It was shown in the first part to this paper how a simple magnetohydrodynamic model can be used to determine the stability of a tokamak plasma’s edge to peeling (external kink) modes. It was found that stability is determined by the value of Δ, a normalized measure of the discontinuity in the radial derivative of the radial perturbation to the magnetic field at the plasma-vacuum interface. To avoid the possibility that numerical divergences near the X-point might lead to misleading conclusions about plasma stability, this paper calculates the value of Δ analytically. This is accomplished by showing that the method of conformal transformations can be applied to systems with a continuously varying nonzero boundary condition and using the technique to obtain analytical expressions for both the vacuum energy and Δ. A conformal transformation is also used to obtain an equilibrium vacuum field surrounding a plasma with a separatrix and X-point. This allows the analytical expressions for the vacuum energy and Δ to be evaluated. The results here, combined with those in the first part of this paper, subsequently provide a quantitative description of the peeling mode’s growth rate as the plasma-vacuum boundary more closely approximates a separatrix with an X-point.

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