Жданов С.К Цветков И.В - Основы физических процессов в плазме и в плазменных установках (2000)
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§ 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:
§ω |
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ɝɞɟ ω Le,i ɥɟɧɝɦɸɪɨɜɫɤɢɟ ɱɚɫɬɨɬɵ ɱɚɫɬɢɰ ɩɥɚɡɦɵ. |
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ɉɭɫɬɶ ɬɟɩɟɪɶ |
ɧɚ |
ɜɦɨɪɨɠɟɧɧɭɸ ɜ |
ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɩɥɚɡɦɭ ɩɚɞɚɟɬ ɩɨɩɟɪɟɱɧɚɹ |
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ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ ɜɨɥɧɚ, ɬɚɤ, ɱɬɨ ɜɟɤɬɨɪ ɫɤɨɪɨɫɬɢ |
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ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɜɨɥɧɵ ɩɟɪɩɟɧɞɢɤɭɥɹɪɟɧ ɜɟɤɬɨɪɭ |
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ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɚ ɜɟɤɬɨɪ |
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ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɷɬɨɣ ɜɨɥɧɵ ȿ |
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ɤɨɥɥɢɧɟɚɪɟɧ (ɩɚɪɚɥɥɟɥɟɧ ɢɥɢ ɚɧɬɢɩɚɪɚɥɥɟɥɟɧ) |
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ɜɟɤɬɨɪɭ B0 (ɪɢɫ.4.6). ȼɧɟɲɧɟɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ |
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ɛɭɞɟɦ ɩɨɦɟɱɚɬɶ ɢɧɞɟɤɫɨɦ «0», ɱɬɨɛɵ ɨɬɥɢɱɚɬɶ ɟɝɨ |
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Ɋɢɫ.4.6. ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ ɜɨɥɧɚ |
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ɨɬ ɫɨɛɫɬɜɟɧɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜɨɥɧɵ. ȼɧɨɜɶ |
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ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɤ |
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ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɜɨɥɧɵ ɜɨɡɞɟɣɫɬɜɭɟɬ ɬɨɥɶɤɨ ɧɚ |
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B&0 ɢ ɟɟ ɜɟɤɬɨɪ ȿ&||B&0 |
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ɞɜɢɠɟɧɢɟ ɱɚɫɬɢɰ ɜɞɨɥɶ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɧɚ ɤɨɬɨɪɨɟ |
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ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɧɟ ɫɤɚɡɵɜɚɟɬɫɹ. |
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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.
•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: |
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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:
E& = E& + |
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ɉɨɞɫɬɚɜɢɜ ɨɩɪɟɞɟɥɹɟɦɭɸ ɷɬɢɦ ɭɫɥɨɜɢɟɦ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜ ɭɪɚɜɧɟɧɢɟ ɢɧɞɭɤɰɢɢ
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1 ∂ |
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ɩɪɢɯɨɞɢɦ ɤ ɭɪɚɜɧɟɧɢɸ ɜɦɨɪɨɠɟɧɧɨɫɬɢ: |
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ɭɪɚɜɧɟɧɢɟ |
ɨɛɥɚɞɚɟɬ |
ɫɥɟɞɭɸɳɢɦ |
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ɡɚɦɟɱɚɬɟɥɶɧɵɦ ɫɜɨɣɫɬɜɨɦ. ȼɵɞɟɥɢɦ ɜ ɩɥɚɡɦɟ |
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ɧɟɤɨɬɨɪɵɣ ɤɨɧɬɭɪ, ɩɪɨɧɢɡɵɜɚɟɦɵɣ ɫɢɥɨɜɵɦɢ ɥɢɧɢɹɦɢ |
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ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ (ɪɢɫ. 4.7), ɢ ɫɦɟɳɚɸɳɢɣɫɹ ɜɦɟɫɬɟ ɫ |
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ɩɥɚɡɦɨɣ. ɉɨɬɨɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɱɟɪɟɡ ɷɬɨɬ ɤɨɧɬɭɪ ɩɨ |
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ɨɩɪɟɞɟɥɟɧɢɸ ɪɚɜɟɧ ɢɧɬɟɝɪɚɥɭ ɨɬ ɜɟɤɬɨɪɚ ɢɧɞɭɤɰɢɢ |
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ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɩɨ ɩɥɨɳɚɞɢ, ɨɯɜɚɬɵɜɚɟɦɨɣ ɷɬɢɦ |
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ɤɨɧɬɭɪɨɦ: |
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Φ = ³BdS =³Bn dS , |
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Ɋɢɫ. 4.7. Ʉ ɬɟɨɪɟɦɟ ɜɦɨɪɨɠɟɧɧɨɫɬɢ |
ɝɞɟ ȼn – ɩɪɨɟɤɰɢɹ ɜɟɤɬɨɪɚ ɢɧɞɭɤɰɢɢ ɧɚ ɧɚɩɪɚɜɥɟɧɢɟ |
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ɧɨɪɦɚɥɢ. ɉɪɨɢɧɬɟɝɪɢɪɨɜɚɜ ɭɪɚɜɧɟɧɢɟ (4.69) ɩɨ ɷɬɨɦɭ |
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ɤɨɧɬɭɪɭ, ɦɵ ɨɛɧɚɪɭɠɢɦ, ɱɬɨ ɩɨɬɨɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɩɪɨɧɢɡɵɜɚɸɳɟɝɨ ɤɨɧɬɭɪ, ɫɨɯɪɚɧɹɟɬɫɹ:
dΦ |
= 0. |
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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.
