Penetration and Amplification of Resonant Perturbations in 3D Ideal-MHD Equilibria

Full text: The nature of ideal-MHD equilibria in three-dimensional geometry is profoundly affected by resonant surfaces, which beget a non analytic dependence of the equilibrium on the boundary. Furthermore, nonphysical currents arise in equilibria with continuously nested magnetic surfaces and smooth pressure and rotational-transform profiles. We demonstrate that three-dimensional, ideal-MHD equilibria with nested surfaces and delta-function current densities that produce a discontinuous rotational transform are well defined and can be computed both perturbatively and using fully-nonlinear equilibrium calculations. The results are of direct practical importance: we predict that resonant magnetic perturbations penetrate past the rational surface (i.e., 'shielding' is incomplete, even in purely ideal-MHD) and that the perturbation is amplified by plasma pressure, increasingly so as stability limits are approached. (author)