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CATEGORIES:DAMTP Astrophysics Seminars
SUMMARY:Metastability of magnetohydrodynamic atmospheres a
nd their relaxation - David Hosking (Princeton)
DTSTART;TZID=Europe/London:20231127T140000
DTEND;TZID=Europe/London:20231127T150000
UID:TALK206419AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/206419
DESCRIPTION:Motivated by explosive releases of energy in space
and fusion plasmas\, this talk considers the nonl
inear convective stability of stratified magnetohy
drodynamic (MHD) equilibria in 2D. We demonstrate
that\, unlike the Schwarzschild criterion in hydro
dynamics (“entropy must increase upwards for conve
ctive stability”)\, the so-called modified Schwarz
schild criterion for 2D MHD (or in any kind of flu
id dynamics with more than one source of pressure)
is a guarantor only of linear stability. As a res
ult\, in 2D MHD (unlike HD) there exist metastable
equilibria that are unstable to nonlinear perturb
ations despite being stable to linear ones. We sho
w that the minimum-energy configurations attainabl
e by these atmospheres via non-diffusive reorganis
ation can be obtained by solving a combinatorial o
ptimisation problem — these ground states are usua
lly 2D and are fairly well reproduced by direct nu
merical 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 colliso
nless plasmas and the Robert-Sommeria-Miller theor
y of 2D vortices) — the minimum-energy states desc
ribed above are the low-temperature limit of this
theory. We show that the predictions of the statis
tical mechanics are in reasonable agreement with d
irect numerical simulations.
LOCATION:MR14 DAMTP and online
CONTACT:Roger Dufresne
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