•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
ε |
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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.
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Ɋɢɫ.4.8. ɇɚɩɪɚɜɥɟɧɢɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɜɨɥɧɵ |
Ɋɢɫ. 4.9. ɉɨɥɹɪɢɡɚɰɢɹ ɩɥɚɡɦɵ ɜ |
ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɤ B&0 ɢ ɟɟ ɜɟɤɬɨɪ ȿ& B&0 |
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
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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: |
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ɗɬɨ ɩɨɞɬɜɟɪɠɞɚɟɬɫɹ ɞɟɬɚɥɶɧɵɦɢ ɪɚɫɱɟɬɚɦɢ[18]. ȼ ɡɚɤɥɸɱɟɧɢɟ ɩɪɢɜɟɞɟɦ (ɞɥɹ ɫɩɪɚɜɨɤ) ɛɟɡ ɜɵɜɨɞɚ ɩɨɥɧɭɸ ɫɬɪɭɤɬɭɪɭ ɬɟɧɡɨɪɚ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɯɨɥɨɞɧɨɣ ɩɥɚɡɦɵ:
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ɞɢɚɝɨɧɚɥɶɧɵɟ |
ɤɨɦɩɨɧɟɧɬɵ ɡɞɟɫɶ ɨɩɪɟɞɟɥɹɸɬɫɹ |
ɩɪɢɜɟɞɟɧɧɵɦɢ ɜɵɲɟ ɮɨɪɦɭɥɚɦɢ, ɚ |
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«ɤɨɫɵɟ» ɤɨɦɩɨɧɟɧɬɵ ɨɩɪɟɞɟɥɹɸɬɫɹ ɜɟɥɢɱɢɧɨɣ: |
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g == − ¦ |
ωBα ωL2α |
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2 2 |
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α =e,iω(ω − ωBα ) |
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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&||B&0 , 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&||B&0 , 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
ε |
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, N 2 ≡ |
k 2c |
2 |
≡ v2 . |
ω 2 |
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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:
ε = |
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ɝɞɟ ɜɜɟɞɟɧɨ ɭɞɨɛɧɨɟ ɨɛɨɡɧɚɱɟɧɢɟ |
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cA = |
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4πn(mi + me ) |
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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
vΦ = vɝɪ |
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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<<c, ɮɚɡɨɜɚɹ ɢ ɝɪɭɩɩɨɜɚɹ ɫɤɨɪɨɫɬɢ ɷɬɨɣ ɜɨɥɧɵ ɫɨɜɩɚɞɚɸɬ ɫ ɚɥɶɜɟɧɨɜɫɤɨɣ
ɫɤɨɪɨɫɬɶɸ:
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ɗɬɨ – ɨɞɢɧ ɢɡ ɜɚɠɧɟɣɲɢɯ ɬɢɩɨɜ ɜɨɥɧɨɜɵɯ ɞɜɢɠɟɧɢɣ |
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ɦɚɝɧɢɬɨɚɤɬɢɜɧɨɣ ɩɥɚɡɦɵ. |
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Ʉɚɤ ɢɡɜɟɫɬɧɨ, ɫɢɥɨɜɵɟ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ |
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Ɋɢɫ. 4.11. Ⱥɥɶɜɟɧɨɜɫɤɚɹ ɜɨɥɧɚ, ɬ.ɟ. |
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ɦɨɠɧɨ ɩɪɢɩɢɫɚɬɶ |
ɨɩɪɟɞɟɥɟɧɧɨɟ |
«ɧɚɬɹɠɟɧɢɟ». |
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ɤɨɥɟɛɚɧɢɟ «ɧɚɬɹɧɭɬɵɯ ɫɬɪɭɧ» – |
ɍɩɪɨɳɟɧɧɨ ɩɨ ɷɬɨɣ |
ɩɪɢɱɢɧɟ ɚɥɶɜɟɧɨɜɫɤɭɸ ɜɨɥɧɭ |
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ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. |
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ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɥɹɬɶ ɫɟɛɟ ɤɚɤ ɤɨɥɟɛɚɧɢɹ «ɧɚɬɹɧɭɬɵɯ |
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ɫɬɪɭɧ» − ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ (ɪɢɫ. 4.11), ɩɪɢ ɷɬɨɦ ɩɥɚɡɦɚ ɤɨɥɟɛɥɟɬɫɹ ɜɦɟɫɬɟ ɫ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ, ɜ ɤɨɬɨɪɨɟ ɨɧɚ ɜɦɨɪɨɠɟɧɚ.
