Measurement of the Townsend Coefficients for Ionization by Collision

Abstract

The photoelectric current between parallel plates in dry air was measured as a function of plate distance for constant field strength and pressure over plate distances ranging from 1 to 7 cm and at a pressure of 1 mm of mercury. The simple Townsend relation $i={i}_{0}{\ensuremath{\epsilon}}^{\ensuremath{\alpha}d}$ was found to give excellent agreement for values of $\frac{X}{p}$ from 40 to 110. The least squares values of $\frac{\ensuremath{\alpha}}{p}$ plotted as a function of $\frac{X}{p}$ lie on a smooth curve which does not fit either the equation $\frac{\ensuremath{\alpha}}{p}=N{\ensuremath{\epsilon}}^{\ensuremath{-}\frac{N{V}_{0}p}{X}}$ suggested by Townsend, nor the empirical relation $\frac{\ensuremath{\alpha}}{p}=A{\ensuremath{\epsilon}}^{\frac{\mathrm{bX}}{p}}$, found by the writer to hold for values of $\frac{X}{p}$ from 20 to 36.5. Voltages and plate distances were measured to within $\frac{1}{10}$ of 1 percent and pressures to \textonehalf{} of 1 percent or better. For $\frac{X}{p}'\mathrm{s}$ from 120 to 160 the current was found to increase with plate distance more rapidly than the simple exponential relation would indicate, as was observed by Townsend for plate distances less than 1 cm at much greater $\frac{X}{p}'\mathrm{s}$. The early appearance of this deviation may be ascribed to the greater sensitivity given by larger plate distances. Both of the relations suggested by Townsend: $i=\frac{{i}_{0}(\ensuremath{\alpha}\ensuremath{-}\ensuremath{\beta}){\ensuremath{\epsilon}}^{(\ensuremath{\alpha}\ensuremath{-}\ensuremath{\beta})d}}{[\ensuremath{\alpha}\ensuremath{-}\ensuremath{\beta}{\ensuremath{\epsilon}}^{(\ensuremath{\alpha}\ensuremath{-}\ensuremath{\beta})d}]},$ which was derived on the assumption that each positive ion produces $\ensuremath{\beta}$ new pairs of ions by collision in 1 cm of path, and $i=\frac{{i}_{0}{\ensuremath{\epsilon}}^{\ensuremath{\alpha}d}}{[1\ensuremath{-}\ensuremath{\gamma}({\ensuremath{\epsilon}}^{\ensuremath{\alpha}d}\ensuremath{-}1)]},$ which assumes $\ensuremath{\gamma}$ new electrons liberated by each positive ion which strikes the cathode, fit the experimental curves equally well. The values of $\frac{\ensuremath{\beta}}{p}$ were observed to increase with $\frac{X}{p}$ as found by Townsend for higher $\frac{X}{p}'\mathrm{s}$. The coefficient $\ensuremath{\gamma}$, which is approximately equal to $\frac{\ensuremath{\beta}}{\ensuremath{\alpha}}$ was observed to increase only very slightly over this small range of $\frac{X}{p}'\mathrm{s}$.