Instability and Turbulent Relaxation in a Stochastic Magnetic Field

Abstract

An analysis of instability dynamics in a stochastic magnetic field is presented for the tractable case of the resistive interchange. Externally prescribed static magnetic perturbations convert the eigenmode problem to a stochastic differential equation, which is solved by the method of averaging. The dynamics are rendered multi-scale, due to the size disparity between the test mode and magnetic perturbations. Maintaining quasi-neutrality at all orders requires that small-scale convective cell turbulence be driven by disparate scale interaction. The cells in turn produce turbulent mixing of vorticity and pressure, which is calculated by fluctuation-dissipation type analyses, and are relevant to pump-out phenomena. The development of correlation between the ambient magnetic perturbations and the cells is demonstrated, showing that turbulence will 'lock on' to ambient stochasticity. Magnetic perturbations are shown to produce a magnetic braking effect on vorticity generation at large scale.Detailed testable predictions are presented. The relations of these findings to the results of available simulations and recent experiments are discussed. I. INTRODUCTIONThe dynamics of instability, relaxation, and turbulence are (taken collectively) fundamental to magnetic confinement physics. Here, 'relaxation' includes the evolution of plasma free energy (in the presence of sources and sinks), and the resulting transport [1]. Relaxation determines plasma confinement and possible bifurcations between different states thereof [2].Recently, a new element has been added to this already challenging problem. Good confinement is no longer deemed sufficient. Rather, good confinement must be achieved along with