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)(z): σX2∼DX2·z/Neff, where DXDX is the diffusion constant and NeffNeff is the effective number of electrons. Experimentally, it has been shown that NeffNeff is smaller than the average number of drift electrons per pad row (N¯). We estimated NeffNeff by means of a simple numerical simulation. The simulation shows that NeffNeff can be as small as ∼30%∼30% of N¯ due to the combined effect of statistical fluctuations in the number of drift electrons (N)(N) and in their multiplication in avalanches.