Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

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Magnetic fields and tokamak plasmas Alan Wootton Then we would have the output from the 'modified Rogowski' coil ∑ s p,τ = c m f m f p dl ∑ m ∫ = c m 4a m + p m l ⎡ ⎣ ⎢ m + 1 + ( ) a a ⎤ p +1⎦ ⎥ for m, p even 3.16 = 0 otherwise 3.17 Equations 3.16 and 3.17 show specifically how, by including a finite number of terms (say p max = m max = 5) we will end up with a set of linear equations relating the measured signals to the required constants c m . We must now solve them to obtain the coefficients c m as functions of the measured s p,τ ; a similar procedure provides the d m as functions of the signals s p,n . The result is not as elegant as the Fourier analysis applicable on a circular contour, where a single coil can be wound to measure each individual Fourier coefficient, but I don’t know another way to represent the fields on a square contour. Of course, instead of using these specially wound coils to measure s p,τ and s p,n directly, the required integrals can always be constructed from individual coil signals of B τ and B n around the contour l. An example of a saddle coil for a particular f = η(1+ξ/R l ) is shown in Figure 3.5. Here R l is the major radius of the contour center. These strange looking coils are actually useful for helping determine plasma position Figure 3.5. A saddle coil suitable for winding on a square vessel 38
Magnetic fields and tokamak plasmas Alan Wootton 4. PLASMA CURRENT Rogowski coil The plasma current is measured by a "Rogowski coil", which is a multi turn solenoid completely enclosing the current to be measured. Figure 4.1 shows an example, the placement of this coil around the plasma is shown in Figure 4.2. The transient plasma current generates a voltage ε which, for a uniform winding density of n A turns per unit length of area A, is (after applying Faraday's Law) ε = n A Aµ 0 dI dt 4.1 from which I p is deduced after time integration. This is just a special case of our general model for how to measure the fields on a contour. Integration can be performed passively with a resistance-capacitance circuit, with active integrators, or numerically on a computer. In each case there is an associated 'integration time constant' τ int . The Rogowski coil must not be sensitive to other than the wanted field components, so that a center return must be used. The angle between the Rogowski coil and the enclosed current is irrelevant, as is the contour on which the coil is wound. plasma Volts Rogowski I p Volts Figure 4.1. A Rogowski coil Figure 4.2. Coil placement around plasma 39
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Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

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