Ɉɬɦɟɬɢɦ, ɱɬɨ ɩɪɢ ɩɪɨɢɡɜɨɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ
ɚɥɶɜɟɧɨɜɫɤɨɣ ɜɨɥɧɵ ɨɤɚɡɵɜɚɟɬɫɹ ɫɥɟɞɭɸɳɢɦ: |
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B&0 |
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ω = kcA , |
cA |
4πnmi |
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ɝɪ = cA . |
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Ƚɪɭɩɩɨɜɚɹ ɫɤɨɪɨɫɬɶ ɚɥɶɜɟɧɨɜɫɤɨɣ |
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ɜɨɥɧɵ, ɨɬɜɟɬɫɬɜɟɧɧɚɹ ɡɚ ɩɟɪɟɧɨɫ |
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ɜɨɥɧɨɣ ɷɧɟɪɝɢɢ, ɩɚɪɚɥɥɟɥɶɧɚ ɜɟɤɬɨɪɭ |
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ɢɧɞɭɤɰɢɢ |
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ɦɚɝɧɢɬɧɨɝɨ |
ɩɨɥɹ. |
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ɇɚɩɨɦɧɢɦ, ɱɬɨ ɮɚɡɨɜɚɹ ɫɤɨɪɨɫɬɶ ɞɥɹ |
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ɥɸɛɨɣ ɜɨɥɧɵ, ɜ ɬɨɦ ɱɢɫɥɟ ɢ ɞɥɹ |
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ɚɥɶɜɟɧɨɜɫɤɨɣ, |
ɩɚɪɚɥɥɟɥɶɧɚ ɜɨɥɧɨɜɨɦɭ |
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ɜɟɤɬɨɪɭ. |
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Ɇɨɞɭɥɢ |
ɝɪɭɩɩɨɜɨɣ |
ɢ |
ɮɚɡɨɜɨɣ |
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ɫɤɨɪɨɫɬɢ ɧɟ |
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ɡɚɜɢɫɹɬ |
ɨɬ |
ɜɟɥɢɱɢɧɵ |
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Ɋɢɫ. |
4.12. |
Ʉɚɱɟɫɬɜɟɧɧɚɹ |
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ɤɚɪɬɢɧɚ |
ɞɢɫɩɟɪɫɢɢ |
ɜɨɥɧɨɜɨɝɨ ɜɟɤɬɨɪɚ. ɗɬɨ ɨɡɧɚɱɚɟɬ, |
ɱɬɨ |
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ɩɨɩɟɪɟɱɧɵɯ |
ɜɨɥɧ |
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ɩɪɢ |
ɩɪɨɞɨɥɶɧɨɦ |
ɜɨɥɧɚ ɧɟ |
ɞɢɫɩɟɪɝɢɪɭɟɬ. |
ɇɨ |
ɷɬɨ |
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ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɢ: 1 – ɫɨɛɫɬɜɟɧɧɨ ɚɥɶɜɟɧɨɜɫɤɚɹ |
ɫɩɪɚɜɟɞɥɢɜɨ ɬɨɥɶɤɨ ɜ ɨɛɥɚɫɬɢ ɧɢɡɤɢɯ |
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ɜɨɥɧɚ (ɨɛɵɤɧɨɜɟɧɧɚɹ, ɥɟɜɚɹ ɩɨɥɹɪɢɡɚɰɢɹ), |
ɱɚɫɬɨɬ. ȼɛɥɢɡɢ ɰɢɤɥɨɬɪɨɧɧɵɯ ɱɚɫɬɨɬ |
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2 – ɛɵɫɬɪɚɹ ɆɁȼ (ɧɟɨɛɵɤɧɨɜɟɧɧɚɹ, ɩɪɚɜɚɹ |
ɫɢɬɭɚɰɢɹ ɦɟɧɹɟɬɫɹ (ɪɢɫ. 4.12). |
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ɩɨɥɹɪɢɡɚɰɢɹ), |
3 – ɨɛɥɚɫɬɶ |
ɝɟɥɢɤɨɧɨɜ, 4 – ȼɑ- |
ɉɨɹɫɧɢɬɶ |
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ɩɨɹɜɥɟɧɢɟ |
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ɜɨɥɧɵ |
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ɫɭɳɟɫɬɜɟɧɧɨɣ |
