Pressure profiles, resonant Pfirsch–Schlüter currents, thermal instabilities, and magnetic island formation

A prescription for constructing the plasma pressure profile in the vicinity of an equilibrium magnetic island is derived by solving a sourced pressure diffusion equation near the island region. For pressure sources and sinks that are relatively constant in space, it is found that the plasma pressure profile is insensitive to pressure sources; thus the pressure profile can be constructed by assuming that the net pressure flux across any topologically toroidal magnetic surface is constant. This construction of the pressure profile is also valid for magnetic islands that are slowly evolving in time. By coupling the pressure evolution equation with the magnetostatic equilibrium equations, the theory is applied to the case of self-consistent construction of pressure-gradient-driven magnetic islands. In particular, the question of resonant Pfirsch–Schlüter current induced magnetic islands and the role of thermal effects on nonlinear magnetic islands is addressed.