Demonstration of Muon-Beam Transverse Phase-Space Compression

We demonstrate efficient transverse compression of a 12.5 MeV/c muon beam stopped in a helium gas target featuring a vertical density gradient and crossed electric and magnetic fields. The muon stop distribution extending vertically over 14 mm was reduced to a 0.25 mm size (RMS) within 3.5 $\mu$s. The simulation including cross sections for low-energy $\mu^+$-$\text{He}$ elastic and charge exchange ($\mu^+\leftrightarrow $ muonium) collisions describes the measurements well. By combining the transverse compression stage with a previously demonstrated longitudinal compression stage, we can improve the phase space density of a $\mu^+ $ beam by a factor of $ 10^{10} $ with $ 10^{-3} $ efficiency.