Single-Particle Electrodynamics - Assassination Science

+ 3 2 r dr s ˙v 2 (n s· ˙v) ˙σ − 3 2 r dr s (n d· ˙v)(n s· ˙v)¨σ − 3 4 r dr s (n d· ˙v)(n s·¨v) ˙σ
− 3 4 r dr s (n d·¨v)(n s· ˙v) ˙σ − 9 4 r dr s (n s· ˙v)( ˙v·σ)¨v − 9 2 r dr s (n s· ˙v)( ˙v· ˙σ) ˙v
− 9 4 r dr s (n s· ˙v)(¨v·σ) ˙v − 3 2 r dr s (n s·¨v)( ˙v·σ) ˙v
+ 3 2 r dr s (n d· ˙v)(n s· ˙v)( ˙v·σ) ˙v + 3 4 r2 s (n s· ˙v) 2 ¨σ + 3 4 r2 s (n s· ˙v)(n s·¨v) ˙σ
− 3 4 r2 s (n s· ˙v) 2 ( ˙v·σ) ˙v + O(ε 3 ).
(G.63)
G.6.18
General retarded field expressions
The retarded field expressions verified explicitly in the program retfield
are
E ′q
1 = −κ 3 (n·n ′ ) ˙v + κ 3 (n· ˙v)n ′ ,
E ′q
2 = κ 3 γ −2 n ′ ,
E ′d
1 = 3κ 5 (n· ˙v) 2 (n·σ ′ )n ′ − 3κ 5 (n·n ′ )(n· ˙v)(n·σ ′ ) ˙v − κ 4 (n·n ′ )(n·σ ′ )¨v
− 3κ 4 (n·n ′ )(n· ˙σ ′ ) ˙v + 3κ 4 (n· ˙v)(n· ˙σ ′ )n ′ + κ 4 (n·¨v)(n·σ ′ )n ′
− κ 3 (n·n ′ )¨σ ′ − κ 3 (n· ˙v) ˙σ ′ + κ 3 (n· ˙σ ′ ) ˙v + κ 3 (n· ¨σ ′ )n ′ ,
E ′d
2 = −3κ 5 (n·n ′ )(n ′′·σ ′ ) ˙v + 3κ 5 (n· ˙v)(n ′′·σ ′ )n ′ + 3κ 5 (n·σ ′ )(n ′′· ˙v)n ′
+ 3κ 4 (n ′′· ˙σ ′ )n ′ − κ 3 γ −2 ˙σ ′ − κ 3 (n· ˙v)σ ′ + κ 3 (n ′·σ ′ ) ˙v
+ κ 3 (v· ˙σ ′ )n ′ − κ 3 ( ˙v·σ ′ )n ′ ,
E ′d
3 = 3κ 5 γ −2 (n ′′·σ ′ )n ′ − κ 3 γ −2 σ ′ ,
B ′q
1 = −κ 3 (n·n ′ )n× ˙v + κ 3 (n· ˙v)n×n ′ ,
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