Pulse Risetimes in Proportional Counters

We present a method of calculating proportional counter pulse shapes for both point and extended ionization tracks. The method is applicable to any counter gas for which the electron drift velocity as a function of the electric field is known. The mobility of the positive ions that are responsible for pulse formation is a parameter of the theory. If we assume there is only one species of positive charge carrier, we can identify it by measuring counter pulse shapes for point ionization tracks and comparing them to calculated pulse shapes. The theory is consistent with measurements of actual pulses in four counter gases: 90% Ar-10% CH4, 90% Ar-10% N2, 90% Kr-10% CO2, and 90% Xe-10% CO2.