Structure of medium Mach number quasi‐parallel shocks: Upstream and downstream waves

Abstract

Satellite observations of quasi‐parallel collisionless shocks document a complex behavior that has proven to be extraordinarily difficult to analyze and interpret. Recent data analyses and computer simulations, however, have revealed that these shocks can be unsteady and cyclically reforming, and have shed some light on the processes that are involved. Despite this progress, a number of issues regarding the ion thermalization at and re‐formation of quasi‐parallel shocks are still not well understood. Previous simulation studies at high Mach numbers have suggested either the convection of far upstream density perturbations into the shock or an instability at the shock interface as mechanisms contributing to the shock re‐formation. On the other hand, simulations at low Mach numbers have shown a steady shock. To understand the transition from steady low Mach number to unsteady high Mach number shocks, we have performed large‐scale one‐dimensional hybrid code simulations at increasing Mach numbers. We find that fast‐mode waves with wavelengths longer than phase‐standing whistlers are excited upstream from the shock by backstreaming ions. At increasing Mach numbers, the phase and group velocities of the dominant waves are reduced until they point back toward the shock. When there is sufficient energy flux in these waves, they lead to unsteady shock behavior and eventually to shock re‐formation. For typical solar wind conditions and an angle of θBn = 30° between the shock normal and the upstream magnetic field, we find the shock to become unsteady at MA ∼ 2.3. Various spectral diagnostics are employed to investigate the properties of the excited upstream and downstream waves. Fast‐mode wave energy that is convected through the shock is partially mode converted into downstream Alfvén and slow‐mode fluctuations. This mechanism may be responsible for some of the turbulence observed downstream of the the Earth's quasi‐parallel bow shock. An analysis of the shock dynamics indicates that there are no characteristic time scales associated with the unsteady medium Mach number shocks.