Page 294 - Fundamentals of Magnetic Thermonuclear Reactor Design

Plasma Control System Chapter | 8 273

where I are the ampere-turns of the poloidal coils and the central solenoid sec- Ii
i
cs)
(,
tions, and b mn are the (m,n) error fields caused by unit deviations δ′, w′ of bm,n(c,s)
,
relevant shifts δ and rotations w of the coils.
A similar procedure is employed to estimate the (m,n) error fields associated
with deviations ∆ kl , () in the toroidal coil system: ∆k,l(φk')
'
φ
k
18 10
′
′
(,
(,
cs)
φ
cs)
B mn ( tor) =∑ ∑ mn ⋅  k ′ ; ′ k l , φ ⋅∆ ( ). (8.65) Bm,n(c,s)(tor)=∑k=118∑l=110bm,
b
φ ∆ ( )

k
,
k
,
kl
,
k =1 = l 1 n(c,s)⋅φk';∆k,l'(φk')⋅∆k,l(φk').
The final form is
cs)
cs)
(,
cs)
(,
B mn ( error) = B (, , ( tor) + B mn ( pol). (8.66) Bm,n(c,s)(error)=Bm,n(c,s)(tor)+Bm,n(c,s)(
,
,
mn
pol).
2
2
(0)
c ()
+
B mn = (B mn ) (B mn , s () ) , Bm,n(0)=Bm,n(c) +Bm,n(s) ,
,
,
2
2
Ψ mn = arctgB mn ) B , c () . Ψm,n=arctg(Bm,n(s))/Bm,n(c).
s ()
(
,
,
mn
As manufacture/assembly deviations are independent and additive, it is rea-
sonable to employ statistical methods in the analysis of error fields.
cs)
Error field modes B (, , are linearly dependent on shifts and tilts (rotations) of Bm,n(c,s)
mn
(, δω ), related
cs)
the coils or their parts. Pre-calculated error field modes b mn, (0,, ,∆ λ bm,n(c,s)(0,δ,w,∆λ)
to unit shifts and tilts, are the coefficients in linear combinations (8.64) and (8.65).
8.7.3 ITER Correction Coils
Despite the stringent tolerances imposed on manufacture/assembly errors of the
ITER magnet system, related error fields may be two to three times higher than
allowed. To suppress these errors below the LMT, a system of correction coils
is provided for in the ITER design (Fig. 8.4) [11].
Eighteen superconducting correction coils are periodically distributed
around the ITER and grouped in three locations: six at the top, six at the bot-
tom, and six at mid-plane. Each pair of coils, located on opposite sides of the
tokamak, is electrically connected in anti-series and magnetically coupled to
provide suppression of the n = 1 error field modes. Each group has three in-
dependent power supplies, which allow the phase adjustment of the correcting
field modes. As a result, nine independent power supplies enable reduction of
three error modes to an acceptable level.
8.8 PLASMA COLUMN POSITION AND SHAPE
RECONSTRUCTION BASED ON MAGNETIC MEASUREMENTS
8.8.1 Basic Principles
The position of a plasma column within the vacuum vessel is one of the main
parameters controlled during a discharge. Its reliable and fast identification is