First principles calculation of the effect of Coulomb collisions in partially ionized gases

Abstract

Coulomb collisions, at appreciable ratios (η) of the electron to the neutral particle density, influence significantly the electron kinetics in particle swarms and in plasmas of gas discharges. This paper introduces a combination of Molecular Dynamics and Monte Carlo simulation techniques, to provide a novel, approximationfree, first principles calculation method for the velocity distribution function of electrons, and related swarm characteristics, at arbitrary η. Simulation results are presented for electrons in argon gas, for density ratios between zero and 10 −1 , representing the limits of a negligible electron density and an almost complete Maxwellization of the velocity distribution function, respectively. PACS numbers: 52.65.-y, 52.25. Fi,

Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions

“…For instance, in the particle-particle-particle-mesh (P 3 M) method, the usual technique used to compute the potential on the simulation grid is refined by additionally computing inside each cell the direct contribution to the force due to near particles [54,55], as is also done in Barnes-Hut tree code [56]. Moreover, hybrid approaches are also available, where either the usual PIC scheme [57], P 3 M [58], or a smooth potential method [59] for the force calculation is combined with Monte Carlo sweeps in velocity space, thereby restoring the collision term in the right-hand side of Boltzmann equation (3). In general, such methods turn out to be computationally costly since they involve iterative evaluations of the systems phase-space distribution function f at each collision step.…”

First-principles particle simulation and Boltzmann equation analysis of negative differential conductivity and transient negative mobility effects in xenon

“…It is plausible that the validity of the approximations listed above can only be checked with an approach that is free of these and makes it possible to compute the VDF without any a priori assumptions. Such a particlebased method relying on first principles has recently been presented in [16]. This method has been cross-checked with BE solutions for the scenario of the "bistabilty" of the Electron Energy Distribution Function (EEDF) [14], an effect that allows the formation of distinctly different EEDF-s at exactly same conditions.…”

Bistable solutions for the electron energy distribution function in electron swarms in xenon: a comparison between the results of first-principles particle simulations and conventional Boltzmann equation analysis

“…The solution of the Boltzmann equation adopted the usual, widely accepted approximations: it (i) searched for the distribution function in the form of two terms, (ii) neglected the electron-electron part of the collision integral for the anisotropic part of the distribution function, (iii) treated Coulomb collisions as binary events, and (iv) truncated the range of the electron-electron interaction beyond a characteristic distance. The particle simulation method [26], being devoid of any of these approximation has provided rst-principles solutions to the problem, via a combination of a Molecular Dynamics simulation method (that described accurately the many-body interactions within the electron gas governed by the full Coulomb potential) and a Monte Carlo method (that handled the interaction of the electrons with the atoms of the background gas). Both methods allowed the computation of the EEDF and the related quantities, and have indicated the existence of two stable solutions for the EEDF for a range of E n / .…”

“…(b) Elastic momentum transfer cross section for electron-Xe atom collisions [27]. The simulation scheme is based on a combination of a Molecular Dynamics (MD) technique and a Monte Carlo (MC) approach [26]. The MD describes the many-body interactions (driven by the inter-particle Coulomb potential) within the classical electron gas, while the MC part handles the interaction of the electron gas with the background (atomic) gas.…”

“…(We note that previous particle-based (Monte Carlo) methods, dealing with Coulomb collisions, are neither free of approximations.) The particle-based simulation technique, used here [26], on the other hand, relaxes all the above major approximations and provides a solution based on rst principles. Therefore we expect this method to be able to evaluate the accuracy of the BE solution that is limited by the approximations adopted, and can verify the effects predicted within the frame of the BE approach, like the EEDF bistability that was introduced above and is studied here in details in Xe gas.…”