Charge Separation Effects on the Profile of a Perpendicular Shock Wave

The profile of a plasma shock wave propagating perpendicular to a magnetic field is studied using a system of moment equations derived from a pair of Boltzmann equations for electrons and ions. The system, rigorously closed for weak shocks, describes a fully ionized plasma in which a long list of dissipative mechanisms and Hall effects are coupled. The charge separation effect which is automatically excluded by the usual weak shock scaling [P. N. Hu, Phys. Fluids 9, 89 (1966) and H. Grad and P. N. Hu, Phys. Fluids 10, 2596 (1967)] is retained in this description by a special nonuniform scaling of the Debye length relative to the shock strength. The shock profiles are obtained from an equation with two essential parameters (combining five dimensionless parameters which occur in the problem). The magnetic field profiles cover the entire range from collision-dominated monotonic profiles to damped oscillatory profiles and the limiting collisionless case of purely oscillatory and solitary wave profiles. The profiles of the electric field and the charge density can also be oscillatory or monotonic, and, in some parameter ranges, have long downstream tails, extending far beyond where the velocity and the magnetic field are undisturbed.