Test particle distribution in a partially ionized plasma

Abstract

Theory and experiments are described for the evolution of the energy distribution of a group of test electrons interacting with a background plasma through electron-electron (e-e), electron-ion (e-i), and elastic electron-neutral (e-n) collisions. The experiments were performed on the afterglow of a pulsed microwave discharge (1010<ne<1012 cm−3, Te∼0.2 eV). The test electrons (4<E<14 eV) were injected into the plasma as a feeble quasi-monoenergetic beam. For the electrons, the e-n mean-free path λ was much smaller than the length of the plasma L, while the e-e mean-free path was much greater. Nonetheless, because of the large neutral-to-electron mass ratio, the dynamic friction and smaller diffusion-in-speed were determined by Coulomb collisions, while frequent e-n collisions maintained the distribution nearly isotropic. As this distribution gradually advanced along the discharge, it was shifted downward in mean energy due to dynamic friction, and broadened because of the distribution of friction path lengths, and because of diffusion-in-energy. The Boltzmann equation governing the beam electrons was reduced, by taking advantage of the smallness of λ/L and m/M, to a simple partial differential equation for the distribution function which was solved analytically. The remarkably close agreement between experiment and theory, including the lack of sensitivity of the latter to all parameters save plasma density and initial test particle energy, suggests wide applicability for the concepts examined here.