Hydrodynamics of shock waves with reflected particles. I. Rankine-Hugoniot relations and stationary solutions

In this work we investigate how reflected particles modify the Rankine-Hugoniot (RH) relations in a simple hydrodynamical framework. It is assumed that the ions are specularly reflected by the cross-shock potential. For simplicity, an exactly perpendicular shock is assumed, thus other reflection mechanisms, such as magnetic mirroring, can be neglected. Momentum and energy terms are introduced to model reflected particles at the shock and the RH conditions are examined using a geometrical entropy condition to distinguish the physically relevant states. Although such shocks have some common features with combustion shocks within a narrow range of reflection parameters, for a wide range of reflection parameters, particularly for highly oblique shocks, Chapman-Jouguet solutions do not exist. It is conjectured that these shocks comprise a distinct class. Decelerated solutions of the RH conditions are shown to exist only under specific conditions for shocks with reflected particles. Velocity flows both parallel and oblique to the perpendicular shock (with respect to an upstream magnetic field) are considered and found to be strongly sheared. (c) 2006 American Institute of Physics.