Princeton University Astroplasmas Seminar

Motivated by explosive releases of energy in fusion, space and astrophysical plasmas, this talk considers the nonlinear stability of stratified magnetohydrodynamic (MHD) equilibria in 2D. I demonstrate that, unlike the Schwarzschild criterion in hydrodynamics (“entropy must increase upwards for stability”), the modified Schwarzschild criterion for 2D MHD (or any kind of fluid dynamics with more than one source of pressure) is a guarantee only of linear stability. As a result, in 2D MHD (unlike HD) there exist metastable equilibria that are unstable to nonlinear perturbations despite being stable to linear ones. I show that the available energy of these equilibria under non-diffusive reorganization of flux tubes can be calculated by solving a combinatorial optimization problem. The reorganized states with minimum energy are, to good approximation, the final states reached by simulations of destabilized equilibria at small Reynolds number. To predict the state reached by turbulent relaxation at large Reynolds number, I construct a statistical mechanical theory based on the maximization of Boltzmann’s mixing entropy (this is analogous to the Lynden-Bell statistical mechanics of stellar systems and collisonless plasmas and the Robert-Sommeria-Miller theory of 2D vortices). I show that the predictions of this statistical mechanics are in remarkable agreement with numerical simulations.
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