scholarly journals On the Theory of Anisotropic Diffusion of Electrons in Gases

1972 ◽  
Vol 25 (1) ◽  
pp. 43 ◽  
Author(s):  
LGH Huxley

It is now recognized that when electrons move in a steady state of motion in a gas in an electric field the process of diffusion is in general anisotropic with a coefficient of diffusion DL along or against the electric force eE that is not the same as the coefficient D for directions normal to eE. A theoretical discussion of this phenomenon based upon the Maxwell?Boltzmann equation is given which also entails consideration of related matters such as the distribution function for an isolated travelling group, the distribution of number density n, the equation of continuity and current density, and the relation of the theory of the travelling group to that of the steady stream.

Author(s):  
Hoyeon Choi ◽  
Yong Gap Park ◽  
Man Yeong Ha

Abstract In this paper, a numerical model was developed to describe the wire-plate electrostatic precipitator, commonly called electronic air cleaners. Electrostatic precipitator have been widely used to control particulate pollutants, which adversely affect human health. In this model, the complex interactions between fluid dynamics, electric fields and particle dynamics are considered. Therefore different approach methods are used in this study for each field, Eulerian reference frame was used for the fluid flow field and the electric field, Lagrangian reference frame used for the particles trajectories. In order to describe corona phenomena around high voltage electrode, electric field and ion current density field in electrostatic precipitator are numerically calculated using the iterative method for corona discharge model suggested by Kim (2010). The most important concept in electrostatic precipitator is the electric force applied to particles through the particle charging phenomena. The charge acquired by the particle in the corona region was obtained by combining the field charge, the diffusion charge and the time available for charging being the residence time of the particle in the corona region. In order to simulate more accurately, the charging model suggested by Lawless (1996) is used for the charging phenomena of particles by corona discharge because this model was designed to predict combination effect of diffusion charge and field charge. The diminution of particle concentration along the collection plate was derived from Deutsch’s theory, and migration velocity of the particle was developed from the condition that the magnitude of Coulomb force is equal to that of Stoke’s resistance force. This model is implemented by UDF in commercial software Fluent and validated with experimental and numerical results from literatures. CFD results had been compared with various experimental data obtained by Penney&Matick, Parasram and Kihm. Our results shows good agreement in terms of distributions of electric potential, current density, electrohydrodynamic flow pattern, and particle trajectories as well as corona current and collection efficiency. From this simulation, the effect of wire arrangement on electrostatic precipitator characteristics and particle charging are investigated. Both inline and staggered arrangements of wire electrode have been considered for fixed values of gas velocity equal to 2m/s. Applied voltage on wire electrode varies 6∼13kV and particle diameter is 4μm. For low voltage condition, staggered arrangement of wire electrode caused the turbulent effect so that collection efficiency increase more than inline arrangement. However, collection efficiency decrease in high voltage condition because electric force applied on particles passing between the wire electrodes is canceled out by both side wire electrodes.


1971 ◽  
Vol 49 (9) ◽  
pp. 1124-1136
Author(s):  
H. W. H. Van Andel

The steady state distribution function for a suprathermal electron cloud injected into a cylindrical plasma is found as a function of position and velocity by solving the Boltzmann equation numerically in the Fokker–Planck approximation with an added term taking into account electron-neutral collisions. The injection is assumed to take place at one end of the cylinder, and an axial magnetic field is assumed present. A number of representative solutions are given for various choices of the parameters of the problem.


1970 ◽  
Vol 4 (1) ◽  
pp. 143-144
Author(s):  
G. J. Lewak

In a previous paper [Lewak (1969), see also Pflrsch (1966) for related treatment], it was shown that the Vlasov equation in the Semi-Lagrangian (S.L.) formulation, may be written in a form resembling the fluid equations.plus Maxwell's equations with the source terms given bywhere n is the determinant of the tensor Tij = ∂gi/∂ζj, and N is the constant mean number density of electrons. The averaging notation < > here is defined bywhere f(σ) is the electron distribution function to be specified. The equations assume for simplicity a uniform fixed ion background, although this is not a necessary restriction and equations (1) and (2) need only an obvious modification to account for ions. The force fields in (1) are related to the electric field E and magnetic field B in the plasma by .


1972 ◽  
Vol 25 (6) ◽  
pp. 685 ◽  
Author(s):  
RE Robson

Non-equilibrium thermodynamics is used to analyse the diffusive processes associated with a swarm of charged particles (ions or electrons) drifting in a neutral gas under the influence of an electric field. A simple approximate phenomenological relationship connecting components of the diffusion tensor with the drift velocity of the swarm is derived and the utility of the formula is illustrated in several cases where previous analyses have been carried out using the Boltzmann equation.


2021 ◽  
Vol 36 (1) ◽  
pp. 420-432
Author(s):  
Mohammad M. Othman ◽  
Sherzad A. Taha ◽  
Saeed O. Ibrahim

In this study, the electron energy distribution function EEDF, the electron swarm parameters, the effective ionization coefficients, and the critical field strength (dielectric strength) in binary He-H2 gas mixture which used as cryogenic for high-temperature superconducting power application, are evaluated by using two-term approximation of the Boltzmann equation over the range of E/N ( the electric field to gas density) from 1 to 100 Td ( 1 Td=10-17 Vcm2) at temperature 77 K and pressure 2MPa, taking into account elastic and inelastic cross-section. Using the calculated EEDF, the electron swarm parameters (electron drift velocity, mean electron energy, diffusion coefficient, electron mobility, ionization and attachment coefficient) are calculated. At low reduced electric field E/N, the EEDF close Maxwellian distribution, at high E/N, due to vibrational excitation of H2 the calculated distribution function is non-Maxwellian. Besides, in the He-H2 mixture, it is found that increasing small amount of H2 enhances to shift the tail of EEDF to the lower energy region, the reduced ionization coefficient α/N. reduced effective ionization coefficient (α-η)/N) decreases, while, reduced attachment coefficient η/N, reduced critical electric field strength (E/N)crt. and critical electric field Ecrt. Increases, because of hydrogen’s large ionization cross-sections. The dielectric strength of 5% H2 in mixture is in good agreement with experimental values, it is found that dielectric strength depend on pressure and temperature. The electron swarm parameters in pure gaseous helium (He) and hydrogen (H2), in satisfying agreement with previous available theoretical and experimental values. The validity of the calculated values has been confirmed by two-term approximation of the Boltzmann equation analysis.


1973 ◽  
Vol 26 (2) ◽  
pp. 135 ◽  
Author(s):  
LGH Huxley

A theoretical discussion is presented of the structure of a stream of electrons moving through a gas under the action of a uniform electric field. The treatment incorporates the phenomenon of longitudinal diffusion in which the coefficient DL can be different from the isotropic coefficient of diffusion D. The treatment also is not restricted to the case in which the aperture through which the stream enters the diffusion chamber is small. The solution satisfies the boundary condition n = 0 at the surface of the anode and everywhere on the cathode except over the plane of the source aperture. The theory therefore provides criteria for the validity of simplified solutions employed hitherto.


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