Multiple Scattering and Energy Loss of a Fast Test Electron Beam in a Plasma

Abstract

For a tenuous monoenergetic electron beam incident on a quiescent plasma, the number and mean energy loss of electrons scattered through angle θ are calculated. The beam density is assumed so low that the collision frequency exceeds the growth rate of unstable plasma oscillations, preventing the development of a two‐stream instability. The resulting test particle quantum Lenard‐Balescu equation is solved. In the very‐small‐θ, multiple scattering regime, the energy loss rate becomes approximately independent of θ, but is about 20% smaller than the “stopping power,” or energy loss rate averaged over θ. Dynamic shielding effects, especially Cerenkov emission of plasma oscillations, contribute significantly to the energy loss rate. Also in the multiple scattering regime, the distribution over θ is approximately Gaussian, as has been shown by other workers, and dynamic shielding results only in small new corrections, principally to the width of the Gaussian. The transition to single scattering, which begins at $\text{θ\hspace{0.17em}≳\hspace{0.17em}5°}$ for parameters considered, is also studied. In the single scattering regime, the distribution over θ is non‐Gaussian, and the energy loss depends strongly on θ. The calculation is quantitatively accurate only for $\text{θ\hspace{0.17em}≲\hspace{0.17em}20°}$ .