Unified solution of the Boltzmann equation for electron and ion velocity distribution functions and transport coefficients in weakly ionized plasmas

Abstract

We present a framework for the solution of Boltzmann's equation in the swarm limit for arbitrary mass ratio, allowing for solutions of electron or ion transport. An arbitrary basis set can be used in the framework, which is achieved by using appropriate quadratures to obtain the required matrix elements. We demonstrate an implementation using Burnett functions and benchmark the calculations using Monte-Carlo simulations. Even though the convergence in transport quantities is always good, the particle distributions did not always converge, highlighting that simple benchmarks can give misleading confidence in a choice of basis. We postulate a different basis, which avoids a spherical harmonic expansion, which is better suited to strong electric fields or sharp features such as low-energy attachment processes.

Electron transport in biomolecular gaseous and liquid systems: theory, experiment and self-consistent cross-sections

“…From a numerical calculation of transport coefficients viewpoint, this manifests itself as poor convergence rates, or convergence that is very sensitive to the numerical technique parameters. This was recently discussed in [104,105]. Furthermore, it could be that in this small region of E/n 0 the hydrodynamic approximation breaks down, and drift and diffusion coefficients alone may not be sufficient to describe the current trace.…”

Physics-informed neural networks for solving the Boltzmann equation of the electron velocity distribution function in weakly ionized plasmas

“…Since introducing dimensionless quantities is useful in numerical calculations 4,28) and it is preferable for the ANN inputs to be distributed on [−1, 1], 29) the physical quantity appearing in the governing equation is converted to the dimensionless quantity. The dimension of the physical quantity considered here can be expressed as a product of time T, length L, mass M, and electric charge Q.…”

“…1,2) These coefficients are required for simulating electron transport and chemistry in plasmas. [3][4][5][6] Furthermore, electron collision cross-section sets have been determined and validated by comparing calculated and measured electron transport coefficients. [7][8][9] The direct numerical solution (DNS) of the BE, which requires no expansion of the EVDF using orthogonal functions, is preferable to calculate the EVDF accurately.…”

“…Maeda and Makabe 12) developed the DNS for investigating the electron swarm transport under RF electric fields in Ar. Their method was used to calculate the electron transport coefficients in CF 4 and CF 4 -Ar mixtures. 13) Sugawara recently developed the DNS for calculating the EVDF under DC uniform electric fields crossed with DC magnetic fields at a right angle.…”

Асимптотика Ядер Интеграла Столкновений Линейного Уравнения Больцмана При Больших Значениях Индекса Для Потенциала Твердых Шаров

“…Такая ситуация возникает, например, в задаче о расчете ФР ионов. Эта задача весьма актуальна для анализа химических реакций в плазме, включающих ионы, определения подвижности ионов, нагрева нейтральной компоненты плазмы и т. д. Подходы к ее решению активно разрабатываются исследователями (см., например, обзор методов решения уравнения Больцмана для заряженных частиц [1], описание нового метода расчета ФР электронов и ионов в слабо ионизованной плазме [2] и ссылки в [2], сравнение результатов расчета ФР ионов с экспериментальными данными [3]).…”