Phase space compression of a positive muon beam in two spatial dimensions

We present the first demonstration of simultaneous phase space compression in two spatial dimensions of a positive muon beam, the first stage of the novel high-brightness muon beam under development by the muCool collaboration at the Paul Scherrer Institute. The keV-energy, sub-mm size beam would enable a factor 10$^5$ improvement in brightness for precision muSR, and atomic and particle physics measurements with positive muons. This compression is achieved within a cryogenic helium gas target with a strong density gradient, placed in a homogeneous magnetic field, under the influence of a complex electric field. In the next phase, the muon beam will be extracted into vacuum.