Low‐Mach number quasi‐parallel shocks: Upstream waves

Abstract

The structure of a low Mach number (Alfvén Mach number MA = 2.2) quasi‐parallel shocks is investigated using a two‐dimensional hybrid (particle ions, massless fluid electrons) code. We have run cases with average magnetic field ‐ shock normal angles of ΘBno = 20°, 30°, and 45°. Initially, phase standing dispersive whistler waves with an upstream directed group velocity are radiated by the shock ramp. As expected, the wave vector of these whistler waves is parallel to the average shock normal direction. The steepness of the shock ramp varies along the shock surface; this leads to a modulation of the whistler wave amplitude at a constant phase, i.e., perpendicular to the wave vector. Subsequently, ions are backstreaming from the shock into the upstream medium. At ΘBno = 30° these ions excite, as in the one‐dimensional hybrid simulations by Omidi et al. (1990), longer wavelength whistler waves by an electromagnetic ion/ion beam instability. The wave normal of these longer wavelength whistler waves is in between the average magnetic field direction and the shock normal. The skewing of the wave normal into the shock normal direction is attributed to a large density gradient of backstreaming ions upstream of the shock ramp in the shock normal direction. At ΘBno = 20° the shock consists of whistlers in the upstream, whose wavelength and shock directed phase velocity increases gradually toward the shock. It is suggested that in this more parallel case remnants of the dispersive whistlers continue to exist further upstream and interact with backstreaming ions. This leads to a change of the wave normal direction as the waves are convected toward the shock. In the 45° case the upstream density of backstreaming ions is greatly reduced. Only close to the shock ramp (within ∼ 5c/ωpi) does the backstreaming ion density exceed 10% of the solar wind density. Wave vectors of small wavelength whistlers in this region are almost aligned with the shock normal.