Back-diffusion of electrons in argon in the presence of an electric field

Abstract

Measurements of electron back-diffusion to plane cold cathodes in a uniform electric field in Ar do not agree satisfactorily with theories derived from first principles. The process has been re-analysed in terms of one-dimensional diffusion and drift with allowance made for the Ramsauer-Townsend effect, which causes the electron's energy and mean free path to vary from its initial value at the cathode to its equilibrium value in the applied field. The analytically obtained expression for the ratio of collected to emitted current densities j/j0, which follows similarity rules, depends on pl, the product of gas pressure and electrode separation, and on the reduced field, E/p. It is found that for values of (E/p)34/(pl)>or approximately=10, j/j0 becomes independent of pl.

Asymptotic calculation of escape factor in atomic plasmas

“…Eliminating from this equation J − e by means of equation (32) and solving for J e /J em , one finds for the escape factor on a reflecting cathode [7,8] f (R) es ≡…”

“…In figure 5 the escape factor in argon is shown for the monoenergetic distribution of emitted electrons with the energy 1 eV. The data are given for both non-reflecting cathodes (R = 0) and reflecting cathodes (R = 0.6; this value is typical for metals at ε 0 about several tenths of electronvolts [7]). It is seen that for non-reflecting cathodes the data given by equation (30) agree with those of Monte Carlo calculations [9].…”

“…Equation (7) represents a rational interpolation between asymptotic behaviours at small and large θ . We stress a relation between this approximation and Padé approximants (e.g.…”

“…[10] and references therein). Such asymptotic interpolations are normally rather accurate, and one can hope that equation (7) would provide a good accuracy at all θ , especially if θ is the only parameter governing f es . Note that equation ( 7) may be transformed to a form similar to that of the Thomson-Loeb formula (3) with 1/Aθ appearing in place of Ce /4V e .…”

“…Unfortunately, this formula, while being quite simple, can hardly be considered theoretically justified, and it is unclear what its accuracy is. Also available are evaluations of the escape factor, in different ranges of the reduced electric field, on the basis of solution of the kinetic equation for the isotropic part of the electron distribution function (EDF) [2][3][4][5][6], with the use of diffusion approximation [7] and by means of Monte Carlo simulations [8,9]. Note that approaches [5,6] are based on using approximations similar to the Thomson-Loeb formula for a formulation of a boundary condition for the isotropic part of the distribution function at the cathode surface.…”