A determination of relativistic shock jump conditions using Monte Carlo techniques

Monte Carlo techniques are used, assuming isotropic elastic scattering of all particles, to calculate jump conditions in parallel relativistic collisionless shocks in the absence of Fermi acceleration. The shock velocity and compression ratios are shown for arbitrary flow velocities and for any upstream temperature. Both single-component electron-positron plasma and two-component proton-electron plasmas are considered. It is shown that protons and electrons must share energy, directly or through the mediation of plasma waves, in order to satisfy the basic conservation conditions, and the electron and proton temperatures are determined for a particular microscopic, kinetic-theory model, namely, that protons always scatter elastically. The results are directly applicable to shocks in which waves of scattering superthermal particles are absent.