Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

Magnetic fields and tokamak plasmas
Alan Wootton
for any path l, with n the normal to a two sided surface S. Applying Stokes theorem
( ∫ A • dl = n • ∇ × AdS
l ∫ for any vector A) to the left hand side of Equation 1.6 gives Equation
S
1.3. Figure 1.1 shows the geometry of a coil used in applying Equation 1.6, Faraday’s Law. The
output signal must be time integrated to obtain the required flux. By taking a small enough coil
the local field B can then be determined. This becomes difficult if very small scale variations in
field exist, because the pick-up coils must then be very small themselves. The surface S includes
any area between the leads; this is minimized by twisting them together. A hand drill is
particularly useful for this.
Integration
Coil
voltage
Surface S
produced
across
leads
leads
Contour l
Figure 1.1. The contour l and surface S of a pick-up coil.
The time integration required to obtain the magnetic field B from the pick-up coil output ε can be
performed either digitally or by an analog circuit.
ε in
Ω
C
Figure 1.2. A passive “ΩC” integration circuit.
ε out
The simplest thing to do is to use a capacitor (C) and resistor (Ω) network, as shown in Figure
1.2. The output voltage is given by
dε out
dt
+ ε out
τ
= ε in
τ
1.7
with τ = ΩC called the integrator time constant. The solution to this equation is
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