Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

Magnetic fields and tokamak plasmas
Alan Wootton
Figure 1.18a and 18b show the computed distortion to a particular surface (A = constant) for d
= 0.25, I zq /I zp = 0 and 2.0. With I zq /I zp = 1.0 the value of height to width is measured to be 1.28,
as compared to the value of 1.25 derived from Equation 1.62.
Figure 1.18a. Contours of vector potential
with I zq /I zp = 0. The larger contour is taken
as a reference in determining the distortion
produced by an applied quadrupole field.
Figure 1.18b Contours of vector potential
with I zq /I zp = 2. The contours have the same
flux values as those shown in Figure 1.18a.
Circuit equations
For some applications we will consider the plasma as a lumped series resistance and inductance,
coupled to other circuits (including a conducting vacuum vessel) by mutual inductances. Figure
1.19 shows how this is represented.
The equation for circuit l consisting of a series self inductance L ll and resistance Ω l , coupled by
mutual inductances M li to other circuits i, is
1.63
The sum over the mutual inductances is for i ≠ l because M ll = L ll is brought out separately. If
the circuit is closed (short circuited), then ε l = 0. If the circuit is open, or connected to a high
input impedance, then I l = 0 and ε l = d/dt(ΣM l,i I i ). The plasma is sometimes represented as one
series inductance-resistance circuit, or sometimes as a number of such circuits in parallel, all
short circuited together. The vacuum vessel is similarly represented as a number of paralleled
resistor-inductor circuits, which can be open circuit (a vessel with an insulating gap) or short
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