Plasma Equilibrium in a Magnetic Field with Stochastic Regions

The nature of plasma equilibrium in a magnetic field with stochastic regions is examined, with particular application to the reconstruction of equilibria for the W7AS stellarator. It is shown that the magnetic differential equation that determines the equilibrium Pfirsch-Schl\"{u}ter 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-Schl\"{u} ter currents. Implications for the numerical calculation of 3D equilibria are discussed, with specific application to the calculation of equilibria for the W7AS stellarator.