Sasa Dujko

Recent advances in the application of Boltzmann equation and fluid equation methods to charged particle transport in non-equilibrium plasmas

The kinetic theory of charged particles in gases has come a long way in the last 60 years or so, but many of the advances have yet to find their way into contemporary studies of low-temperature plasmas. This review explores the way in which this gap might be bridged, and focuses in particular on the analytic framework and numerical techniques for the solution of Boltzmanns equation for both electrons and ions, as well as on the development of fluid models and semi-empirical formulae. Both hydrodynamic and non-hydrodynamic regimes are considered and transport properties are calculated in various configurations of dc and ac electric and magnetic fields. We discuss in particular the duality in transport coefficients arising from non-conservative collisions (attachment, ionization).

Monte Carlo studies of non-conservative electron transport in the steady-state Townsend experiment

An investigation of the spatial relaxation of the electrons and benchmark calculations of spatially resolved non-conservative electron transport in model gases has been carried out using a Monte Carlo simulation technique. The Monte Carlo code has been specifically developed to study the spatial relaxation of electrons in an idealized steady-state Townsend (SST) experiment in the presence of non-conservative collisions. Calculations have been performed for electron transport properties with the aim of providing the benchmark required to verify the codes used in plasma modelling. Both the spatially uniform values and the relaxation profiles of the electron transport properties may serve as an accurate test for such codes. The explicit effects of ionization and attachment on the spatial relaxation profiles are considered using physical arguments. We identify the relations for the conversion of hydrodynamic transport properties to those found in the SST experiment. Our Monte Carlo simulation code and sampling techniques appropriate to these experiments have provided us with a way to test these conversion formulae and their convergence.

Kinetic phenomena in electron transport in radio-frequency fields

Abstract We discuss the application of swarm physics based techniques to study the time resolved kinetic phenomena that may be of interest to modeling of radio-frequency (rf) plasma, the relevance of such studies for the data that are being used and models that are being developed. Kinetic phenomena may not be predicted by extrapolation of the dc data or single particle trajectories and require full kinetic treatment or detailed simulations. Our exact solutions to the Boltzmann equation by direct numerical procedure (DNP) and Monte Carlo simulations (MCSs) revealed such phenomena as: anomalous longitudinal diffusion, time resolved negative differential conductivity, absolute negative mobility in afterglow and in rf fields, complex waveforms of transport coefficients due to phases between electric and magnetic fields, due to cyclotronic motion and all the comparisons performed so far between the two techniques and with results of the exact solutions to the Boltzmann equation by the group from James Cook University have showed excellent agreement. While the data used nowadays in plasma modeling are basically for dc fields, one has to include effects due to magnetic and time resolved magnetic field and also the kinetic phenomena in plasma modeling as these may affect the electron transport in real collisional processing plasmas. Thus we believe that kinetic and Monte Carlo based codes should be tested against swarm transport benchmarks, including results for time resolved E ( t ) and E ( t )× B ( t ) fields.

Low-energy electron and positron transport in gases and soft-condensed systems of biological relevance

We present a study of electron and positron transport in water in both the gaseous and liquid states using a Boltzmann equation analysis and a Monte-Carlo simulation technique. We assess the importance of coherent scattering processes when considering transport of electrons/positrons in dense gases and liquids. We highlight the importance of electron and positron swarm studies and experiments as a test of the accuracy and completeness of cross-sections, as well as a technique for benchmarking Monte-Carlo simulations. The thermalization of low-energy positrons (<150 eV) in water is discussed and the sensitivity of the profiles to the form of the cross-sections in this energy region, and assumptions in the microscopic processes, is considered.

High-order fluid model for streamer discharges: I. Derivation of model and transport data

Streamer discharges pose basic problems in plasma physics, as they are very transient, far from equilibrium and have high ionization density gradients; they appear in diverse areas of science and technology. This paper focuses on the derivation of a high-order fluid model for streamers. Using momentum transfer theory, the fluid equations are obtained as velocity moments of the Boltzmann equation; they are closed in the local mean energy approximation and coupled to the Poisson equation for the space charge generated electric field. The high-order tensor in the energy flux equation is approximated by the product of two lower order moments to close the system. The average collision frequencies for momentum and energy transfer in elastic and inelastic collisions for electrons in molecular nitrogen are calculated from a multi-term Boltzmann equation solution. We then discuss, in particular, (1) the correct implementation of transport data in streamer models; (2) the accuracy of the two-term approximation for solving Boltzmanns equation in the context of streamer studies; and (3) the evaluation of the mean-energy-dependent collision rates for electrons required as an input in the high-order fluid model. In the second paper in this sequence, we will discuss the solutions of the high-order fluid model for streamers, based on model and input data derived in this paper.

