Whistler Critical Mach Number Concept Revisited

Abstract

<p><br>The formation of a collisionless shock is the result of a balance between nonlinear steepening and processes that counteract this steepening. Dispersive shocks are shocks in which dispersive processes counterbalance the front steepening and are formed when the dispersive spatial scale exceeds scales associated with resistive processes. Oblique dispersive shocks are characterized by a phase standing wave precursor adjacent to the magnetic ramp. The whistler critical Mach number is defined as the maximum Mach number for which a linear whistler wave can phase stand upstream of the shock front. It was widely accepted that if the Mach number exceeds , linear whistler waves propagating along the shock normal are not able to "phase stand" in the upstream flow, and "& mldr;the shock will be initiated by a monotonic ramp." (Kennel et al., 1985, https://doi.org/10.1029/gm034p0001). In this study, we present results of numerical simulations and observations of shocks with that reveal the occurrence of an alternative scenario. For both the shock resulting from kinetic particle-in-cell simulations and that observed by MMS, the propagation direction of the precursor deviates from the shock normal direction. As a result, the velocity of the surface of constant phase along the shock normal exceeds the phase speed of these waves. It is shown that the propagation of the surface of constant phase along the shock normal occurs at a velocity that is nearly equal to the shock speed. Hence, these waves are "phase standing along the shock normal" in spite of .<br></p>