Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

Magnetic fields and tokamak plasmas
Alan Wootton
z
plasma
η
Contour l
ξ
R
R l
Figure 7.5. Geometry used for a non-circular contour.
An analogy with our cosinusoidally wound Rogowski coil and sinusoidally wound saddle coil
would be a modified Rogowski coil measuring the first symmetric (in vertical position) moment
s 1,τ
= ∫ ξB τ
dl
7.18
l
and a saddle coil measuring the first asymmetric (in vertical position) moment
λ 1
= − ρ
2R l
⎡
1+ a 2
⎛ ⎞
p
⎜
⎝ ρ 2
⎠
⎟ ⎛
Λ + 1 ⎞ ⎛
⎜
⎝ 2
⎟ + ln
ρ ⎞
⎜ ⎟ −1 + 2R ∆ ⎤
l g
⎢
⎥
⎣ ⎢
⎠ ⎝ a p ⎠ ρ 2
⎦ ⎥
7.19
To interpret what these coils will measure, we can write an equation for the components B τ and
B n on our chosen contour (for a rectangular contour they will be either B η or B ξ ). Because the
only variables in the equations for an assumed circular equilibrium are the geometric
displacement ∆ g , Λ and minor radius a p , we must be able to derive expressions for the measured
coil outputs s 1,τ and s 1,n in terms of these variables. For example, if our contour is a square of
half height and half width a, centered at R = R l , we must find
( ) 7.20
s 1,τ
= s 1, τ
I p
,Λ,∆ g
, a p
, a, R l
s 1,n
= s 1,n ( I p
, Λ,∆ g
, a p
,a, R l ) 7.21
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