Two‐dimensional simulations of supercritical quasi‐parallel shocks: Upstream waves, downstream waves, and shock re‐formation

Abstract

Two‐dimensional hybrid (particle ions, massless fluid electrons) simulations of quasi‐parallel collisionless shocks are carried out in order to investigate the upstream wave properties, the shock re‐formation process, and the downstream turbulence. The two‐dimensional simulations confirm the results of earlier one‐dimensional simulations. When backstreaming diffuse ions are retained re‐formation of a shock with an upstream magnetic field ‐ shock normal angle of ΘBno = 30° occurs as a result of upstream low‐frequency waves which steepen, become pulsationlike structures and take over as the re‐formed shock. The upstream waves are initially aligned with the shock normal; later in the run the waves become more and more aligned with the upstream magnetic field. However, when approaching the shock, the wave vectors are refracted in the region of increasing diffuse ion density into the shock normal direction so that shock re‐formation is again coherent along the shock surface. In addition, re‐formation on a smaller scale and out of phase along the shock front is due to more or less specularly reflected ions. Re‐formation of a ΘBno = 10° shock is due to locally at the shock ramp emerging waves. These are attributed to the so‐called interface instability in the region of partial overlap between the incident cold solar wind and part of the hot downstream distribution. These waves emerge in phase along the shock surface and thus re‐formation is in this more parallel case also coherent along the shock. At medium Alfvén Mach number (MA ∼ 5) shocks, upstream waves which are aligned with the upstream magnetic field are convected into the shock and produce ripples on the shock surface. At higher Mach number (MA ∼ 9) the shock surface becomes less coherent and the local value of the shock normal ‐ magnetic field angle varies greatly. The re‐formation length scale is larger than in the lower Mach number case. The turbulence downstream reflects the two mechanisms of shock reformation: in the ΘBno = 30° case the upstream pulsations are mode converted when convected through the shock layer. In the ΘBno = 10° case the downstream turbulence results from the local instability at the shock front.