On the approximation of transport properties in structured materials using momentum-transfer theory

In this paper, we present a fluid model for electrons and positrons in structured and soft-condensed matter utilizing dilute gas phase cross-sections together with a structure factor for the medium. Generalizations of the Wannier energy and Einstein (Nernst–Townsend) relations to account for coherent scattering effects present in soft-condensed matter are presented along with new expressions directly relating transport properties in the dilute gas and the structured matter phases. The theory is applied to electrons in a benchmark Percus–Yevick model and positrons in liquid argon, and the accuracy is tested against a multi-term solution of Boltzmann's equation (White and Robson 2011 Phys. Rev. E 84 031125)

Positron transport in water vapour

Transport properties of positron swarms in water vapour under the influence of electric and magnetic fields are investigated using a Monte Carlo simulation technique and a multi-term theory for solving the Boltzmann equation. Special attention is paid to the correct treatment of the non-conservative nature of positronium (Ps) formation and its explicit and implicit influences on various positron transport properties. Many interesting and atypical phenomena induced by these influences are identified and discussed. Calculated transport properties for positrons are compared with those for electrons, and the most important differences are highlighted. The significant impact of a magnetic field on non-conservative positron transport in a crossed field configuration is also investigated. In general, the mean energy and diffusion coefficients are lowered, while for the measurable drift velocity an unexpected phenomenon arises: for certain values of the reduced electric field, the magnetic field enhances the drift. The variation of transport coefficients with the reduced electric and magnetic fields is addressed using physical arguments with the goal of understanding the synergistic effects of Ps formation and magnetic field on the drift and diffusion of positrons in neutral gases

Transition from Townsend to glow discharge: subcritical, mixed or supercritical

The full parameter space of the transition from Townsend to glow discharge is investigated numerically in one space dimension in the classical model: with electrons and positive ions drifting in the local electric field, impact ionization by electrons ($\alpha$ process), secondary electron emission from the cathode ($\gamma$ process) and space charge effects. We also perform a systematic analytical small current expansion about the Townsend limit up to third order in the total current that fits our numerical data very well. Depending on $\gamma$ and system size pd, the transition from Townsend to glow discharge can show the textbook subcritical behavior, but for smaller values of pd, we also find supercritical or some intermediate ``mixed'' behavior. The analysis in particular lays the basis for understanding the complex spatio-temporal patterns in planar barrier discharge systems.Comment: 12 pages, 10 figures, submitted to Phys. Rev.

Rate coefficients for vibrational excitation of CF₄ in crossed RF electric and magnetic fields

Knowledge of electron transport coefficients as well as detailed understanding of the kinetic phenomena that may occur in rf plasma are two basic demands in plasma modeling nowdays. Transport coefficients obtained under conditions of crossed RF electric and magnetic fields are the input data necessary for fluid models of plasma reactors such as ICP (inductively coupled plasmas). In particular, the behaviour of the transport coefficients is important for a fundamental understanding of processes leading to RF plasma maintenance. However, modeling of RF plasmas often relies on application of DC swarm data. Hence, there are some critical steps in plasma modeling. Apart from the application of time resolved fields in our calculations another critical step is proper inclusion of the effects of magnetic field as well as adequate treatment of the electron transport which is non-local in space and not fully relaxed in time.\ud \ud The aim of this work is to investigate behavior of the rate coefficients for vibrational excitation under the influence of crossed RF fields in pure CF₄. CF₄ is one of the most frequently used gases in plasma applications in ultra large scale integrated (ULSI) circuit technologies. Therefore, a great effort has been made in order to complete sets of cross sections and related electron swarm data in order to employ them in plasma modeling. The structure of cross section with the predominant inelastic electron scattering process at low energy range require non-trivial treatment of the electron transport. Rapidly rising cross section for vibrational excitation in the region of Rarnsauer-Townsend minimum induce a strong anisotropy of the electron velocity distribution function (EVDF) and the most common techniques employed for calculating the electron transport parameters in plasma modeling may fail. Therefore the only recourse for CF₄ is the exact techniques such as the multi-term theory for solving the Boltzmann equation or Monte Carlo simulations.\ud \ud Our calculations based on Monte Carlo simulation technique show that the effect of the magnetic field is strong and consequently produces complex behavior of the electron swarm transport coefficients and kinetic phenomena that should be accounted for in plasma models. In particular, we show the rate coefficients for vibrational excitation in order to analyze and understand electron kinetics at the region of Ramsauer-Townsend minimum

