Electrostatic instabilities of a finite electron beam propagating in a cold magnetized plasma

For a better understanding of the high-frequency waves observed during active experiments of electron-beam injection into the ionospheric plasma, we do a complete investigation of the electrostatic-beam--plasma instabilities that do occur in such a situation. The electron beam is cold, it is aligned with the vacuum magnetic field, and has a finite radius; the background plasma is cold and homogeneous. We study both analytically and numerically the dispersion equation of the different branches and follow the dependence of the temporal and spatial growth rates with the beam and plasma parameters. Simultaneously we investigate the different types of instabilities (radiated or confined to the beam) in the various frequency ranges which are of interest. We give an analytical criterion for the convective or absolute character of these instabilities, taking into account the two-dimensional wave propagation along and across the vacuum magnetic field.