Magnetic island effects on axisymmetric equilibria

Abstract

The plasma magnetohydrodynamics equilibrium equation in the vicinity of a single, thin magnetic island region is derived. First, the pressure profile in the vicinity of an island is determined using the continuity of transport fluxes across the island assuming a diffusive form for the fluxes. Then, by considering the island-induced magnetic perturbation, the structure of the current density around an island is examined. The modifications of the pressure and current density in the vicinity of a magnetic island lead to an equation that describes the toroidal equilibrium of the plasma. An “effective” axisymmetric Grad–Shafranov equation is constructed by taking a helical average over the toroidal equilibrium. Thus, we can take account of the three-dimensional magnetic island effects for a thin island in a two-dimensional equation. As with the Grad–Shafranov equation, the calculation does not employ a large aspect ratio or small β approximation; however, it uses a small island width (w≪r)s expansion. Finally, we determine the time-varying signal that would be observed on a probe measuring a scalar quantity such as the pressure when a magnetic island structure is rotating relative to the probe.