Perpendicular collisionless shock wave instability

Completes an investigation into the effects of temperature, density, and magnetic field gradients on the linear instability of longitudinal waves in perpendicular collisionless shocks. The dispersion relation for the propagation of Bernstein modes in an inhomogeneous plasma is derived and solved in the limits alpha =0, alpha >or approximately=1, where alpha = beta e kv d / Omega e and v d is the net drift velocity. For warm ion shocks the temperature gradient can result in a significant increase in the growth rate. For typical experimental conditions, however, this increase is cancelled out by the stabilizing effect of the magnetic field gradient The latter effect increases with wavenumber; typically, waves with k>or approximately=k e are stabilized and the maximum growth rate now occurs for the m=1 mode (k approximately 0.1 k e ), where k e is the electron Debye wavenumber.