A Collisional Model of the Positive Ion Collection by a Cylindrical Langmuir Probe

Abstract

This article presents a new theoretical model of ion collection by a cylindrical Langmuir probe at medium and higher pressures which we call the "modified TALBOT and CHOU model". The model makes use of the following theories; (a) the kinetic theory by CHOU, TALBOT and WILLIS [6, 71 and (b) the theory by ZAKRZEWSKI and KOPICZYNSKI [lo, 1 I]. The basic idea is to calculate the decrease of probe ion current due to collisions with neutrals according [6, 71 and the increase of the ion current due to destruction of an orbital motion according [lo, I I]. The computed results are presented in the form of graphs suitable for probe data interpretation at medium and higher pressures. The applicability of the results at particular plasma conditions is also discussed.

Langmuir Probe Diagnostics for Medium Pressure and Magnetised Low-Temperature Plasma

“…The advantage of the new model [12] of the ion collection by a cylindrical Langmuir probe consists mainly in the fact that it is valid for any K, i.e. for OIK,<oo as long as the condition of the OML regime of the probe is fulfilled (DA53).…”

“…On the contrary to the calculations of the yz factor which have been made by Zakrzewski and Kopiczynski the correction factor yz* depends on the ratio of the electron to ion temperature z=(TJT$. We suggested in [12] to call this new model the "modified Talbot and Chou model" since it refines the "classical" kinetic Chou and Talbot theory [43,44].…”

“…Comparison of the theory [12] with the Chen-Talbot [27] and with the Zakrzewski-Kopiczynski 151,521 theories has been made by Kudrna in [58]. He calculated also the dependence of the directly measurable quantity D?I,* on K, with Dn as a parameter.…”

“…Up to now the Zakrzewski and Kopiczynski model [51] has been tested in several papers [12,52,59,60]. In [12,52] the authors used the X-band microwave interferometer for the independent determination of the relative values of the electron density.…”

“…[12]) namely by the Knudsen number for ions and electrons K,, = /Z,JR, (where A,,, is the mean free path for ions/electrons and Rp the probe radius) and by the Debye number Dn = R/AD, LD=(E~~TJ (q02nejj1'2 is the Debye length, c0 is the permittivity of vacuum, k the Boltzmann constant, T, the electron temperature, go the elementary charge and n, the electron density). Another parameter which influences the collection of charged particles by a probe is the "anisothermicity parameter" of a plasma namely the ratio of the electron to ion temperature, z = TJ Ti.…”