Kinetic Theory Approach to Electrostatic Probes

Abstract

A spherical electrostatic (Langmuir) probe in a slightly ionized plasma is studied from a kinetic theory point of view. The two-sided distribution function method of Lees, which embodies the Mott-Smith approach, is used. The velocity space is divided into two regions along the straight cone tangent to the spherical probe, and different distribution functions are defined in the two regions. On satisfying the two relevant moments of the distribution function (continuity and number density flux) three simultaneous ordinary nonlinear differential equations, which are appropriate to all values of the Debye length, collision mean free path and probe potential, are obtained for determining the ion and electron number densities, and the potential. These equations reduce to the usual linear flux equations when the mean free path is much shorter than the probe radius and the Debye length. The equations are first linearized and solved for the case of small probe potential. Explicit solutions are given for the current-voltage characteristics and the distributions of the number densities and the potential. The general case of arbitrary probe potential is also studied. Results for the characteristics and for the potential drop in the sheath are presented for some representative cases. Many of the results which are obtained do not appear in the original simplified Langmuir model. The modifications required to take into account the curvilinear orbits of the charged particles are discussed.

Cooled electrostatic probe.

“…The goal of a true plasma theory requires the description of the potential and electron density variations in the vicinity of the probe. The problem of the variation of the electrostatic potantial near a probe immersed in a continuum plasma has been studied by Cohen, 12 Lam, 20 -21 Wasserstrom, Su, and Probstein, 10 and Waymouth. 13 A basic conclusion drawn by all of these theories is the existence of a sheath region having a potential drop that is usually a large fraction of the probe potential, followed by a transition region containing the remaining potential variation.…”

Movement and dispersal of inhomogeneities in plasma

“…In the general case, no such calculations have yet been done. For weakly ionized plasma in the absence of a magnetic field, the problem is treated in [87]. by (1.7) have the form* N = 0, n(-~V~p + eDeVN) = 2e n(e/31VN + ~iV~p)…”

Kinetic and thermodynamic treatment for the exact solution of the unsteady Rayleigh flow problem of a rarefied homogeneous charged gas

“…The kinetic equation of gas flow based on the Boltzmann equation has obvious peculiarities in comparison with the macroscopic description found by using the Navier-Stokes equations, see [15,19]. Since it is very difficult to solve the full Maxwell-Boltzmann equations, various approximations have been suggested, such as the Chapman-Enskog procedure, Krook's model, and Lee's moment method [31][32][33][34] for the solution of the Boltzmann equation. Lees et al [33] applied the two-sided Maxwellian distribution to the problem of a conductive heat transfer.…”