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A 10 MeV/c $\mu^+$ beam was stopped in helium gas of a few mbar in a magnetic field of 5 T. The muon 'swarm' has been efficiently compressed from a length of 16 cm down to a few mm along the magnetic field axis (longitudinal compression) using electrostatic fields. The simulation reproduces the low energy interactions of slow muons in helium gas. Phase space compression occurs on the order of microseconds, compatible with the muon lifetime of 2 $\mu$s. This paves the way for preparation of a high quality muon beam., Comment: 5 pages, 6 figures

We report on Muonium (Mu) emission into vacuum following {\mu}+ implantation in mesoporous thin SiO2 films. We obtain a yield of Mu into vacuum of (38\pm4)% at 250 K temperature and (20\pm4)% at 100 K for 5 keV {\mu}+ implantation energy. From the implantation energy dependence of the Mu vacuum yield we determine the Mu diffusion constants in these films: D250KMu = (1.6 \pm 0.1) \times 10-4 cm2/s and D100KMu = (4.2\pm0.5)\times10-5 cm2/s. Describing the diffusion process as quantum mechanical tunneling from pore-to-pore, we reproduce the measured temperature dependence T^3/2 of the diffusion constant. We extract a potential barrier of (-0.3 \pm 0.1) eV which is consistent with our computed Mu work-function in SiO2 of [-0.3,-0.9] eV. The high Mu vacuum yield even at low temperatures represents an important step towards next generation Mu spectroscopy experiments., Comment: 5 pages, 5 Figures