Fast Magnetic Field Penetration Into Plasmas due to Hall Resistivity

The Hall resistivity is shown to modify the rate and the nature of the magnetic field evolution in short-duration plasmas. Two different cases are studied. In the first case the magnetic field penetrates a plasma along a backgrond magnetic field, and is then governed by a diffusion equation with a complex diffusion coefficient. In the collisionless limit the governing equation is equivalent to the Schrodinger equation for a free particle, and the magnetic field propagates the way a wave packet expands by dispersion ratherthg than by diffusion. The wave packet expdnds by dispersion rather than by diffusion. The mechanism of penetration here is that of whistler waves. We discuss the competition between magnetic field penetration and plamsa pushing by the magnetic pressure and also the effect of the displacement current. In the second case an aximuthal magnetic field propagates axially into a hollow cylindrical plasma. When the radial current flows inward the magnetic field penetrates into the plasma by a Hall-induced shock wave. However, when the radial current flows outward, the magnetic field does not penetrate. Moreover, the magnetic field is expelled from an initially magnetized plasma. Both penetration and expulsion are shown to result naturally from the frozen-in law. The radial boundary conditions and the conservation of magnetic field flux and energy are discussed.