No 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 ;

SummaryThe theory is developed of the structure of a stream of electrons and ions drifting under the action of a uniform field and diffusing in a gas when either or both ionization by collision and electron attachment are present. The cases considered include a point source and a line source, and in the latter case the influence of a magnetic field is discussed.The investigation provides a theoretical basis for methods of measuring electron attachment, about to be put into practice.

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 functionfri(c) 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.

Recent determinations of attachment and ionization coefficients have been carried out using a number of different techniques including (i) a method due in the first instance to Lozier using an electron beam (Craggs, Thorburn, and Tozer 1957; Tozer, Thorburn, and Craggs 1958), (ii) a development of Townsend's Driginal method of determining ionization coefficients by the measurement of ionization currents between parallel plane electrodes of variable separation (Geballe and Harrison 1952, 1953), and (iii) a modification of Doehring's method depending on measurements of time of flight (Chanin, Phelps, and Biondi 1959). In experiments of the second and third type it is not possible to estimate experimentally the mean energy of the electrons and, if the coefficients are to be expressed as functions of electron energy, it is necessary to use the results of independent experiments.