Electrostatic Waves in Beam-Plasma Systems

By describing systems composed of a plasma and a set of moving nonrelativistic charged particle streams by means of collective coordinates, it is possible to discuss the collective interactions of the components of the system. The dispersion relation of an infinite beam-plasma system is found by requiring that the coupled equations of motion of these coordinates have a simultaneous solution. For a finite plasma the interaction is discussed in the limit where the time necessary for a beam particle to traverse the plasma is short. Two types of growing plasma waves are then possible. The first type is due to the coupling of the growing beam modes to the plasma modes. The second type occurs when the frequency of the beam oscillations match the background plasma frequency and leads to a linear growth of the plasma waves.