Kinetic Theory of Charged Particle Swarms in Neutral Gases

Abstract

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 ...

Time-of-flight observation of electron swarm in methane

“…15,18 Besides the transformation above, the solution f͑z , v ជ , t͒ for Eq. ͑2͒ can be expressed in a multiterm formula by the density gradient expansion method ͑e.g., Kumar et al 1 …”

“…The spatiotemporal evolution of the electron swarm has been studied since 1969, e.g., by Parker and Lowke, 2 Thomas, 3 Skullerud, 4 Tagashira et al, 5 Kumar et al, 1 and other investigators. These investigations describe the electron swarm envisaging the spatial distribution at a certain time, which accords to the continuity equation ͑or "diffusion equation"͒ derived from the Boltzmann equation.…”

“…The macroscopic behavior of an isolated electron swarm can be described by the Boltzmann equation, leading to the continuity equation by integrating over velocity space. The swarm parameters, such as the drift velocity and the diffusion coefficient appearing in the continuity equation, have an inclination to converge to a set of constant values as time elapses ͑e.g., Kumar et al 1 ͒. In this regard, it may be appropriate to refer to the electron ensemble in this kind of equilibrium state as an "electron swarm.…”

Three species one-dimensional kinetic model for weakly ionized plasmas

“…However, a better understanding of the basic dynamics involved in momentum and energy transfers among plasma species in presence of self-consistent or imposed electromagnetic fields would require kinetic models for a feasible local description. The resulting highly non-linear equations are usually arduous to solve analytically, even numerically, without further simplification or linearisation procedures [1][2][3][4] .…”

Anisotropic Dispersion of a Charged Particle Swarm in a Turbulent Gas in an Electrostatic Field

“…Thus a swarm of charged particles released into the gas from a source drifts under the influence of an applied electrostatic field E and simultaneously diffuses by virtue of collisions with gas molecules. In the so-called hydrodynamic regime (Kumar et al 1980), the swarm has relaxed to a state where its density nCr, t) varies only slowly over distances of the order of the mean free path between collisions and in times of the order of the mean free time between collisions. Under these circumstances, Fick's law of diffusion [see equation (7) below] holds and, in the language of fluid mechanics (Monin and Yaglom 1971), the swarm is said to be a 'passive additive', which is characterised by 'molecular' transport coefficients K (mobility) and D (diffusion tensor) respectively.…”