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.

• Received 20 July 2001

DOI:https://doi.org/10.1103/PhysRevLett.88.101103