Kinetic theory of instability in the interaction of an electron beam and plasma with an arbitrary anisotropic electron velocity distribution function

Based on the kinetic approach, this work investigates the stability of the system consisting of a fast electron beam and a dense plasma at an arbitrary (anisotropic) electron velocity distribution function. It is shown that during the interaction of a fast electron beam with a cold plasma, both the conditions for losing stability and the increment do not depend on the form of the electron distribution function (EDF) of a plasma and are determined only by the ratio of the electron beam energy to the mean energy in a plasma. With an increase in the mean electron energy in the plasma, it becomes necessary to take into account the moments of the EDF following for energy moment. It was found that the plasma anisotropy has a significant effect on both the stability loss conditions and the increment. The physical reason for this effect is the shift in the plasma frequency due to the Doppler effect caused by the plasma anisotropy in the coordinate system moving along with the beam. Other findings include a region of anomalous dispersion of the electron beam - plasma system and regions of negative group velocity of perturbations in such system. Physical interpretations are proposed for all the observed effects.