Abstract: Astrophysical, space and fusion plasmas frequently exhibit explosive releases of energy. Motivated by such events, I consider in this talk the nonlinear stability of stratified magnetohydrodynamic equilibria to interchanges of straight magnetic-flux tubes. I demonstrate that, even under this restricted class of motions, plasma equilibria can be linearly stable while nonlinearly unstable, i.e., metastable. When destabilized, they can release their stored energy explosively. I show that the available energy with respect to interchanges can be determined accurately by solving a combinatorial optimization problem. The states with least energy are, to good approximation, the final states reached by simulations of the relaxation of metastable equilibria, provided that turbulent mixing is suppressed by viscosity. To predict the result of fully turbulent relaxation, I construct a statistical mechanical theory based on the maximization of Boltzmann's mixing entropy. This theory is analogous to the Lynden-Bell statistical mechanics of stellar systems and collisionless plasmas. The theory reproduces well the results of numerical simulations for sufficiently large initial perturbations to the metastable equilibrium.
Host: Prof. Vladimir Zhdankin and Prof. Carl Sovinec