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 Boltzmann's 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).

Periodic electron spatial structures in gases occur within a window of voltages and pressures. Recent accurate solutions of Boltzmann's equation portray this effect, but offer little physical insight into the causes of windowing. Here we show for the first time how such insight can be obtained using the fluid model established by Robson, White, and Petrović [Rev. Mod. Phys. 77, 1303 (2005)10.1103/RevModPhys.77.1303], with an appropriate generalization of the heat flux ansatz. Conversely, the success in portraying windowing itself becomes a stringent test of the integrity of this fluid model, which can then be applied to a wider range of problems.

Since the 1950s there has been great progress in the fundamental kinetic theory of charged particles (electrons, positrons, muons and ions) in gases, but many of the ideas and results have still to find their way into modern low temperature plasma physics. This paper stresses the bigger picture, in the context of the kinetic theory of gases and fluid modelling, with a view to reconciling the plasma and swarm literature. We focus especially on the importance of a unified approach to transport analysis, appropriate to all types of charged particles in all situations. We discuss both plasmas and swarms in general, and make recommendations for 'best practice' in both kinetic theoretical and fluid modelling.

It is shown how the accuracy of fluid models of charged particles in gases can be improved significantly by direct substitution of swarm transport coefficient data, rather than cross sections, into the average collision terms. This direct substitution method emerges in a natural way for fluid formulations in which the role of the mean energy is transparent, whatever the mass of the charged particles in equation (ions or electrons), and requires no further approximations. The procedure is illustrated by numerical examples for electrons, including the operational window of E/N for an idealized Franck-Hertz experiment. Using the same fluid formulation, we develop an aliasing method to estimate otherwise unknown mobility data for one type of particle, from known mobility data for another type of particle. The method is illustrated for muons in hydrogen, using tabulated data for protons in the same gas.

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