A multi-term solution of the nonconservative Boltzmann equation for the analysis of temporal and spatial non-local effects in charged-particle swarms in electric and magnetic fields

A multi-term solution of the Boltzmann equation has been developed and used to investigate the temporal and spatial relaxation of charged-particle swarms and associated phenomena induced by non-local effects under the influence of electric and magnetic fields crossed at arbitrary angles when nonconservative collisions are operative. The hierarchy resulting from a spherical harmonic decomposition of the Boltzmann equation in both the hydrodynamic and non-hydrodynamic regimes is solved numerically by representing the speed dependence of the phase-space distribution function in terms of an expansion in Sonine polynomials about a variety of Maxwellian based weighting functions. Temporal and spatial relaxation profiles of various charged-particle swarm transport properties are presented for certain model and real gases over a range of field strengths and angles between the fields. It was found that the magnetic field strength and angle between the fields have an ability to control the relaxation process: in general, these parameters can be used to enhance or suppress the oscillatory features in the relaxation profiles of various transport properties. The explicit and implicit effects of nonconservative collisions on the drift and diffusion elements in varying configurations of radio-frequency electric and magnetic fields are considered using physical arguments.

On the use of Monte Carlo simulations to model transport of positrons in gases and liquids.

In this paper we make a parallel between the swarm method in physics of ionized gases and modeling of positrons in radiation therapy and diagnostics. The basic idea is to take advantage of the experience gained in the past with electron swarms and to use it in establishing procedures of modeling positron diagnostics and therapy based on the well-established experimental binary collision data. In doing so we discuss the application of Monte Carlo technique for positrons in the same manner as used previously for electron swarms, we discuss the role of complete cross section sets (complete in terms of number, momentum and energy balance and tested against measured swarm parameters), we discuss the role of benchmarks and how to choose benchmarks for electrons that may perhaps be a subject to experimental verification. Finally we show some samples of positron trajectories together with secondary electrons that were established solely on the basis of accurate binary cross sections and also how those may be used in modeling of both gas filled traps and living organisms.

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. 6 Author to whom any correspondence should be addressed.

Non-equilibrium transport of positron and electron swarms in gases and liquids

The transport properties of positron and electron swarms in gases and liquids find application in many and varied fields. In this paper we present a time-dependent multi-term solution of Boltzmanns equation valid for electrons and positrons, and benchmark it against an independent Monte-Carlo simulation where possible. The transport properties of positrons in dilute gaseous and liquid argon are considered and compared. The sensitivity of the macroscopic transport properties to the anisotropic nature of elastic scattering is highlighted. The temporal non-locality of diffusion for electron swarms in gases under the influence of time-dependent electric and magnetic fields is addressed through the consideration of their associated relaxation profiles.

Non-conservative electron transport in CF4 in electric and magnetic fields crossed at arbitrary angles

A Monte Carlo simulation technique is used to investigate electron transport in carbon tetrafluoride (CF4) for an arbitrary configuration of electric and magnetic fields. We investigate the way in which the transport coefficients and other swarm properties are influenced by the electric and magnetic field strengths and the angle between the fields. In addition, the sensitivity of transport data on the presence of non-conservative collisions (attachment/ionization) is analysed. It is found that the difference between the two sets of transport coefficients, bulk and flux, resulting from the explicit effects of non-conservative collisions, can be controlled either by the variation of the magnetic field strengths or by the angles between the fields. This study was initiated in order to obtain the transport data for input into the fluid models of magnetron and inductively coupled plasma discharges as well as several types of high energy particle detectors, and has resulted in a database of such transport data. Values and general trends in the profiles of mean energy, collision frequency, rate coefficients, drift velocity elements and diffusion tensor are reported here.