Nonlocal analysis of finite-beam-driven instabilities

Abstract

Electrostatic waves in an electron–beam–plasma system are studied in the low-temperature-beam regime and the warm-beam regime. The field-aligned electron beam is assumed to have a Gaussian density profile. The fully kinetic integral eigenmode equation in wave-number space is used to describe the nonlocal behavior of these waves. The case of strongly magnetized electrons and unmagnetized ions, which corresponds to the waves in a frequency range from the lower-hybrid to the electron plasma frequency, is examined in detail. Three groups of wave modes are found. The first group consists of modes that have dispersive properties similar to the uniform, infinite beam–plasma system. Depending on the beam width, the growth rates are, however, strongly reduced. The modes are localized, with the maximum amplitudes at the center of the beam. The behavior of the wave modes is interpreted as an emission of perturbations from the unstable region toward the surrounding medium which is stable to these perturbations. The second group, surface modes, are localized at the periphery of the beam region and are less unstable than the unstable modes of the first group. The third group represents natural oscillations of the background plasma. These modes are nearly unaffected by the beam. Their frequencies are very close to those expected in the uniform thermal plasma and all the modes are damped. The main effect of the beam appears as an exclusion of the modes from the beam region.