Precision Measurements of the Townsend Energy Ratio for Electron Swarms in Highly Uniform Electric Fields

Abstract

SummaryA detailed account is given of the solution to the problems associated with the use of the Townsend-Huxley method of measuring the ratio of drift speed to diffusion coefficient for very low energy electron swarms. The elimination of radial components of the electric field within the diffusion chamber is shown to be the major experimental problem, especially in the case of the comparatively weak electric fields which must be used for some of the measurements in the near· thermal region. The experimental techniques and procedures, which are described in some detail, enable measurements to be made in this region with an accuracy comparable to that which has been achieved at higher electron energies. I. INTRODUOTIONOne of the methods of examining collision phenomena between low energy electrons and gas molecules is to measure the ratio of the drift velocity W to the diffusion coefficient D of an electron swarm moving under the influence of an electric field E in a gas at a pressure p. Since WjD is a pressure-dependent quantity, the experimental results are always given either in terms of DjfL, where fL is defined as the ratio WjE, or of kv a parameter closely related to the Townsend energy factor, k T , which is defined as the ratio of the mean energy of agitation of the electrons to the mean thermal energy of the molecules of the gas through which the electron swarm moves. These quantities are related by the expression whereBoth k1 and DjfL are functions of the ratio EjN and are also, in general, functions of the gas temperature.An examination of a number of possible sources of error in the TownsendHuxley method for measuring k1 has been made by Crompton and Jory (1962), who showed that, by careful attention to the choice of experimental parameters and conditions, results with errors of less than I % can be achieved for measurements of k1 in hydrogen at 293°K over the range in E jp of O· 1-5·0 V cm -1 torr-I, for which the lowest value of k1 is approximately 2. If the measurements are to be extended to lower values of E jp, the data lose much of their significance unless

DT/µ andDL/µ for electrons in NO

“…At the same time, the high end of our range is in very good agreement with the results of Lakshminarasimha and Lucas [8]. None of the studies are of the highest possible accuracy developed by Crompton and coworkers [30], but since there are no data available from such an experiment the present results should be the most reliable for the time being. Thus, we suggest that some modifications of the available cross sections [17] may be required to put the calculated drift coefficients in agreement with our results.…”

On the Theory of Anisotropic Diffusion of Electrons in Gases

“…The first assumption appeared reasonable prior to the experimental and theoretical work that revealed the extent of the anisotropicity in certain circumstances (Wagner, Davis, and Hurst 1967;Parker and Lowke 1969). The second assumption, although violating the normally accepted boundary condition n = 0 over the cathode except at the source hole, appeared to be justified by the success which the formula based on jt, enjoyed in predicting consistent values of the ratio D/W from a large body of experimental data (Huxley and Crompton 1955;Crompton and Jory 1962;Crompton, Elford, and Gascoigne 1965). A detailed analysis by Hurst and Liley (1965), while retaining the assumption of isotropic diffusion in regions of the apparatus removed from the boundaries, showed that the experimental results could be accounted for on the assumption of artificial reflection coefficients at the electrodes.…”

Electron Drift And Diffusion In Deuterium At 293°K

“…The useful parameter kl can be obtained from the rat.io of diffusion coefficient to mobility by the use of the relation kl = (D/fL)(kT/e)-l, (2) where fL = W/E, k is Boltzmann's constant, T is the temperature, and e is the electronic charge. The slight decrease in the values of D/fL (amounting to a maximum of 0'7% at E/p = 0·3) as the pressure is reduced at a given value of E/p is instrumental in origin and is of t.he same form as the change expected from the influence of the finit.e size of the source hole in the apparatus (Crompton and Jory 1962;Crompt.on, Elford, and Gascoigne 1965). Crompton and Jory's calculations suggest an upper limit of 0·8% for this effect under t.he present experimental conditions and so the average values in Table 2 should still lie within the claimed accuracy.…”

“…The ratio of diffusion coefficient to mobility was measured by the Townsend-Huxley lateral diffusion method using apparatus and techniques identical with those described by Crompton, Elford, and Gascoigne (1965). Small errors caused by contact potential differences over the surfaces presented to the electron stream were eliminated, or compensated for, by the application of a small potential difference between the guard rings and the end plates of the apparatus (Crompton, Elford, and Gascoigne 1965). Two sets of measurements were taken in the same apparatus but with different collecting electrodes requiring different compensating potentials.…”