The physics of swarms and some basic questions of kinetic theory

Abstract This report provides an introduction to the physics of swarms to those interested in kinetic theory. After a brief historical sketch the principles of experiments and their phenomenological analysis are discussed. The relation of this analysis to kinetic theory and the potential of the experiments for studying the nature of hydrodynamic regime and the nonhydrodynamic effects is pointed out. Recent advances in the kinetic theory of swarms in free space are surveyed. They include results such as the generalised Einstein relations and others from the momentum transfer theory, which point to some interesting properties of the many averages that occur in kinetic theory and their relation to thermodynamics, as well as the more technical advances in analysing the structure of the collision operator and solutions of kinetic equations which have lead to very precise calculations of the transport coefficients. The use of theory and experiment in precise determination of cross-sections, potentials and reaction rates is illustrated. Observations showing the effects of finite enclosures are summarised and a theory of swarms in a finite enclosure is outlined. The implications of the subject for kinetic theory are discussed.

[1]  I. Amdur,et al.  Kinetic Theory of Gases , 1959 .

[2]  Kailash Kumar.  Matrix Elements of the Boltzmann Collision Operator in a Basis Determined by an Anisotropic Maxwellian Weight Function including Drift , 1980 .

[3]  R. Robson.  Generalized Einstein Relation and Negative Differential Conductivity in Gases , 1984 .

[4]  H. Skullerud.  On the calculation of ion swarm properties by velocity moment methods , 1984 .

[5]  R. Crompton,et al.  Diffusion and drift of electrons in gases , 1974 .

[6]  F. B. Hildebrand,et al.  Introduction To Numerical Analysis , 1957 .

[7]  R. Hegerberg,et al.  Diffusion, Attachment and Attachment Cooling of Thermal Electrons in Oxygen and Oxygen Mixtures , 1983 .

[8]  Gregory H. Wannier,et al.  On an anomaly in the mobility of gaseous ions , 1970, Bell Syst. Tech. J..

[9]  P. M. Prenter.  Splines and variational methods , 1975 .

[10]  E. A. Mason,et al.  Influence of resonant charge transfer on ion diffusion and generalized Einstein relations. , 1982 .

[11]  E. A. Mason,et al.  Moment theory of electron drift and diffusion in neutral gases in an electrostatic field , 1979 .

[12]  R. Robson.  Nonlinear Diffusion of Ions in a Gas , 1975 .

[13]  M. Elford,et al.  The Momentum Transfer Cross Section for Electrons in Helium Derived from Drift Velocities at 77°K , 1970 .

[14]  G. Wannier.  On a Conjecture about Diffusion of Gaseous Ions , 1973 .

[15]  N. Mermin.  E Pluribus Boojum: the physicist as neologist , 1981 .

[16]  G. Braglia.  Theory of electron motion in gases , 1980 .

[17]  D. Albritton.  Energy Dependences of Ion-Neutral Reactions Studied in Drift Tubes , 1979 .

[18]  K. Kumar.  The Chapman-Enskog solution of the Boltzmann equation: a reformulation in terms of irreducible tensors and matrices , 1967 .

[19]  R. Robson,et al.  Mobility and diffusion. I. Boltzmann equation treatment for charged particles in a neutral gas , 1973 .

[20]  T. Kihara.  The Mathematical Theory of Electrical Discharges in Gases. B. Velocity-Distribution of Positive Ions in a Static Field , 1953 .

[21]  G. Wannier.  Motion of gaseous ions in strong electric fields , 1953 .

[22]  Robert Robson,et al.  Kinetic Theory of Charged Particle Swarms in Neutral Gases , 1980 .

[23]  Graeme A. Bird,et al.  Direct Simulation and the Boltzmann Equation , 1970 .

[24]  R. Robson,et al.  Diffusivity of Charge Carriers in Semiconductors in Strong Electric Fields , 1973 .

[25]  Kailash Kumar,et al.  Electron Diffusion in Finite Enclosures , 1975 .

[26]  R. Crompton.  The Contribution of Swarm Techniques to the Solution of Some Problems in Low Energy Electron Physics , 1970 .

[27]  L. Viehland,et al.  Application of the three-temperatue theory of gaseous ion transport , 1979 .

[28]  F. Molinet.  Existence, uniqueness and properties of the solutions of the Boltzmann kinetic equation for a weakly ionized gas. I. , 1977 .

[29]  R. Robson.  A Thermodynamic Treatment of Anisotropic Diffusion in an Electric Field , 1972 .

[30]  G. Haddad,et al.  Model Calculations of Negative Differential Conductivity in Gases , 1984 .

[31]  H. Drange.  The Linearized Boltzmann Collision Operator for Cut-Off Potentials , 1975 .

[32]  J. Bardsley,et al.  Monte Carlo simulation of ion motion in drift tubes , 1977 .

[33]  T. G. Cowling,et al.  The mathematical theory of non-uniform gases , 1939 .

[34]  Lawrence H. Luessen,et al.  Electrical Breakdown and Discharges in Gases , 1983 .

[35]  E. A. Mason,et al.  Three-temperature theory of gaseous ion transport , 1979 .

[36]  G. C. Pomraning,et al.  Linear Transport Theory , 1967 .

[37]  H. Skullerud.  Kinetic Theory Analysis of Electron Attachment Cooling in Oxygen , 1983 .

[38]  J. Gillis,et al.  Linear Differential Operators , 1963 .

[39]  R. Robson,et al.  The determination of ion-atom interaction potentials , 1974 .

[40]  L. Viehland.  Gaseous ion transport coefficients , 1982 .

[41]  S. Hunter,et al.  Comparison between the Boltzmann and Monte Carlo simulation methods for the determination of electron swarm transport coefficients in molecular hydrogen , 1979 .

[42]  B. Bederson,et al.  Total Electron-Atom Collision Cross Sections at Low Energies-A Critical Review , 1971 .

[43]  R. Robson.  Boundary Effects in Solution of Boltzmann's Equation for Electron Swarms , 1981 .