱɟɧɶ ɛɵɫɬɪɨ − ɜ ɪɚɜɧɨɜɟɫɧɨɣ ɒɬɪɢɯɨɜɚɹ ɥɢɧɢɹ - ɡɚɦɟɧɚ σ (r) ɫɬɭɩɟɧɶɤɨɣ ɜ ɤɚɧɚɥɨɜɨɣ ɦɨɞɟɥɢ ɩɥɚɡɦɟ ne ~ exp(-r/r0) (ɚ ɫ ɧɟɣ ɢ ɩɪɨɜɨɞɢɦɨɫɬɶ (σ ~ ne)), ɬɚɤ ɱɬɨ ɬɨɤɨɩɪɨɜɨɞɹɳɢɣ ɤɚɧɚɥ ɫɨɫɪɟɞɨɬɨɱɟɧ ɭ ɨɫɢ. ɇɚ ɪɚɞɢɭɫɟ, ɛɨɥɶɲɟɦ rɨ (ɪɢɫ. 8.7), ɩɪɨɜɨɞɢɦɨɫɬɶɸ ɩɥɚɡɦɵ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ. Ɉɞɧɚɤɨ ɫɜɹɡɚɬɶ ɤɨɥɢɱɟɫɬɜɟɧɧɨ ɬɨɤ I, ɪɚɞɢɭɫɵ r0 ɢ R, ɦɨɳɧɨɫɬɶ w ɭɞɚɥɨɫɶ ɒɬɟɧɛɟɤɭ, ɬɨɥɶɤɨ ɜɜɟɞɹ ɩɪɢɧɰɢɩ ɦɢɧɢɦɭɦɚ ɦɨɳɧɨɫɬɢ "min w". ɉɪɢ ɡɚɞɚɧɧɨɦ ɬɨɤɟ I ɢ ɪɚɞɢɭɫɟ R ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ
r0 ɬɚɤɨɟ, ɱɬɨɛɵ ɜɵɞɟɥɹɸɳɚɹɫɹ ɜ ɪɚɡɪɹɞɟ ɦɨɳɧɨɫɬɶ ɛɵɥɚ ɦɢɧɢɦɚɥɶɧɨɣ (ɩɨɡɠɟ ɞɨɤɚɡɚɥɢ, ɱɬɨ ɩɪɢɧɰɢɩ " min w " ɫɩɪɚɜɟɞɥɢɜ ɧɟ ɜɫɟɝɞɚ, ɧɨ ɜ ɞɭɝɟ ɫɩɪɚɜɟɞɥɢɜ). ɋɭɳɟɫɬɜɟɧɧɨ, ɱɬɨ ɦɚɤɫɢɦɚɥɶɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ Ɍɤ (ɫɦ. ɪɢɫ.8.7) ɜɟɫɶɦɚ ɫɥɚɛɨ ɡɚɜɢɫɢɬ ɨɬ ɨɯɥɚɠɞɟɧɢɹ ɞɭɝɢ (ɜɚɠɟɧ ɬɨɥɶɤɨ ɬɟɩɥɨɨɬɜɨɞ ɨɬ ɤɚɬɨɞɚ) ɢ ɪɚɫɬɟɬ ɫ ɜɤɥɚɞɵɜɚɟɦɨɣ ɦɨɳɧɨɫɬɶɸ ɧɟɫɤɨɥɶɤɨ ɦɟɞɥɟɧɧɟɟ, ɱɟɦ ɤɨɪɟɧɶ ɤɜɚɞɪɚɬɧɵɣ ɢɡ ɦɨɳɧɨɫɬɢ. ɉɪɢ ɜɵɫɨɤɨɦ ɞɚɜɥɟɧɢɢ (p ≥ 10 ɚɬɦ) ɢ ɜɵɫɨɤɨɣ ɬɟɦɩɟɪɚɬɭɪɟ (Ɍ ≥ 12000Ʉ) ɨɱɟɧɶ ɫɭɳɟɫɬɜɟɧɧɵɦ ɨɤɚɡɵɜɚɟɬɫɹ ɨɯɥɚɠɞɟɧɢɟ ɢɡɥɭɱɟɧɢɟɦ, ɨɧɨ ɭɧɨɫɢɬ ɞɨ 90% ɦɨɳɧɨɫɬɢ. ȼ ɩɨɫɥɟɞɧɢɟ ɝɨɞɵ ɜɵɫɨɤɢɣ ɫɜɟɬɨɜɨɣ ɄɉȾ ɞɭɝ ɜɵɫɨɤɨɝɨ ɞɚɜɥɟɧɢɹ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɸɬ ɞɥɹ ɨɫɜɟɳɟɧɢɹ ɞɨɪɨɝ. Ɉɛɥɚɫɬɶ ɚɧɨɞɚ
Ɉɛɥɚɫɬɶ ɚɧɨɞɚ ɬɚɤ-ɠɟ, ɤɚɤ ɢ ɩɪɢɤɚɬɨɞɧɚɹ, ɜɟɫɶɦɚ ɬɨɧɤɚɹ, ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɧɟɣ ɡɚɜɢɫɢɬ ɨɬ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɚɧɨɞɚ, ɚ ɢɯ ɞɜɚ. ɉɟɪɜɵɣ ɪɟɠɢɦ ɞɢɮɮɭɡɧɵɣ ɢɦɟɟɬ ɦɟɫɬɨ ɩɪɢ ɛɨɥɶɲɨɣ ɩɥɨɳɚɞɢ ɚɧɨɞɚ ɢ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ j ≤ 102Ⱥ/ɫɦ2 , ɬɨɤ ɪɚɫɩɪɟɞɟɥɟɧ ɩɨ ɜɫɟɦɭ ɚɧɨɞɭ ɢ ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɨɱɟɧɶ ɦɚɥɨ (1 ÷ 3 ȼ) (ɢ ɞɚɠɟ ɛɵɜɚɟɬ ɨɬɪɢɰɚɬɟɥɶɧɵɦ). ȼɬɨɪɨɣ ɪɟɠɢɦ: ɟɫɥɢ ɩɥɨɳɚɞɶ ɚɧɨɞɚ ɦɚɥɚ (ɬɨɤ ɜɵɯɨɞɢɬ ɧɚ ɤɪɚɹ ɢ ɬ.ɞ.), ɬɨ ɩɪɢ ɧɟɤɨɬɨɪɨɦ ɬɨɤɟ (ɡɚɜɢɫɢɬ ɨɬ ɦɧɨɝɢɯ ɩɪɢɱɢɧ) ɬɨɤ ɫɨɛɢɪɚɟɬɫɹ ɜ ɩɹɬɧɨ (ɢɥɢ ɩɹɬɧɚ) ɫ ɩɥɨɬɧɨɫɬɶɸ j = 102 Ⱥ/ɫɦ2. Ⱥɧɨɞɧɵɟ ɩɹɬɧɚ ɨɛɪɚɡɭɸɬ ɩɪɚɜɢɥɶɧɵɟ ɝɟɨɦɟɬɪɢɱɟɫɤɢɟ ɮɢɝɭɪɵ (!), ɢɧɨɝɞɚ ɛɟɝɚɸɬ, ɧɨ ɬɨɠɟ ɩɨ ɭɩɨɪɹɞɨɱɟɧɧɵɦ ɬɪɚɟɤɬɨɪɢɹɦ (ɤɪɭɝɢ, ɨɜɚɥɵ,...). Ɇɟɯɚɧɢɡɦɵ ɧɟ ɢɡɜɟɫɬɧɵ. Ɂɚɠɢɝɚɧɢɟ ɞɭɝɢ
Ɂɚɠɢɝɚɧɢɟ ɞɭɝɢ ɦɨɠɧɨ ɩɪɨɢɡɜɟɫɬɢ, ɫɨɟɞɢɧɹɹ ɷɥɟɤɬɪɨɞɵ (ɨɫɧɨɜɧɵɟ ɢɥɢ ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɟ, ɤɚɤ ɜ ɢɝɧɢɬɪɨɧɟ), ɚ ɡɚɬɟɦ ɪɚɡɴɟɞɢɧɹɹ ɢɯ. ɉɪɨɰɟɫɫ ɡɚɠɢɝɚɧɢɹ ɞɭɝɢ ɩɪɢ ɪɚɡɦɵɤɚɧɢɢ ɰɟɩɢ (ɩɪɢ ɪɚɡɴɟɞɢɧɟɧɢɢ ɷɥɟɤɬɪɨɞɨɜ) ɨɛɴɹɫɧɹɟɬɫɹ ɥɨɤɚɥɶɧɵɦ ɪɚɡɨɝɪɟɜɨɦ ɷɥɟɤɬɪɨɞɨɜ ɜɫɥɟɞɫɬɜɢɟ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɦɟɠɞɭ ɧɢɦɢ ɩɥɨɯɨɝɨ ɤɨɧɬɚɤɬɚ, ɤɨɝɞɚ ɢɡ-ɡɚ ɛɨɥɶɲɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɩɪɨɢɫɯɨɞɢɬ ɧɚɝɪɟɜ ɦɟɫɬɚ ɤɨɧɬɚɤɬɚ ɞɨ ɬɟɪɦɨɷɦɢɫɫɢɢ ɢ ɪɚɡɪɹɞ ɡɚɠɢɝɚɟɬɫɹ. Ɍɚɤɨɣ ɠɟ ɩɪɨɰɟɫɫ ɩɪɨɢɫɯɨɞɢɬ ɢ ɩɪɢ ɪɚɡɦɵɤɚɧɢɢ ɬɨɤɚ ɜ ɫɢɥɶɧɨɬɨɱɧɵɯ ɜɵɤɥɸɱɚɬɟɥɹɯ ɫ ɨɛɪɚɡɨɜɚɧɢɟɦ ɜɪɟɞɧɵɯ ɞɭɝ, ɤɨɬɨɪɵɟ ɜɵɠɢɝɚɸɬ ɷɥɟɤɬɪɨɞɵ. Ⱦɪɭɝɨɣ ɫɩɨɫɨɛ ɨɛɪɚɡɨɜɚɧɢɹ ɞɭɝɢ − ɷɬɨ ɢɨɧɢɡɚɰɢɹ ɜ ɦɟɠɷɥɟɤɬɪɨɞɧɨɦ ɩɪɨɦɟɠɭɬɤɟ ɩɪɢ ɩɨɞɚɱɟ ɩɨɜɵɲɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɢ ɜɵɛɨɪ ɮɨɪɦɵ ɷɥɟɤɬɪɨɞɨɜ, ɫɩɨɫɨɛɫɬɜɭɸɳɟɣ ɪɚɡɪɹɞɭ (ɨɛɵɱɧɨ ɨɫɬɪɢɟ). ȿɫɥɢ ɜ ɬɥɟɸɳɟɦ ɪɚɡɪɹɞɟ ɭɜɟɥɢɱɢɜɚɬɶ ɫɢɥɭ ɬɨɤɚ (ɩɭɬɟɦ ɫɧɢɠɟɧɢɹ ɜɧɟɲɧɟɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɢɥɢ ɩɨɜɵɲɚɹ ɗȾɋ ɢɫɬɨɱɧɢɤɚ ε), ɬɨ ɩɪɢ ɛɨɥɶɲɨɣ ɫɢɥɟ ɬɨɤɚ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɷɥɟɤɬɪɨɞɚɯ ɬɪɭɛɤɢ ɧɚɱɢɧɚɟɬ ɩɚɞɚɬɶ, ɪɚɡɪɹɞ ɛɵɫɬɪɨ ɪɚɡɜɢɜɚɟɬɫɹ, ɩɪɟɜɪɚɳɚɹɫɶ ɜ ɞɭɝɨɜɨɣ. ȼ ɛɨɥɶɲɢɧɫɬɜɟ ɫɥɭɱɚɟɜ ɩɟɪɟɯɨɞ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɫɤɚɱɤɨɦ ɢ ɧɟɪɟɞɤɨ ɜɟɞɟɬ ɤ ɤɨɪɨɬɤɨɦɭ ɡɚɦɵɤɚɧɢɸ. ɍɝɨɥɶɧɚɹ ɞɭɝɚ
ɍɝɨɥɶɧɚɹ ɞɭɝɚ ɢɫɬɨɪɢɱɟɫɤɢ ɢɡɜɟɫɬɧɚ ɫ 1802 ɝ., ɢɡɭɱɟɧɚ, ɩɨɠɚɥɭɣ, ɥɭɱɲɟ ɜɫɟɯ ɞɪɭɝɢɯ, ɩɪɢɱɟɦ ɤɨɧɤɪɟɬɧɨ ɜ ɜɨɡɞɭɯɟ. Ⱦɭɝɨɜɵɟ ɫɜɟɬɢɥɶɧɢɤɢ, ɫɜɟɱɚ əɛɥɨɱɤɨɜɚ, ɩɟɪɜɵɟ ɫɜɚɪɤɢ, ɧɚɜɚɪɢɜɚɧɢɟ ɦɟɬɚɥɥɨɜ ɜɟɥɢɫɶ ɫ ɭɝɨɥɶɧɵɦɢ ɞɭɝɚɦɢ. ɇɨ ɭ ɧɢɯ ɛɵɥ ɛɨɥɶɲɨɣ ɧɟɞɨɫɬɚɬɨɤ: ɨɞɢɧ ɢɡ ɷɥɟɤɬɪɨɞɨɜ ɫɝɨɪɚɥ ɛɵɫɬɪɟɟ ɞɪɭɝɨɝɨ. Ȼɵɥ ɢɡɨɛɪɟɬɟɧ ɪɹɞ ɭɫɬɪɨɣɫɬɜ, ɪɟɝɭɥɢɪɭɸɳɢɯ ɩɨɞɚɱɭ ɭɝɥɟɣ, ɢɯ ɜɵɩɭɫɤɚɥɚ ɩɪɨɦɵɲɥɟɧɧɨɫɬɶ. ɇɨ ɜ ɫɟɪɟɞɢɧɟ 19-ɝɨ ɜɟɤɚ əɛɥɨɱɤɨɜ ɩɪɟɞɥɨɠɢɥ ɩɟɪɟɣɬɢ ɨɬ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɤ ɩɟɪɟɦɟɧɧɨɦɭ: ɭ ɝɟɧɟɪɚɬɨɪɨɜ ɡɚɦɟɧɢɬɶ ɤɨɥɥɟɤɬɨɪ ɧɚ
ɬɨɤɨɫɴɟɦɧɵɟ ɤɨɥɶɰɚ. Ɍɨɤ ɛɭɞɟɬ ɦɟɧɹɬɶ ɡɧɚɤ, ɭɝɥɢ ɛɭɞɭɬ ɝɨɪɟɬɶ ɨɞɢɧɚɤɨɜɨ. ɋ ɷɬɨɝɨ ɦɨɦɟɧɬɚ "ɛɨɪɶɛɚ" ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ (ɨɧ ɢ ɞɨ ɫɢɯ ɩɨɪ ɧɭɠɟɧ ɨɱɟɧɶ ɦɧɨɝɢɦ ɩɨɬɪɟɛɢɬɟɥɹɦ − ɨɬ ɷɥɟɤɬɪɢɱɟɤ ɩɪɢ ɛɨɥɶɲɢɯ I, ɞɨ ɷɥɟɤɬɪɨɧɢɤɢ − ɩɪɢ ɦɚɥɵɯ I) ɫ ɩɟɪɟɦɟɧɧɵɦ (ɟɝɨ ɦɨɠɧɨ ɬɪɚɧɫɩɨɪɬɢɪɨɜɚɬɶ, ɡɧɚɱɢɬ, ɫɬɪɨɢɬɶ ɦɨɳɧɵɟ ɷɥɟɤɬɪɨɫɬɚɧɰɢɢ, ɱɬɨ ɜɵɝɨɞɧɟɟ) ɩɪɨɞɨɥɠɚɥɚɫɶ ɩɪɢɦɟɪɧɨ ɞɨ 20-ɯ ɝɝ. XX ɜ. Ʉɨɧɟɱɧɨ, ɩɨɛɟɞɢɥ ɩɟɪɟɦɟɧɧɵɣ. ɉɥɚɡɦɚ ɭɝɨɥɶɧɨɣ ɞɭɝɢ ɜ ɚɬɦɨɫɮɟɪɟ ɪɚɜɧɨɜɟɫɧɚɹ, ɯɨɬɹ ɩɨ ɟɟ ɞɥɢɧɟ ɬɟɦɩɟɪɚɬɭɪɚ ɦɟɧɹɟɬɫɹ ɛɨɥɟɟ ɱɟɦ ɜ ɞɜɚ ɪɚɡɚ (ɨɬ 12000 ɞɨ ~ 5000Ʉ). Ʉɚɬɨɞɧɨɟ ɩɚɞɟɧɢɟ ɫɧɢɠɚɟɬɫɹ ɜɩɥɨɬɶ ɞɨ 10 ȼ (!), ɚɧɨɞɧɨɟ ɬɨɠɟ ɩɨɪɹɞɤɚ 10 ȼ, ɨɫɬɚɥɶɧɨɟ (ɧɟɫɤɨɥɶɤɨ ɜɨɥɶɬ) ɩɪɢɯɨɞɢɬɫɹ ɧɚ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ. ȼȺɏ ɞɨ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɡɧɚɱɟɧɢɹ ɬɨɤɚ ɩɚɞɚɸɳɚɹ, ɡɚɬɟɦ ɧɚɩɪɹɠɟɧɢɟ ɫɤɚɱɤɨɦ ɭɦɟɧɶɲɚɟɬɫɹ, ɜɨɡɧɢɤɚɟɬ ɲɢɩɟɧɢɟ («ɲɢɩɹɳɚɹ ɞɭɝɚ»), ɢ ȼȺɏ ɫɬɚɧɨɜɢɬɫɹ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ. ɂɧɬɟɪɟɫɧɨ, ɱɬɨ ɤɚɬɨɞ (Ɍɤ ≈ 3500 Ʉ) ɯɨɥɨɞɧɟɟ ɚɧɨɞɚ (Ɍɚ ≈ 4200 Ʉ). §53. ɂɫɤɪɨɜɨɣ ɢ ɤɨɪɨɧɧɵɣ, ȼɑ- ɢ ɋȼɑ- ɪɚɡɪɹɞɵ ɂɫɤɪɨɜɨɣ ɪɚɡɪɹɞ
ɂɫɤɪɨɜɨɣ ɪɚɡɪɹɞ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɢɦɩɭɥɶɫɧɵɣ, ɟɝɨ ɢɡɭɱɚɥɢ ɢ ɞɨ ɩɨɹɜɥɟɧɢɹ ɢɫɬɨɱɧɢɤɨɜ ɬɨɤɚ: ɬɪɟɧɢɟɦ ɡɚɪɹɠɚɥɢ ɤɨɧɞɟɧɫɚɬɨɪɵ ("ɥɟɣɞɟɧɫɤɢɟ ɛɚɧɤɢ"), ɫɨɛɢɪɚɥɢ ɚɬɦɨɫɮɟɪɧɨɟ ɷɥɟɤɬɪɢɱɟɫɬɜɨ ɜ ɩɪɟɞɝɪɨɡɨɜɵɯ ɭɫɥɨɜɢɹɯ. ȼ Ɋɨɫɫɢɢ ɜ XVIII ɜ. ɪɚɛɨɬɚɥɢ Ɇ. Ʌɨɦɨɧɨɫɨɜ ɢ Ƚ. Ɋɢɯɦɚɧ, ɜ Ⱥɦɟɪɢɤɟ ȼ.