Calculation of nonlocal EDF using a one-dimensional Boltzmann equation solver

Abstract

A method for the calculation of the nonlocal electron distribution function (EDF) with programs commonly used for solving the one-dimensional Boltzmann kinetic equation (e.g., COMSOL Multiphysics) was proposed and implemented. The capabilities of the proposed method were illustrated using the example of the positive column plasma in argon. Significant differences between the local and nonlocal EDFs were observed, especially at the plasma periphery. This can result in significant differences in the electron transport coefficients and reaction rate constants for electron-induced processes. The proposed approach increases the precision of the numerical modeling of gas discharge devices and equipment.

Features of the EEDF formation in the dusty plasma of the positive column of a glow discharge

“…Taking into account these parameters, calculations were carried out both in the local and nonlocal approximations according to the Holstein-Tsendin method described above. As in previous works [25][26][27], the COMSOL multiphysics software package [31] was used for the calculations. This software has a built-in two-term Boltzmann model for calculating the local EEDF.…”

“…This software has a built-in two-term Boltzmann model for calculating the local EEDF. In the previous works [26][27][28], this solver was adapted for solving the nonlocal kinetic equation using the Holstein-Tsendin method.…”

“…In the Holstein-Tsendin model, the nonlocal EEDF depends on only one variable, namely the total energy ; thus, the kinetic equation after volume-averaging has the same form for the local approximation (see below equations ( 9) and ( 13)). This made it possible to implement [26][27][28][29][30] the adaptation procedure of the standard local Boltzmann solver to obtain a nonlocal EEDF using the Holstein-Tsendin method [19,24]. As a result, it has been possible to significantly expand the applicability of well-known software packages [29][30][31][32] available to a wide range of users for modeling of the EEDF in gas-discharge plasma and leading to an improvement of the obtained results.…”

“…In the previous research [12,13], the parabolic potential was used, which often does not correspond to the Boltzmann distribution of electrons in plasma realized in practice. It was shown in [26] that replacing the parabola with a more realistic dependence corresponding to the Bessel plasma density profile resulted in noticeable differences in the form of the nonlocal EEDF and other electron characteristics even in a simple (without dust particles) plasma. On the other hand, with an increase in the density of dust particles, the dependences of eϕ(r) can be realized more sharply than those occurring in a simple plasma without dust (for more information, see, e.g.…”

“…In the present work, the effect of dust particles on the formation of the nonlocal EEDF in the positive column of the glow discharge in argon is investigated. It is based on the previous studies [26][27][28] on the influences of various processes on the formation of the nonlocal EEDF. The technique of adapting a standard local Boltzmann solver for the calculation of the nonlocal EEDF in dusty plasma is implemented.…”