In the first part to this papercite{part1} it was shown how a simple Magnetohydrodynamic model could be used to determine the stability of a Tokamak plasmas edge to a Peeling (External Kink) mode. Stability was found to be determined by the value of $Delta$, a normalised measure of the discontinuity in the radial derivative of the radial perturbation to the magnetic field at the plasma-vacuum interface. Here we calculate $Delta$, but in a way that avoids the numerical divergences that can arise near a separatrices X-point. This is accomplished by showing how the method of conformal transformations may be generalised to allow their application to systems with a non-zero boundary condition, and using the technique to obtain analytic expressions for both the vacuum energy and $Delta$. A conformal transformation is used again to obtain an equilibrium vacuum field surrounding a plasma with a separatrix. This allows the subsequent evaluation of the vacuum energy and $Delta$. For a plasma-vacuum boundary that approximates a separatrix, the growth rate $gamma$ normalised by the Aflven frequency $gamma_A$ is then found to have $ln(gamma/gamma_A)=-{1/2} ln (q/q)$. Consequences for Peeling mode stability are discussed.
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