Magnetic field penetration and electron heating in weakly nonuniform plasmas

The simultaneous magnetic field penetration and electron heating in plasmas of nonuniform density and of azimuthal cylindrical symmetry are studied. The penetration is caused by both the convective skin effect and the pressure gradient. The shock penetration of the current layer into a cold unmagnetized plasma is shown to result in equal magnetic field energy and electron thermal energy. A direct relation is shown between the heating of an electron along its orbit and the deviation from the frozen-in law. General Hugoniot relations are presented for the shock penetration into warm magnetized plasmas. The profiles of the magnetic field and of the electron thermal energy are found in the steady skin layer that is formed in the case of no penetration.