2009/02/20 by Webster, A. J.
#FOS: Physical sciences #Plasma Physics (physics.plasm-ph)
paper · doi:10.48550/arxiv.0902.3587
In the first part to this paper\citepart1 it was shown how a simple Magnetohydrodynamic model could be used to determine the stability of a Tokamak plasma's edge to a Peeling (External Kink) mode. Stability was found to be determined by the value of Δ', 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 Δ', but in a way that avoids the numerical divergences that can arise near a separatrice's 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 Δ'. 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 Δ'. For a plasma-vacuum boundary that approximates a separatrix, the growth rate γ normalised by the Aflven frequency γA is then found to have ln(γ/γA)=-1/2 ln (q'/q). Consequences for Peeling mode stability are discussed.