A multi-term solution of the space–time Boltzmann equation for electrons in gases and liquids

Abstract

In a recent paper [1] the scattering and transport of excess electrons in liquid argon in the hydrodynamic regime was investigated, generalizing the seminal works of Lekner and Cohen [2, 3] with modern scattering theory techniques and kinetic theory. In this paper, the discussion is extended to the non-hydrodynamic regime through the development of a full multi-term space-time solution of Boltzmann's equation for electron transport in gases and liquids using a novel operator-splitting method. A Green's function formalism is considered that enables flexible adaptation to various experimental systems. The spatio-temporal evolution of electrons in liquids in the hydrodynamic regime is studied for a benchmark model Percus-Yevick liquid as well as for liquid argon. The temporal evolution of Franck-Hertz oscillations are observed for liquids, with striking differences in the spatio-temporal development of the velocity distribution function components between the uncorrelated gas and true liquid approximations in argon. Transport properties calculated from the non-hydrodynamic theory in the long time limit, and under steady-state Townsend conditions, are benchmarked against hydrodynamic transport coefficients. arXiv:1509.00867v1 [physics.comp-ph] 31 Aug 2015

Integral Cross Sections for Electron–Zinc Scattering over a Broad Energy Range (0.01–5000 eV)

“…The two-term approximation did break down for reduced fields above this with transport coefficients differing by up to 40% at the maximum field considered. 19,20 We observe an almost order of magnitude lower bulk drift and diffusion for the recommended cross section set at very low E/n 0 (∼10 −3 Td). This is entirely due to the higher magnitude elastic MTCS for the recommended set compared to the White et al 7 set in the thermal energy regime (∼10 −1 Td).…”

“…Finally, we note that we calculated transport coefficients for gaseous Zn at 750 K using a well benchmarked, multiterm solution of Boltzmann's equation. 19,20 For comparison, we also applied the twoterm approximation 21 over the same range of E/n 0 . Here, we found that the results from the multiterm and two-term solvers agreed to better than a few percent for reduced fields less than 100 Td.…”

Toward a complete and comprehensive cross section database for electron scattering from NO using machine learning

“…To assess the quality of our initial set of electron-NO cross sections, we apply a well-benchmarked multi-term solution of Boltzmann's equation [32,49,50] in order to calculate swarm transport coefficients for comparison to measured values in the literature. Chronologically, electron-NO swarm measurements include drift velocities and transverse characteristic energies by Skinker et al [51] and Bailey et al [52], transverse characteristic energies by Townsend [53], drift velocities and attachment coefficients by Parkes et al [54], transverse characteristic energies and ionisation coefficients by Lakshminarasimha et al [55], transverse and longitudinal characteristic energies by Mechlińska-Drewko et al [56], and, most recently, drift velocities and longitudinal diffusion coefficients by Takeuchi et al [33] (for both pure NO and admixtures of NO in Ar).…”

Positron Scattering from Gas-Phase Beryllium and Magnesium: Theory, Recommended Cross Sections, and Transport Simulations

“…Finally, for each species, a comparison of the positron versus electron transport behavior is presented and discussed. In what follows, we implement a well benchmarked multiterm solution of Boltzmann's equation 44 for the calculation of the transport coefficients in gaseous Be and Mg, and we have found that the two-term approximation 45,46 is generally sufficient for the coefficients presented, over the range of E/n 0 considered. Our physical discussions below will focus on the rates and the drift velocities.…”