Calculation of field distortion by a large-gained avalanche in a gas counter

Simulation performed by using the continuity equation of electrons and positive ions is applied to examine the three-dimensional formation and the time evolution of an electron avalanche in a cylindrical gas counter. The field made by space charge is calculated exactly and concurrently by the relaxation method in the evolution. The gas multiplication for photon detection is consistently estimated for an Ar-based mixture by not using any adjustable parameter for geometrical dependency. Field distortion at the time of the finish of the evolution is studied systematically. The distortion is concentrated in a small region of angle in case of a large diameter of the anode. The shape of the distortion is calculated for several distributions of the initial charge. The distortion is enhanced by the distribution that occupies small area in the transverse plain in the avalanche. Change of the field distortion depending on the anode diameter and the initial charge distribution is shown quantitatively by these calculations. The transition to a streamer by the continuous supply of electrons is suggested to depend strongly on the charge distribution in an avalanche.