Fast magnetic-field penetration into plasmas due to the Hall field

The enhancement of magnetic-field penetration into short-duration plasmas by the dissipationless Hall field is examined. Magnetic-field penetration along a background magnetic field is focused on, where the inductive Hall electric field enables the magnetic field to penetrate as a whistler wave. It is shown that the magnetic-field evolution, when governed simultaneously by both whistler wave propagation and collisional diffusion, is described by a diffusion equation with a complex diffusion coefficient. The imaginary part of this coefficient is proportional to the Hall resistivity associated with the background magnetic field. In the collisionless limit the governing equation is equivalent to the Schrödinger equation for a free particle, and the magnetic field propagates the way a free-particle wave packet expands by dispersion rather than by diffusion. This study was motivated by the enhanced magnetic-field penetration recently observed in the anode plasma of a magnetically insulated ion diode.