A comparison of kinetic and fluid models of the positive column of discharges in inert gases

Abstract

The models of a positive column of an inert gas discharge at low pressures and small currents are developed in the frameworks of nonlocal kinetic and local fluid theories. Both models are based on the joint solution of the corresponding kinetic equation, ion-motion equation and Poisson equation that permit one to describe bulk plasma and near-wall sheaths of space charge. The theories differ principally in the descriptions of the electron component of a plasma. In the fluid theory the radial flux of electrons is a combination of field and diffusive fluxes, but in the kinetic model a similar representation is impossible. A comparison of the distribution functions and macroscopic properties calculated by kinetic and fluid theories for the discharge under the same conditions is performed. This comparison is carried out for the models of the positive column developed under the assumption of plasma quasi-neutrality and with regard to the deviations from quasi-neutrality. The use of the fluid theory beyond its application range (low pressures and small currents) does not reflect the physical picture of discharge sustenance and leads to incorrect results with respect to several parameters.

Self-Consistent Description of Radial Space-Charge Confinement in DC Column Plasmas

“…A numerical solution of this equation to describe the electron kinetics in inhert gas dc column plasmas has been performed by several authors [4,[13][14][15][16][17][18][19][20][21][22] recently. Most of these approaches [4,13,15,[17][18][19][20][21][22] are based on the two-term expansion of the electron velocity distribution (EVD) into spherical harmonics. In the other approaches [14,16], particle simulation techniques have been used to solve the kinetic equation.…”

“…In the other approaches [14,16], particle simulation techniques have been used to solve the kinetic equation. However, most of these authors assumed roughly simplified model functions for the radial space-charge potential [4,15,16,19,22,23] or used a potential function resulting from corresponding electrical probe measurements [17,18,21].…”

“…Up to now, only some authors [4,13,14,22,23] have made initial attempts to apply a nonlocal electron kinetic treatment inside a self-consistent positive column model, which includes the determination of the radial space-charge field. Hartig and Kushner [13] deduced the radial field from the radial ambipolar flux avoiding the solution of Poisson's equation.…”

“…Hartig and Kushner [13] deduced the radial field from the radial ambipolar flux avoiding the solution of Poisson's equation. Behnke et al [4] and Golubovskii et al [22,23] started with an electron kinetic treatment for a given roughly simplified model potential and determined afterwards a new estimate of the potential assuming quasi-neutrality [4,23] or solving Poisson's equation [22]. However, they did not consistently take into account the coupling of the equations by applying the resulting potential function in an additional treatment of the electron and ion kinetics.…”

“…Except for the recent work of Golubovskii et al [22], all these authors avoided the additional coupling of the electron kinetic treatment with a balancing of important excited atom states and described the charge carrier production very roughly by taking into account direct ionization of ground state atoms only. The self-consistent coupling of the spatially resolved treatments of the excited atom kinetics and the electron kinetics is described, in [17,18,21,22].…”