On the design of temporal cerenkov detectors that have optimal algorithms for the unique reconstruction of muon tracks

Abstract

A general condition providing the unambiguous reconstruction of an azimuthal muon track, which is necessary in the design of both temporal and amplitude detectors, is found analytically. Two designs of temporal Cerenkov detectors that allow one (unlike conventional strings of detectors) to recover all the parameters of the muon track and admit the partition of the obtained set of equations into two independent sets of lower dimensions are proposed. Optimal algorithms for calculating the muon track parameters are found with this approach. One of the designs proposed allows for an analytical solution to the set of equations.