Stability of a force-free Hall equilibrium and release of magnetic energy

Abstract

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.