LOW-MACH NUMBER QUASI-PARALLEL SHOCKS - UPSTREAM WAVES

The structure of a low Mach number (Alfven Mach number M(A) = 2.2) qua si-parallel shocks is investigated using a two-dimensional hybrid (par ticle ions, massless fluid electrons) code. We have run cases with ave rage magnetic field - shock normal angles of THETA(Bno) = 20-degrees, 30-degrees, and 45-degrees. Initially, phase standing dispersive whist ler waves with an upstream directed group velocity are radiated by the shock ramp. As expected, the wave vector of these whistler waves is p arallel to the average shock normal direction. The steepness of the sh ock 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 shoc k into the upstream medium. At THETA(Bno) = 30-degrees these ions exci te, 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 wave s is in between the average magnetic field direction and the shock nor mal. 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 THETA(Bno) = 20-d egrees the shock consists of whistlers in the upstream, whose waveleng th and shock directed phase velocity increases gradually toward the sh ock. It is suggested that in this more parallel case remnants of the d ispersive whistlers continue to exist further upstream and interact wi th backstreaming ions. This leads to a change of the wave normal direc tion as the waves are convected toward the shock. In the 45-degrees ca se the upstream density of backstreaming ions is greatly reduced. Only close to the shock ramp (within approximately 5c/omega(pi)) does the backstreaming ion density exceed 10% of the solar wind density. Wave v ectors of small wavelength whistlers in this region are almost aligned with the shock normal.