Electron thermalization in gases

The energy relaxation of energetic electrons is determined with a moment method solution of the hard sphere Lorentz–Fokker–Planck equation. The convergence of the expansion of the electron speed distribution function in speed polynomials is rapid and the energy relaxation can be written explicitly as a sum of a small number of exponential terms characterized by the lowest eigenvalues of the Lorentz–Fokker–Planck equation. The decay of the directed velocity is examined with a discrete ordinate method. The rate of convergence vs the number of quadrature points is extremely rapid and for particular values of the initial electron energy, an exact result can be obtained.