Structure of a Perpendicular Shock Wave in a Plasma

Abstract

Based on the Boltzmann equations for fully ionized gases, analytic solutions of weak perpendicular shock waves are obtained. The result shows that all weak shock waves (in ionized gases as well as in nonionized gases) have similar profiles given by the hyperbolic-tangent function of the distance. The shock thickness is found to depend on four basic parameters, namely, the mean free path of the gas, the length of penetration, the Larmor radius based on thermal speed, and the mass ratio of electron and ion. From the explicit expression of the shock thickness, various significant cases are derived and discussed. The most interesting case occurs when the mean free path is larger than the electron length of penetration, which is in turn larger than the electron Larmor radius; it is found that both the scaled and the actual shock thickness can be smaller than the length of penetration—a result contrary to that obtained for collisionless plasmas.