Transition scale at quasiperpendicular collisionless shocks: Full particle electromagnetic simulations

One-dimensional full particle simulations of almost perpendicular supercritical collisionless shocks over a wide Alfvén Mach number range are presented. The physical ion to electron mass ratio has been used; however, due to computer time limitations a value of the ratio of the electron plasma frequency to the electron gyrofrequency of 4 has been assumed. The shock structure in the density and magnetic field consists of a foot, formed by reflected ions, and a steeper ramp leading to an overshoot. It is shown that the shock ramp scale in units of the upstream ion inertial length is more or less constant and close to 1 over the Mach number regime investigated, i.e., up to $MA≈14$⁠. Further, the convective ion gyroradius in units of the upstream ion inertial length is also constant with the Mach number when the gyroradius is evaluated with the magnetic field strength in the overshoot. Thus the shock transition also scales with the convected gyroradius. When a hyperbolic tangent function is fitted to the density profile the neglect of the overshoot essentially results, for high Mach number shocks, in a fit of the foot and not of the ramp, i.e., the shock transition scale is grossly overestimated. The simulations suggest that in a regime above the critical Mach number the nonlinear steepening is balanced by gyroviscosity of the reflected ions as the shock ramp scale is given by the convected gyroradius in the overshoot. At higher Mach numbers the shock becomes unsteady the ramp scale can become as small as several electron inertial length during a part of the reformation cycle. At still higher Mach number microinstabilities in the foot may have growth times much shorter than the inverse ion gyrofrequency so that they can lead to ion heating, and a steady resistive shock will result.