Colloquium: Physically based fluid modeling of collisionally dominated low-temperature plasmas

Abstract

This colloquium examines the theoretical modeling of nonequilibrium low-temperature ͑tens of thousands of degrees͒ plasmas, which involves a juxtaposition of three distinct fields: atomic and molecular physics, for the input of scattering cross sections; statistical mechanics, for the kinetic modeling; and electromagnetic theory, for the simultaneous solution of Maxwell's equations. Cross sections come either from single-scattering beam experiments or, at very low energies ͑Ͻ0.5 eV͒, from multiple-scattering experiments on "swarms" in gases-the free diffusion or large Debye length limit of a plasma, where they are embedded in transport coefficient data. The same Boltzmann kinetic theory that has been developed to a high level of sophistication over the past 50 years, specifically for the purpose of unfolding these transport data, can be employed for low-temperature plasmas with appropriate modification to allow for self-consistent rather than externally prescribed fields. A full kinetic treatment of low-temperature plasmas is, however, a daunting task and remains at the developmental level. Fortunately, since the accuracy requirements for modeling plasmas are generally much less stringent than for swarms, such a sophisticated phase-space treatment is not always necessary or desirable, and a computationally more efficient but correspondingly less accurate macroscopic theoretical model in configuration space at the fluid level is often considered sufficient. There has been a proliferation of such fluid modeling in recent times and this approach is now routinely used in the design and development of a large variety of plasma technologies, ranging from plasma display panels to plasma etching reactors for microelectronic device fabrication. However, many of these models have been developed empirically with specific applications in mind, and rigor and sophistication vary accordingly. In this colloquium, starting from the governing Boltzmann kinetic equation, a unified, general formulation of fluid equations is given for both ions and electrons in gaseous media with transparent and internally consistent approximations, all benchmarked against established results. Thereby a fluid model is obtained that is appropriate for practical application but at the same time is based on a firmer physical foundation. CONTENTS

Transport coefficients and cross sections for electrons in water vapour: Comparison of cross section sets using an improved Boltzmann equation solution

“…Nevertheless, this region needs special attention from a different perspective, in view of the continued confusion 28 surrounding transport coefficient definition in the presence of nonconservative collisions (ionization and attachment). 29,35,36 Thus names are sometimes assigned to drift velocities according to the experiment in which they are measured, e.g., time-of-flight, arrival time spectra, steady state Townsend, and pulsed Townsend drift velocities, although as has been pointed out a number of times, this is neither desirable nor necessary, given that there are just two fundamental types of transport properties, which can be defined independently of any experimental arrangement. The measurable and universal transport coefficients (independent of experiment) are the "bulk" transport coefficients 35 which appear in the diffusion equation.…”

METHES: A Monte Carlo collision code for the simulation of electron transport in low temperature plasmas

“…The kinetic modeling on the basis of microscopic collision cross sections is possible either by numerically solving the Boltzmann equation for the electron distribution [5][6][7], or by tracking the stochastic motion of the individual electrons by means of Monte Carlo simulation [1,[8][9][10][11][12]. For steady-state conditions kinetic modeling can provide transport parameters and reaction rates that are the necessary input parameters for macroscopic fluid models used in low-temperature plasmas and gas discharges [13].…”

A Monte Carlo simulation of ion transport at finite temperatures

“…Indirectly, transport coefficients can be used to verify the completeness and the absolute magnitude of the cross sections in the sets [1,9] that are to be used in Monte Carlo (MC) and particle in cell models of plasmas [14,15]. There is a critical shortage of data for most ions in most gases that are interesting for applications [16].…”