Energy loss of fast nonthermal electrons in plasmas

Simple analytical expressions for equilibration times of nonrelativistic monoenergetic electrons in plasmas are evaluated in the ‘‘weak’’-beam approximation when the density of the monoenergetic electrons is much smaller than the plasma density. The equilibration time is defined as the time needed by the beam of monoenergetic electrons to lose most of its energy as a result of collisions with plasma particles having a Maxwellian energy distribution. The process of the energy equilibration is treated as a statistical superposition of both elastic (electron-electron, electron-ion, and electron–neutral-particle) and inelastic (electron–neutral-particle) collisions in the plasma. The possibility of collisionless equilibration is also discussed. Comparison of the equilibration times with the Spitzer relaxation times indicates that the former times are more appropriate for an estimate of the energy loss of the ‘‘weak’’ electron beams in highly ionized plasmas. The approach of this work can be generalized in a straightforward way to beam-plasma and beam-gas systems with ionic and neutral-particle beams.