Жданов С.К Цветков И.В - Основы физических процессов в плазме и в плазменных установках (2000)
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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 ) εe , 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:
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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 |
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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”
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
τee = K |
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ɝɞɟ σc ɤɭɥɨɧɨɜɫɤɨɟ ɫɟɱɟɧɢɟ, ɚ vTe – ɬɟɩɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ. ɉɨɞɫɬɚɜɥɹɹ
ɡɧɚɱɟɧɢɟ ɤɭɥɨɧɨɜɫɤɨɝɨ ɫɟɱɟɧɢɹ σc ɢɡ (1.23) ɢ vTe = |
3Te me , ɩɨɥɭɱɢɦ: |
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ɋɬɪɨɝɢɣ ɪɚɫɱɟɬ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ Ʉ<2. Ⱥɧɚɥɨɝɢɱɧɵɣ ɪɚɫɱɟɬ ɞɥɹ ɢɨɧɨɜ ɞɚɟɬ
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ɝɞɟ Z1,2 - ɤɪɚɬɧɨɫɬɢ ɢɨɧɢɡɚɰɢɢ. ɋɪɚɜɧɢɦ τee ɢ τii: ɞɥɹ ɪɚɜɧɵɯ ɬɟɦɩɟɪɚɬɭɪ Te=Ti , ɩɪɟɞɩɨɥɚɝɚɟɦ Z1=Z2=1:
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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
(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:
(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
ɜmi me (~50 ɞɥɹ ɜɨɞɨɪɨɞɧɨɣ ɩɥɚɡɦɵ) ɪɚɡ ɛɨɥɶɲɟ.
ȼɨɛɳɟɦ 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]:
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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 |
= − |
Te − Ti |
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dTi |
= |
Te − Ti |
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dt |
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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 + Ti0 = 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]:
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4.5 10 |
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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 |
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D (∆x)2 / 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 |
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D = 1/3λvT , |
(1.51) |
ɝɞɟ vT = 3 T - ɬɟɩɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɱɚɫɬɢɰ ɝɚɡɚ. |
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ɂɡɜɟɫɬɧɵ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɜɹɡɤɨɫɬɢ η ɢ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ κ ɝɚɡɚ: |
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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 61 n(x − λ )vT − 61 n(x + λ)vT − 13 λvT ∂∂nx .
Ɇɵ ɜɢɞɢɦ, ɱɬɨ ɩɥɨɬɧɨɫɬɶ ɩɨɬɨɤɚ ɨɤɚɡɵɜɚɟɬɫɹ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɣ ɝɪɚɞɢɟɧɬɭ ɤɨɧɰɟɧɬɪɚɰɢɢ. Ʉɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ ɡɞɟɫɶ ɢ ɟɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬ ɞɢɮɮɭɡɢɢ (1.51). Ⱥɧɚɥɨɝɢɱɧɨ, ɪɚɫɫɦɚɬɪɢɜɚɹ ɩɟɪɟɧɨɫ ɬɟɩɥɚ,
ɢɭɱɢɬɵɜɚɹ, 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
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∂T |
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∂T |
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T(x − λ ) − |
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T(x + λ )¸ |
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nλv |
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≡ −κ |
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, κ ≈ |
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nλv |
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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 |
∂vy |
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η ~ pτ , |
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ɝɞɟ ɪ – ɞɚɜɥɟɧɢɟ, ɚ τ - ɜɪɟɦɹ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ. ɉɨɫɤɨɥɶɤɭ ɞɥɹ ɨɞɧɨɤɨɦɩɨɧɟɧɬɧɨɝɨ ɝɚɡɚ p=nT, ɚ τ=λ/vT, ɬɨ ɩɨɥɭɱɚɟɦ
η ~ pτ ~ nT |
λ = mn T λ |
m |
= |
1 mnλvT , |
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vT |
m 3T |
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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
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ȿɫɥɢ ɜ ɪɚɜɟɧɫɬɜɨ (1.51) ɩɨɞɫɬɚɜɢɬɶ ɡɧɚɱɟɧɢɟ λ ɢɡ ɜɵɪɚɠɟɧɢɹ (1.22) ɢ ɩɪɢɧɹɬɶ |
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vT |
= 3 T |
, ɬɨ ɩɨɥɭɱɢɦ |
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3 3 T 5/ 2 |
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D = 4πe4 L n m . |
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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:
j |
