Density shocks in the relativistic expansion of highly charged one component plasmas

In a previous paper we showed that dynamical density shocks occur in the non-relativistic expansion of dense single component plasmas relevant to ultrafast electron microscopy; and we showed that fluid models capture these effects accurately. We show that the non-relativistic decoupling of the relative and center of mass motions ceases to apply and this coupling leads to novel behavior in the relativistic dynamics under planar, cylindrical, and spherical symmetries. In cases where the relative motion of the bunch is relativistic, we show that a dynamical shock emerges even in the case of a uniform bunch with cold initial conditions; and that density shocks are in general enhanced when the relative motion becomes relativistic. Furthermore, we examine the effect of an extraction field on the relativistic dynamics of a planar symmetric bunch.