Page 291 - Fundamentals of Magnetic Thermonuclear Reactor Design

270 Fundamentals of Magnetic Thermonuclear Reactor Design

8.7 CORRECTION OF ERROR FIELDS
8.7.1 Effect of Error Fields on Plasma Processes

In tokamaks the poloidal magnetic field minor deviations from the ideal axial
−
4
Bm,n/Bt0≤10−4 symmetry with amplitudes B mn / B ≤ 10 (error fields) may give rise to the
t0
,
so-called locked (i.e. non-rotating) modes. Values B m,n are amplitudes of Fou-
rier harmonics of the normal component of a magnetic field on the plasma ratio-
nal magnetic surfaces q = m/n (the safety factor) with m poloidal and n toroidal
numbers.
Low-order error field modes, such as (1.1), (2.1) and (3.1), interact with the
rational q surfaces in the plasma and drive the formation of magnetic islands. If
islands are not stabilised, they slow down the plasma rotation and, if the natural
rotation is insufficient, the rotating MHD mode locks and the adverse effect of
error fields is amplified. The locked modes may considerably limit the operating
domain of any tokamak, resulting in a degraded energy/particle confinement or
a plasma current disruption not only at the early discharge stage, but also at later
discharge stages. A systematic study of the locked mode evolution mechanism
allowed a semi-empirical estimation of the acceptable level of error fields (and
how to correct them).
As the plasma ‘sensitivity’ to the locked modes tends to grow with increas-
ing the major radius and toroidal field of tokamaks, this problem is likely to be
much more serious for reactor-scale machines, including ITER, than for experi-
mental devices. In the case of ITER, it can be solved if the following require-
ments are met simultaneously:
l High precision of the magnet manufacturing and assembly,
l Comprehensive accounting and, where possible, elimination of factors that
may disturb the field axial symmetry, and
l Presence of correction coils.
Extrapolation of experimental data for a combination of error field modes
(m, n) = (1,1), (2,1), (3,1) for the B m,n normal component of error fields to
ITER parameters allowed the following multi-mode criterion (referred to as the
locked mode threshold or LMT) to be formulated for Ohmic operation at low
plasma density:

2
2
2
B 3-mode = W 11 ⋅ B 1,1 +W 21 ⋅ B 2,1 +W 31 ⋅ B , (8.49)
3,1
B3-mode=W11⋅B1,12+W21⋅B2,12+W31⋅B3,12≤5×10−5⋅Bt0
≤×510 −5 ⋅ B t0
where assigned weights W = 0.2, W = 1.0, W = 0.8, respectively; B = 5.3 T
31
21
11
t0
is the toroidal field at the major radius R = 6.2 m. As one can see, the LMT
criterion imposes considerable restrictions on error fields in tokamak reactors.
Experimentally, it is found that the locking mode (m,n) = (2,1) is the most dan-
gerous and, accordingly, attention is focused on minimising and correcting this
error field component. The “3-mode” error field criterion and criteria on the