Single-Particle Electrodynamics - Assassination Science

where
P (n)
aq (r d , r s ) = 0,
P (n)
ad (r d, r s ) = ˙σ·E a n(r d , r s ),
P (n)
aµ (r d , r s ) = ˙σ·B a n(r d , r s ),
F (n)
aq (r d , r s ) = λE q n(r d , r s ),
F (n)
ad (r d, r s ) = λ(σ·∇)E a n(r d , r s ) + (σ· ˙v)E a n(r d , r s ) + ˙σ×B a n(r d , r s ),
F (n)
aµ (r d , r s ) = λ(σ·∇)B a n(r d , r s ) + (σ· ˙v)B a n(r d , r s ) − ˙σ×E a n(r d , r s )
N N(n)
aq (r d , r s ) = 0,
+ λσ×J a n,
N N(n)
ad (r d , r s ) = λσ×E a n(r d , r s ),
N N(n)
aµ (r d , r s ) = λσ×B a n(r d , r s ),
where n is the inverse power of R of the retarded fields in question (or M for
the Maxwell field of the magnetic dipole), and a and b = q, d or µ.
Defining, for convenience, the quantity
˜µ 2 ≡ d 2 + µ 2
which appears for all dually-symmetric dipole self-interactions, the program
radreact of Section G.6 finds the following final equations of motion:
P self
= − 2 3 qdη 1( ˙v· ˙σ) − 2 3 ˜µ2 η 1 ( ˙σ· ¨σ) − 1 30 ˜µ2 η 1 ( ˙v·σ)( ˙v· ˙σ)
+ 2 3 qdη 0(¨v· ˙σ) + 2 3 ˜µ2 η 0 ( ˙σ·... σ) + 1 3 ˜µ2 η 0 ( ˙v·σ)(¨v· ˙σ)
− 1 3 ˜µ2 η 0 ( ˙v· ˙σ)(¨v·σ), (6.128)
F self = − 3 2 µ2 η ′ 3 ˙v − 1 2 ˜µ2 η ′ 3 ˙v − 1 2 q2 η 1 ˙v − 2 3 qdη 1 ¨σ + 4
15 ˜µ2 η 1
...
v + 2 3 ˜µ2 η 1 ˙v 2 ˙v
− 1 3 ˜µ2 η 1 ˙σ 2 ˙v + 1 3 ˜µ2 η 1 ( ˙v·σ)¨σ + 1 15 ˜µ2 η 1 ( ˙v·σ) 2 ˙v − 1 6 ˜µ2 η 1 ( ˙v· ˙σ) ˙σ
289