Probe measurements of electron-energy distributions in plasmas: what can we measure and how can we achieve reliable results?

Abstract

An electric-probe method for the diagnostics of electron-distribution functions (EDFs) in plasmas is reviewed with emphasis on receiving reliable results while taking into account appropriate probe construction, various measurement errors and the limitations of theories. The starting point is a discussion of the Druyvesteyn method for measurements in weakly ionized, low-pressure and isotropic plasma. This section includes a description of correct probe design, the influence of circuit resistance, ion current and plasma oscillations and probe-surface effects on measurements. At present, the Druyvesteyn method is the most developed, consistent and routine way to measure the EDF. The following section of the review describes an extension of the classical EDF measurements into higher pressures, magnetic fields and anisotropic plasmas. To date, these methods have been used by a very limited number of researchers. Therefore, their verification has not yet been fully completed, and their reliable implementation still requires additional research. Nevertheless, the described methods are complemented by appropriate examples of measurements demonstrating their potential value.

Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas

“…[17,18,44] where bi-modal distribution functions (distribution function of 2 populations of particles at different temperatures) have been used. Other results are published in the literature describing effects of non-Maxwellians on the Langmuir probe measurements [36][37][38][39][40][41][42][43][44][45][46][47]. The bi-modal approximation is the first efficient way to describe NMDFs, but it assumes the superposition of two populations of particles at the Maxwellian equilibrium and the self-consistency is very restricted since in this bi-modal description the plasma is enough collisional to assure a MDF for each species but do not allow collisions between these two populations.…”

“…(ii) Another example is the discrepancy of the Langmuir probe interpretation [36][37][38][39][40][41][42][43][44][45][46][47] with respect to the Thomson scattering measurements [48,49] of the electron temperature which has been associated with the presence of super-thermal particles [17,18] (i.e., bulk and super-thermal populations, both at different thermodynamic equilibrium). The Langmuir probe is one of the most used diagnostic for low temperature plasmas.…”

Ramsauer-Townsend minimum in methane — modified effective range analysis

“…It was shown previously in pioneering work for argon [3] that including an empirical polarization potential is necessary to reproduce theoretically the R-T minimum. The sub-eV electron energies are important for tokomak edge regions, radiation counters and electrical discharges [4,5], with the R-T minimum determining electron temperatures in plasmas [6].…”

Energy spectra of Penning electrons in non-local plasma at middle and high pressures

“…The energy spectra of the Penning electrons were obtained by measuring the second derivative of the probe VA-characteristic (d 2 I/dV 2 ) with respect to the scanning voltage applied, which, according to the Druyvesteyn's relation, is proportional to the EEDF [8]. The so-called "modulation method" [8] was used.…”

“…The so-called "modulation method" [8] was used. The recording system is typical for the probe measurements [5].…”