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

TL;DR

This paper investigates the factors affecting the effective number of electrons in TPCs, focusing on diffusion effects and their impact on measurement accuracy, revealing that normal diffusion has minimal influence on N_eff.

Contribution

The study extends previous models by evaluating the impact of diffusion perpendicular to the pad-row direction on N_eff in TPCs.

Findings

Diffusion normal to the pad-row direction has a negligible effect on N_eff.

N_eff is significantly smaller than the average number of drift electrons due to fluctuations.

De-clustering effects cause N_eff to depend on drift distance, but are minor in the studied prototypes.

Abstract

For time projection chambers (TPCs) the accuracy in measurement of the track coordinates along the pad-row direction deteriorates with the drift distance (z): Resolution**2 = D**2 * z / N_eff, where D 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>). In the previous work we estimated N_eff by means of a simple numerical simulation for argon-based gas mixtures, taking into account the diffusion of electrons only in the pad-row direction [1]. The simulation showed that N_eff could be as small as 30% of <N> because of the combined effect of statistical fluctuations in the number of drift electrons (N) and in their multiplication in avalanches. In this paper, we evaluate the influence of the diffusion normal to the pad-row direction on the effective number of electrons. The de-clustering of the drift electrons due to the diffusion makes N_eff drift-distance dependent. However, its effect was found to be too small to explain the discrepancy between the values of N_eff measured with two TPC prototypes different in size.