Calculation of Electric Microfield Distributions
Calculation of Electric Microfield Distributions
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a r e i r -r/X -ar/Xi u (r) = — ^ t — J l e _e I » a -1 2 -r/X v S (r) =-5-^ . (A-6) APPENDIX B EVALUATION OF T U)/T (0) o o In this appendix we evaluate the term T (£)/T (o). To do this we first evaluate the ring graph sum presented in Fig. (1.4a), lnT o (i) -~-4- I i-^'^l - / dr 2 ... dr j=l J- x u(r 01 ,£)v(r 12 ) ••• v(r )u(r ,£) (B-l) As in Appendix A, we make use of the Fourier transforms to write 2 ■*■ In T (£) = ~ P l / -^_ u (q,£)u(-q,Ji)e" 1 (q). (B-2) Z (2tt) J Since T (o) simply req...uires T (£=0) it follows that o ' o 2 + in T (£)/T (0) = ~ P j? / dq e _1 (q) {u(q,£)u(-q,A) - u 2 (q)} Z (2it) J 2 ->• f ■»■ - ~Pfl f dq -1, . f £»q -v 2 2, .
(2tt ) 3 2 = -yL , (B-3) 4(a 2 +l) 2 where in Eq.(B3) L = Zz ; a = r A; e = e/r 2 , (B-4) o o o o 105 106 and r is the ion sphere radius defined by the expression 4tt 3 , r r P-l. (B-5) APPENDIX C CALCULATION OF y In this appendix we evaluate the integrals in Eq.(1.2.17), 2 2 V ■ H" / d? 10 d? 20 ^v S (r 12 )] 2 /2 x {u S (r 10 ;£)u S (r 2() ;£) - u S (r 1Q )u S (r^)} .
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To quickly assess the difficulty of the text, read a short excerpt:
a r e i r -r/X -ar/Xi u (r) = — ^ t — J l e _e I » a -1 2 -r/X v S (r) =-5-^ . (A-6) APPENDIX B EVALUATION OF T U)/T (0) o o In this appendix we evaluate the term T (£)/T (o). To do this we first evaluate the ring graph sum presented in Fig. (1.4a), lnT o (i) -~-4- I i-^'^l - / dr 2 ... dr j=l J- x u(r 01 ,£)v(r 12 ) ••• v(r )u(r ,£) (B-l) As in Appendix A, we make use of the Fourier transforms to write 2 ■*■ In T (£) = ~ P l / -^_ u (q,£)u(-q,Ji)e" 1 (q). (B-2) Z (2tt) J Since T (o) simply req...uires T (£=0) it follows that o ' o 2 + in T (£)/T (0) = ~ P j? / dq e _1 (q) {u(q,£)u(-q,A) - u 2 (q)} Z (2it) J 2 ->• f ■»■ - ~Pfl f dq -1, . f £»q -v 2 2, .
(2tt ) 3 2 = -yL , (B-3) 4(a 2 +l) 2 where in Eq.(B3) L = Zz ; a = r A; e = e/r 2 , (B-4) o o o o 105 106 and r is the ion sphere radius defined by the expression 4tt 3 , r r P-l. (B-5) APPENDIX C CALCULATION OF y In this appendix we evaluate the integrals in Eq.(1.2.17), 2 2 V ■ H" / d? 10 d? 20 ^v S (r 12 )] 2 /2 x {u S (r 10 ;£)u S (r 2() ;£) - u S (r 1Q )u S (r^)} .
What to read after Calculation of Electric Microfield Distributions?
You can find similar books in the "Read Also" column, or choose other free books by Iglesias, Carlos a to read onlineMoreLess
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