Session AM2: Plasma Kinetics

Challenge for more precise e- and ion-transport in gases and liquids

The full potential of technologies driven by non-equilibrium electron and ion processes in gases, liquids and soft-matter can only be realised once the basic physics has been mastered. The central component in this pursuit is an ever increasing need for the precise determination of electron and ion transport in such media. Over the last few decades, the group at James Cook University and collaborators have developed a suite of multi-term Boltzmann equation solutions to treat temporal and spatial non-locality for electrons and ions in electric and magnetic fields in gaseous systems. In this presentation, we will highlight recent developments including (i) a space-time multi-term solution of Boltzmann's equation; (ii) a unified treatment of electron and ion solutions of Boltzmann's equation which avoids mass ratio expansions; (iii) the treatment dense gases and liquids, including coherent scattering, screened potentials and (self) trapped bubble state effects, the latter of which can give rise to fractional transport behaviour, and (iv) the application to consider the self-consistency of cross-sections for electrons in biomolecules.   

Effect of Coulomb collisions on low temperature plasma characteristics

This presentation discusses the effects of electron-electron and electron-ion Coulomb collisions on the electron distribution function and transport coefficients obtained from the Boltzmann equation for simple gas discharge conditions. Such Boltzmann results are commonly used as inputs for fluids models or to interpret experimental data, but usually without taking into account Coulomb collisions. Proper inclusion of Coulomb collisions in the Boltzmann equation involves complex nonlinear collision terms acting on both the isotropic and anisotropic parts of the distribution function. In this presentation, different Coulomb collision effects are illustrated on the basis of local Boltzmann calculation results for argon gas. It is shown that the anisotropic part of the electron-electron collision term, generally neglected in the low-temperature plasma literature, can in certain cases have a large effect on the electron mobility and is essential when describing the transition towards the Coulomb collision dominated regime characterized by Spitzer transport coefficients. Finally, a brief overview is presented of the discharge conditions for which different Coulomb collision effects occur in different gases.   

Developments in the kinetic theories of ion and electron swarms in the 1960's and 70's

The two decades from 1960 to 1980 saw a quite fantastic development in diverse areas in physics, and so also in the quantitative treatment and deeper understanding of the behaviour of isolated electrons and ions in gases -- that is "charged particle swarm physics". This evolution was strongly correlated with the contemporary advances in computer technology, and of new and accurate experimental methods for finding the charged particle transport parameters, as drift velocities, diffusion coefficients and reaction rates', as well as with development in neighbouring fields as plasma physics and the physics of electronic and molecular collisions. In 1960, low energy electron behaviour could already be calculated with reasonable accuracy in the so-called two-term approximation, while ion behaviour could only be treated at very weak elecric fields. By 1980, though, reasonably complete theories had been developed for perhaps most cases in interest - which is reflected in a number of reviews, books and journal articles published in the early 80's. We will give a guided tour through the developments in this period and the basic theories behind; The Boltzmann equation in difference-differential form (for electrons), or in integral equation form (preferred by mathematicians), and the Maxwell transfer equations ("moment theories"). We will also indicate how the interaction between different studies of the same basic processes have led to the elimination of shortcomings, and a better understanding, choosing a few test cases for illustration.   

Kinetic and fluid descriptions of charged particle swarms in gases and nonpolar fluids: Theory and applications

In this work we review the progress achieved over the last few decades in the fundamental kinetic theory of charged particle swarms with the focus on numerical techniques for the solution of Boltzmann's equation for electrons, as well as on the development of fluid models. We present a time-dependent multi term solution of Boltzmann's equation valid for electrons and positrons in varying configurations of electric and magnetic fields. The capacity of a theory and associated computer code will be illustrated by considering the heating mechanisms for electrons in radio-frequency electric and magnetic fields in a collision-dominated regime under conditions when electron transport is greatly affected by non-conservative collisions. The kinetic theory for solving the Boltzmann equation will be followed by a fluid equation description of charged particle swarms in both the hydrodynamic and non-hydrodynamic regimes, highlighting (i) the utility of momentum transfer theory for evaluating collisional terms in the balance equations and (ii) closure assumptions and approximations. The applications of this theory are split into three sections. First, we will present our 1.5D model of Resistive Plate Chambers (RPCs) which are used for timing and triggering purposes in many high energy physics experiments. The model is employed to study the avalanche to streamer transition in RPCs under the influence of space charge effects and photoionization. Second, we will discuss our high-order fluid model for streamer discharges. Particular emphases will be placed on the correct implementation of transport data in streamer models as well as on the evaluation of the mean-energy-dependent collision rates for electrons required as an input in the high-order fluid model. In the last segment of this work, we will present our model to study the avalanche to streamer transition in non-polar fluids. Using a Monte Carlo simulation technique we have calculated transport coefficients for electrons in liquid argon and liquid xenon. We employ the two model processes in which only momentum and only energy are exchanged to account for structure dependent coherent elastic scattering at low energies. The specific treatment of inelastic collisions in our model will be also discussed using physical arguments.   

Kinetic modeling of active plasma resonance spectroscopy

The term ``active plasma resonance spectroscopy'' (APRS) refers to a plasma diagnostic method which employs the natural ability of plasmas to resonate close to the plasma frequency. Essential for this method is an appropriate model to determine the relation between the resonance parameters and demanded plasma parameters. Measurements with these probes in plasmas of a few Pa typically show a broadening of the spectrum that cannot be predicted by a fluid model. Thus, a kinetic model is necessary.\\ A general kinetic model of APRS probes, which can be described in electorstatic approximation, valid for all pressures has been presented [1]. This model is used to analyze the dynamic behavior of such probes by means of functional analytic methods. One of the main results is, that the system response function $Y(\omega)$ is given in terms of the matrix elements of the resolvent of the dynamic operator evaluated for values on the imaginary axis. The spectrum of this operator is continuous which implies a new phenomenon related to anomalous or non-collisional dissipation. Based on the scalar product, which is motivated by the kinetic free energy, the non-collisional damping can be interpreted: In a periodic state, the probe constantly emits plasma waves which propagate to “infinity”. The free energy simply leaves the “observation range” of the probe which is recorded as damping.\\ The kinetic damping, which depends on the mean kinetic energy of the electrons, is responsible for the broadening of a resonance peak in the measured spectrum of APRS probes. The ultimate goal is to determine explicit formulas for the relation between the broadening of the resonance peak and the ``equivalent electron temperature'', especially in the case of the spherical Impedance Probe and the Multipole Resonance Probe.\\ $[1]$ J. Oberrath and R.P. Brinkmann, Plasma Scources Sci. Technol. {\bf 23}, 045006 (2014).