title: Kullback-Leibler entropy in the electron distribution shape relaxation for electron-atom thermalization.
abstract: We study the thermalization of energetic electrons dilutely dispersed in inert gas atomic moderators, with and without the presence of an external electric field. We investigate the shape relaxation of the electron distribution function relative to the steady-state distribution by means of the Kullback-Leibler entropy. The departure of the distribution function from a local Maxwellian parametrized by the temperature of the electrons is also considered with a functional analogous to the Kullback-Leibler entropy. For neon and argon as moderators, we found no evidence for the formation of a local Maxwellian followed by a slower relaxation to equilibrium. The momentum-transfer cross section for e-Ne collisions is almost constant with energy, whereas the e-Ar momentum-transfer cross section has a deep Ramsauer-Townsend minimum and a strong energy dependence. The role of the Ramsauer minimum in the relaxation processes is investigated. The time-dependent Lorentz-Fokker-Planck equation is solved for the speed distribution of the electrons with a finite difference method. A pseudospectral method is also used to investigate the spectral properties of the Fokker-Planck operator. In spite of the multi-exponential time dependence of the speed distribution function, we show that a single average relaxation time can be defined to characterize the relaxation to equilibrium.
authors.affiliation: Institute of Applied Mathematics, Vancouver, British Columbia, Canada, V6T 1Z2.
authors.forename: Reinel
authors.initials: R
authors.lastname: Sospedra-Alfonso
authors.forename: Bernie D
authors.initials: BD
authors.lastname: Shizgal