Multiple switch-off slow shock solutions

Numerical simulations of the slow-mode switch-off shock with a time-dependent, implicit hybrid plasma simulation code in a bounded domain produce more than one type of internal structure for the same physical parameters, depending on the downstream boundary conditions. Time-steady switch-off slow shocks with large-amplitude trailing waves are obtained with downstream boundaries that either allow incoming ion cyclotron waves or set the magnetic field component transverse to the shock normal equal to zero. Time-steady switch-off slow shocks with no trailing waves are obtained with downstream boundaries that set the electric field according to Ed= -udxBd (ud and Bd are the downstream plasma fluid velocity and the downstream magnetic field, respectively, and are obtained for given upstream conditions by solving the Rankine-Hugoniot relations); for example, the electric field is set to zero for simulations performed in the rest frame of the downstream plasma. Both switch-off slow shocks with and without trailing waves satisfy the Rankine-Hugoniot conditions. Shocks with trailing wave trains are stable to changes in the downstream boundary conditions. Although both shocks with and without the trailing wave trains are linearly stable with respect to changes in the upstream magnetic field, only shocks with no trailing wave trains are nonlinearly stable. These results may explain observations of slow shocks in the magnetotail in which the expected trailing wave train is absent