Shock front nonstationarity of supercritical perpendicular shocks

The shock front nonstationarity of perpendicular shocks in super‐critical regime is analyzed by examining the coupling between “incoming” and “reflected” ion populations. For a given set of parameters including the upstream Mach number ( M A ) and the fraction α of reflected to incoming ions, a self‐consistent, time‐stationary solution of the coupling between ion streams and the electromagnetic field is sought for. If such a solution is found, the shock is stationary; otherwise, the shock is nonstationary, leading to a self‐reforming shock front often observed in full particle simulations of quasi‐perpendicular shocks. A parametric study of this numerical model allows us to define a critical α crit between stationary and nonstationary regimes. The shock can be nonstationary even for relatively low M A (2–5). For a moderate M A (5–10), the critical value α crit is about 15 to 20%. For very high M A (>10), α crit saturates around 20%. Moreover, present full simulations show that self‐reformation of the shock front occurs for relatively low β i and disappears for high β i , where β i is the ratio of upstream ion plasma to magnetic field pressures. Results issued from the present theoretical model are found to be in good agreement with full particle simulations for low β i case; this agreement holds as long as the motion of reflected ions is coherent enough (narrow ion ring) to be described by a single population in the model. The present model reveals to be “at variance” with full particle simulations results for the high β i case. Present results are also compared with previous hybrid simulations.