Speaker: Joshua W. Burby, University of Texas at Austin
Abstract: In three dimensional toroidal domains without symmetry, the standard magnetohydrodynamic (MHD) equilibrium model used for magnetic confinement fusion does not generally support smooth solutions. This leads to both unphysical singular plasma currents on resonant flux surfaces and non- or slow convergence of numerical approximations under refinement. In this work, we present an improved equilibrium principle derived from a simple statistical model for plasma fluctuations. Instead of being static, we assume that the plasma magnetic field is ergodically and rapidly fluctuating relative to the MHD time scale. By averaging the resulting force, we derive a variational equilibrium problem for the statistical mean magnetic field which depends on fluctuation variance. Then, through asymptotics, numerical simulations, and a Grad-Shafranov type argument, we show that the variational principle supports smooth solutions for specific fluctuation statistics chosen to minimally modify the standard equilibrium modeling paradigm. Physically, this model smooths singular current sheets with a length scale determined by the magnetic field fluctuations.