Жданов С.К Цветков И.В - Основы физических процессов в плазме и в плазменных установках (2000)
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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) |
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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 ~ t , ɢ ɦɨɠɧɨ ɜɜɟɫɬɢ, ɤɚɤ ɝɨɜɨɪɹɬ,
ɚɜɬɨɦɨɞɟɥɶɧɭɸ ɩɟɪɟɦɟɧɧɭɸ,
x
ξ = 1 , (3.34)
2 Dɦɚɝβmax t
ɝɞɟ βmax - ɧɨɪɦɢɪɨɜɤɚ, ɬɚɤɚɹ ɱɬɨ |
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β( x,t ) = f (ξ )βmax . |
(3.35) |
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ɉɪɨɮɢɥɶ f(ξ), ɤɚɤ ɫɥɟɞɭɟɬ ɢɡ (3.33), ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɪɚɜɧɟɧɢɸ |
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d |
( f |
df |
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dξ |
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dξ |
2 dξ |
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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: |
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ω = ω( k&) . |
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(4.1) |
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Ɂɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɩɨɡɜɨɥɹɟɬ ɨɩɪɟɞɟɥɢɬɶ ɮɚɡɨɜɭɸ ɫɤɨɪɨɫɬɶ ɜɨɥɧɵ |
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ω( k&) |
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k& |
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vɮ |
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(4.2) |
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k |
k |
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ɢ ɟɟ ɝɪɭɩɩɨɜɭɸ ɫɤɨɪɨɫɬɶ |
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∂ω( k&) |
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vɝɪ |
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(4.3) |
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∂k |
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Ƚɪɭɩɩɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɨɥɧɵ ɨɩɪɟɞɟɥɹɟɬ ɩɟɪɟɧɨɫ ɜɨɥɧɨɜɨɣ ɷɧɟɪɝɢɢ ɢ ɩɨɷɬɨɦɭ ɧɢɤɨɝɞɚ ɧɟ
ɦɨɠɟɬ ɩɪɟɜɵɲɚɬɶ ɫɤɨɪɨɫɬɶ ɫɜɟɬɚ ɜ ɜɚɤɭɭɦɟ vɝɪ < 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 |
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~& |
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ɩɨɥɟ ɜɨɥɧɵ E,B ɫɥɟɞɭɟɬ ɨɩɪɟɞɟɥɹɬɶ ɢɡ ɭɪɚɜɧɟɧɢɣ Ɇɚɤɫɜɟɥɥɚ: |
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~& |
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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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c |
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4π ~& |
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1 ∂E |
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rot B |
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∂t |
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(4.5) |
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c |
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div E |
4πρq |
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~& |
= 0 . |
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divB |
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~ ~& |
− ɧɚɜɟɞɟɧɧɚɹ ɜ ɫɪɟɞɟ ɩɨɥɟɦ ɜɨɥɧɵ ɩɥɨɬɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ |
ɡɚɪɹɞɚ ɢ |
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Ɂɞɟɫɶ ρq , j |
