Measurements of Discharge Characteristics of Geiger-Mueller Counters

An experimental method is presented for determining directly the voltage-time relationship of a counter wire during the interval which begins with the initiation of the discharge and ends when the wire has achieved its maximum negative potential. The procedure allows for the measurement of times ranging from 2.0×${10}^{-7\mathrm{}}$ second to 1.0×${10}^{-4\mathrm{}}$ second, and wire potentials between 20 volts and 350 volts. Studies indicate that over a considerable range of wire and cylinder voltages and wire system capacities the relation $E=-\left(\frac{Q}{c}\right) {log}_{10} (\frac{t}{t_0}+1)$ satisfactorily represents the observations. Here $E$ is the potential of the counter wire, $t$ the time, $Q$ a function of cylinder voltage and $t_0$ a constant for a given counter. $t$ is, of course, measured from the instant when $E=0\mathrm{}$. It follows from this relation that the current in the counter is inversely proportional to the time (for $t\gg t_0$, which is of the order of magnitude of 3.0×${10}^{-8\mathrm{}}$ second). In a particular case where conditions are such that the counter "overshoots" (the voltage pulse $E_{max}$ from the counter exceeds in magnitude the difference between starting potential and cylinder potential) experiment reveals $Q$ to vary with the cylinder potential and with the capacity of the wire system in a manner determined by $Q=\frac{c{E}_{max}}{\beta }$, where $\beta$ is a constant and the dependence upon cylinder potential is contained in the dependence of $E_{max}$ upon that quantity. For this case of overshooting, the foregoing formula results in $t=t_0({10}^{\frac{\beta E}{E_{max}}}-1)$. If we confine ourselves to constant values of the cylinder voltage, the corresponding $Q$'s are constant, so that $c{E}_{max}$ is constant and we may consequently write $t=t_0({10}^{\frac{\mathrm{Ec}}{Q}}-1)$ where $Q$ does not vary with $c$. These expressions for $t$ have been established by the experiment only for $\mathrm{}\left|E\right|\mathrm{}$ not in excess of $0.8\left|E_{max}\right|$ and for $t>\mathrm{}2.0\mathrm{}\times {10}^{-7\mathrm{}}$ second. Discharge characteristics were measured for a series of pressures of an argon-oxygen mixture and in each case a relation of the logarithmic form indicated was found to represent the data. An argon-alcohol counter, generally spoken of as "self-quenching," has characteristics of the same form. When cylinder voltage is adjusted for equality of pulse size, $t_0$ is inversely proportional to pressure.