A multi-term Boltzmann equation analysis of electron swarms in gases

Over the past few years multidimensional self-consistent plasma simulations including complex chemistry have been developed which are promising tools for furthering our understanding of reactive gas plasmas and for reactor design and optimization. These simulations must be benchmarked against experimental data obtained in well-characterized systems such as the Gaseous Electronics Conference (GEC) reference cell. Two-dimensional simulations relevant to the GEC Cell are reviewed in this paper with emphasis on fluid simulations. Important features observed experimentally, such as off-axis maxima in the charge density and hot spots of metastable species density near the electrode edges in capacitively-coupled GEC cells, have been captured by these simulations.

show abstract

“…are needed. These can also be obtained as the appropriate integrals over the distribution function [ 38 ].…”

Section: Model Formulationmentioning

confidence: 99%

Two-Dimensional Self-Consistent Radio-Frequency Plasma Simulations Relevant to the Gaseous Electronics Conference Rf Reference Cell

Lymberopoulos¹,

Economou²

1995

J. Res. Natl. Inst. Stand. Technol.

137

106

View full text Add to dashboard Cite

show abstract

“…The multi-term approximation is a solution method for the BE that further improves the approximation accuracy, and it has been reported that about six terms are required in CH 4 gas. 14) There is an open-source software MultiBolt. 15) Although several different advanced methods are known as exact solution methods for the BE, the most well-known one is the Monte Carlo (MC) method.…”

Section: Introductionmentioning

confidence: 99%

An improved calculation scheme of electron flow in a propagator method for solving the Boltzmann equation

Kobayashi¹,

Sugawara

Ikeda³

2023

Jpn. J. Appl. Phys.

View full text Add to dashboard Cite

In order to accurately evaluate the electron acceleration process in the time evolution calculation of electron velocity distribution function (EVDF) based on the Boltzmann equation, an improved scheme blending upwind and central differences is introduced into the propagator method (PM). While the previous PM based on the upwind scheme needs fine cells to obtain an accurate EVDF at low electric fields, the improved PM is robust against coarse cells, which allows the reduction of the cell resolution. Calculations of the EVDF in Ar under RF electric fields demonstrated that the blending scheme can provide satisfactorily accurate results even with cells about tenfold larger than the upwind case at low reduced electric fields below 1 Td, which leads to much shorter computational time because the reduction of number of cells satisfactorily compensates the complexity of the blending scheme. This technique has been built into a new user-friendly PM software named BOSPROM.

show abstract

“…When the anisotropy of the EVDF is significant, we need to consider higher-order terms. Yachi et al (1988Yachi et al ( , 1991 performed a six-term BE analysis using the Galerkin method. Loffhagen and Winkler (1996) developed a calculation scheme treating the expansion terms being time-dependent in a BE analysis with six to eight terms.…”

Section: Introductionmentioning

confidence: 99%

A relaxation-accelerated propagator method for calculations of electron energy distribution function and electron transport parameters in gas under dc electric fields

Sugawara¹

2017

Plasma Sources Sci. Technol.

View full text Add to dashboard Cite

A propagator method (PM), a numerical technique to solve the Boltzmann equation (BE) for the electron velocity or energy distribution function (EVDF/EEDF) of electron swarms in gases, was customized to obtain the equilibrium solution quickly. The PM calculates the number of electrons in cells defined in velocity space using an operator called the propagator or Green's function. The propagator represents the intercellular transfer of electrons corresponding to the electron velocity change due to the acceleration by the electric field and the collisional events with gas molecules. The relaxation of the EVDF to its drift equilibrium solution proceeds with iterative propagator operations for the EVDF. Merits of the PM are that the series expansion of the EVDF as done in the BE analyses is not required and that time evolution of the electron swarm can be observed if necessary. On the other hand, in case only the equilibrium solution of the EVDF is wanted, the relaxation can be accelerated numerically. A demonstration achieved a shortening of the computational time by about three orders of magnitude. Furthermore, this scheme was applied to calculations of a set of electron transport parameters required in fluid-model simulations, i.e. the effective ionization frequency, the centroid drift velocity and the longitudinal diffusion coefficient, using the zeroth-, first-and second-order moment equations derived from the BE. A detailed description on the PM calculation was presented.

show abstract

A multi-term Boltzmann equation analysis of electron swarms in gases

Cited by 32 publications

References 16 publications

Two-Dimensional Self-Consistent Radio-Frequency Plasma Simulations Relevant to the Gaseous Electronics Conference Rf Reference Cell

Two-Dimensional Self-Consistent Radio-Frequency Plasma Simulations Relevant to the Gaseous Electronics Conference Rf Reference Cell

An improved calculation scheme of electron flow in a propagator method for solving the Boltzmann equation

A relaxation-accelerated propagator method for calculations of electron energy distribution function and electron transport parameters in gas under dc electric fields

Contact Info

Product

Resources

About