Penetration and expulsion of magnetic fields in plasmas due to the Hall field

The axial penetration of an azimuthal magnetic field into a short-duration hollow cylindrical plasma is studied. When the process is so fast that the ion motion is small and the plasma dissipative resistivity, electron inertia, and pressure are small, the evolution of the magnetic field is governed by the Hall field. When the radial current flows inward, the magnetic field penetrates in the form of a Hall-induced shock wave with a narrow current channel. When outward, the magnetic field does not penetrate the plasma. Moreover, in the latter case the magnetic field is expelled from an initially magnetized plasma. The increase and decrease of the magnetic field intensity in the cylindrical plasma are shown to result naturally from the frozen-in law.