Ɏɪɚɧɤɥɢɧ. Ɉɧ ɩɪɟɞɥɨɠɢɥ ɩɟɪɜɨɟ ɨɛɴɹɫɧɟɧɢɟ ɷɥɟɤɬɪɢɱɟɫɤɢɦ ɹɜɥɟɧɢɹɦ: ɷɥɟɤɬɪɢɱɟɫɬɜɨ − "ɧɟɜɟɫɨɦɚɹ ɠɢɞɤɨɫɬɶ" (ɜɪɨɞɟ "ɬɟɩɥɨɪɨɞɚ"), ɟɟ ɢɡɛɵɬɨɤ − ɡɧɚɤ (+), ɧɟɞɨɫɬɚɬɨɤ − ɡɧɚɤ (-). ȿɫɥɢ ɫɨɟɞɢɧɢɬɶ ɢɯ ɩɪɨɜɨɞɧɢɤɨɦ, ɬɨ (+) ɩɨɬɟɱɟɬ ɤ (-)... Ɍɚɤ, ɜ ɷɥɟɤɬɪɨɬɟɯɧɢɤɟ ɬɨɤ ɢ ɞɨ ɫɢɯ ɩɨɪ ɬɟɱɟɬ ɨɬ (+) ɤ (-)!.. Ɋɟɚɥɶɧɨɟ ɢɡɭɱɟɧɢɟ ɨɱɟɧɶ ɛɵɫɬɪɨ ɩɪɨɬɟɤɚɸɳɢɯ ɢɫɤɪɨɜɵɯ ɪɚɡɪɹɞɨɜ ɫɬɚɥɨ ɜɨɡɦɨɠɧɨ ɫ ɩɨɹɜɥɟɧɢɟɦ ɤɚɦɟɪ ȼɢɥɶɫɨɧɚ, ɩɪɢɛɨɪɨɜ ɫɤɨɪɨɫɬɧɨɝɨ ɮɨɬɨɝɪɚɮɢɪɨɜɚɧɢɹ, ɤɚɬɨɞɧɵɯ ɨɫɰɢɥɥɨɝɪɚɮɨɜ. Ɉɤɚɡɚɥɨɫɶ, ɱɬɨ ɢɫɤɪɚ ɦɨɠɟɬ ɡɚɝɨɪɚɬɶɫɹ ɜ ɩɥɨɬɧɨɦ (ɞɚɜɥɟɧɢɟ ɩɨɪɹɞɤɚ ɚɬɦɨɫɮɟɪɵ ɢ ɛɨɥɶɲɟ) ɝɚɡɟ ɩɪɢ ɛɨɥɶɲɨɣ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. ɉɟɪɜɢɱɧɚɹ ɥɚɜɢɧɚ ɛɵɫɬɪɨ ɩɨɥɹɪɢɡɭɟɬɫɹ − ɷɥɟɤɬɪɨɧɵ ɨɬɯɨɞɹɬ ɜ ɫɬɨɪɨɧɭ ɚɧɨɞɚ, ɚ ɢɨɧɵ ɩɪɚɤɬɢɱɟɫɤɢ ɫɬɨɹɬ. ɉɪɢ ɨɛɪɚɡɨɜɚɧɢɢ ɥɚɜɢɧɵ ɩɪɨɢɫɯɨɞɢɬ ɦɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɣ ɫ ɛɵɫɬɪɵɦ ɜɵɫɜɟɱɢɜɚɧɢɟɦ, ɮɨɬɨɷɮɮɟɤɬ ɫɨɡɞɚɟɬ ɧɨɜɵɟ ɷɥɟɤɬɪɨɧɵ, ɧɨɜɵɟ ɥɚɜɢɧɵ ɜɛɥɢɡɢ ɨɫɧɨɜɧɨɣ, ɨɧɢ ɜɬɹɝɢɜɚɸɬɫɹ ɜ ɨɫɧɨɜɧɭɸ ɥɚɜɢɧɭ, ɪɚɫɬɟɬ ɟɟ ɨɛɴɟɞɢɧɟɧɧɵɣ ɡɚɪɹɞ, ɪɚɫɬɟɬ ɫɨɡɞɚɜɚɟɦɨɟ ɢɦ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ E. Ʉɨɝɞɚ ɷɬɨ ɩɨɥɟ ȿ ɩɪɢɦɟɪɧɨ ɫɬɚɧɟɬ ɪɚɜɧɵɦ ɜɧɟɲɧɟɦɭ ȿ0, ɜɨɡɧɢɤɚɟɬ ɬɨɧɤɢɣ ɩɪɨɜɨɞɹɳɢɣ ɤɚɧɚɥ − ɫɬɪɢɦɟɪ, ɫɨɟɞɢɧɹɸɳɢɣ ɷɥɟɤɬɪɨɞɵ (ɫɬɪɢɦɟɪ ɦɨɠɟɬ ɛɵɬɶ ɧɚɩɪɚɜɥɟɧ ɤ ɥɸɛɨɦɭ ɷɥɟɤɬɪɨɞɭ ɢɥɢ ɫɪɚɡɭ ɤ ɨɛɨɢɦ). ɋɤɨɪɨɫɬɶ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɫɬɪɢɦɟɪɨɜ (ɛɨɥɟɟ 108 ɫɦ/ɫ) ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ ɫɤɨɪɨɫɬɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɷɥɟɤɬɪɨɧɧɵɯ ɥɚɜɢɧ, ɨɩɪɟɞɟɥɹɟɦɨɣ ɩɨɞɜɢɠɧɨɫɬɶɸ ɷɥɟɤɬɪɨɧɨɜ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɞɥɹ ɪɚɡɜɢɬɢɹ ɫɬɪɢɦɟɪɚ ɧɟɨɛɯɨɞɢɦɨ ɜɵɩɨɥɧɟɧɢɟ ɞɜɭɯ ɭɫɥɨɜɢɣ: 1) ɩɨɥɟ ɥɚɜɢɧɵ ɫɪɚɜɧɢɜɚɟɬɫɹ ɫ ɜɧɟɲɧɢɦ ɩɨɥɟɦ (E ∼ E0); 2) ɢɡɥɭɱɟɧɢɟ ɩɟɪɟɞɧɟɝɨ ɮɪɨɧɬɚ ɥɚɜɢɧɵ ɞɨɫɬɚɬɨɱɧɨ ɞɥɹ ɮɨɬɨɢɨɧɢɡɚɰɢɢ ɧɭɠɧɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɚɬɨɦɨɜ ɝɚɡɚ. ɋɨɛɫɬɜɟɧɧɨ ɫɬɪɢɦɟɪ ɫɥɚɛɨɩɪɨɜɨɞɹɳɢɣ, ɧɨ ɩɟɪɟɞ ɫɚɦɵɦ ɡɚɦɵɤɚɧɢɟɦ ɦɟɠɷɥɟɤɬɪɨɞɧɨɝɨ ɩɪɨɦɟɠɭɬɤɚ ɜɞɨɥɶ ɧɟɝɨ ɩɪɨɯɨɞɢɬ ɜɨɥɧɚ ɫɤɚɱɤɚ ɩɨɬɟɧɰɢɚɥɚ, ɨɛɪɚɡɭɟɬɫɹ ɯɨɪɨɲɨ ɩɪɨɜɨɞɹɳɢɣ ɤɚɧɚɥ, ɢ ɭɠɟ ɩɨ ɧɟɦɭ ɩɪɨɯɨɞɢɬ ɛɨɥɶɲɨɣ ɬɨɤ − ɫɨɛɫɬɜɟɧɧɨ ɢɫɤɪɚ. Ƚɚɡ ɜ ɤɚɧɚɥɟ ɫɢɥɶɧɨ ɧɚɝɪɟɜɚɟɬɫɹ, ɜɨɡɧɢɤɚɟɬ ɫɤɚɱɨɤ ɞɚɜɥɟɧɢɹ − ɡɜɭɤɨɜɚɹ ɜɨɥɧɚ (ɜ ɦɨɥɧɢɢ − ɝɪɨɦ). (ɂɡɥɨɠɟɧɢɟ ɜɟɫɶɦɚ ɭɩɪɨɳɟɧɧɨɟ, ɧɨ ɛɨɥɟɟ ɚɤɤɭɪɚɬɧɨɟ ɧɚɦɧɨɝɨ ɞɥɢɧɧɟɟ, ɚ ɩɨɥɧɨɣ ɹɫɧɨɫɬɢ ɜɫɟ ɪɚɜɧɨ ɧɟɬ...) ȿɫɥɢ ɦɟɠɷɥɟɤɬɪɨɞɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɛɨɥɶɲɨɟ, ɩɨɥɟ ȿ
ɧɟɨɞɧɨɪɨɞɧɨɟ, ɧɚ ɤɨɧɰɟ ɫɬɢɦɟɪɚ ɦɨɠɟɬ ɨɛɪɚɡɨɜɚɬɶɫɹ ɯɨɪɨɲɨ ɩɪɨɜɨɞɹɳɢɣ ɭɱɚɫɬɨɤ - ɥɢɞɟɪ (ɪɢɫ. 8.8), ɱɬɨ ɯɚɪɚɤɬɟɪɧɨ ɞɥɹ ɦɨɥɧɢɣ, ɝɞɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɨɛɪɚɡɭɟɬɫɹ ɧɟɫɤɨɥɶɤɨ ɥɢɞɟɪɨɜ, ɩɨ ɫɭɳɟɫɬɜɭ, ɧɟɫɤɨɥɶɤɨ ɪɚɡɪɹɞɨɜ ɫ ɜɪɟɦɟɧɧɵɦɢ ɫɞɜɢɝɚɦɢ ɜ ɞɟɫɹɬɤɢ ɦɢɥɥɢɫɟɤɭɧɞ. ɂɫɤɪɨɜɨɣ ɪɚɡɪɹɞ ɩɨɥɭɱɢɥ ɩɪɢɦɟɧɟɧɢɟ ɜ ɩɪɨɦɵɲɥɟɧɧɨɫɬɢ, ɷɬɨ ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ "ɷɥɟɤɬɪɨɷɪɨɡɢɨɧɧɵɣ" ɫɩɨɫɨɛ ɨɛɪɚɛɨɬɤɢ ɦɟɬɚɥɥɨɜ, ɡɚɩɚɬɟɧɬɨɜɚɧɧɵɣ ɜ ɪɹɞɟ ɫɬɪɚɧ. Ȼɨɥɟɟ ɩɨɞɪɨɛɧɨ ɨɛ ɢɫɤɪɨɜɨɦ ɪɚɡɪɹɞɟ ɫɦ. [34]. Ʉɨɪɨɧɧɵɣ ɪɚɡɪɹɞ.