Key Factors in Fluid Modelling of Plasmas and Swarms

In this paper we start with general fluid equations for both ions and electrons in neutral gases, obtained as velocity moments of Boltzmann's cquation. Two distinct approximations are required for these exact equations to be of allY practical use:\ud 1. The collision transfer terms (right hand side of the fluid equations) must be approximated, and\ud II. Some closure ansatz (hypothesis) is required for the "streaming terms" (left hand side of the fluid equations), to ensure that the number of equations corresponds to the number of unknowns.\ud For step I, swarm (frce diffusion) limit results using, e.g., momentum transfer theory, may be taken over directly to low temperature plasmas, but step II remains problematic, with little guide from swarm physics, and serious doubts about existing assumptions in the plasma literature. We focus on electron fluid equations with closure at the level of momentum and energy balance, which requires an accurate heat flux ansatz in order to produce physically meaningful results. The crucial nature of this ansatz is illustrated using a simple benchmark calculation for infinite plane parallel geometry, where we show for the first time how periodic spatial structures (Franck-Hertz oscillations) may be generated from fluid equations

Negative Differential Resistance, Oscillations and Constrictions of Low Pressure, Low Current Discharges

A brief review is given of the recent experimental and theoretical studies of low current diffuse discharges. Two models are developed, one that is based on phenomenological description by effective discharge circuit parameters and the other which is based on the calculation of the field profile from the ion distribution for uniform field. In the first case the physical process responsible for the development of the negative differential resistance is the dependence of the secondary electron yield on current through modification of the field close to the cathode. Experimental systems were developed to provide observables that include : breakdown voltage, voltampere characteristics (which in the low current limit is represented very well by a negative differential resistance), limits and the profile of the low current oscillations, frequency and damping of the induced oscillations, current growth coefficient and the onsets for constrictions. All of the observables are very well predicted by the theory based on the data taken from independent sources, once the steady state secondary electron yield has been fitted to predict the breakdown voltage

Negative absolute electron mobility, Joule cooling and the second law

A number of recent theoretical investigations of electron motion in attaching gases demonstrate the possibility of a steady-state situation in which the electric current opposes the applied field. This phenomenon, which has been called “negative absolute electron mobility”, implies a Joule cooling effect and an associated negative entropy production, suggesting, at first glance, a possible violation of the second law of thermodynamics. In this article we show that the entropy production has in fact two components, the expected negative contribution due to “Joule cooling,” and an additional positive part arising from “attachment heating.” We insist that the total entropy production be positive, in accordance with the second law, and this has the practical implication that the measurable (“bulk”) electron drift velocity must always be positive, even though the actual average (“flux”) velocity may be negative. We discuss the phenomenon physically and take as a numerical example electrons in Ar/F2 mixtures, using Monte Carlo simulation and approximate momentum transfer theory methods to highlight the distinction between the two types of transport coefficient

Kinetic theory of electrons and positrons in dense gaseous and liquid systems

The recent resurgence of interest in positron transport in gases has been driven both by new fundamental positron-atom/molecule cross scattering sections [1, 2], and by the richness and novelty of the associated transport phenomena [3, 4]. In particular the phenomenon of negative differential conductivity (NDC) induced by positronium formation continues to be a focus of attention of kinetic theorists and modellers [5, 6], and there are other interesting effects yet to be explained. Although this work in gaseous systems is largely motivated by intrinsic physical interest, there are a number of important technological and medical applications (e.g. PET scans) which provide an additional imperative for such studies and in particular their extension to dense systems (liquid\ud and soft-condensed), the subject of this presentation. Investigations of positron transport in dense systems so far have been very limited [7]. One can draw to some extent on the extensive transport theory literature for electrons in dense gases and liquids [8], and both electrons and positrons in gases, but there is no straightforward way of directly adapting this existing transport theory: A new theory is needed, in which the effects of both non-reactive coherent scattering by many atoms in the dense gaseous and liquid phases, and reactive collisions are accounted for, through a dynamic structure factor S(K,W) and the positronium formation at cross section respectively

Relaxation processes of electrons and positrons in gases in electric and magnetic fields across at arbitrary angles

A multi-term solution of the Boltzmann equation has been developed and used to investigate the temporal relaxation of charged-particle swarms under the influence of electric and magnetic fields crossed at arbitrary angles. A Monte Carlo simulation technique has been used to verify the Boltzmann equation analysis under hydrodynamic conditions and for an independent study of spatial relaxation of the electrons under non-hydrodynamic conditions. We present results for model and real gases highlighting the explicit influence of the magnetic field and non-conservative collisions on temporal and spatial relaxation characteristics, including the existence of transiently negative electron diffusivity. We present results for thermalization of the positrons in nitrogen highlighting the applicability of our theory for contemporary kinetic studies in the domain of positron physics

Monte Carlo studies of the magnetic field effects on spatial relaxation of electron swarms

An investigation of spatial relaxation of the electrons in model gases in the presence of electric and magnetic fields is carried out over a wide range of values of electric and magnetic field strengths and angles between the fields. A Monte Carlo simulation technique has been specifically\ud developed to study the synergism of magnetic field effects and non-conservative collisions on spatial relaxation of the electrons. It was shown that the application of a magnetic field significantly alters the relaxation profiles of the electron mean energy, average velocity and rate\ud coefficients. In general, the magnetic field and the angle between the fields can be used to futher control the spatial relaxation of the electron transport properties