Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

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Magnetic fields and tokamak plasmas Alan Wootton 7. Position and β I + l i /2 for the circular equilibrium An ‘exact’ circular equilibrium Consider the pickup coils shown in Figure 7.1. Two coils (B ω1 , B ω2 ) measure the poloidal field at the inner and outer equator, each at a distance b from some center at R = R l . A saddle coil measures the difference in flux between the inner and outer equator. Instead of the partial flux loops (i.e. the saddle coil) shown in Figure. 7.1, two complete flux loops could be used, as in the plan view of Figure 7.2. We want to know what these coils tell us for our circular equilibrium. plasma R-b B ω1 Saddle Coil Ψ 1 R+b Bω2 Fig 7.1. Saddle and B ω coils Ψ 2 Fig 7.2. A plan view of poloidal flux loops The original equilibrium was derived in a coordinate system (r,θ,φ) based on the plasma geometric center R g . We must translate the results to a coordinate system (ρ,ω,φ) based on for example the center of a circular contour centered at R = R l , which might be the vacuum vessel center. Details are seen in Figure 7.3. 70
Magnetic fields and tokamak plasmas Alan Wootton z ρ ω ∆g r θ plasma with geometric center R R g contour with center R l Figure 7.3. The coordinate systems associated with the geometric center R g , and an external contour center R l . Then R = R l + ρcos(ω), z = ρsin(ω), and let ∆ g = R g - R l be the displacement of the plasma geometric center from the contour center. Remembering that we are only dealing with r > a, the plasma minor radius, and taking ∆g/a p
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Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

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