Ion cyclotron beam mode-whistler mode plasma instabilities and their role in parallel shock wave structures

The instability generated by two ion beams of arbitrary relative strength counterstreaming parallel to an external magnetic field in the presence of a charge and current neutralizing electron background has been analyzed using the linear Vlasov equation. This analysis extends previous theories by including the effects of finite temperatures in one or both ion beams. Using the Nyquist method, marginal stability curves for arbitrary beam strengths are obtained. For the case of a weak, hot ion beam interacting with a cold plasma whistler mode, an explicit expression for the growth rate (proportional to beam strength) has been obtained. The parameters are then chosen to be applicable to parallel shock waves, modeled as two interpenetrating ion beams. It is found that at the leading edge of the shock wave unstable whistlers may stand in the shock frame for all shock Alfvén Mach numbers MA⩾2.77. Furthermore, it is found that such unstable modes may exist for a wide range of points in the shock interior. The turbulent spectrum that results from a shock of fixed strength has a narrow bandwidth about the wavenumber of the stationary leading edge mode. These results significantly extend the previous cold theory and further support the contention that this instability is a viable mechanism for generating large amplitude turbulent structure in a collisionless shock wave.