Structure of a shock-induced stationary current wave in a conducting material with a transverse magnetic field

In this paper, a two-fluid model of a plane stationary shock wave in a conductor is proposed, and the current structure of the wave is considered. For an ideal hydrodynamic discontinuity, it is shown that the field and current distributions consists of a wide diffusion zone of shockfree material and a small-scale zone of high-frequency oscillations related to relaxation of the electron density to the ion density. The structure of the oscillation zone is considered with variation in the properties of the material and with possible variation in the electric conductivity in the shock wave. The time required for the attainment of an equilibrium density of charges is calculated. It is shown that, for conducting materials, the shock-induced current is determined by compressibility and is almost entirely concentrated in the diffusion zone. The width of this zone is determined by the electric conductivity of the material in the initial state and does not depend on the properties of the material behind the wave front.