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ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ. ɗɬɢ ɜɟɥɢɱɢɧɵ ɧɟ ɹɜɥɹɸɬɫɹ ɩɨɥɧɨɫɬɶɸ ɧɟɡɚɜɢɫɢɦɵɦɢ, ɚ, ɤɚɤ ɷɬɨ ɫɥɟɞɭɟɬ ɢɡ (4.5), ɫɜɹɡɚɧɵ ɫɨɨɬɧɨɲɟɧɢɟɦ
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= −div j |
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(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,
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exp( −iωt + ikr&) = ( |
−iω )exp( −iωt + ikr&) , |
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exp( −iωt + ikr&) = ( ik )exp( −iωt + ikr&), |
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ɬɨ ɭɪɚɜɧɟɧɢɹ (4.5) ɩɪɢ ɬɚɤɨɣ ɩɨɞɫɬɚɧɨɜɤɟ ɩɪɟɜɪɚɳɚɸɬɫɹ ɜ ɚɥɝɟɛɪɚɢɱɟɫɤɢɟ: |
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ω ~& |
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k × E |
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c B , |
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iω ~& |
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ik E |
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&~& |
= 0 . |
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ɉɟɪɜɨɟ ɢɡ ɷɬɢɯ ɫɨɨɬɧɨɲɟɧɢɣ ɜɵɪɚɠɚɟɬ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɜɨɥɧɵ ɱɟɪɟɡ ɷɥɟɤɬɪɢɱɟɫɤɨɟ
~& = c & × ~& B ω k E ,
ɢ ɩɪɢ ɬɚɤɨɦ ɨɩɪɟɞɟɥɟɧɢɢ, ɨɱɟɜɢɞɧɨ, ɩɨɫɥɟɞɧɟɟ ɢɡ ɫɨɨɬɧɨɲɟɧɢɣ (4.7) ɫɬɚɧɨɜɢɬɫɹ ɬɨɠɞɟɫɬɜɨɦ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɨɨɬɧɨɲɟɧɢɹ (4.7) ɫɜɨɞɹɬɫɹ ɤ ɫɥɟɞɭɸɳɢɦ:
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ik E |
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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: |
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4πi |
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ε (ω ,k ) = δ + |
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σ (ω ,k ), |
(4.10) |
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ɝɞɟ ɩɟɪɜɨɟ ɫɥɚɝɚɟɦɨɟ − ɟɞɢɧɢɱɧɚɹ ɞɢɚɝɨɧɚɥɶɧɚɹ ɦɚɬɪɢɰɚ. ɉɨɫɤɨɥɶɤɭ, ɜ ɫɢɥɭ (4.6), ɧɚɜɟɞɟɧɧɚɹ ɩɥɨɬɧɨɫɬɶ ɡɚɪɹɞɚ ɞɨɥɠɧɚ ɛɵɬɶ ɫɜɹɡɚɧɚ ɫ ɧɚɜɟɞɟɧɧɨɣ ɩɥɨɬɧɨɫɬɶɸ ɬɨɤɚ
ɫɨɨɬɧɨɲɟɧɢɟɦ |
~& |
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ωρq = k j |
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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:
( Nεij2 − δij +
ɝɞɟ ɜɟɥɢɱɢɧɚ
N 2 = §¨kc·¸2 © ω ¹
ki k j |
)E j = 0 , |
k 2 |
(4.11)
(4.12)
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:
Det( |
εij (ω ,k ) |
− δ |
+ |
ki k j |
) = 0 . |
(4.13) |
N 2 |
|
|||||
|
ij |
|
k 2 |
|
||
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:
ε |
|
= ε |
|
(δ |
− |
ki k j |
) + ε |
|
ki k j |
, |
(4.14) |
|
|
|
l k2 |
||||||||
|
ij |
|
tr |
ij |
|
k2 |
|
|
|||
ɚ ɞɢɫɩɟɪɫɢɨɧɧɨɟ ɭɪɚɜɧɟɧɢɟ, ɤɚɤ ɥɟɝɤɨ ɩɪɨɜɟɪɢɬɶ, ɩɪɢɜɨɞɢɬɫɹ ɤ ɜɢɞɭ:
|
εij (ω ,k ) |
|
|
ki k j |
|
ε |
l |
§ |
ε |
tr |
· |
2 |
||
Det( |
|
|
− δ |
+ |
|
) = |
|
¨ |
|
− 1¸ |
= 0 . |
|||
N 2 |
k 2 |
N 2 |
N 2 |
|||||||||||
|
ij |
|
|
© |
¹ |
|
||||||||
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɤɚɤ ɦɵ ɜɢɞɢɦ, ɫɭɳɟɫɬɜɭɸɬ ɞɜɟ ɜɨɡɦɨɠɧɨɫɬɢ ɜɵɩɨɥɧɢɬɶ ɷɬɨ ɭɫɥɨɜɢɟ:
εl = 0 , |
(4.15) |
εtr = N 2 . |
(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 = N 2 . |
(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
εl ≡ |
ki k j |
εij . |
k2 |
§ 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): |
|
|
ε = 1 − (ω p / ω )2 , |
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 |
>> vT ,vT . |
(4.20) |
|
|
k |
e i |
|
|
|
|
|
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) |
r2 |
|||
|
D |
