Perturbation of Electron Energy Distribution by a Probe

Abstract

In order to determine electron‐energy distribution in a plasma, the electron current to a probe is measured as a function of potential on the probe. If the rate of removal of high‐energy electrons by measurement is comparable with the rate of replenishment by the various plasma processes, serious perturbation of the electron‐energy distribution will result as a consequence of the act of measurement. A criterion for deciding when this effect may be ignored is presented herein. It is based on the hypothesis that when the depletion time constant τ_d of electrons of a particular energy by a given probe in a given plasma is large compared with the time for electrons to fill out a Maxwellian tail by Coulomb collisions as given by Montgomery and Tidman, perturbation of the electron‐energy distribution is negligible. The depletion time constant is τ_d = 2.9V (mv² / 2kT_e) / (A_p·v), where V is plasma volume, A_p is the probe area, v is electron velocity, and T_e is electron temperature. The criterion for no perturbation of the electron‐energy distribution then becomes N»1.5 × 10⁴ T² A_p, in which N is the total number of electrons in the plasma, T is the temperature in degrees Kelvin, and A_p is the probe area in square centimeters. It is shown that even if the criterion is not satisfied, probe measurements of the electron‐energy distribution may still be made by using a pulsed or transient system with pulses of length τ_p, provided 1/ω_p « τ_p « τ_d, where ω_p is the electron plasma frequency.