Ʉɨɪɨɧɧɵɣ ɪɚɡɪɹɞ − ɫɚɦɨɫɬɨɹɬɟɥɶɧɵɣ ɪɚɡɪɹɞ, Ɋɢɫ. 8.8. ɋɯɟɦɚ ɥɢɞɟɪɚ, ɩɪɨɪɚɫɬɚɸɳɟɝɨ ɨɬ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɨɫɬɪɢɹ ɩɨ ɩɭɬɢ, ɩɪɨɥɨɠɟɧɧɨɦɭ ɤɨɬɨɪɵɣ ɜɨɡɧɢɤɚɟɬ ɬɨɥɶɤɨ ɩɪɢ ɫɬɪɢɦɟɪɚɦɢ, ɤɨɬɨɪɵɟ, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɜɬɹɝɢɜɚɸɬ ɭɫɥɨɜɢɢ ɨɱɟɧɶ ɛɨɥɶɲɨɣ ɥɚɜɢɧɵ ɧɟɨɞɧɨɪɨɞɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɯɨɬɹ ɛɵ ɭ ɨɞɧɨɝɨ ɢɡ ɷɥɟɤɬɪɨɞɨɜ (ɨɫɬɪɢɟ − ɩɥɨɫɤɨɫɬɶ, ɧɢɬɶ − ɩɥɨɫɤɨɫɬɶ, ɞɜɟ ɧɢɬɢ, ɧɢɬɶ ɜ ɰɢɥɢɧɞɪɟ ɛɨɥɶɲɨɝɨ ɪɚɞɢɭɫɚ ɢ ɬ.ɞ.). ɍɫɥɨɜɢɹ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɢ ɪɚɡɜɢɬɢɹ ɤɨɪɨɧɵ ɪɚɡɥɢɱɧɵɟ ɩɪɢ ɪɚɡɧɨɣ ɩɨɥɹɪɧɨɫɬɢ "ɨɫɬɪɢɹ" (ɧɚɡɨɜɟɦ ɬɚɤ ɷɥɟɤɬɪɨɞ, ɜɛɥɢɡɢ ɤɨɬɨɪɨɝɨ ȿ ɫɢɥɶɧɨ ɧɟɨɞɧɨɪɨɞɧɨ). ȿɫɥɢ ɨɫɬɪɢɟ − ɤɚɬɨɞ (ɤɨɪɨɧɚ "ɨɬɪɢɰɚɬɟɥɶɧɚɹ"), ɬɨ ɡɚɠɢɝɚɧɢɟ ɤɨɪɨɧɵ ɩɨ ɫɭɳɟɫɬɜɭ ɩɪɨɢɫɯɨɞɢɬ ɬɚɤ ɠɟ, ɤɚɤ ɜ ɬɥɟɸɳɟɦ ɪɚɡɪɹɞɟ, ɬɨɥɶɤɨ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɟɪɜɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ Ɍɚɭɧɫɟɧɞɚ α (ɬɚɤ ɤɚɤ ɩɨɥɟ ȿ ɫɢɥɶɧɨ ɧɟɨɞɧɨɪɨɞɧɨɟ) ɜ ɜɨɡɞɭɯɟ (ɩɪɚɤɬɢɱɟɫɤɢ ɜɚɠɧɵɣ ɫɥɭɱɚɣ) ɧɚɞɨ ɭɱɢɬɵɜɚɬɶ ɩɪɢɥɢɩɚɧɢɟ (ɧɚɥɢɱɢɟ ɤɢɫɥɨɪɨɞɚ), ɬɚɤ ɱɬɨ x1
³ (α ( x) − a
n
( x))dx = ln(1 + γ −1 ) ,
(8.26)
0
ɝɞɟ x1 − ɪɚɫɫɬɨɹɧɢɟ ɞɨ ɬɨɱɤɢ, ɜ ɤɨɬɨɪɨɣ ȿ ɭɠɟ ɬɚɤ ɦɚɥɨ, ɱɬɨ ɢɨɧɢɡɚɰɢɹ ɧɟ ɩɪɨɢɫɯɨɞɢɬ: E ≈ 0. ȼ ɬɚɤɨɣ ɤɨɪɨɧɟ ɟɫɬɶ ɫɜɟɱɟɧɢɟ ɬɨɥɶɤɨ ɞɨ ɪɚɫɫɬɨɹɧɢɹ, ɬɨɠɟ ɩɪɢɦɟɪɧɨ, ɪɚɜɧɨɝɨ x1. ȿɫɥɢ "ɨɫɬɪɢɟ" - ɚɧɨɞ (ɤɨɪɨɧɚ "ɩɨɥɨɠɢɬɟɥɶɧɚɹ"), ɬɨ ɤɚɪɬɢɧɚ ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɹɟɬɫɹ: ɨɤɨɥɨ ɨɫɬɪɢɹ ɧɚɛɥɸɞɚɸɬɫɹ ɫɜɟɬɹɳɢɟɫɹ ɧɢɬɢ, ɤɚɤ ɛɵ ɪɚɡɛɟɝɚɸɳɢɟɫɹ ɨɬ ɨɫɬɪɢɹ (ɪɢɫ. 8.9). ȼɟɪɨɹɬɧɨ, ɷɬɨ ɫɬɪɢɦɟɪɵ ɨɬ ɥɚɜɢɧ, ɡɚɪɨɠɞɟɧɧɵɯ ɜ ɨɛɴɟɦɟ ɮɨɬɨɷɥɟɤɬɪɨɧɚɦɢ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɢ ɤɪɢɬɟɪɢɣ ɡɚɠɢɝɚɧɢɹ ɞɪɭɝɨɣ − ɬɚɤɨɣ, ɤɚɤ ɞɥɹ ɨɛɪɚɡɨɜɚɧɢɹ ɫɬɪɢɦɟɪɚ. ȼ ɥɸɛɨɦ ɤɨɪɨɧɧɨɦ ɪɚɡɪɹɞɟ ɫɭɳɟɫɬɜɟɧɧɚ ɧɟɨɞɧɨɪɨɞɧɨɫɬɶ ȿ, ɬ.ɟ. ɤɨɧɤɪɟɬɧɚɹ ɝɟɨɦɟɬɪɢɹ ɷɥɟɤɬɪɨɞɨɜ. ɉɨɥɧɨɣ ɹɫɧɨɫɬɢ ɜ ɦɟɯɚɧɢɡɦɟ ɝɨɪɟɧɢɹ ɪɚɡɪɹɞɚ ɧɟɬ, ɧɨ ɷɬɨ ɧɟ ɦɟɲɚɟɬ ɩɪɢɦɟɧɟɧɢɸ ɤɨɪɨɧɧɵɯ ɪɚɡɪɹɞɨɜ ɜ ɩɪɨɦɵɲɥɟɧɧɨɫɬɢ (ɷɥɟɤɬɪɨɮɢɥɶɬɪɵ); ɜ ɫɱɟɬɱɢɤɚɯ Ƚɟɣɝɟɪ-Ɇɸɥɥɟɪɚ ɬɨɠɟ ɪɚɛɨɬɚɟɬ ɤɨɪɨɧɧɵɣ ɪɚɡɪɹɞ. ɇɨ ɨɧ ɛɵɜɚɟɬ ɢ ɜɪɟɞɟɧ, ɧɚɩɪɢɦɟɪ, ɧɚ ɜɵɫɨɤɨɜɨɥɶɬɧɵɯ ɥɢɧɢɹɯ (Ʌȿɉ) ɤɨɪɨɧɧɵɟ ɪɚɡɪɹɞɵ ɫɨɡɞɚɸɬ
