Robert Robson

Moment theory of electron drift and diffusion in neutral gases in an electrostatic field

We develop a rigorous kinetic theory of electron (or light ion) transport processes in neutral gases in an electrostatic field. The theory does not depend upon the usual approximation of the electron velocity distribution by the first two terms of an expansion in spherical harmonics. We use a modification of the moment method developed by Viehland and Mason for ion transport. There are no restrictions on the field strength or cross sections, and both elastic and inelastic collisions are considered. The smallness of the ion–molecule mass ratio simplifies the evaluation of the matrix elements and allows calculations to be carried to very high orders of approximation if necessary. Three examples (in all of which the differential cross section is assumed isotropic) are treated in numerical detail to establish the main features of the present theory: electrons in a rigid‐sphere gas, in argon, and in methane. When only elastic collisions occur, the two‐term approximation is adequate, even if the cross section h...

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).

Physics of reacting particle swarms in gases

A wide variety of reactive phenomena in gaseous swarms is studied using an extension of momentum‐transfer flight theory. Empirical formulas, such as the generalized Einstein relations and the Wannier energy relation are derived, with modifications due to reactive effects made explicit. The emphasis throughout is on simple mathematics and succinct physical reasoning.

Development of swarm transport theory in radio-frequency electric and crossed electric and magnetic fields

The advancements associated with modern day technology demands incorporation of the best physical understanding and the most accurate modelling of charged particle motion in gases. In recent times there have been major advances in the fundamental swarm transport theory, and this is the subject of the present paper. We start from 1986, when “multi-term” solutions of Boltzmann’s equation for static electric fields had been developed to a sophisticated level, and proceed through to the present day, where the theory is motivated far more by application to industrial processes, which involve both electric and magnetic fields , either static or time varying. We present a unified time-dependent multi-term solution of Boltzmann’s equation, emphasising the common methods and techniques underlying the treatment of all these situations, whether they be for electron or ion swarms. New and significant numerical results are presented to highlight the rich and diverse range of phenomena which are observed.

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.

Introductory Transport Theory for Charged Particles in Gases

Many areas of physics research depend upon a good physical understanding of charged particle transport processes in gases, a statement which is as true now as it was in the early part of the last century, when modern physics was taking shape. Gas lasers, multi-wire drift chambers used in high energy particle detectors, muon-catalysed fusion in hydrogen and its isotopes and low-temperature plasma processing technology are just a few examples of experiments and processes in which electrons, ions or muons play a key role. The macroscopic properties of these non-equilibrium systems can best be found by averaging microscopic collision properties over a velocity distribution function, calculated from solution of Boltzmanns kinetic equation, using recently developed techniques. This is the realm of the modern kinetic theory of gases, and is the theme of this book.

Electron drift velocities in He and water mixtures: measurements and an assessment of the water vapour cross-section sets.

The drift velocity of electrons in mixtures of gaseous water and helium is measured over the range of reduced electric fields 0.1-300 Td using a pulsed-Townsend technique. Admixtures of 1% and 2% water to helium are found to produce negative differential conductivity (NDC), despite NDC being absent from the pure gases. The measured drift velocities are used as a further discriminative assessment on the accuracy and completeness of a recently proposed set of electron-water vapour cross-sections [K. F. Ness, R. E. Robson, M. J. Brunger, and R. D. White, J. Chem. Phys. 136, 024318 (2012)]. A refinement of the momentum transfer cross-section for electron-water vapour scattering is presented, which ensures self-consistency with the measured drift velocities in mixtures with helium to within approximately 5% over the range of reduced fields considered.

The mobility of potassium ions in gas mixtures

The reduced mobility of K+ ions in He, Ne, Ar, H2 and N2 and in mixtures of He-Ne, Ne-Ar and H2-N2 has been measured at 293 K over the range 20<or=E/N(Td)<or=100 using the Bradbury-Nielsen time-of-flight technique. A theory has been developed which predicts the deviations from Blancs Law in situations where only elastic scattering occurs. The measured deviations in mixtures of He-Ne and Ne-Ar are in good qualitative agreement with the predictions of this theory. In H2-N2 mixtures the measured deviations are of opposite sign and differ in magnitude from the predictions of the recent theory of Mason and Hahn (1972). The measured values of the reduced mobility of the ions in the pure gases are estimated to be in error by less than +or-2% over the whole range of E/N and the errors in the measured deviations from Blancs Law are considered to be less than +or-0.4%.

Transport coefficients and cross sections for electrons in water vapour: comparison of cross section sets using an improved Boltzmann equation solution.

This paper revisits the issues surrounding computation of electron transport properties in water vapour as a function of E/n(0) (the ratio of the applied electric field to the water vapour number density) up to 1200 Td. We solve the Boltzmann equation using an improved version of the code of Ness and Robson [Phys. Rev. A 38, 1446 (1988)], facilitating the calculation of transport coefficients to a considerably higher degree of accuracy. This allows a correspondingly more discriminating test of the various electron-water vapour cross section sets proposed by a number of authors, which has become an important issue as such sets are now being applied to study electron driven processes in atmospheric phenomena [P. Thorn, L. Campbell, and M. Brunger, PMC Physics B 2, 1 (2009)] and in modeling charged particle tracks in matter [A. Munoz, F. Blanco, G. Garcia, P. A. Thorn, M. J. Brunger, J. P. Sullivan, and S. J. Buckman, Int. J. Mass Spectrom. 277, 175 (2008)].

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.