Жданов С.К Цветков И.В - Основы физических процессов в плазме и в плазменных установках (2000)
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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
tɡɚɩ |
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ɢ ɫɦɟɳɚɟɬɫɹ ɡɚ ɫɱɟɬ ɞɪɟɣɮɚ ɩɨɩɟɪɟɤ ɩɨɥɹ ɧɚ ɪɚɫɫɬɨɹɧɢɟ |
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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:
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ɋɚɦɢ «ɛɚɧɚɧɵ» ɦɨɝɭɬ ɫɭɳɟɫɬɜɨɜɚɬɶ, ɧɟ ɪɚɡɪɭɲɚɹɫɶ, ɩɨɤɚ ɱɚɫɬɨɬɚ ɫɬɨɥɤɧɨɜɟɧɢɣ ɞɨɫɬɚɬɨɱɧɨ ɦɚɥɚ
ν < νɛɚɧ = |
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ɪɟɠɢɦɚɯ ɢ ɱɚɫɬɵɯ ɫɬɨɥɤɧɨɜɟɧɢɣ, |
ν > νɉɒ , ɢ ɪɟɞɤɢɯ ɫɬɨɥɤɧɨɜɟɧɢɣ, |
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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 = νɉɒ .
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.
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:
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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 vE = c B . ɉɨɷɬɨɦɭ ɬɨɤɚ ɧɟ ɛɭɞɟɬ,
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:
< ∆ >= ρ |
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me vE c |
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< ∆ >= ρ |
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E
ɝɞɟ vE = c B , ɚ ɡɚɪɹɞɵ ɱɚɫɬɢɰ ɩɨ ɜɟɥɢɱɢɧɟ ɫɱɢɬɚɸɬɫɹ ɨɞɢɧɚɤɨɜɵɦɢ.
Ɂɚɪɹɞɵ ɜ ɫɪɟɞɧɟɦ “ɪɚɡɨɣɞɭɬɫɹ” ɧɚ ɜɟɥɢɱɢɧɭ
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( m + m )c2 E |
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∆ =< ∆ > + < ∆ >= |
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ɍɦɧɨɠɢɜ ɷɬɭ ɜɟɥɢɱɢɧɭ ɧɚ ɡɚɪɹɞ ɢ ɧɚ ɩɥɨɬɧɨɫɬɶ, ɩɨɥɭɱɢɦ ɞɢɩɨɥɶɧɵɣ ɦɨɦɟɧɬ Ɋ ɟɞɢɧɢɰɵ ɨɛɴɟɦɚ |
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n( m + m )c2 E |
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ɢ ɩɨɩɟɪɟɱɧɭɸ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɤɨɦɩɨɧɟɧɬɭ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɩɥɚɡɦɵ
ε |
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(2.103) |
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ȼ ɨɛɟɢɯ ɮɨɪɦɭɥɚɯ ρm = n( me + mi ) - ɦɚɫɫɨɜɚɹ ɩɥɨɬɧɨɫɬɶ ɩɥɚɡɦɵ.
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 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 |
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ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɬɨɤ ɬɟɱɟɬ ɩɨɞ ɭɝɥɨɦ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɢ ɡɚɤɨɧ Ɉɦɚ ɞɥɹ ɩɥɚɡɦɵ ɜɵɝɥɹɞɢɬ
ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ [13]: |
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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 |
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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:
R& |
= −0.71n |
( b& )T |
− |
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], b& = |
B& |
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(2.107) |
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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 |
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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′ |
= |
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(2.108ɛ) |
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ɇɨ ɞɥɹ ɩɪɨɬɟɤɚɧɢɹ ɬɨɤɚ ɩɨɩɟɪɟɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɭɠɧɚ ɫɨɫɬɚɜɥɹɸɳɚɹ ɷɮɮɟɤɬɢɜɧɨɝɨ ɩɨɥɹ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɚɹ ɢ ɤ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ, ɢ ɤ ɬɨɤɭ - ɷɬɨ ɬɚɤ ɧɚɡɵɜɚɟɦɨɟ ɯɨɥɥɨɜɫɤɨɟ ɩɨɥɟ:
& |
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&& |
ω Beτ ei |
&& |
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= |
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(2.109) |
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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 |
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& c F& |
× B& |
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vd = |
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= |
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(2.110) |
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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 |
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& |
= ¦nev&d |
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× p |
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= c |
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(2.111) |
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ɉɨɹɜɥɟɧɢɟ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɬɨɤɨɜ ɜɫɥɟɞɫɬɜɢɟ ɧɟɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɪɢɱɢɧ − ɫɩɟɰɢɮɢɱɟɫɤɚɹ ɨɫɨɛɟɧɧɨɫɬɶ ɩɥɚɡɦɵ, ɩɪɢɫɭɳɚɹ ɟɣ ɜɫɟɝɞɚ, ɤɨɝɞɚ ɟɫɬɶ ɤɚɤɢɟ-ɥɢɛɨ
ɧɟɨɞɧɨɪɨɞɧɨɫɬɢ ɩɥɚɡɦɵ. |
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ɂɡ ɬɟɨɪɢɢ ɦɚɝɧɟɬɢɡɦɚ [15] ɢɡɜɟɫɬɧɨ, ɱɬɨ ɧɚɦɚɝɧɢɱɟɧɢɟ ɫɪɟɞɵ I& |
ɢ ɩɥɨɬɧɨɫɬɶ ɦɨɥɟɤɭɥɹɪɧɵɯ ɬɨɤɨɜ |
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ȼ ɩɥɚɡɦɟ ɧɚɦɚɝɧɢɱɟɧɢɟ ɪɚɜɧɨ ɫɭɦɦɟ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ ɱɚɫɬɢɰ ɜ ɟɞɢɧɢɰɟ ɨɛɴɟɦɚ: |
I& = n < & > ɢ, |
