Plasma equilibrium in a magnetic field with stochastic regions

The nature of plasma equilibrium in a magnetic field with stochastic regions is examined. It is shown that the magnetic differential equation that determines the equilibrium Pfirsch–Schlüter currents can be cast in a form similar to various nonlinear equations for a turbulent plasma, allowing application of the mathematical methods of statistical turbulence theory. An analytically tractable model, previously studied in the context of resonance-broadening theory, is applied with particular attention paid to the periodicity constraints required in toroidal configurations. It is shown that even a very weak radial diffusion of the magnetic field lines can have a significant effect on the equilibrium in the neighborhood of the rational surfaces, strongly modifying the near-resonant Pfirsch–Schlüter currents. Implications for the numerical calculation of three-dimensional equilibria are discussed.