Computer Simulation of an Electron Swarm at low E/p in Helium

328

208

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 ...

Section: (B) Position-independent Boltzmann Equation and Mobility Equmentioning

confidence: 99%

“…As an example of the last kind, we mention the work of McIntosh (1974). He studied the space-time development of a highly localized pulse of electrons, and noticed a 'pear-shaped' component in the density distribution nCr, t).…”

Section: (B) Position-independent Boltzmann Equation and Mobility Equmentioning

confidence: 99%

Kinetic Theory of Charged Particle Swarms in Neutral Gases

Kumar¹,

Skullerud²,

Robson³

1980

328

208

“…For very light ions (or electrons), this parameter is most important and the indications are (Skullerud 1974) that it is the so-called collision frequency for energy transfer, (2m/M)v, which ought to appear in place of v. In this case, the constant terms in equations (14) may be significant (McIntosh 1974;Skullerud 1974). However, when ion and neutral molecule masses are not very much different, these expressions should be at least qualitatively correct.…”

Section: Centroid and Mean Square Width Of Pulsementioning

confidence: 99%

“…An alternative to the rigorous analytic approach is to simulate the electron or ion swarm on a computer (McIntosh 1974). This has proved particularly useful in demonstrating the pear-shaped asymmetry· of the swarm which must arise from nonlinear diffusive effects (Kumar and Robson 1973).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Diffusion of Ions in a Gas

Robson¹

1975

“…and the mean energy of the swarm <e). McIntosh (1974) determined corresponding transport parameters for helium at E/N = 3 ·03 Td. Lucas and Saelee (1975), using a similar technique to that of Lucas (1972), obtained a set of transport coefficients for a number of idealized collision models.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo Simulation of Electron Swarms in H2

Hunter¹

1977

A Monte Carlo simulation of the motio'n of an electron swarm in molecular hydrogen has been studied in the range E/N = 1,4-170 Td. The simulation was performed for 400-600 electrons at several values of E/N for two different sets of inelastic collision cross sections at high E/N. ,Results were obtained for the longitudinal diffusion coefficient DL , lateral diffusion coefficient D, swarm drift velocity W, average swarm energy D at high values of E/N.