《Table 2 Detection efficiency and acceptance of the beam with different sample sizes》

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《Conceptual design and update of the 128-channel μSR prototype spectrometer based on musrSim》

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Simulations of scanning the asymmetry along the z-axis were performed with the detector length of 10 mm（radius of the detector ring=150 mm or 90 mm）to verify the relation between the asymmetry and location.For these specific simulations，107muons were simulated to suppress statistical fluctuations.Ideally，a virtual detector with zero length can exactly detect the asymmetry in each point along the z-axis according to Eq.（5）.However，we cannot determine the energy deposition used to confirm whether the deposited event is a muon decay event.A detector with a length of 10 mm is sufficiently small to detect the asymmetry in its location.For the two-ring structure，each ring has 64 scintillators（see Table 1）.The width of each segment is 13.5 mm，resulting in the detector ring with a radius of 150 mm.For the four-ring structure，each ring has32 detectors.Similar to the fly-past device in EMU，the radius of the cruciform（see Fig.1）is approximately80 mm.Detectors should be placed outside the cruciform or degraders.Therefore，the minimum radius of the detector ring that can be chosen is 90 mm.Figure 8 shows scanning of the asymmetry using degraders with different thicknesses along the z-axis in the ZF.Theoretical results were calculated using Eq.（5）.The simulation results in Fig.8 are consistent with their corresponding theoretical ones.The space occupied by the spectrometer is in the region（-350，350）mm along the z-axis.In this region，detectors that use thicker degraders can achieve higher asymmetries.When detectors are further away from the sample，higher asymmetries can be achieved but the asymmetry increases slowly after z=150 mm.Comparing detector rings with different radii but the same degrader thickness，asymmetries increase quickly with a smaller radius（90 mm）.Furthermore，detectors with smaller radius can achieve higher asymmetries in the interested region along the z-axis.To achieve high asymmetries，the tworing spectrometer should be updated to a four-ring one.According to the analysis，a detector ring can be placed after 150 mm to achieve the highest asymmetry and another detector ring can be mounted before 150 mm to cover more solid angle for the four-ring spectrometer.Therefore，the outer detector ring with a length of 100 mm is set up after 150 mm.To ensure that the inner and outer rings have the same covered solid angle，the length of the inner ring is set to 40 mm.