40 pages, 36 figures
Motivated by explosive releases of energy in fusion, space and astrophysical plasmas, we consider 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 for any kind of fluid dynamics with more than one source of pressure) guarantees only linear stability. As a result, in 2D MHD (unlike in hydrodynamics) 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 reorganization can be determined by solving a combinatorial optimization problem. We find inter alia that these minimum-energy states are usually 2D, even when the original metastable equilibrium was 1D. We demonstrate with direct numerical simulations that these 2D states are fairly accurate predictors of the final state reached by laminar relaxation of metastable equilibria at small Reynolds number. To describe relaxation at large Reynolds number, we construct a statistical mechanical theory based on the maximization of Boltzmann's mixing entropy that is analogous to the Lynden-Bell statistical mechanics of self-gravitating systems and collisionless plasmas, and to the Robert-Sommeria-Miller (RSM) theory of 2D vortex turbulence. The minimum-energy states described above are, we show, the low-temperature limit of this theory. We demonstrate that the predictions of the statistical mechanics are in reasonable agreement with direct numerical simulations.
10 pages, 13 figures. Submitted for publication
6 pages, 3 figures
28 pages, 19 figures, submitted to ApJ
17 pages, 8 figures. To be published in The Planetary Science Journal
14 pages, 14 figures, submitted to MNRAS
16 pages, 9 figures, Accepted for publication in MNRAS
11 pages, 6 figures, accepted for publication in ApJ
12 pages, 13 figures, submitted to MNRAS
13 pages, 13 figures
12 pages, 20 figures, 4 tables. Accepted by MNRAS. A summary video is at this https URL &ab_channel=NTHUCosmology
Accepted by the RAA journal
6 pages, 5 figures
38 pages, 15 figures. To appear in the edition of the Central European Astrophysical Bulletin dedicated to the proceedings of the Hvar Stellar Meeting 2023
Submitted to Physics of Plasmas. Comments welcome
4 pages, 1 figure; to appear in proceedings of ADASS XXXIII
18 pages, 11 figures, accepted for publication in A&A
12 pages, 8 figures
9 pages, 5 figures, accepted for publication in APJL
18 pages plus Appendices, 9 figures plus 37 figures in Appendices. Accepted by MNRAS
Submitted to JINST
Accepted for publication in the Monthly Notices of the Royal Astronomical Society
to be published in MNRAS
4 pages, 4 figures
13 pages, 10 figures
11 pages, 5 figures, 1 table
12 pages, 6 figures
22 pages, 3 figures