Burnett function expansions with a bi-Maxwellian weight function for electron swarm physics

In the solution of Boltzmann's equation by polynomial expansion techniques it is important to choose the weight function as close as possible to the actual distribution function in order to ensure rapid convergence. In the case of electron motion through neutral gases in the presence of external electric and magnetic fields, the so-called moment method has had considerable success. The method is essentially a polynomial expansion of the electron velocity distribution function about a Maxwellian weight function at some arbitrary temperature. By choosing the temperature carefully in order to approximate the actual distribution adequate convergence can usually be obtained. However when the interactions between the electrons and the molecules is `soft' and/or reactive processes cause a significant increase in the population of the high energy tail of the distribution function, convergence of the expansion rapidly deteriorates and may not be achieved. In this article we investigate the use of a bi-Maxwellian weight function to improve convergence by the use of a model interaction between the electrons and molecules. The idea being that a Maxwellian at the lower temperature should be sufficient to characterise the electrons in the bulk of the distribution, while a second Maxwellian of smaller amplitude but at a some what higher temperature is used to characterised the electrons in the high energy tail of the distribution

Transport coefficients for electrons in water vapor: definition, measurement, and calculation

Comparison of experimental and theoretical transport data for electron swarms in water vapour over a wide range of fields provides a rigorous test of (e(-), H(2)O) scattering cross sections over a correspondingly broad range of energies. That like should be compared with like is axiomatic, but the definition of transport coefficients at high fields, when non-conservative processes are significant, has long been contentious. This paper revisits and distills the most essential aspects of the definition and calculation of transport coefficients, giving numerical results for the drift velocity and ionisation coefficient of electrons in water vapour. In particular, the relationship between the theoretically calculated bulk drift velocities of [K. F. Ness and R. E. Robson, Phys. Rev. A 38, 1446 (1988)] and the experimental "arrival time spectra" drift velocity data of Hasegawa et al. [J. Phys. D 40(8), 2495 (2007)] is established. This enables the Hasegawa et al. data to be reconciliated with the previous literature, and facilitates selection of the best (e(-), H(2)O) cross section set

Visualization of ion and electron velocity distribution functions in electric and magnetic fields

The Boltzmann equation for ions and electrons in gases subject to arbitrarily oriented electric and magnetic fields is solved by a recently developed unified 'multiterm' theory (White et al 1999a), and attention is focused on portrayal of the velocity distribution function. In particular, we take 'slices' in velocity space to elucidate the effects of changing orientation angle, magnetic field strength and the ion to gas molecule mass ratio. The first results for electrons in CO2 and ion swarms in electric and magnetic fields are presented in this way. The implications of symmetries are discussed

Computation of electron and ion transport properties in gases

A unified multi-term solution of Boltzmann's equation is used to investigate transport properties and velocity distribution functions of charged particles in gases under the influence of an electric field. The effects of the charged-particle to neutral-particle mass ratio on the convergence of the polynomials expansion techniques employed are addressed physically

Electron transport coefficients in O2 magnetron discharges

Electron transport coefficients required for the modelling of bulk electron transport in an O2 magnetron discharge are calculated from solution of the non-conservative Boltzmann equation. The influence on the transport coefficients (rate coefficients, drift velocity vector elements, diffusion tensor elements) of the electric and magnetic field strengths and their orientation with respect to each other have been systematically investigated over ranges consistent with practical operation. The results represent the first multi-term solution of the non-conservative Boltzmann's equation for electric and magnetic fields at arbitrary orientations

Non-equilibrium electron transport in gases: influence of magnetic fields on temporal and spatial relaxation

The ability to control the temporal and spatial relaxation of electron swarms in gases through application of an orthogonal magnetic field is examined via solutions of Boltzmann's equation. Multi-term solutions of Boltzmann's equation are presented for two specific applications: temporal relaxation in the time-dependent hydrodynamic regime, and spatial relaxation in the steady state non-hydrodynamic regime. We highlight the commonality of methods and techniques for handling the velocity dependence of the phase-space distribution function as well as their point of departure for treating the spatial dependence. We present results for model and real gases highlighting the explicit influence of the magnetic field on spatial and temporal relaxation characteristics, including the existence of transiently negative diffusion coefficients

The v = 0→1 vibrational cross-section for e-H2 scattering: an unresolved problem with wide implications

Controversy has surrounded the determination of the v= 0 → 1 vibrational cross-section for e–H2 scattering for some thirty years: differences exist between values measured in crossed-beam experiments, which agree well with ab-initio quantum mechanical values, and cross sections derived from swarm experiments. These differences are far larger than the estimated errors associated with all three determinations, which will all remain under something of a cloud until the discrepancy is resolved. Following the suggestion of Buckman et al. [1], research on this problem has recently refocused on the transport theory used to determine cross sections from swarm data. This paper will review the results and implications of this recent research and will present new results on the validity of conventional semi-classical transport theory. We consider approximations used in contemporary solutions of the semi-classical Boltzmann equation including steady-state hydrodynamic assumptions. In addition, we address the validity of the semi-classical Boltzmann equation itself with particular reference to conservation of angular momentum and to the importance of taking into account the essentially fermionic nature of electrons in transport theory

Electron transport coefficients in CF4 magnetized plasma discharges

Electron transport coefficients for electron swarms in carbon tetrafluoride (CF4) in the presence of uniform static electric and magnetic fields crossed at arbitrary angles to each other are calculated using a Monte Carlo simulation technique. We focus on the way in which the transport coefficients are influenced by electric and magnetic field strengths and the angle between the fields. The investigation has resulted in a database of transport data which is applicable for a wide range of potential applications, although we focused upon the provision\ud and correct implementation of swarm data within the fluid modeling of a magnetron or inductively coupled plasma discharges