Page 397 - Fundamentals of Magnetic Thermonuclear Reactor Design

Mechanics of Magnetic Fusion Reactors Chapter | 12 375

FIGURE A.12.1.1 Estimation of mutual magnetic stiffness of ring currents I i and I j . u 1 = 0;
u 2 = u are horizontal displacements of coils along the х axis.

magnetic stiffness will be determined for an equivalent pair of ring currents.
The coils are taken to be absolutely stiff. We denote the unit vectors of coordi-
nate axes as e , e and e .
x
y
z
,
In the general case u( = u i − uh = z i − z ), the force directed at the i-th coil (u=ui−uj, h=zi−zj)
j
j
from the j-th coil may be written as
F ij =−c ij ( PF) u ( i − u ), Fij=−cij(PF)(ui−uj),
j
where
 ( −z z ) − 2 ( R 2 + R 2 ) cos Ψ+ RR 3cos 2 Ψ )

2
( +
c (PF ) = µ 0 I IR R j ∫ π   i j i j   i j d Ψ
ij i
ij
2 0  2 2 − RR cos ) 2  52
  R i + R j 2 i j Ψ+ z i   cijPF=µ 2IiIjRiRj∫0πzi−zj −2Ri2
( − z j
2
0
2
()
m
( ≠i j C ij () = C ji m ) is the mutual magnetic stiffness of the i-th and the j-th coils. +Rj2cosΨ+RiRj3+cos ΨRi2+Rj2−
,
i≠j,cij(m)=cji(m)
2
2RiRjcosΨ+zi−zj 5/2 dΨ