An estimation of the effective number of electrons contributing to the coordinate measurement with a TPC

For time projection chambers (TPCs) the accuracy in measurement of track coordinates along the pad row direction deteriorates with the drift distance ( z ) : σ X 2 ∼ D X 2 · z / N eff , where D X is the diffusion constant and N eff is the effective number of electrons. Experimentally, it has been shown that N eff is smaller than the average number of drift electrons per pad row ( N ¯ ) . We estimated N eff by means of a simple numerical simulation. The simulation shows that N eff can be as small as ∼ 30 % of N ¯ due to the combined effect of statistical fluctuations in the number of drift electrons ( N ) and in their multiplication in avalanches.