Geant4 simulation of the PSI LEM beam line: energy loss and muonium formation in thin foils and the impact of unmoderated muons on the $\mu$SR spectrometer

TL;DR

This paper uses Geant4 simulations to analyze muon energy loss and muonium formation in thin foils within the PSI low-energy muon spectrometer, highlighting the impact of unmoderated muons on experimental measurements.

Contribution

The study models muonium formation and energy losses in the start detector, revealing the importance of unmoderated muons in accurately reproducing experimental data.

Findings

Simulated and measured time-of-flight spectra agree when unmoderated muons are included.

Energy losses and muonium formation significantly affect muon beam parameters.

Beam size and asymmetry are sensitive to line settings and sample geometry.

Abstract

The PSI low-energy $\mu$SR spectrometer is an instrument dedicated to muon spin rotation and relaxation measurements. Knowledge of the muon beam parameters such as spatial, kinetic energy and arrival-time distributions at the sample position are important ingredients to analyze the $\mu$SR spectra. We present here the measured energy losses in the thin carbon foil of the muon start detector deduced from time-of-flight measurements. Muonium formation in the thin carbon foil (10 nm thickness) of the muon start detector also affect the measurable decay asymmetry and therefore need to be accounted for. Muonium formation and energy losses in the start detector, whose relevance increase with decreasing muon implantation energy ($<10$ keV), have been implemented in Geant4 Monte Carlo simulation to reproduce the measured time-of-flight spectra. Simulated and measured time-of-flight and beam spot agrees only if a small fraction of so called "unmoderated" muons which contaminate the mono-energetic muon beam of the $\mu$SR spectrometer is introduced. Moreover the sensitivity of the beam size and related upstream-downstream asymmetry for a specially shaped "nose" sample plate has been studied for various beam line settings, which is of relevance for the study of thermal muonium emission into vacuum from mesoporous silica at cryogenic temperatures.