ɡɚɦɟɬɧɵɟ ɩɨɬɟɪɢ. Ʉɨɪɨɧɵ ɛɵɜɚɸɬ ɩɪɟɪɵɜɢɫɬɵɦɢ ɫ ɪɚɡɥɢɱɧɵɦɢ − ɭ ɱɚɫɬɨɬɚɦɢ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɞɨ 104 Ƚɰ, ɭ ɨɬɪɢɰɚɬɟɥɶɧɵɯ − ɞɨ 106 Ƚɰ − ɚ ɷɬɨ ɪɚɞɢɨɞɢɚɩɚɡɨɧ, ɩɨɦɟɯɢ. Ɇɟɯɚɧɢɡɦ ɩɪɟɪɵɜɢɫɬɨɫɬɢ ɪɚɡɪɹɞɚ ɭ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɤɨɪɨɧɵ, ɜɢɞɢɦɨ, ɫɜɹɡɚɧ ɫ ɬɟɦ, ɱɬɨ ɷɥɟɤɬɪɨɧɵ Ɋɢɫ. 8.9. ɋɬɪɢɦɟɪ ɨɬ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɫɬɟɪɠɧɹ ɞɢɚɦɟɬɪɨɦ 2 ɫɦ ɧɚ ɩɥɨɫɤɨɫɬɶ ɧɚ ɪɚɫɫɬɨɹɧɢɢ 150 ɫɦ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɧɚɩɪɹɠɟɧɢɢ 125 ɫɬɪɢɦɟɪɨɜ ɜɬɹɝɢɜɚɸɬɫɹ ɜ ɚɧɨɞ, ɤȼɬ; ɫɩɪɚɜɚ - ɪɚɫɱɟɬ, ɩɪɨɜɟɞɟɧɵ ɷɤɜɢɩɨɬɟɧɰɢɚɥɶɧɵɟ ɩɨɜɟɪɯɧɨɫɬɢ, ɰɢɮɪɵ ɨɤɨɥɨ ɤɪɢɜɵɯ - ɞɨɥɢ ɨɬ ɩɪɢɥɨɠɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ, ɩɨɥɨɠɢɬɟɥɶɧɵɟ ɨɬɫɱɢɬɚɧɧɵɟ ɨɬ ɩɥɨɫɤɨɫɬɢ; ɫɥɟɜɚ - ɮɨɬɨɝɪɚɮɢɹ ɫɬɪɢɦɟɪɨɜ ɜ ɬɟɯ ɠɟ ɨɫɬɨɜɵ ɷɤɪɚɧɢɪɭɸɬ ɭɫɥɨɜɢɹɯ ɚɧɨɞ, ɧɨɜɵɟ ɫɬɪɢɦɟɪɵ ɧɟ ɦɨɝɭɬ ɫɨɡɞɚɜɚɬɶɫɹ, ɩɨɤɚ ɨɫɬɨɜɵ ɧɟ ɭɣɞɭɬ ɤ ɤɚɬɨɞɭ. Ɍɨɝɞɚ ɚɧɨɞ "ɨɬɤɪɨɟɬɫɹ" ɢ ɤɚɪɬɢɧɚ ɩɨɜɬɨɪɢɬɫɹ. Ⱦɥɹ ɨɬɪɢɰɚɬɟɥɶɧɨɣ ɤɨɪɨɧɵ ɫɭɳɟɫɬɜɟɧɧɨ ɧɚɥɢɱɢɟ ɜ ɜɨɡɞɭɯɟ ɤɢɫɥɨɪɨɞɚ − ɧɟɦɧɨɝɨ ɨɬɨɣɞɹ ɨɬ ɤɨɪɨɧɵ ɷɥɟɤɬɪɨɧɵ ɩɪɢɥɢɩɚɸɬ ɤ ɤɢɫɥɨɪɨɞɭ, ɨɬɪɢɰɚɬɟɥɶɧɵɟ ɢɨɧɵ ɷɤɪɚɧɢɪɭɸɬ ɨɫɬɪɢɟ, ɢ ɩɨɤɚ ɨɧɢ ɧɟ ɭɣɞɭɬ ɤ ɚɧɨɞɭ, ɪɚɡɪɹɞ ɩɪɟɤɪɚɳɚɟɬɫɹ. ɉɨɫɥɟ ɭɯɨɞɚ ɢɨɧɨɜ ɪɚɡɪɹɞ ɜɨɡɧɢɤɧɟɬ ɜɧɨɜɶ ɢ ɤɚɪɬɢɧɚ ɩɨɜɬɨɪɢɬɫɹ. ȼɵɫɨɤɨɱɚɫɬɨɬɧɵɟ (ȼɑ) ɪɚɡɪɹɞɵ
~ ~ ȼ ȼɑ-ɞɢɚɩɚɡɨɧɟ (10-1 ÷ 102 ɆȽɰ) ɩɪɢɧɹɬɨ ɪɚɡɥɢɱɚɬɶ E ɢ H ɬɢɩɵ ɪɚɡɪɹɞɨɜ − ɩɨ ɨɩɪɟɞɟɥɹɸɳɟɦɭ ɜɟɤɬɨɪɭ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ȼ ɥɚɡɟɪɧɨɣ ɬɟɯɧɢɤɟ ~ ɢɫɩɨɥɶɡɭɸɬ E (ɟɦɤɨɫɬɧɵɟ) ɪɚɡɪɹɞɵ, ɩɨɦɟɳɚɹ ɪɚɛɨɱɢɣ ɨɛɴɟɦ ɜ ɤɨɧɞɟɧɫɚɬɨɪ, ɤ ɩɥɚɫɬɢɧɚɦ ɤɨɬɨɪɨɝɨ ɩɨɞɜɨɞɹɬ ȼɑ-ɧɚɩɪɹɠɟɧɢɟ (ɩɥɚɫɬɢɧɵ ɢɧɨɝɞɚ ɩɪɹɦɨ ɜɜɨɞɹɬ ɜ ɨɛɴɟɦ, ɢɧɨɝɞɚ ɢɡɨɥɢɪɭɸɬ ɞɢɷɥɟɤɬɪɢɤɨɦ − ɨɛɵɱɧɨ ɫɬɟɤɥɨɦ). Ɇɨɳɧɨɫɬɢ ɷɬɢɯ ɪɚɡɪɹɞɨɜ ɧɟɛɨɥɶɲɢɟ (ɢɯ ɡɚɞɚɱɚ ɩɨɞɞɟɪɠɚɬɶ ɢɨɧɢɡɚɰɢɸ), ɧɨ ~ E ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɜɟɥɢɤɢ − ɞɨ ɞɟɫɹɬɤɨɜ ɤɷȼ. ɉɪɢɦɟɧɟɧɢɟ ȼɑ ɢɧɞɭɤɰɢɨɧɧɵɯ ɩɨɥɟɣ Ɋɢɫ. 8.10. ɂɧɞɭɤɰɢɨɧɧɵɣ ɪɚɡɪɹɞ ɜ ɬɪɭɛɤɟ ɪɚɞɢɭɫɨɦ R, ɜɫɬɚɜɥɟɧɧɨɣ ɜ ɞɥɢɧɧɵɣ ɫɨɥɟɧɨɢɞ; r0 - ɪɚɞɢɭɫ ɩɥɚɡɦɵ, ɫɩɪɚɜɚ ~ ( H -ɩɨɥɟɣ) ɭɠɟ ɫ ɤɨɧɰɚ – ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɩɨ ɪɚɞɢɭɫɭ 40-ɯ ɝ. ɫɬɚɥɨ ɜɟɫɶɦɚ ɲɢɪɨɤɢɦ, ɯɨɬɹ, ɜ ɨɫɧɨɜɧɨɦ, ɜ ɜɢɞɟ ȼɑ-ɩɟɱɟɣ. ȼɟɡɞɟ, ɝɞɟ ɧɭɠɧɨ ɱɢɫɬɨɟ ɬɟɩɥɨ ɢ
~ ɟɫɬɶ ɩɪɨɜɨɞɹɳɚɹ ɫɪɟɞɚ, H ɩɨɥɹ ɧɟɡɚɦɟɧɢɦɵ. ɗɬɨ ɢ ɩɪɨɢɡɜɨɞɫɬɜɨ ɩɨɥɭɩɪɨɜɨɞɧɢɤɨɜɵɯ ɦɚɬɟɪɢɚɥɨɜ, ɢ ɡɨɧɧɚɹ ɩɥɚɜɤɚ ɱɢɫɬɵɯ ɦɟɬɚɥɥɨɜ, ɢ ɫɜɟɪɯɱɢɫɬɵɟ ɯɢɦɢɱɟɫɤɢɟ ɫɨɟɞɢɧɟɧɢɹ ɢ ɞɚɠɟ ɛɵɬɨɜɵɟ ɩɟɱɢ. ɉɪɚɜɞɚ, ɜ ɷɬɢɯ ɭɫɬɪɨɣɫɬɜɚɯ ɩɨɱɬɢ ɧɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɫɨɝɥɚɫɨɜɚɧɢɹ ɝɟɧɟɪɚɬɨɪɚ ɢ ɧɚɝɪɭɡɤɢ − ɫɨɨɬɧɨɲɟɧɢɟ ɪɟɚɤɬɢɜɧɨɝɨ ɢ ɚɤɬɢɜɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɧɚɝɪɭɡɤɢ ɦɟɧɹɟɬɫɹ ɦɚɥɨ. Ⱥ ɜɨɬ ɜ ɪɚɡɪɹɞɚɯ ɞɟɥɨ ɫɥɨɠɧɟɟ: ɢɡɦɟɧɟɧɢɟ ɩɚɪɚɦɟɬɪɨɜ ɫɪɟɞɵ ɪɚɡɪɹɞɚ (ɫɨɩɪɨɬɢɜɥɟɧɢɟ, ɫɚɦɨɢɧɞɭɤɰɢɹ, ɜɡɚɢɦɨɢɧɞɭɤɰɢɹ − ɫɜɹɡɶ ɫ ɢɧɞɭɤɬɨɪɨɦ) ɦɨɝɭɬ ɦɟɧɹɬɶɫɹ ɜ ɲɢɪɨɤɢɯ ɩɪɟɞɟɥɚɯ. Ɉɛɵɱɧɨ ɢɧɞɭɤɬɨɪ − ɤɚɬɭɲɤɚ (ɛɵɜɚɟɬ ɢ ɨɞɢɧ ɜɢɬɨɤ!), ɜɧɭɬɪɢ ɤɨɬɨɪɨɣ ɢ ɩɪɨɢɫɯɨɞɢɬ ɪɚɡɪɹɞ (ɪɢɫ. 8.10). ~ ~ ɉɟɪɟɦɟɧɧɨɟ H ɩɨɥɟ ɧɚɩɪɚɜɥɟɧɨ ɜɞɨɥɶ ɨɫɢ ɤɚɬɭɲɤɢ, ɩɨɥɟ E ɚɤɫɢɚɥɶɧɨ ɤ ~ ɧɟɣ. Ⱦɥɹ ɩɨɞɞɟɪɠɚɧɢɹ ɪɚɡɪɹɞɚ ɧɭɠɧɨɟ E ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɶɲɟ, ɱɟɦ ɞɥɹ ɟɝɨ ɡɚɠɢɝɚɧɢɹ. ɉɨɷɬɨɦɭ ɨɛɵɱɧɨ ɜɜɨɞɹɬ ɜ ɨɛɴɟɦ ɬɨɧɤɢɣ ɦɟɬɚɥɥɢɱɟɫɤɢɣ ɷɥɟɤɬɪɨɞ, ɨɧ ɪɚɡɨɝɪɟɜɚɟɬɫɹ, ɞɚɟɬ ɬɟɪɦɨɷɥɟɤɬɪɨɧɵ (ɢɧɨɝɞɚ ɱɚɫɬɢɱɧɨ ɢɫɩɚɪɹɟɬɫɹ), ɢɧɢɰɢɢɪɭɟɬ ɪɚɡɪɹɞ, ɩɨɫɥɟ ɱɟɝɨ ɟɝɨ ɭɞɚɥɹɸɬ. ȼɨ ɜɪɟɦɹ ɪɚɛɨɬɵ ɦɨɳɧɨɫɬɶ ɜɜɨɞɢɬɫɹ ɩɨɬɨɤɨɦ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɷɧɟɪɝɢɢ: <S> = (ɫ/4π)<ȿɇ> ,
(8.27)
ɚ ɨɬɜɨɞɢɬɫɹ ɱɚɳɟ ɜɫɟɝɨ ɩɨɬɨɤɨɦ ɝɚɡɚ (ɨɧ ɢɨɧɢɡɭɟɬɫɹ ɢ ɭɧɨɫɢɬ ɷɧɟɪɝɢɸ). ɇɨ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ ɷɧɟɪɝɢɹ ɩɪɨɧɢɤɚɟɬ ɜ ɩɥɚɡɦɭ (ɩɪɨɜɨɞɧɢɤ) ɧɚ ɝɥɭɛɢɧɭ ɯ, ɫɩɚɞɚɹ ɩɨ ɷɤɫɩɨɧɟɧɬɟ ɟɯɪ(-ɯ/δ), ɝɞɟ δ − ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ ɫɤɢɧɫɥɨɣ, ɢ ɟɝɨ ɭɫɥɨɜɢɥɢɫɶ ɫɱɢɬɚɬɶ ɝɥɭɛɢɧɨɣ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɩɨɬɨɤɚ:
δ2 = ɫ2/(2πσω) ,
(8.28)
ɝɞɟ σ − ɩɪɨɜɨɞɢɦɨɫɬɶ ɩɪɨɜɨɞɧɢɤɚ, ω − ɱɚɫɬɨɬɚ ȼɑ ɩɨɥɹ. Ɉɱɟɜɢɞɧɨ, ɪɟɠɢɦ ɪɚɛɨɬɵ ɭɫɬɚɧɨɜɤɢ ɡɚɜɢɫɢɬ ɨɬ ɫɨɨɬɧɨɲɟɧɢɹ R ɢ ɜɟɥɢɱɢɧɵ δ. ȿɫɥɢ δ < R, ɬɨ ɷɧɟɪɝɢɹ ɩɨɝɥɨɳɚɟɬɫɹ, ɜ ɫɥɨɟ ɬɨɥɳɢɧɨɣ δ, ɨɛɪɚɡɭɹ ɩɪɨɜɨɞɹɳɢɣ ɰɢɥɢɧɞɪ. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨ ɪɚɞɢɭɫɭ ɬɟɦɩɟɪɚɬɭɪɵ Ɍ ɢ ɩɪɨɜɨɞɢɦɨɫɬɢ σ ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɚ ɪɢɫ. 8.11, ɩɨ ɫɭɳɟɫɬɜɭ, ɷɬɨ ɩɨɥɧɵɣ ɚɧɚɥɨɝ ɤɚɧɚɥɨɜɨɣ ɦɨɞɟɥɢ ɞɭɝɢ, ɟɟ ɧɚɡɵɜɚɸɬ "ɦɨɞɟɥɶɸ ɦɟɬɚɥɥɢɱɟɫɤɨɝɨ ɰɢɥɢɧɞɪɚ". ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɪɟɚɥɶɧɨ ɦɨɠɧɨ ɭɩɪɚɜɥɹɬɶ ɞɚɜɥɟɧɢɟɦ p (ɠɟɥɚɬɟɥɶɧɨ ɩɨɛɨɥɶɲɟ!) ɢ ɩɨɬɨɤɨɦ <ȿɇ>, ɨɩɪɟɞɟɥɹɟɦɵɦ
Ɋɢɫ. 8.11. ɋɯɟɦɚɬɢɱɟɫɤɢɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨ ɪɚɞɢɭɫɭ ɬɟɦɩɟɪɚɬɭɪɵ (ɚ), ɩɪɨɜɨɞɢɦɨɫɬɢ (ɛ) ɢ ɞɠɨɭɥɟɜɚ ɬɟɩɥɚ (ɜ) ɜ ɢɧɞɭɤɰɢɨɧɧɨɦ ɪɚɡɪɹɞɟ; ɲɬɪɢɯɨɜɚɹ ɥɢɧɢɹ - ɡɚɦɟɧɚ σ (r) ɫɬɭɩɟɧɶɤɨɣ ɜ ɦɨɞɟɥɢ ɦɟɬɚɥɥɢɱɟɫɤɨɝɨ ɰɢɥɢɧɞɪɚ, J – ɬɟɩɥɨɜɨɣ ɩɨɬɨɤ, S0 ɩɨɬɨɤ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɷɧɟɪɝɢɢ, δ - ɬɨɥɳɢɧɚ ɫɤɢɧɫɥɨɹ
ɚɦɩɟɪɜɢɬɤɚɦɢ: <ȿɇ> ~ IN (ɝɞɟ I − ɬɨɤ, N − ɱɢɫɥɨ ɜɢɬɤɨɜ ɧɚ ɟɞɢɧɢɰɭ ɞɥɢɧɵ ɢɧɞɭɤɬɨɪɚ). ɋȼɑ-ɪɚɡɪɹɞɵ
