Electron beam excitation of upstream waves in the whistler mode frequency range

We examine whistler mode instabilities arising from electron beams in interplanetary space at 1 AU. Both parallel and obliquely propagating solutions are considered. We demonstrate that the generation of two simultaneous whistler mode waves is possible, and even reasonably likely, for beam parameters frequently encountered upstream of the Earth's bow shock and at interplanetary shocks. We also explore the generation of left-hand polarized waves at whistler mode frequencies under these same conditions. We offer both parametric variations derived from numerical solutions of the various instabilities as well as an analytical treatment of the problem which succeeds in unifying the various numerical results.