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SUMMARY:Metastability of magnetohydrodynamic atmospheres and their relaxat
 ion - David Hosking (Princeton)
DTSTART:20231127T140000Z
DTEND:20231127T150000Z
UID:TALK206419@talks.cam.ac.uk
CONTACT:Roger Dufresne
DESCRIPTION:Motivated by explosive releases of energy in space and fusion 
 plasmas\, this talk considers the nonlinear convective stability of strati
 fied magnetohydrodynamic (MHD) equilibria in 2D. We demonstrate that\, unl
 ike the Schwarzschild criterion in hydrodynamics (“entropy must increase
  upwards for convective stability”)\, the so-called modified Schwarzschi
 ld criterion for 2D MHD (or in any kind of fluid dynamics with more than o
 ne source of pressure) is a guarantor only of linear stability. As a resul
 t\, in 2D MHD (unlike HD) there exist metastable equilibria that are unsta
 ble to nonlinear perturbations despite being stable to linear ones. We sho
 w that the minimum-energy configurations attainable by these atmospheres v
 ia non-diffusive reorganisation can be obtained by solving a combinatorial
  optimisation problem — these ground states are usually 2D and are fairl
 y well reproduced by direct numerical simulations at small Reynolds number
 . For the case of relaxation at large Reynolds number\, we construct a sta
 tistical mechanical theory based on the maximisation of Boltzmann’s mixi
 ng 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 abov
 e are the low-temperature limit of this theory. We show that the predictio
 ns of the statistical mechanics are in reasonable agreement with direct nu
 merical simulations.
LOCATION:MR14 DAMTP and online
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