A high-brightness low energy positive muon beam for future precision muon-based experiments

The muCool project aims at developing a novel device that reduces the phase space of a standard low energy positive muon beam, $\mu+(\mathrm{E} \sim$ few MeV), by a factor of ten orders of magnitude with $\mathrm{O}\left(10^{-4}\right)$ efficiency. The phase space compression is achieved by stopping a standard $\mu+$ beam in cryogenic helium gas. The stopped $\mu+$ are manipulated into a small spot using complex electric and magnetic fields in combination with gas density gradients. The muons are extracted from there into the vacuum and in a field-free region. Various aspects of this compression scheme have been demonstrated. They include the proof of the longitudinal and transversal compression, obtained first in two stages. The combination of the measured longitudinal and transversal compression stages corresponds to a phase space compression factor of $10^{10}$ with an efficiency of $10^{-3}$, as predicted. We will present the achieved results, where the combination of the transverse and longitudinal compression has been obtained, and measured using scintillators coupled to siliconphotomultipliers. We will discuss the next steps focused on studying the extraction and reacceleration scheme. The integration of such a cooling scheme into the incoming High-Intensity Muon Beam Lines at PSI, aiming at delivering up to $10^{10}$ muons/s will represent a major milestone for future precision experiments based on muons.