Fundamental issues in fluid modeling: direct substitution and aliasing methods.

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.

Fluid-model analysis of electron swarms in a space-varying field: nonlocality and resonance phenomena.

The physically based, benchmarked fluid model developed by Robson et al. [R. E. Robson, R. D. White, and Z. Lj. Petrovic, Rev. Mod. Phys. 77, 1303 (2005)] and extended to analyze electron swarms in a spatially homogeneous electric field under conditions corresponding to the Franck-Hertz experiment [P. Nicoletopoulos and R. E. Robson, Phys. Rev. Lett. 100, 124502 (2008)] is generalized to investigate the nonlocal response and resonance phenomena associated with electrons subject to an externally prescribed, spatially varying electrostatic field. Analytic expressions are first derived for the mean velocity, energy, and heat flux of electrons in a harmonically varying field, and expressions are then given for fields with more general spatial dependences. Numerical examples are given for both benchmark model cross sections and a real gas.

Periodic electron structures in gases: a fluid model of the "window" phenomenon.

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 Petrovic [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.