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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)
&& |
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ϕ ~ eikr , |
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ɩɪɢɯɨɞɢɦ ɤ ɫɥɟɞɭɸɳɟɦɭ ɪɟɡɭɥɶɬɚɬɭ: |
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1 |
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1 |
1 |
1 |
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|||
ε = 1 + |
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, |
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≡ |
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+ |
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, |
(4.22) |
k 2r2 |
r2 |
r2 |
r2 |
||||||
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D |
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D |
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De |
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Di |
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ɨɩɪɟɞɟɥɹɸɳɟɦɭ ɞɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɥɚɡɦɵ ɜ ɫɬɚɬɢɱɟɫɤɨɦ ɩɪɟɞɟɥɟ, ɫɩɪɚɜɟɞɥɢɜɨɦ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɭɫɥɨɜɢɹ, ɨɛɪɚɬɧɨɝɨ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ (4.19):
vɮ |
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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:
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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,
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Ⱦɚɥɟɟ, ɫ ɩɨɦɨɳɶɸ (4.24) ɜɵɱɢɫɥɹɟɦ ɫɤɨɪɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ, ɚ ɡɚɬɟɦ ɢ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ, ɢɧɞɭɰɢɪɭɟɦɨɝɨ ɜɨɥɧɨɣ. Ɋɟɡɭɥɶɬɚɬ ɨɤɚɡɵɜɚɟɬɫɹ ɫɥɟɞɭɸɳɢɦ:
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Ʉɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ ɦɟɠɞɭ ɩɥɨɬɧɨɫɬɶɸ ɬɨɤɚ ɢ ɧɚɩɪɹɠɟɧɧɨɫɬɶɸ ɩɨɥɹ ɜɨɥɧɵ ɞɚɟɬ ɜɟɥɢɱɢɧɭ ɩɪɨɜɨɞɢɦɨɫɬɢ ɩɥɚɡɦɵ, ɤɨɬɨɪɚɹ ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɩɪɟɞɟɥɟ ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɨɣ
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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: |
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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:
men0e~v&e + mi n0i ~v&i = 0 .
ɗɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɩɨɡɜɨɥɹɟɬ ɜɵɪɚɡɢɬɶ ɨɞɧɭ ɫɤɨɪɨɫɬɶ ɱɟɪɟɡ ɞɪɭɝɭɸ, ɧɚɩɪɢɦɟɪ ɢɨɧɧɭɸ ɫɤɨɪɨɫɬɶ ɱɟɪɟɡ ɷɥɟɤɬɪɨɧɧɭɸ ɫɤɨɪɨɫɬɶ:
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ɍɪɚɜɧɟɧɢɹ (4.26) ɜ ɪɟɡɭɥɶɬɚɬɟ ɫɜɨɞɹɬɫɹ ɤ ɨɞɧɨɦɭ, ɧɚɩɪɢɦɟɪ, ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɛɭɞɟɬ
ɫɥɟɞɭɸɳɢɦ: |
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∂ve |
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men0e ∂t = − |
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ɢ ɬɟɩɟɪɶ ɭɠɟ ɧɟɫɥɨɠɧɨ ɜɵɱɢɫɥɢɬɶ ɫɤɨɪɨɫɬɢ ɢ ɫ ɢɯ ɩɨɦɨɳɶɸ ɩɥɨɬɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ. Ⱦɥɹ ɝɚɪɦɨɧɢɱɟɫɤɨɣ ɜɨɥɧɵ ɨɧɚ ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɨɣ:
~& |
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ɢ ɜɧɨɜɶ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɣ ɩɨɥɸ ɜɨɥɧɵ. Ɂɞɟɫɶ νei |
= τei−1 |
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− ɱɚɫɬɨɬɚ ɷɥɟɤɬɪɨɧ-ɢɨɧɧɵɯ ɫɬɨɥɤɧɨɜɟɧɢɣ, σ − |
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ɩɪɨɜɨɞɢɦɨɫɬɶ ɩɥɚɡɦɵ. Ⱦɥɹ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɩɨɥɭɱɚɟɦ:
ε = 1 − |
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/ m )] |
