The statistics of avalanche electrons in micro-strip and micro-gap gas chambers

The fundamental limit to the energy resolution of proportional counters is determined by the combined effects of two factors: statistical fluctuation in the number of electrons formed in the primary ionization, and the avalanche-to-avalanche fluctuation in gas amplification. Because the latter is usually larger than the former, the magnitude of the avalanche variance dominates the statistical portion of the energy resolution. This variance was calculated numerically for typical geometries used in three types of proportional counters: wire chambers, micro-strip gas chambers and micro-gap chambers. The results show that the spatial dependence of the electric field has a strong influence on the variance.