Perpendicular ion beam instability: Solutions to the linear dispersion relation

A 200-eV Xe+ ion beam directed perpendicular to the terrestrial magnetic field in the F region ionosphere produced very narrow band electrostatic emissions just above multiples of the hydrogen cyclotron frequency. Although the plasma conditions associated with the ion beam were undoubtedly very complex, we consider first a simple ion beam in a background ionosphere. The dispersion relation for flute mode waves and an unmagnetized perpendicular ion beam is solved for a diffuse H+ plasma and then for a combination of dense O+ and diffuse H+. These solutions account for most of the wave properties, including the observation of narrow spectral peaks separated by the hydrogen cyclotron frequency and the observation of no spectral peaks below 2000 Hz. We cannot dismiss field-aligned currents associated with the Xe+ beam as an alternate source of free energy for the narrow band emissions. However, our intention here is to examine closely the Xe+ beam as a source for directly exciting the plasma waves