Metastability of magnetohydrodynamic atmospheres and their relaxation

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• David Hosking (Princeton)
• Monday 27 November 2023, 14:00-15:00
• MR14 DAMTP and online.

If you have a question about this talk, please contact Roger Dufresne.

Motivated by explosive releases of energy in space and fusion plasmas, this talk considers the nonlinear convective stability of stratified magnetohydrodynamic (MHD) equilibria in 2D. We demonstrate that, unlike the Schwarzschild criterion in hydrodynamics (“entropy must increase upwards for convective stability”), the so-called modified Schwarzschild criterion for 2D MHD (or in any kind of fluid dynamics with more than one source of pressure) is a guarantor 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. We show that the minimum-energy configurations attainable by these atmospheres via non-diffusive reorganisation can be obtained by solving a combinatorial optimisation problem — these ground states are usually 2D and are fairly well reproduced by direct numerical simulations at small Reynolds number. For the case of relaxation at large Reynolds number, we construct a statistical mechanical theory based on the maximisation of Boltzmann’s mixing entropy (this is analogous to the Lynden-Bell statistical mechanics of self-gravitating systems and collisonless plasmas and the Robert-Sommeria-Miller theory of 2D vortices) — the minimum-energy states described above are the low-temperature limit of this theory. We show that the predictions of the statistical mechanics are in reasonable agreement with direct numerical simulations.

This talk is part of the DAMTP Astrophysics Seminars series.

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