Energy exchange between a test charge and an unstable electron beam

An investigation is made of the interaction between a test charge and an electron beam which is convectively unstable against plasma oscillations. An analysis is made of the negative-mass instability of the longitudinal motion. Expressions are derived for the reaction force exerted by the electron plasma polarized by the moving charge and for the diffusion tensor arising from electric field fluctuations. The approximation of uniform rectilinear motion of a test particle is used to estimate the systematic and diffusion components of the rates of change in its energy. It is shown that in this case, interaction with an unstable electron beam leads to acceleration of the particle in respect to the longitudinal degree of freedom (antifriction) and under certain conditions enhances the friction effect (cooling) in respect to the transverse degrees of freedom. An assessment is made of the possibility of obtaining an overall positive friction effect by using a special “sweeping” procedure whereby the longitudinal velocity of the electron beam is changed in a specific manner consistent with the cooling process.