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 ($\frac{\alpha }{p}$) ($\alpha$ 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 $\frac{X}{p}=20\mathrm{}$ and $\frac{X}{p}=38\mathrm{}$ may be represented at 22°C by $\frac{\alpha }{p}=(5.76\mathrm{}\pm 1.56)\times {10}^{-7\mathrm{}}{e}^{\frac{(0.245\mathrm{}\pm 0.003)X}{p}}.$ In this region the Townsend equation $i=i_0{e}^{\alpha d}$ for electron ionization alone was found to hold up to the passage of a spark. Between $\frac{X}{p}=44\mathrm{}$ and 176 the curve $\frac{\alpha }{p}=F\left(\frac{X}{p}\right)$ is represented by $\frac{\alpha }{p}=(1.166\mathrm{}\pm 0.022)\times {10}^{-4\mathrm{}}{(\frac{X}{p}-32.1\mathrm{}\pm 1.4)}^2.$ The portion of the curve between $\frac{X}{p}=200\mathrm{} \mathrm{and} 1000$ may be represented by ${(\frac{\alpha }{p}+3.65)}^2=\frac{0.21X}{p}$. These results are in excellent agreement with those of Masch but differ by an order of magnitude and more from those of Ayres below $\frac{X}{p}=70\mathrm{}$. The deviations from $i=i_0{e}^{\alpha d}$ (due to a secondary process of ionization) were first observed at $\frac{X}{p}=100\mathrm{}$. These deviations yield values of a coefficient $\beta$ due to the secondary ionization mechanism in terms of Townsend's equation $i=\frac{i_0(\alpha -\beta )e^{(\alpha -\beta )d}}{(\alpha -\beta e^{(\alpha -\beta )d})}$ which extend from $\frac{X}{p}=100\mathrm{}$ to $\frac{X}{p}=1000\mathrm{}$. To obtain consistent values of $\beta$ it was found necessary to reduce the initial photoelectric current density from the cathode to less than ${10}^{-13\mathrm{}}$ amp./${\mathrm{cm}}^2$. Current densities of magnitude greater than ${10}^{-12\mathrm{}}$ amp./${\mathrm{cm}}^2$ give rise to space charge field distortion and consequently falsify values of the secondary coefficient. The values of $\frac{\alpha }{p}$ and $\frac{\beta }{p}$ 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 $\beta$ 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 $\frac{\alpha }{p}$ and $\frac{\beta }{p}$ 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.