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 a 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 quasiperpendicular 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.