This colloquium examines the theoretical modeling of nonequilibrium low-temperature ͑tens of thousands of degrees͒ plasmas, which involves a juxtaposition of three distinct fields: atomic and molecular physics, for the input of scattering cross sections; statistical mechanics, for the kinetic modeling; and electromagnetic theory, for the simultaneous solution of Maxwell's equations. Cross sections come either from single-scattering beam experiments or, at very low energies ͑Ͻ0.5 eV͒, from multiple-scattering experiments on "swarms" in gases-the free diffusion or large Debye length limit of a plasma, where they are embedded in transport coefficient data. The same Boltzmann kinetic theory that has been developed to a high level of sophistication over the past 50 years, specifically for the purpose of unfolding these transport data, can be employed for low-temperature plasmas with appropriate modification to allow for self-consistent rather than externally prescribed fields. A full kinetic treatment of low-temperature plasmas is, however, a daunting task and remains at the developmental level. Fortunately, since the accuracy requirements for modeling plasmas are generally much less stringent than for swarms, such a sophisticated phase-space treatment is not always necessary or desirable, and a computationally more efficient but correspondingly less accurate macroscopic theoretical model in configuration space at the fluid level is often considered sufficient. There has been a proliferation of such fluid modeling in recent times and this approach is now routinely used in the design and development of a large variety of plasma technologies, ranging from plasma display panels to plasma etching reactors for microelectronic device fabrication. However, many of these models have been developed empirically with specific applications in mind, and rigor and sophistication vary accordingly. In this colloquium, starting from the governing Boltzmann kinetic equation, a unified, general formulation of fluid equations is given for both ions and electrons in gaseous media with transparent and internally consistent approximations, all benchmarked against established results. Thereby a fluid model is obtained that is appropriate for practical application but at the same time is based on a firmer physical foundation. CONTENTS

The kinetic theory of charged test particles in a neutral gas, in the presence of static and uniform electric and magnetic fields, is reviewed. The effects of inelastic processes and reactions are included. The general space-time development of the swarms is considered and the relation between the nonhydrodynamic anQ hydrodynamic developments is pointed out. The transport coefficients are identified as statistical averages over the configuration-space and phase-space distributions. The evaluation of these averages by computer simulations is briefly discussed.The main emphasis, however, is on the Boltzmann equation treatment of the problem. Transport coefficients of any order are obtained as velocity moments of the solutions of the corresponding kinetic equations derived from the Boltzmann equation. These equations have similar structure and may be solved by similar methods. Methods of solution are classified and examined in detail for precise calculation of drift and diffusion. Illustrative examples are given.Several representations of the Boltzmann collision integral suitable for use in these calculations are examined. A discussion of the calculation of matrix elements and the relationship between different matrix representations is given. Complete expressions to all orders in the Fokker-Planck expansion and in the expansions for the operator components of the spherical harmonic decomposition in the differential form are given. The advantages of using the adjoint of the collision operator and the cold gas collision operator in these derivations and in applications are shown and utilized. Phys., 1980, 33, 343-448 AbstractThe kinetic theory of charged test particles in a neutral gas, in the presence of static and uniform electric and magnetic fields, is reviewed. The effects of inelastic processes and reactions are included. The general space-time development of the swarms is considered and the relation between the nonhydrodynamic anQ hydrodynamic developments is pointed out. The transport coefficients are identified as statistical averages over the configuration-space and phase-space distributions. The evaluation of these averages by computer simulations is briefly discussed. The main emphasis, however, is on the Boltzmann equation treatment of the problem. Transport coefficients of any order are obtained as velocity moments of the solutions of the corresponding kinetic equations derived from the Boltzmann equation. These equations have similar structure and may be solved by similar methods. Methods of solution are classified and examined in detail for precise calculation of drift and diffusion. Illustrative examples are given.Several representations of the Boltzmann collision integral suitable for use in these calculations are examined. A discussion of the calculation of matrix elements and the relationship between different matrix representations is given. Complete expressions to all orders in the Fokker-Planck expansion and in the expansions for the operator components of the spherical harmonic ...

We outline a new kinetic theory for positrons in soft matter, which blends together cross sections for positrons scattering from single molecules, with the structure function of the medium as a whole. Numerical results are presented for positrons in liquid argon, where negative differential conductivity arises from both positron formation and the structure of the medium.

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