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= − D |
dni |
− b |
dϕ |
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(1.55) |
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dx |
dx |
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i |
i |
i |
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ɝɞɟ bi - ɩɨɞɜɢɠɧɨɫɬɶ ɢɨɧɨɜ, ϕ - ɩɨɬɟɧɰɢɚɥ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. Ⱥɧɚɥɨɝɢɱɧɨ ɩɨɬɨɤ ɷɥɟɤɬɪɨɧɨɜ ɪɚɜɟɧ:
j |
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= − D |
dne |
+ b |
dϕ |
, |
(1.56) |
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dx |
dx |
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e |
e |
e |
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ɝɞɟ be - ɩɨɞɜɢɠɧɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ. Ɍɚɤ ɤɚɤ ɩɥɚɡɦɚ ɜ ɰɟɥɨɦ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɚ, ɬɨ, ɩɪɢɧɹɜ
ne=ni=n ɢ |
dni |
= |
dne |
= |
dn |
, ɢ ɢɫɤɥɸɱɢɜ |
dϕ |
ɢɡ ɭɪɚɜɧɟɧɢɣ (1.55) ɢ (1.56), ɨɛɧɚɪɭɠɢɦ, ɱɬɨ |
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dx |
dx |
dx |
dx |
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ɩɥɨɬɧɨɫɬɶ ɩɨɬɨɤɚ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɝɪɚɞɢɟɧɬɭ ɟɟ ɤɨɧɰɟɧɬɪɚɰɢɢ:
j = − |
Dibe + Debi dn |
= − Da |
dn |
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. |
(1.57) |
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b + b |
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dx |
dx |
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i e |
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Ʉɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ ɦɟɠɞɭ ɩɥɨɬɧɨɫɬɶɸ ɩɨɬɨɤɚ ɱɚɫɬɢɰ ɢ ɝɪɚɞɢɟɧɬɨɦ ɤɨɧɰɟɧɬɪɚɰɢɢ ɢ ɟɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬ ɚɦɛɢɩɨɥɹɪɧɨɣ ɞɢɮɮɭɡɢɢ:
D = |
Dibe + Debi |
. |
(1.58) |
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a |
bi +be |
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ɍɱɢɬɵɜɚɹ, ɱɬɨ, ɫɨɝɥɚɫɧɨ ɫɨɨɬɧɨɲɟɧɢɸ ɗɣɧɲɬɟɣɧɚ, ɩɨɞɜɢɠɧɨɫɬɶ ɱɚɫɬɢɰ ɢ |
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ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɞɢɮɮɭɡɢɢ ɫɜɹɡɚɧɵ ɦɟɠɞɭ ɫɨɛɨɣ ɫɨɨɬɧɨɲɟɧɢɹɦɢ |
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be,i = (|e|D/T)e,i, |
(1.59) |
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ɚ ɬɚɤɠɟ, ɭɱɢɬɵɜɚɹ, ɱɬɨ, ɫɨɝɥɚɫɧɨ ɜɵɪɚɠɟɧɢɸ (1.54), ɞɨɥɠɧɨ ɛɵɬɶ De>>Di ɢ, ɤɚɤ ɫɥɟɞɫɬɜɢɟ, ɷɥɟɤɬɪɨɧɵ ɡɧɚɱɢɬɟɥɶɧɨ ɩɨɞɜɢɠɧɟɟ ɢɨɧɨɜ, ɩɨɥɭɱɚɟɦ
D = D |
§ |
1 |
+ |
Te |
· |
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¨ |
¸ . |
(1.60) |
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T |
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a |
i |
© |
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¹ |
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i |
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Ɉɱɟɜɢɞɧɨ, ɢɦɟɸɬ ɦɟɫɬɨ ɧɟɪɚɜɟɧɫɬɜɚ Di<Da<<De, ɤɚɤ ɢ ɞɨɥɠɧɨ ɛɵɬɶ, ɫɨɝɥɚɫɧɨ ɥɨɝɢɤɟ ɧɚɲɢɯ ɪɚɫɫɭɠɞɟɧɢɣ: ɚɦɛɢɩɨɥɹɪɧɨɟ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɭɫɢɥɢɜɚɟɬ ɩɟɪɟɧɨɫ ɢɨɧɧɨɣ ɤɨɦɩɨɧɟɧɬɵ ɩɥɚɡɦɵ ɢ, ɬɟɦ ɫɚɦɵɦ, ɷɮɮɟɤɬɢɜɧɨ ɭɜɟɥɢɱɢɜɚɟɬ ɤɨɷɮɮɢɰɢɟɧɬ ɞɢɮɮɭɡɢɢ ɩɥɚɡɦɵ ɜ ɰɟɥɨɦ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɞɢɮɮɭɡɢɢ ɢɨɧɨɜ; ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ - ɛɨɥɟɟ ɩɨɞɜɢɠɧɨɣ ɤɨɦɩɨɧɟɧɬɵ ɩɥɚɡɦɵ - ɫɢɬɭɚɰɢɹ ɨɛɪɚɬɧɚɹ.
Ⱦɥɹ ɢɡɨɬɟɪɦɢɱɟɫɤɨɣ ɩɥɚɡɦɵ, ɤɨɝɞɚ Te = Ɍi , ɩɨɥɭɱɚɟɦ
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 / L m . |
(1.61) |
c |
|
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
j = σE = −σ |
dϕ |
, |
(1.65) |
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dx |
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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 ɧɟɜɫɟɝɞɚ, 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
(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:
σ |
T |
3/ 2 |
T 3/ 2 . |
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e |
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(1.70) |
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e |
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Lc |
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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]:
σ = 1.96σ T 3/ 2 |
, |
σ |
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0.9 1013 |
, c−1ɷȼ−3/ 2 . |
(1.71) |
|
1 |
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1 e |
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( Lc |
/ 10 ) |
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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 n2 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:
(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) |