Free Path Formulae for the Coefficient of Diffusion D and Velocity of Drift W of Ions and Electrons in Gases

Abstract

SummaryIn derivations of formulae for D and W for electrons by the method of free paths (Huxley 1957a(Huxley , 1957b) the assumption was made that along a number of successive free paths an electron travels at essentially the same speed c. As this assumption is not true of ions it would not be legitimate to apply the formulae to the motion of ions in gases without further discussion. However, the formulae are in fact valid for ionic motion and in what follows they are established in a more general form. OOEFFICIENT OF DIFFUSION DOonsider a large number p of free paths xIl X 2, • •• , xn all traversed at the same speed 0 by the ion or electron, but not necessarily consecutively.If lo is the mean free path then Let {j be the mean speed of the ion (with speed 0) relative to the molecules which move at random and let N be the number of molecules in unit volume.The sum of the times spent in traversing the paths x k is t=plojc, that is to say, p=ctjlo' But p={jtNm:r 2 , consequently lo=(cj{j) N1t(j2=lo(0). For electrons {j =c; lo =ljN 1t(j2. (j is the limiting value of the impact parameter beyond which deflections of the ions are unimportant.Oonsider a diffusing group of n electrons or ions. In the absence of an electric or magnetic field the rate of increase of the mean of the squares of the distance of the n particles from a fixed origin is given by the well-known formula di2jdt=6D.In time t let the kth particle traverse a succession of free paths xk,m so that its vector position changes from r Ok at time t=O to r k at time t. That is, Also, if ro is the position of the centroid of the group, n n nro= ~ r k = ~ r Ok ;

Relaxation of transient ionization in the lower ionosphere

“…This reaction has a threshold at about 4 eV [Huxley and Crompton, 1974]. As shown in Figure 1, the electron temperature will decrease very quickly to below this (t < 0.1 ms), and will probably only be above this threshold while the ionization mechanism is still active, although decaying.…”

Transport coefficients and cross sections for electrons in water vapour: Comparison of cross section sets using an improved Boltzmann equation solution

“…In general, the variation of the transport coefficients with E/n 0 (the ratio of the applied electric field E to the target number density n 0 ) is a macroscopic reflection of the way microscopic cross sections depend upon energy, and indeed this provides the rationale for the so-called "swarm method" for inverting transport data to obtain cross sections. 19 However, we emphasize at the outset that we are not involved with any such inversion scheme in this paper. Unlike beam experiments, swarm experiments are "many/multiple scattering" experiments.…”

“…18 One of the key discriminating tests on the completeness and accuracy of any given cross section set is provided through electron swarm experiments. [19][20][21] In swarm experiments, electrons are passed through a gas at known pressure and temperature under the influence of a uniform electric field. Currents are interpreted in terms of drift and diffusion and other transport coefficients.…”

A Monte Carlo study of photoelectron extraction efficiency from CsI photocathodes into Xe–CH4 and Ne–CH4 mixtures

“…In the field of gaseous radiation detectors, and the emission of photoelectrons from CsI in particular, the effect has been investigated experimentally and by Monte Carlo simulation, see [7][8][9][10][11][12][13][14][15] and references therein, where the dependence on gas and mixture composition, reduced applied electric field E/N (E is the field strength and N the number density) and incident photon energy E ph was analyzed. In the broader field of swarm physics [16], which is fundamental to gas discharge and plasma physics, electron back-diffusion has been investigated for more than half a century, together with reflection effects and induced secondary emission [17][18][19][20][21][22][23][24][25][26]. In [24][25][26] Monte Carlo simulation was used to examine electron back-diffusion to an emitting frontier (cathode) in argon and nitrogen, showing in particular, as we also verified in [14], that transmission is very sensitive to the electron initial energy ε 0 and energy distribution profile, increasing in general with decreasing ε 0 , with full transmission for ε 0…”