Plasma heating by relativistic electron beams: Correlations between experiment and theory

The streaming instability is the primary heating mechanism in most, if not all, experiments in which the beam is injected into partially or fully ionized gas. In plasma heating experiments, the relativistic beam must traverse an anode foil before interacting with the plasma. The linear theory for such a scattered beam is discussed, including a criterion for the onset of the kinetic interaction. A nonlinear model of the two-stream instability for a scattered beam is developed. Using this model, data from ten experiments are unfolded to obtain the following correlations: i) for a fixed anode foil, the dependence of the plasma heating on the beam-to-plasma density ratio is due to anode foil scattering, ii) for a fixed beam-to-plasma density ratio, the predicted change in the magnitude of plasma heating as a function of the anode foil is in agreement with experiment, and iii) the plasma heating tentatively appears to be proportional to the beam kinetic energy density and beam pulse length. For a fixed anode foil, theory also predicts that the energy deposition is improved by increasing the beam electron energy γmc². Presently, no experiment has been performed to confirm this aspect of the theory.