On the Swarm Method for Determining the Ratio of Electron Drift Velocity to Diffusion Coefficient

Abstract

SummaryThe use of data from swarm experiments for electron energies approaching those corresponding to thermal equilibrium demands results of greater precision than has hitherto been available. In order to examine the possibility of producing such data, the swarm method for detennining WID has been extensively examined over a range of values of the parameter Elp where the agreement between the results of recent investigations is not good. A number of factors influencing the accuracy of measurements of this type are discussed. The results for hydrogen which are presented are considered to be subject to an error of less than 1 %. I. INTRODUCTIONThe results of swarm methods for determining the ratio WID of electron drift velocity to diffusion coefficient have found application in a number of recent papers in which collision phenomena between low energy electrons and gas molecules have been discussed (Gerjouy and Stein 1955;Huxley 1956Huxley , 1959Shkarofsky, Bachynski, and Johnston 1961;Frost and Phelps 1961). For some of these applications, more especially those dealing with collision phenomena for electrons with mean energy of several electron-volts, the accuracy of existing data is sufficiently good. Not only are the results of a number of investigations substantially in agreement for this energy range but the degree of accuracy to which they have been obtained is adequate for most purposes. On the other hand, for those applications where the difference in energy between the electrons and gas molecules is important, small errors in the determination of WID become significant as this difference approaches zero. Unfortunately it is in this energy range that the measurements become more difficult and the agreement between the results from various laboratories is not good.In this paper an account is given of a systematic investigation of the swarln method for determining WID using an apparatus which enables the dimensions of the diffusion chamber to be quickly and simply varied. A number of possible sources of error has been investigated both theoretically and experimentally, as a result of which it has been possible to determine the experimental procedures which lead to results of maximum accuracy. The results which have been obtained where these procedures were followed show good agreement over a wide range of values of the experimental parameters and it is considered that the values of WID in hydrogen from O'1<Elp<5'OVcm-1 mIllHg-l which are

Transport Coefficients for Low Energy Electrons in Crossed Electric and Magnetic Fields

“…The same solution applies when the hole is regarded as a dipole source and the receiving electrode as a geometrical plane (Huxley and Zaazou 1949). As for the case with no magnetic field (Crompton and Jory 1962), h has been chosen to ensure that equations (5) are applicable also for the case of zero electron concentration at each electrode. may be shown to be given by where…”

“…2) the ratio of the current received by the central disk to the total current can be measured in the absence of the magnetic field. The ratio WID can be calculated from this current ratio in the usual way (Crompton and Jory 1962). From the results of the two experiments W",I W z can then be calculated.…”

“…For a given gas pressure, measurements were made in the absence of the magnetic field with the leads from the segments of the collecting electrode connected together in such a way as to form a central disk and surrounding annulus. For a range of values of electric field strength E, restricted as described below, measurements of the ratio of currents received by the disk and annulus were made and from these measurements values of WID determined as described, for example, by Crompton and Jory (1962). The leads were then rearranged in such a way that the collecting electrode took the form of two semicircular segments and the ratio of the currents received by these segments was measured at each value of E for a range of values of the magnetic field strength B.…”

“…The ratios of currents received by the segments of the receiving electrode were measured using the equipment described by Crompton and Jory (1962), which enables ratios of currents as small as 5 X 10-13 A to be measured to within 0·1 % for nearly equal currents while maintaining all sections of the receiving electrode to within 0·2 m V of earth potential.…”

“…The work described in the present paper was initiated to provide experimental results for W M of accuracy comparable with those becoming available for the more commonly measured transport coefficients, namely the drift velocity W and the coefficient of diffusion D. Huxley's method (Huxley and Zaazou 1949) has been used since it is more flexible in its application than Townsend's method and has the advantage that the theory upon which it is based does not rely on an approximation whose validity is questionable (Section II). The reliability of the method and the techniques used was established by following the procedure of Crompton and Jory (1962), that is by taking an extensive series of results for a wide range of those experimental parameters that can be conveniently varied, in this instance the pressure and the electric field and magnetic field strengths. Both the experiment itself, and the interpretation of the results from it in terms of W M, are less straightforward than those for measuring Wand WID.…”