Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

Magnetic fields and tokamak plasmas
Alan Wootton
plasma
diamagnetic loop
integrator gate
compensating coil
•
•
Ω
balance resistor
C
Ω i
Ci
_
Figure 14.5. A diamagnetic coil compensating system
An alternative technique is to wrap two simple toroidal flux loops around the vessel, but at
different minor radii. Such a configuration is shown in Figure 14.4. Let two concentric loops
have radii b 1 and b 2 , and let R l be the major radius of the loops. Then, remembering that B φe =
B φ0 R l /R, we have after time integration
⎡
Φ(b i
) = 2πR l
B φ0
R l
− R 2 2
⎢
l
− b i
⎣
( ) 1 2
⎡
Φ(b i
) = 2πR l
B φ0
R l
− R 2 2
⎢
l
− b i
⎣
( ) 1 2
⎤
⎥ +δΦ 14.24
⎦
⎤
⎥ +δΦ 14.25
⎦
δΦ = Φ(b 1
) − k( Φ(b 2
) − Φ(b 1
)); k =
b 1
2
b 2 2 − b 1
2
R
l
2
− b 12
+ R 2 2
− b 2
R l
+
R 2 2
+ b
l 1
l
14.26
111