A Hall--Drift Induced Magnetic Field Instability

In the presence of a strong magnetic field and under conditions as realized in the crust and the superfluid core of neutron stars the Hall–drift dominates the field evolution. We show by a linear analysis that for a sufficiently strong large–scale background field depending at least quadratically on position in a plane conducting slab an instability occurs which rapidly generates small–scale fields. Their growth rates depend on the choice of the boundary conditions, increase with the background field strength and may reach ${10}^3$ times the ohmic decay rate. The effect of that instability on the rotational and thermal evolution of neutron stars is discussed.