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電離計数管の電極に誘導される誘導電荷

Induced charge on the electrode of ionization counters

坂佐井 馨  

Sakasai, Kaoru

グリーンの相反定理に基づき、電離計数管の電極間に点電荷がある場合、それによって電極に誘導される誘導電荷を解析的に導出した。電極の形状は平行平板及び円筒型を仮定した。平行平板型の場合、電荷分布はベッセル関数を含んだ積分で表され、円筒型は変形ベッセル関数を含んだ積分で表される。計数管の電流信号はその誘導電荷の時間微分で求められるため、これらの表式は計数管の電流信号を評価するのに有用である。

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.

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