Ɍɚɤɢɟ ɪɚɡɪɹɞɵ ɧɚɱɚɥɢ ɩɪɢɦɟɧɹɬɶ ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɜ ɦɨɞɟɥɹɯ ɬɟɪɦɨɹɞɟɪɧɵɯ ɭɫɬɚɧɨɜɨɤ (ɧɟ ɨɱɟɧɶ ɭɫɩɟɲɧɨ ɧɚ ɫɬɚɞɢɢ ɪɚɡɪɹɞɚ) ɢ ɜ ɩɥɚɡɦɨɯɢɦɢɱɟɫɤɢɯ ɭɫɬɚɧɨɜɤɚɯ. ɉɪɢ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬɚɯ (ɝɢɝɨɝɟɪɰɵ) ɫɭɳɟɫɬɜɟɧɧɵ ɝɟɨɦɟɬɪɢɱɟɫɤɢɟ ɫɨɨɬɧɨɲɟɧɢɹ, ɜɚɠɧɵ ɩɪɟɥɨɦɥɟɧɢɹ ɢ ɨɬɪɚɠɟɧɢɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɜɨɥɧɵ. ɋȼɑɷɧɟɪɝɢɹ ɜɟɫɶɦɚ ɞɨɪɨɝɚɹ, ɧɨ ɨɤɚɡɵɜɚɟɬɫɹ, ɱɬɨ ɢɫɩɨɥɶɡɭɹ ɪɚɡɪɹɞ ɜ ɋȼɑɩɥɚɡɦɨɬɪɨɧɚɯ ɦɨɠɧɨ ɜɜɟɫɬɢ ɜ ɩɥɚɡɦɭ ɞɨ 90% ɋȼɑ ɷɧɟɪɝɢɢ [35]. ɇɚɢɛɨɥɟɟ ɢɫɩɨɥɶɡɭɟɦɵɟ ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɫɯɟɦɵ ɋȼɑ-ɪɚɡɪɹɞɨɜ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 8.12. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜ ɫɯɟɦɟ (ɪɢɫ. 8.12) ɩɨɱɬɢ ɜɫɹ ɦɨɳɧɨɫɬɶ ɩɨɝɥɨɳɚɟɬɫɹ ɜ ɫɬɪɭɟ ɝɚɡɚ (ɩɪɟɜɪɚɳɚɸɳɟɣɫɹ ɜ ɩɥɚɡɦɭ): ɜɧɟɲɧɹɹ ɩɨɜɟɪɯɧɨɫɬɶ ɫɬɨɥɛɚ ɩɥɚɡɦɵ ɢ ɜɧɭɬɪɟɧɧɹɹ ɩɨɜɟɪɯɧɨɫɬɶ ɜɨɥɧɨɜɨɞɚ ɨɛɪɚɡɭɸɬ ɤɨɚɤɫɢɚɥɶɧɭɸ ɥɢɧɢɸ ɞɥɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɜɨɥɧɵ − ɷɧɟɪɝɢɹ ɜ ɫɬɨɥɛ ɜɬɟɤɚɟɬ ɩɨ ɪɚɞɢɭɫɭ (ɤɚɤ ɜ ȼɑ-ɪɚɡɪɹɞɟ). ɂɧɬɟɪɟɫɧɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɦɟɯɚɧɢɡɦ ɩɪɨɛɨɹ ɜ ɋȼɑ (ɧɨ ɧɟ ȼɑ!) ɞɢɚɩɚɡɨɧɟ ɩɨɯɨɠ ɧɚ ɦɟɯɚɧɢɡɦ ɩɪɨɛɨɹ ɜ ɬɥɟɸɳɟɦ ɪɚɡɪɹɞɟ (ɨɛɪɚɡɨɜɚɧɢɟ ɥɚɜɢɧ, ɫɬɚɰɢɨɧɚɪɧɵɣ ɤɪɢɬɟɪɢɣ ɩɪɨɛɨɹ (8.19), ɤɪɢɜɵɟ ɡɚɜɢɫɢɦɨɫɬɢ Ɋɢɫ. 8.12. ɋɯɟɦɚ ɪɚɡɪɹɞɚ ɜ ɜɨɥɧɨɜɨɞɟ, ɩɨɞɞɟɪɠɢɜɚɟɦɨɝɨ H01 ɜɨɥɧɨɣ: ɚ) ɫɟɱɟɧɢɟ ɜɨɥɧɨɜɨɞɚ E = f(p) - ɚɧɚɥɨɝɢ ɤɪɢɜɵɯ ɉɚɲɟɧɚ, ɞɢɚɦɟɬɪɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɶɸ ɬɪɭɛɤɢ, ɩɥɚɡɦɚ ɡɚɬɟɧɟɧɚ; ɫɪɚɜɧɢɦɨɫɬɶ ɩɨɪɨɝɨɜɵɯ ɡɧɚɱɟɧɢɣ ɛ) ɪɚɫɩɪɟɞɟɥɟɧɢɟ ȿ ɜɞɨɥɶ ɲɢɪɨɤɨɣ ɫɬɟɧɤɢ ɜɨɥɧɨɜɨɞɚ ȿ/p), ɨ ɧɟɦ ɩɨɞɪɨɛɧɨ ɦɨɠɧɨ ɩɪɨɱɢɬɚɬɶ ɜ [33]. Ɉɩɬɢɱɟɫɤɢɣ ɩɪɨɛɨɣ
Ɉɩɬɢɱɟɫɤɢɣ ɩɪɨɛɨɣ − ɥɚɡɟɪɧɚɹ ɢɫɤɪɚ, ɫɚɦɵɣ ɦɨɥɨɞɨɣ ɜɢɞ ɝɚɡɨɜɨɝɨ ɪɚɡɪɹɞɚ. ȼɩɟɪɜɵɟ ɧɚɛɥɸɞɚɥɫɹ ɜ 1963ɝ. ɜ ɮɨɤɭɫɟ ɥɭɱɚ ɝɢɝɚɧɬɫɤɨɝɨ ɪɭɛɢɧɨɜɨɝɨ ɥɚɡɟɪɚ ɫ ɦɨɳɧɨɫɬɶɸ 30 Ɇȼɬ ɞɥɢɬɟɥɶɧɨɫɬɶɸ ɢɦɩɭɥɶɫɚ 3⋅10-4 ɫ, ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ ȿ ≈ 6⋅106 ȼ/ɫɦ. əɜɥɟɧɢɟ ɛɵɥɨ ɧɟɨɞɧɨɡɧɚɱɧɵɦ, ɩɪɢɜɥɟɤɥɨ ɲɢɪɨɤɨɟ ɜɧɢɦɚɧɢɟ ɢ ɭɠɟ ɢɡɭɱɟɧɨ ɧɟ ɯɭɠɟ ɞɪɭɝɢɯ ɪɚɡɪɹɞɨɜ. Ʉ ɥɚɡɟɪɧɨɣ ɢɫɤɪɟ ɩɪɢɦɟɧɢɦ ɧɟɫɬɚɰɢɨɧɚɪɧɵɣ ɤɪɢɬɟɪɢɣ ɩɪɨɛɨɹ (8.17), ɩɪɢɱɟɦ ɪɨɥɶ ɩɨɬɟɪɶ ɷɥɟɤɬɪɨɧɨɜ Ya ɢ Yd ɦɨɠɟɬ ɞɚɠɟ ɨɤɚɡɚɬɶɫɹ ɧɟ ɫɭɳɟɫɬɜɟɧɧɨɣ − ɜɪɟɦɹ ɨɱɟɧɶ ɦɚɥɨ, ɜɫɟ ɨɩɪɟɞɟɥɹɟɬ ɫɨɡɞɚɧɢɟ ɷɥɟɤɬɪɨɧɨɜ, ɥɚɜɢɧ. ɇɨ ɜɨɬ "ɡɚɬɪɚɜɨɱɧɵɣ" ɷɥɟɤɬɪɨɧ ɦɨɠɟɬ ɪɨɞɢɬɶɫɹ ɜ ɪɟɡɭɥɶɬɚɬɟ ɦɧɨɝɨɮɨɬɨɧɧɨɝɨ ɮɨɬɨɷɮɮɟɤɬɚ (ɩɨ ɫɭɳɟɫɬɜɭ ɤɜɚɧɬɨɜɨɝɨ ɹɜɥɟɧɢɹ). ɂɧɬɟɪɟɫɧɨ, ɱɬɨ ɟɫɬɶ ɛɨɥɶɲɨɟ ɫɯɨɞɫɬɜɨ ɩɪɨɰɟɫɫɨɜ ɩɪɨɛɨɹ ɜ ɨɩɬɢɱɟɫɤɨɦ ɢ ɋȼɑ ɞɢɚɩɚɡɨɧɚɯ − ɧɚɩɪɢɦɟɪ, ɪɚɫɱɟɬɵ ɩɨɪɨɝɨɜ ɩɪɨɛɨɹ ɢ ɫɪɚɜɧɟɧɢɟ ɢɯ ɫ ɷɤɫɩɟɪɢɦɟɧɬɨɦ. Ɋɚɡɜɢɬɢɟ ɥɚɡɟɪɨɜ ɢ ɩɨɜɵɲɟɧɢɟ ɢɯ ɦɨɳɧɨɫɬɢ ɩɪɢɜɟɥɨ ɤ ɬɨɦɭ, ɱɬɨ ɟɳɟ ɜ 1976ɝ. ɭ ɧɚɫ ɫɦɨɝɥɢ ɡɚɠɟɱɶ "ɢɫɤɪɭ" ɜ ɜɨɡɞɭɯɟ ɞɥɢɧɧɨɣ 8 ɦ, ɚ ɪɟɤɨɪɞɧɵɟ ɞɥɢɧɵ ɛɵɥɢ ɛɨɥɶɲɟ ɞɟɫɹɬɤɚ ɦɟɬɪɨɜ.
