A New Formula for the Accurate Evaluation of Magnetic Spectrometers’ Performance With Nonuniform Fields

We present a new and highly accurate formula to evaluate muon momentum and its resolution for magnetic spectrometers with high variability of field distribution. A full derivation of the model is given, along with a comparison with the classic approach. The statistical validation is performed using 3D numerical simulation of the particle flight within the magnetized volume of the spectrometer. In the presence of high variation in field profiles, for the considered study cases, the proposed formula provides an average accuracy of 2%, as compared to 18% and 33% of its classical counterparts. This improvement is achieved with no increase in the computational cost, providing a fast, simple, and reliable tool for the design of spectrometers’ magnets.