Time dependent electron distribution functions and degradation spectra: A comparison of the Spencer—Fano equation and the Boltzmann equation

Abstract

The thermalization of electrons in gaseous moderators for initial nonequilibrium distributions not far removed from thermal energies has been studied previously with a Fokker—Planck equation for electron distribution. For electron energies in the keV to eV energy range an approach based on the Spencer—Fano equation has also been used. The present paper considers a detailed comparison of the two approaches to electron thermalization. The Spencer—Fano equation is analogous to the Fokker—Planck equation but with the moderator temperature set to zero, that is, with the cold gas approximation. The effect of the cold gas approximation on the time evolution of the nonequilibrium distributions and on the calculation of thermalization times is discussed in detail. The cold gas approximation is shown to be the basis for most of the concepts used in radiation chemistry and physics to study electron degradation. Applications to the thermalization of electrons in the inert gases are considered. The analysis is restricted to elastic electron-moderator collisions.