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ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (2.9), |
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Ɍɚɤ ɤɚɤ ɞɜɢɠɟɧɢɟ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɟ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ, ɢɦɟɟɬ ɞɜɟ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ, ɬɨ, ɩɪɨɢɡɜɨɞɹ ɭɫɪɟɞɧɟɧɢɟ, ɢ ɨɛɨɡɧɚɱɢɜ&p =nT , ɩɨɥɭɱɚɟɦ
&j = −c rot |
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ȼɷɬɨɣ ɮɨɪɦɟ ɡɚɩɢɫɢ ɭɱɢɬɵɜɚɸɬɫɹ ɞɪɟɣɮɨɜɵɟ ɬɨɤɢ, ɜɨɡɧɢɤɚɸɳɢɟ ɜɫɥɟɞɫɬɜɢɟ ɝɪɚɞɢɟɧɬɚ ɩɥɨɬɧɨɫɬɢ
ɢɝɪɚɞɢɟɧɬɚ 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
τ |
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4πσ |
δ 2 |
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δ 2 |
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s |
c2 |
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Dɦɚɝ |
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ɝɞɟ σ - ɩɪɨɜɨɞɢɦɨɫɬɶ; |
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Dɦɚɝ |
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c2 |
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(3.2) |
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4πσ |
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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 |
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L>>ρi |
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Zni-ne=0. |
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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
v& = |
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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 v&α .
( 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 |
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∂ t + div( ρv&) = 0 . |
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(3.4) |
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• ɍɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɟɞɢɧɢɰɵ ɨɛɴɟɦɚ ɩɥɚɡɦɵ (ɫɨɯɪɚɧɟɧɢɹ ɢɦɩɭɥɶɫɚ): |
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dv& |
1 & |
& |
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ρ |
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j |
× B − p + F , |
(3.5) |
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dt |
c |
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ɝɞɟ p=pe+pi - ɩɨɥɧɨɟ ɞɚɜɥɟɧɢɟ ɩɥɚɡɦɵ, ɪɚɜɧɨɟ ɫɭɦɦɟ ɞɚɜɥɟɧɢɣ ɷɥɟɤɬɪɨɧɨɜ ɢ
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& |
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dv& |
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∂ v& |
& & |
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ɢɨɧɨɜ, |
F |
- ɜɧɟɲɧɹɹ ɫɢɥɚ (ɧɚɩɪɢɦɟɪ, ɫɢɥɚ ɬɹɠɟɫɬɢ), |
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= |
∂ t |
+ ( v )v |
− ɩɨɥɧɚɹ |
dt |
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 ); |
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div B& = 0 ; |
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& |
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1 ∂ B& |
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rot E |
= − |
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∂ t |
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4π & |
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rot B |
= |
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ɉɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɜɫɟ ɩɪɨɰɟɫɫɵ ɦɟɞɥɟɧɧɵɟ ɢ ɬɨɤɚɦɢ ɫɦɟɳɟɧɢɹ ɦɨɠɧɨ |
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ɩɪɟɧɟɛɪɟɱɶ, ɱɬɨ ɢ ɢɫɩɨɥɶɡɨɜɚɧɨ ɜ ɩɨɫɥɟɞɧɟɦ ɢɡ ɭɪɚɜɧɟɧɢɣ (3.6). |
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• Ɂɚɤɨɧ Ɉɦɚ (ɫɨɝɥɚɫɧɨ ɪɚɛɨɬɟ [13]): |
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1 & |
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j |
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E′ = |
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× B , |
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σ |
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cn |
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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 & &
ɩɥɚɡɦɵ; cne|e| j × B - ɯɨɥɥɨɜɫɤɨɟ ɩɨɥɟ.
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:
& |
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1 & |
& |
1 & |
& |
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= σ ®E + |
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× B − |
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× B + |
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n|e|c |
n|e| |
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¿ |
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• ɍɪɚɜɧɟɧɢɟ ɫɨɫɬɨɹɧɢɹ - ɷɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɜɢɞɚ: p = p( ρ ,T ) .
(3.8)
(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 «ɝɚɡɨɜ» − «ɝɚɡɚ» ɷɥɟɤɬɪɨɧɨɜ ɫ ɤɨɧɰɟɧɬɪɚɰɢɟɣ ne ɢ «ɝɚɡɚ» ɢɨɧɨɜ ɫ
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 ~ ργ . ɉɪɢ ɷɬɨɦ
ɢɡɦɟɧɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɫɥɟɞɭɟɬ ɫɨɨɬɧɨɲɟɧɢɸ T ~ ργ −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.