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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
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ve − vi |
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0e e |
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ɢɥɢ ɦɟɠɞɭ ɢɨɧɚɦɢ ɢ ɷɥɟɤɬɪɨɧɚɦɢ
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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 |
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me ei |
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µ = |
memi . |
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e2e2 n |
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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 ne,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:
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Ʉɪɨɦɟ ɦɨɞɟɥɢ ɩɥɚɡɦɵ ɫ ɩɨɫɬɨɹɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ, ɱɚɫɬɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɦɨɞɟɥɶ ɩɨɥɢɬɪɨɩɵ, ɜ ɤɨɬɨɪɨɣ ɞɚɜɥɟɧɢɟ ɢ ɬɟɦɩɟɪɚɬɭɪɚ ɩɥɚɡɦɵ ɩɪɟɞɩɨɥɚɝɚɸɬɫɹ ɫɬɟɩɟɧɧɵɦɢ ɮɭɧɤɰɢɹɦɢ ɩɥɨɬɧɨɫɬɢ:
pe,i = ne,iTe,i ~ neγ,ie ,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»:
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ɧɚɩɪɢɦɟɪ, |
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ɝɚɪɦɨɧɢɱɟɫɤɢɦɢ, ɜɵɱɢɫɥɹɟɦ ɜɨɡɦɭɳɟɧɢɟ ɩɥɨɬɧɨɫɬɢ ɢ ɫɤɨɪɨɫɬɢ ɤɨɦɩɨɧɟɧɬ ɩɥɚɡɦɵ: |
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ωm |
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csα ɞɥɹ «ɫɤɨɪɨɫɬɢ ɡɜɭɤɚ» |
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ɝɞɟ, ɩɨ ɚɧɚɥɨɝɢɢ ɫ ɝɚɡɨɦ, ɞɥɹ ɤɪɚɬɤɨɫɬɢ ɜɜɟɞɟɧɨ ɨɛɨɡɧɚɱɟɧɢɟ |
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ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɤɨɦɩɨɧɟɧɬɵ ɩɥɚɡɦɵ. ɍɦɧɨɠɢɜ ɧɚɣɞɟɧɧɵɟ ɫɤɨɪɨɫɬɢ ɤɨɦɩɨɧɟɧɬ ɩɥɚɡɦɵ ɧɚ ɡɚɪɹɞ ɢ ɧɟɜɨɡɦɭɳɟɧɧɭɸ ɩɥɨɬɧɨɫɬɶ, ɩɪɨɫɭɦɦɢɪɨɜɚɜ ɡɚɬɟɦ ɪɟɡɭɥɶɬɚɬ ɩɨ ɫɨɪɬɚɦ ɱɚɫɬɢɰ, ɜɵɱɢɫɥɹɟɦ ɩɥɨɬɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ:
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n0α eα2 ω |
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ȼɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶ, ɞɚɥɟɟ, ɨɩɪɟɞɟɥɟɧɢɹɦɢ (4.9), (4.10) ɩɨɥɭɱɚɟɦ ɬɟɧɡɨɪ ɩɪɨɜɨɞɢɦɨɫɬɢ:
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σ p,q ( k ,ω ) = |
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ɚ ɡɚɬɟɦ ɢ ɬɟɧɡɨɪ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ: |
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ε p,q ( k ,ω ) ≡ δp,q + |
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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 − ¦ |
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ɢ ɩɨɩɟɪɟɱɧɭɸ |
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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 |
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ω → 0 , ɩɪɨɞɨɥɶɧɚɹ |
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ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɨɣ |
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ɱɬɨ ɫɨɜɩɚɞɚɟɬ ɫ (4.22), |
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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 ɩɨɤɚɡɚɬɟɥɢγ 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, ɧɨɤɨɧɟɱɧɵɦɢ, ɢɡ ɮɨɪɦɭɥɵ (4.32) ɩɪɢɛɥɢɠɟɧɧɨ ɩɨɥɭɱɚɟɦ:
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ɱɬɨ ɫɨɜɩɚɞɚɟɬ ɫ ɪɟɡɭɥɶɬɚɬɨɦ ɤɢɧɟɬɢɱɟɫɤɨɣ ɬɟɨɪɢɢ [18] ɩɪɢ ɜɵɛɨɪɟ γ α |
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