The Townsend Coefficients and Spark Discharge

Abstract

A quantitative study has been made of the prespark current between plane parallel electrodes in purified ${\mathrm{N}}_{2}$. The results yield the relationship between ($\frac{X}{p}$) ($X$ in volts/cm, $p$ pressure in mm of Hg) and ($\frac{\ensuremath{\alpha}}{p}$) ($\ensuremath{\alpha}$ is the number of new pairs of ions created by one electron in advancing one cm in the direction of the field). The range in values of $\frac{X}{p}$ covered is from 20 to 1000. The portion of the data between $\frac{X}{p}=20$ and $\frac{X}{p}=38$ may be represented at 22\ifmmode^\circ\else\textdegree\fi{}C by $\frac{\ensuremath{\alpha}}{p}=(5.76\ifmmode\pm\else\textpm\fi{}1.56)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}{e}^{\frac{(0.245\ifmmode\pm\else\textpm\fi{}0.003)X}{p}}.$ In this region the Townsend equation $i={i}_{0}{e}^{\ensuremath{\alpha}d}$ for electron ionization alone was found to hold up to the passage of a spark. Between $\frac{X}{p}=44$ and 176 the curve $\frac{\ensuremath{\alpha}}{p}=F(\frac{X}{p})$ is represented by $\frac{\ensuremath{\alpha}}{p}=(1.166\ifmmode\pm\else\textpm\fi{}0.022)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}{(\frac{X}{p}\ensuremath{-}32.1\ifmmode\pm\else\textpm\fi{}1.4)}^{2}.$ The portion of the curve between $\frac{X}{p}=200 \mathrm{and} 1000$ may be represented by ${(\frac{\ensuremath{\alpha}}{p}+3.65)}^{2}=\frac{0.21X}{p}$. These results are in excellent agreement with those of Masch but differ by an order of magnitude and more from those of Ayres below $\frac{X}{p}=70$. The deviations from $i={i}_{0}{e}^{\ensuremath{\alpha}d}$ (due to a secondary process of ionization) were first observed at $\frac{X}{p}=100$. These deviations yield values of a coefficient $\ensuremath{\beta}$ due to the secondary ionization mechanism in terms of Townsend's equation $i=\frac{{i}_{0}(\ensuremath{\alpha}\ensuremath{-}\ensuremath{\beta}){e}^{(\ensuremath{\alpha}\ensuremath{-}\ensuremath{\beta})d}}{(\ensuremath{\alpha}\ensuremath{-}\ensuremath{\beta}{e}^{(\ensuremath{\alpha}\ensuremath{-}\ensuremath{\beta})d})}$ which extend from $\frac{X}{p}=100$ to $\frac{X}{p}=1000$. To obtain consistent values of $\ensuremath{\beta}$ it was found necessary to reduce the initial photoelectric current density from the cathode to less than ${10}^{\ensuremath{-}13}$ amp./${\mathrm{cm}}^{2}$. Current densities of magnitude greater than ${10}^{\ensuremath{-}12}$ amp./${\mathrm{cm}}^{2}$ give rise to space charge field distortion and consequently falsify values of the secondary coefficient. The values of $\frac{\ensuremath{\alpha}}{p}$ and $\frac{\ensuremath{\beta}}{p}$ as functions of $\frac{X}{p}$ are applied to the Townsend criterion for spark breakdown between plane parallel electrodes and yield a curve for sparking potential plotted against the product of pressure and electrode separation in agreement with the experimental data of Strutt and Hurst. Since the quantity $\ensuremath{\beta}$ cannot be due to ionization by positive ions in the gas it must be ascribed to electron liberation at the cathode either by positive ion impact or by a photoelectric effect. The character of the variation of $\frac{\ensuremath{\alpha}}{p}$ and $\frac{\ensuremath{\beta}}{p}$ as functions of $\frac{X}{p}$ lends support to the hypothesis that it is the photoelectric effect at the cathode which is the effective secondary mechanism under these conditions.