Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

Magnetic fields and tokamak plasmas
Alan Wootton
Figure 19.2. The currents flowing in a vessel or shell with toroidal
(i.e. longitudinal) and poloidal (i.e. transverse) gaps.
There are two types of insulating breaks, as shown in Figure 19.1 and Figure 19.2, (taken from
Mukhovatov and Shafranov). For transverse gaps (Figure 19.1) any symmetric component of
current must flow on the vessel surfaces. However, non symmetric components, introduced for
example by axisymmetric plasma motion, will produce volume currents. At the gap the non
symmetric currents flow in opposite directions. They will produce a local vertical field, which
must affect the plasma position, as well as the interpretation of magnetic coil signals. The two
(surface and bulk) currents have different decay times, as discussed later.
If both a transverse and a longitudinal gap exists, Figure 19.2 shows that for the non symmetric
components the placing of the break in poloidal angle is important. A longitudinal gap at the
outer equator does not distort the field, while a gap at the top or bottom does.
x
d
a
b
z
Figure 19.3. The geometry of a conducting shell or vessel.
We are concerned with the currents induced in a resistive vacuum vessel lying outside the
plasma, and their effects on all the measurements we have discussed. As a characteristic
example, consider a homogeneous field B = B 0 sin(ωt) parallel to the plane of a conducting plate;
the inner and outer boundaries of the plate are at a distance b and a from the symmetry plane (see
Figure 19.3). Maxwell's equations reduce to
∇ × ( ∇ × B) = −µ 0
σ ∂B
∂t
19.1
When the ratio of the plate thickness to the layer thickness is much less than unity, i.e. d/b > d skin , (i.e. at high frequency) we have a thick plate, and we can consider
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