ɞɢɫɩɟɪɫɢɢ |
ɦɨɠɧɨ |
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ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. ɂɡɜɟɫɬɧɨ, ɱɬɨ ɥɸɛɭɸ ɩɥɨɫɤɨ ɩɨɥɹɪɢɡɨɜɚɧɧɭɸ ɜɨɥɧɭ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ ɫɨɜɨɤɭɩɧɨɫɬɢ ɞɜɭɯ ɜɨɥɧ ɩɨɥɹɪɢɡɨɜɚɧɧɵɯ ɩɨ ɤɪɭɝɭ – «ɥɟɜɨ- ɢ ɩɪɚɜɨ ɩɨɥɹɪɢɡɨɜɚɧɧɵɯ». ȿɫɥɢ ɧɚɩɪɚɜɥɟɧɢɟ ɜɪɚɳɟɧɢɹ ɨɤɚɡɵɜɚɟɬɫɹ ɪɟɡɨɧɚɧɫɧɵɦ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɜɪɚɳɟɧɢɹ ɩɥɚɡɦɟɧɧɵɯ ɱɚɫɬɢɰ, ɚ ɦɵ ɡɧɚɟɦ, ɱɬɨ ɢɨɧɵ ɢ ɷɥɟɤɬɪɨɧɵ ɩɥɚɡɦɵ
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&||B&0 , ɪɢɫ. 4.10,ɛ)
ȼɷɬɨɦ 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 |
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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 = vɝɪ cA , |
(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
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Ɋɢɫ. 4.13. Ʉɚɱɟɫɬɜɟɧɧɚɹ ɤɚɪɬɢɧɚ |
Ɋɢɫ. 4.14. Ʉɚɱɟɫɬɜɟɧɧɵɣ ɯɚɪɚɤɬɟɪ ɞɢɫɩɟɪɫɢɢ |
ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɦɚɝɧɢɬɨɡɜɭɤɨɜɨɣ |
ɦɚɝɧɢɬɨɡɜɭɤɨɜɵɯ ɜɨɥɧ ɜ ɨɛɥɚɫɬɢ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬ: |
ɜɨɥɧɵ: ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ |
1 – ɨɛɥɚɫɬɶ ɦɚɝɧɢɬɧɨɝɨ ɡɜɭɤɚ, 2 – |
ɪɚɡɪɟɠɟɧɢɣ ɢ ɫɠɚɬɢɣ ɜɟɥɢɱɢɧɵ |
ɧɢɠɧɟɝɢɛɪɢɞɧɵɟ ɜɨɥɧɵ, 3 – ɜɟɪɯɧɟɝɢɛɪɢɞɧɵɟ |
ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ |
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:
v2 = |
B2 |
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+ γ |
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γβ¸ . |
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4πnm |
nm |
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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
ωɇȽ |ωBeωBi|, |
(4.85) |
ɬɨ ɟɫɬɶ ɨɧɚ ɫɨɜɩɚɞɚɟɬ ɫɨ ɫɪɟɞɧɢɦ ɝɟɨɦɟɬɪɢɱɟɫɤɢɦ ɢɡ ɰɢɤɥɨɬɪɨɧɧɵɯ ɱɚɫɬɨɬ, ɚ ɬɚɤɠɟ ɜɟɪɯɧɟɝɢɛɪɢɞɧɚɹ ɱɚɫɬɨɬɚ, ɩɪɢɛɥɢɠɟɧɧɨ ɪɚɜɧɚɹ (ɩɨɞɪɨɛɧɟɟ ɫɦ. [18])
ωȼȽ |
ωLe2 +ωBe2 . |
(4.86) |
ȼ ɨɛɥɚɫɬɢ ɱɚɫɬɨɬ ω <ωɇȽ |
ɜ ɩɥɚɡɦɟ ɜɨɡɦɨɠɧɨ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɦɚɝɧɢɬɨɡɜɭɤɨɜɵɯ ɜɨɥɧ, ɜ |
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ɨɛɥɚɫɬɢ ɱɚɫɬɨɬ ω >ωɇȽ |
ɜɨɡɦɨɠɧɨ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɯ ɜɨɥɧ, ɜ ɨɛɥɚɫɬɢ |
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ɱɚɫɬɨɬ ωɇȽ |
<ω <<ωȼȽ ɱɢɫɬɨ ɩɨɩɟɪɟɱɧɨɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɜɨɥɧ ɧɟɜɨɡɦɨɠɧɨ. |
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