Abstract
The Fokker‐Planck equation describing the scattering and energy loss of hot electrons in a mirror‐confined, hot‐electron plasma is solved, neglecting the effect of hot‐electron self‐scattering, but including the effect of hot‐electron scattering against neutrals, ions, and cold electrons. For a class of initial‐value problems (no source), expressions for the time‐asymptotic form of the distribution function f, the density n, and the mean‐square velocity per contained particle 〈υ2〉 are obtained. For a distribution function with an initial Maxwellian or Druyvestian tail scattering against constant density neutrals, f ∼ υβ for small velocity υ and large time t. For a Maxwellian tail, ln n ∼ t2/3 and 〈υ2〉 ∼ t2/9; for a Druyvestian tail, ln n ∼ t4/3 and 〈υ2〉 ∼ t−2/9. Numerical calculations showing the transition to the asymptotic form of the decay are presented. For the case of steady‐state injection of hot electrons, expressions for f, n, and 〈υ2〉 are obtained in terms of the given source distribution function.
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