Induced charge on the electrode of ionization counters

Sakasai, Kaoru  

Based on the Green's reciprocation theorem, the charge distributions on the electrode of ionization counters induced by a point charge that exist between the electrodes have been derived in a closed form. The shape of the electrodes were assumed to be parallel plates or cylindrical. In the case of parallel plate electrodes, the distribution can be expressed by an integral of Bessel function of zero order. On the other hands, in the case of cylindrical electrodes, the distribution can be expressed by an integral of modified Bessel function of zero order. These expressions will be useful to calculate current signals of counters because the current signal can be obtained by differentiating the charge distribution.