Effect of finite dimensions on the electric field configuration of cylindrical proportional counters

Three dimensional electrostatic fields in cylindrical proportional counters have been computed to high accuracy using a zero-th order boundary element technique. The effects of finite bounds of the detector on the resulting field configuration have been studied in detail. It has been observed that electric field configurations at the mid-plane of cylindrical proportional counters can be considered to be identical (deviations less than 10%) to that of an infinitely long detector only if the aspect ratio [λ=(l/b)] of the detector is greater than 2.0. Significant amount of deviation from the analytical solution (valid for infinitely long detectors) has been observed for a large percentage of the detector volume for the complete range of λ considered in the study (0.25<λ<10.0). The deviations have been found to be significant close to the anode wire and the cathode cylinder where the nature of the field configuration matters most. Attempts have been made to quantify the deviations as functions of λ, and, for a given λ, as functions of the distance from the mid-plane.