Stability of a force-free Hall equilibrium and release of magnetic energy. (arXiv:1906.07936v1 [astro-ph.SR])

Stability of a force-free Hall equilibrium and release of magnetic energy. (arXiv:1906.07936v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Kitchatinov_L/0/1/0/all/0/1">Leonid Kitchatinov</a>

Conservation of magnetic helicity by the Hall drift does not prevent Hall
instability of helical fields. This conclusion follows from stability analysis
of a force-free spatially-periodic Hall equilibrium. The growth rates of the
instability scale as $sigma propto B^{3/4}eta^{1/4}$ with the field strength
$B$ and magnetic diffusivity $eta$ and can be large compared to the rate of
resistive decay of the background field. The instability deviates the magnetic
field from the force-free configuration. The unstable eigenmodes include a fine
spatial structure which evolves into current sheets at the nonlinear stage of
the instability. The instability catalyses the resistive release of magnetic
energy. The energy is released in a sequence of spikes, every spike emits
several percent of the total energy. A numerically defined scaling for the
energy released in a single spike permits an extrapolation to astrophysically
relevant values of the Hall number. The instability can be relevant to magnetic
energy release in a neutron star crust and, possibly, in stellar coronae.

Conservation of magnetic helicity by the Hall drift does not prevent Hall
instability of helical fields. This conclusion follows from stability analysis
of a force-free spatially-periodic Hall equilibrium. The growth rates of the
instability scale as $sigma propto B^{3/4}eta^{1/4}$ with the field strength
$B$ and magnetic diffusivity $eta$ and can be large compared to the rate of
resistive decay of the background field. The instability deviates the magnetic
field from the force-free configuration. The unstable eigenmodes include a fine
spatial structure which evolves into current sheets at the nonlinear stage of
the instability. The instability catalyses the resistive release of magnetic
energy. The energy is released in a sequence of spikes, every spike emits
several percent of the total energy. A numerically defined scaling for the
energy released in a single spike permits an extrapolation to astrophysically
relevant values of the Hall number. The instability can be relevant to magnetic
energy release in a neutron star crust and, possibly, in stellar coronae.

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