ɋɩɢɫɨɤ ɰɢɬɢɪɨɜɚɧɧɨɣ ɥɢɬɟɪɚɬɭɪɵ. 1. Ɋɨɦɚɧɨɜɫɤɢɣ Ɇ.Ʉ. ɗɥɟɦɟɧɬɚɪɧɵɟ ɩɪɨɰɟɫɫɵ ɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɱɚɫɬɢɰ ɜ ɩɥɚɡɦɟ. – Ɇ: ɂɡɞ. ɆɂɎɂ, 1984. 2. Zhdanov S.K., Kurnaev V.A., Pisarev A.A. Lectures on Plasma Physics. M: MEPhI, 1998. 3. Ⱥɥɟɤɫɚɧɞɪɨɜ Ⱥ.Ɏ., Ɋɭɯɚɞɡɟ Ⱥ.Ⱥ. Ʌɟɤɰɢɢ ɩɨ ɷɥɟɤɬɪɨɞɢɧɚɦɢɤɟ ɩɥɚɡɦɨɩɨɞɨɛɧɵɯ ɫɪɟɞ. Ɇ: ɂɡɞ. ɆȽɍ, 1999. 4. Ɏɨɪɬɨɜ ȼ.ȿ., əɤɭɛɨɜ ɂ.Ɍ. ɇɟɢɞɟɚɥɶɧɚɹ ɩɥɚɡɦɚ. Ɇ: ɗɧɟɪɝɨɚɬɨɦɢɡɞɚɬ, 1994. 5. Ɏɢɡɢɱɟɫɤɚɹ ɷɧɰɢɤɥɨɩɟɞɢɹ \ɩɨɞ ɪɟɞ. ɉɪɨɯɨɪɨɜɚ Ⱥ.Ɇ. \, ɬ.2. Ɇ: ɋɨɜɟɬɫɤɚɹ ɷɧɰɢɤɥɨɩɟɞɢɹ, 1990. 6. Ɏɢɡɢɱɟɫɤɢɟ ɜɟɥɢɱɢɧɵ. ɋɩɪɚɜɨɱɧɢɤ\ɩɨɞ ɪɟɞ. Ƚɪɢɝɨɪɶɟɜɚ ɂ.ɋ., Ɇɟɣɥɢɯɨɜɚ ȿ.Ɂ.\. Ɇ: ɗɧɟɪɝɨɚɬɨɦɢɡɞɚɬ, 1991. 7. ɋɦɢɪɧɨɜ Ȼ.Ⱥ. Ɏɢɡɢɤɚ ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɵ. Ɇ.: ɇɚɭɤɚ, 1978, ɫ.132, ɡɚɞɚɱɚ 2.23. 8. Ⱥɥɟɤɫɟɟɜ Ȼ.ȼ., Ʉɨɬɟɥɶɧɢɤɨɜ ȼ.Ⱥ. Ɂɨɧɞɨɜɵɣ ɦɟɬɨɞ ɞɢɚɝɧɨɫɬɢɤɢ ɩɥɚɡɦɵ. Ɇ.: ɗɧɟɪɝɨɚɬɨɦɢɡɞɚɬ, 1988. 9. Ɏɪɚɧɰ-Ʉɚɦɟɧɟɰɤɢɣ Ⱦ.Ⱥ. Ʌɟɤɰɢɢ ɩɨ ɮɢɡɢɤɟ ɩɥɚɡɦɵ. - Ɇ.: Ⱥɬɨɦɢɡɞɚɬ, 1964. 10. Ⱥɪɰɢɦɨɜɢɱ Ʌ.Ⱥ. ɍɩɪɚɜɥɹɟɦɵɟ ɬɟɪɦɨɹɞɟɪɧɵɟ ɪɟɚɤɰɢɢ. - Ɇ.: Ɏɢɡɦɚɬɝɢɡ, 1961. 11. Ɍɪɭɛɧɢɤɨɜ Ȼ.Ⱥ. Ɍɟɨɪɢɹ ɩɥɚɡɦɵ. - Ɇ.:ɗɧɟɪɝɨɚɬɨɦɢɡɞɚɬ, 1996. 12. Ʌɭɤɶɹɧɨɜ ɋ.ɘ., Ʉɨɜɚɥɶɫɤɢɣ ɇ.Ƚ. Ƚɨɪɹɱɚɹ ɩɥɚɡɦɚ ɢ ɭɩɪɚɜɥɹɟɦɵɣ ɹɞɟɪɧɵɣ ɫɢɧɬɟɡ. Ɇ.:ɆɂɎɂ, 1997. 13. Ȼɪɚɝɢɧɫɤɢɣ ɋ.ɂ. ȼɨɩɪɨɫɵ ɬɟɨɪɢɢ ɩɥɚɡɦɵ. - Ɇ.: Ⱥɬɨɦɢɡɞɚɬ, 1963, ɬ.1, ɫ.208-209. 14. Ƚɚɥɟɟɜ Ⱥ.Ⱥ., ɋɚɝɞɟɟɜ Ɋ.Ɂ. ȼɨɩɪɨɫɵ ɬɟɨɪɢɢ ɩɥɚɡɦɵ. - Ɇ.: Ⱥɬɨɦɢɡɞɚɬ, 1973. 15. Ɍɚɦɦ ȿ.ɂ. Ɉɫɧɨɜɵ ɬɟɨɪɢɢ ɷɥɟɤɬɪɢɱɟɫɬɜɚ. - Ɇ.: Ƚɨɫɬɟɯɢɡɞɚɬ, 1946, ɫ.432. 16. Ʌɟɨɧɬɨɜɢɱ Ɇ.Ⱥ., Ɉɫɨɜɟɰ ɋ.Ɇ. - Ⱥɬɨɦɧɚɹ ɷɧɟɪɝɢɹ, 1956, ʋ3. 17. Ʉɚɞɨɦɰɟɜ Ȼ.Ȼ. Ʉɨɥɥɟɤɬɢɜɧɵɟ ɹɜɥɟɧɢɹ ɜ ɩɥɚɡɦɟ. - Ɇ: ɇɚɭɤɚ, 1976. 18. Ⱥɥɟɤɫɚɧɞɪɨɜ Ⱥ.Ɏ., Ȼɨɝɞɚɧɤɟɜɢɱ Ʌ.ɋ., Ɋɭɯɚɞɡɟ Ⱥ.Ⱥ. Ɉɫɧɨɜɵ ɷɥɟɤɬɪɨɞɢɧɚɦɢɤɢ ɩɥɚɡɦɵ. - Ɇ: ȼɵɫɲɚɹ ɲɤɨɥɚ, 1978. 19. ɂɜɚɧɨɜ Ⱥ.Ⱥ. Ɏɢɡɢɤɚ ɫɢɥɶɧɨɧɟɪɚɜɧɨɜɟɫɧɨɣ ɩɥɚɡɦɵ. - Ɇ.: Ⱥɬɨɦɢɡɞɚɬ, 1977, ɫ.11-23. 20. Ʌɢɮɲɢɰ ȿ.Ɇ., ɉɢɬɚɟɜɫɤɢɣ Ʌ.ɉ. Ɏɢɡɢɱɟɫɤɚɹ ɤɢɧɟɬɢɤɚ (ɋɟɪɢɹ: «Ɍɟɨɪɟɬɢɱɟɫɤɚɹ ɮɢɡɢɤɚ», ɬɨɦ ɏ). - Ɇ: ɇɚɭɤɚ, 1979. 21. Ʉɢɧɝɫɟɩ Ⱥ.ɋ. ȼɜɟɞɟɧɢɟ ɜ ɧɟɥɢɧɟɣɧɭɸ ɮɢɡɢɤɭ ɩɥɚɡɦɵ. - Ɇ: ɂɡɞ. ɆɎɌɂ, 1996. 22. Ʉɚɞɨɦɰɟɜ Ȼ.Ȼ. Ɏɢɡɢɤɚ ɩɥɚɡɦɵ ɢ ɩɪɨɛɥɟɦɚ ɭɩɪɚɜɥɹɟɦɵɯ ɬɟɪɦɨɹɞɟɪɧɵɯ ɪɟɚɤɰɢɣ. Ɇ.:ɂɡɞ.Ⱥɇ ɋɋɋɊ, 1958. 23. ɒɚɮɪɚɧɨɜ ȼ.Ⱦ. Ɏɢɡɢɤɚ ɩɥɚɡɦɵ ɢ ɩɪɨɛɥɟɦɚ ɭɩɪɚɜɥɹɟɦɵɯ ɬɟɪɦɨɹɞɟɪɧɵɯ ɪɟɚɤɰɢɣ. - Ɇ.: ɂɡɞ.Ⱥɇ ɋɋɋɊ, 1958, ɬ.2 24. Ɋɚɣɡɟɪ ɘ.ɉ. Ɉɫɧɨɜɵ ɫɨɜɪɟɦɟɧɧɨɣ ɮɢɡɢɤɢ ɝɚɡɨɪɚɡɪɹɞɧɵɯ ɩɪɨɰɟɫɫɨɜ, Ɇɨɫɤɜɚ, ɇɚɭɤɚ, 1980 25. Ⱦɢɦɢɬɪɨɜ ɋ.Ʉ., Ɏɟɬɢɫɨɜ ɂ.Ʉ., Ʌɚɛɨɪɚɬɨɪɧɵɣ ɩɪɚɤɬɢɤɭɦ ɩɨ ɮɢɡɢɤɟ ɝɚɡɨɪɚɡɪɹɞɧɨɣ ɩɥɚɡɦɵ ɢ ɩɭɱɤɪɜ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ, ɆɂɎɂ, 1989 26. Ⱥɪɰɢɦɨɜɢɱ Ʌ.Ⱥ., Ʌɭɤɶɹɧɨɜ ɋ.ɘ. Ⱦɜɢɠɟɧɢɟ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɢ ɦɚɝɧɢɬɧɵɯ ɩɨɥɹɯ, Ɇ. 1972. 27. Ƚɥɚɡɟɪ, Ɉɫɧɨɜɵ ɷɥɟɤɬɪɨɧɧɨɣ ɨɩɬɢɤɢ, Ɇɨɫɤɜɚ, 1957, ɫɬɪ.64 28. Ʉɟɥɶɦɚɧ ȼ.Ɇ., əɜɨɪ ɋ.ə., ɗɥɟɤɬɪɨɧɧɚɹ ɨɩɬɢɤɚ, Ɇɨɫɤɜɚ, 1959, ɫ.125 29. Ʉɚɩɰɨɜ ɇ.Ⱥ., ɗɥɟɤɬɪɨɧɢɤɚ, Ɇɨɫɤɜɚ, 1956, ɫɬɪ.138 30. Ƚɪɚɧɨɜɫɤɢɣ ȼ.Ʌ. ɗɥɟɤɬɪɢɱɟɫɤɢɣ ɬɨɤ ɜ ɝɚɡɚɯ, Ɇɨɫɤɜɚ, 1971. 31. Ⱦɨɛɪɟɰɨɜ Ʌ.ɇ., Ƚɚɦɚɸɧɨɜɚ Ɇ.ȼ., ɗɦɢɫɫɢɨɧɧɚɹ ɷɥɟɤɬɪɨɧɢɤɚ, Ɇɨɫɤɜɚ, 1966. 32. ɉɪɨɬɚɫɨɜ ɘ.ɋ., ɑɭɜɚɲɟɜ ɋ.ɇ., Ɏɢɡɢɱɟɫɤɚɹ ɷɥɟɤɬɪɨɧɢɤɚ ɝɚɡɨɪɚɡɪɹɞɧɵɯ ɭɫɬɪɨɣɫɬɜ, Ɇɨɫɤɜɚ, 1992, ɫ.352 33. Ɋɚɣɡɟɪ ɘ.ɉ. Ɏɢɡɢɤɚ ɝɚɡɨɜɨɝɨ ɪɚɡɪɹɞɚ. Ɇ: ɇɚɭɤɚ, 1992. 34. Ʌɨɞɡɢɧɫɤɢɣ ɗ.Ⱦ., Ɏɢɪɫɨɜ Ɉ.Ȼ. Ɍɟɨɪɢɹ ɢɫɤɪɵ. Ɇ: Ⱥɬɨɦɢɡɞɚɬ, 1975. 35. Ɋɭɫɚɧɨɜ Ⱦ., Ɏɪɢɞɦɚɧ Ⱥ.Ⱥ. Ɏɢɡɢɤɚ ɯɢɦɢɱɟɫɤɢ ɚɤɬɢɜɧɨɣ ɩɥɚɡɦɵ. Ɇ: 1984.
