Magnetic field penetration due to the Hall field in (almost) collisionless plasmas*

The fast penetration of magnetic fields into plasmas due to the Hall field is described. The penetration occurs in nonuniform plasmas of a characteristic length smaller than the ion skin depth, it is much faster than the ion motion, and its rate is independent of the resistivity. Some previous results are described: a shock penetration of the magnetic field accompanied by a large energy dissipation, and field expulsion from an initially magnetized plasma. It is then shown how the Hall field can enhance the penetration into a plasma surrounded by vacuum. Finally, it is demonstrated how the evolution of the magnetic field in a plasma that conducts current between electrodes depends crucially on its evolution near the electrodes, when a realistic density profile is taken into account.