Perturbation of Electron Energy Distribution by a Probe

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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 τd 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 τd = 2.9V (mv2 / 2kTe) / (Ap·v), where V is plasma volume, Ap is the probe area, v is electron velocity, and Te is electron temperature. The criterion for no perturbation of the electron-energy distribution then becomes N»1.5 × 104 T2 Ap, in which N is the total number of electrons in the plasma, T is the temperature in degrees Kelvin, and Ap 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 τp, provided 1/ωp « τp « τd, where ωp is the electron plasma frequency.