Electron scattering and transport in liquid argon

Abstract

The transport of excess electrons in liquid argon driven out of equilibrium by an applied electric field is revisited using a multi-term solution of Boltzmann's equation together with ab initio liquid phase cross-sections calculated using the Dirac-Fock scattering equations. The calculation of liquid phase cross-sections extends previous treatments to consider multipole polarisabilities and a non-local treatment of exchange, while the accuracy of the electron-argon potential is validated through comparison of the calculated gas phase cross-sections with experiment. The results presented highlight the inadequacy of local treatments of exchange that are commonly used in liquid and cluster phase cross-section calculations. The multi-term Boltzmann equation framework accounting for coherent scattering enables the inclusion of the full anisotropy in the differential cross-section arising from the interaction and the structure factor, without an a priori assumption of quasi-isotropy in the velocity distribution function. The model, which contains no free parameters and accounts for both coherent scattering and liquid phase screening effects, was found to reproduce well the experimental drift velocities and characteristic energies.

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

“…With an increase in density, several important density effects become significant, most notably (i) the coherent scattering from multiple scattering centres, (ii) the screening of the long range polarization potential due to induced multipoles in the bulk, and (iii) the contribution of the bulk to the effective potential experienced by the electron. Transport coefficients such as drift velocities and characteristic energies calculated in the hydrodynamic regime with our hydrodynamic multi-term Boltzmann equation solution were in good agreement with swarm experiment measurements in both gas-and liquid-phase argon [17]. In this work we extend the discussion to an investigation of liquid state in the non-hydrodynamic regime, using the same electronargon potentials and cross-sections presented in [1].…”

Assessment of the self-consistency of electron-THF cross sections using electron swarm techniques: Mixtures of THF–Ar and THF–N2

“…The quasielastic 70 momentum transfer cross section of THF is much larger than that of argon, between one and two orders larger below 1 eV (compare the "current" argon elastic momentum-transfer profile in Fig. 1 of Boyle et al 69 with the THF quasielastic momentum-transfer profile in Fig. 3).…”

“…For the present study, where we compare experimentally measured and simulated drift velocities and the effective Townsend ionization coefficient, we calculate time-of-flight and steady-state Townsend coefficients for each of these, respectively. For details, the reader is referred to the approaches used in the work of Casey et al 67 and Boyle et al 68,69 that have been systematically benchmarked and validated against independent kinetic theory solutions and Monte Carlo methods.…”

Generalized balance equations for charged particle transport via localized and delocalized states: Mobility, generalized Einstein relations, and fractional transport

“…To find an expression for the diffusion coefficient, we must apply density gradient expansions to all average quantities in the momentum and energy balance equations (24) and (25). For the mean energy we have, to first spatial order [16] ≈ ε + γ · 1 n ∂n ∂r ,…”

“…Rather than performing a direct solution of Boltzmann's equation, as considered in [16], in this study we embrace a more physical insight and explore the relationships between the measured macroscopic transport properties and the underlying microscopic processes (as determined by the appropriate collision frequencies). This is a philosophy that has been adopted in swarm physics, and now is routinely applied in a variety of fields including low-temperature plasma physics [17][18][19][20][21], positron physics [22][23][24], liquid particle detectors [25,26] and radiation damage [27][28][29].…”