Almost Longitudinal Instabilities in a Plasma-Beam System

A plasma-beam system immersed in a magnetic field B0 is investigated under the assumption that the plasma is stationary, cold, uniform, and extended and that the beam of charged particles is uniform in density and moving in a direction parallel to that of B0. Instabilities which are almost longitudinal are investigated with respect to conditions of occurrence, strength and type of instabilities, and dependence on the angle between the direction of B0 and the direction of the excited waves. Two logically distinct types of waves which occur are defined and investigated. An almost longitudinal Čerenkov wave has a phase velocity equal to the projection of the beam velocity in the direction of the wave. An almost longitudinal cyclotron wave has a frequency equal to the Doppler-shifted gyrofrequency of the particles in the beam. Typical examples are analyzed numerically and presented graphically. Certain simple analytical expressions which apply to the significant regions of instability are derived and tabulated.