  A new muon source has been proposed to conduct muon spin
rotation/relaxation/resonance ($\mu$SR) measurements at China Spallation
Neutron Source (CSNS). Only 1 Hz of the CSNS proton beams (25 Hz in total) will
be allocated for muon production. To make better use of muons in every pulse,
an ultrahigh-array $\mu$SR spectrometer (UHAM) with thousands of detector
channels is under design. Due to such a high granularity of detectors, multiple
counting events generated from particle scattering or spiral motions of
positrons in a strong longitudinal field should be carefully considered in the
design. Six different structures were modeled and simulated based on two types
of angular orientations (parallel arrangement and pointing arrangement) and
three kinds of spectrometer geometries (cylinder, cone and sphere). A quality
factor, $Q$, was proposed to evaluate the performance of these structures by
integrating their impacts on the overall asymmetry, the counting rate and the
percentage of multiple counts. According to the simulation, the conical
structure with detectors pointing to the sample has the highest $Q$ in both
zero field and longitudinal field. The results also show that all kinds of
structures cannot be operated under strong longitudinal fields with a strength
over 2 T. The full simulation of a $\mu$SR spectrometer can provide good
guidance for the construction of the UHAM in the upcoming upgrade of CSNS.

Instrumentation and Detectors