Nonrelativistic collisionless shocks in unmagnetized electron-ion plasmas

We show that the Weibel-mediated collisionless shocks are driven at nonrelativistic propagation speed (0.1c < V < 0.45c) in unmagnetized electron-ion plasmas by performing two-dimensional particle-in-cell simulations. It is shown that the profiles of the number density and the mean velocity in the vicinity of the shock transition region, which are normalized by the respective upstream values, are almost independent of the upstream bulk velocity, i.e., the shock velocity. In particular, the width of the shock transition region is similar to 100 ion inertial lengths, independent of the shock velocity. For these shocks the energy density of the magnetic field generated by the Weibel-type instability within the shock transition region reaches typically 1%-2% of the upstream bulk kinetic energy density. This mechanism probably explains the robust formation of collisionless shocks, for example, driven by young supernova remnants, with no assumption of an external magnetic field in the universe.