Transit-time scattering and heating of a relativistic electron beam in strong Langmuir turbulence

Abstract

A Fokker–Planck theory is developed to describe the diffusion in momentum space of a beam of relativistic electrons due to multiple transit-time interactions with an ensemble of coherent Langmuir wave packets. The theory incorporates two ingredients: a perturbed-orbit calculation of the momentum change of a test particle during a single transit-time interaction, and an ensemble average of the resulting Fokker–Planck coefficients based on the statistical properties of strong Langmuir turbulence. An approximate analytic solution of the Fokker–Planck equation is obtained for the case of a strongly collimated beam, and is used to interpret measurements of energy and pitch-angle scattering in relativistic-electron-beam (REB) experiments. Fokker–Planck coefficients are also calculated for a weakly collimated beam. It is shown that the theory correctly predicts the amount of energy scattering in REB experiments, but underestimates the pitch-angle scattering regardless of the distribution of wave packet orientations and the degree of collimation of the beam. This discrepancy may be a product of the approximate wave-packet structure assumed in the analysis, or of systematic errors in the experimental data; alternatively, it may imply that a non-transit-time process is responsible for part of the pitch-angle scattering observed.