Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

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Magnetic fields and tokamak plasmas Alan Wootton fields, can be used. The plasma fields can be calculated if external conductor currents are known. Using just the plasma fields alone may have advantages in terms of requiring fewer moments to accurately describe the data. 86
Magnetic fields and tokamak plasmas Alan Wootton 10. PLASMA POSITION Position by multipole moments Let us apply the concept of multipole moments as described in section 9 to the geometry shown in Figure 10.1, using the notation of Shafranov, Equations 9.7 through 9.10. Assume S φ contains only the plasma and vacuum regions so that µ = µ 0 and L* = ∆*. The term ∫dS φ in Equation 9.7 is over the plasma surface, in a coordinate system centered in the plasma, while the term ∫dl is evaluated in a laboratory frame. The two coordinate systems are related by plasma position; therefore Equation 9.7 must provide information on the plasma position. Z φ R Z ρ ω R Z ∆z η ξ z x R R l 1a R R c l 1b 1c ∆ R Figure 10.1. The geometry used in section 10. There is a contour l, centered on R = R l , with a local rectalinear system (η,ξ), and a second coordinate system based within the plasma, (z,x), centered at R = R c , the plasma current center, defined later. Note that ξ = x +∆ R , η = z + ∆ z , R c = R l + ∆ R , and R = R c + x = R l + ξ. To be convenient, the moments (i.e. the choice of f m ) should, in the large aspect ratio limit (x 2 +iz 2 )/R p 2
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Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

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