Phase Rotation, Cooling And Acceleration Of Muon Beams: A Comparison Of   Different Approaches
  Experimental and theoretical activities are underway at CERN with the aim of examining the feasibility of a very-high-flux neutrino source. In the present scheme, a high-power proton beam (some 4 MW) bombards a target where pions are produced. The pions are collected and decay to muons under controlled optical condition. The muons are cooled and accelerated to a final energy of 50 GeV before being injected into a decay ring where they decay under well-defined conditions of energy and emittance.   We present the most challenging parts of the whole scenario, the muon capture, the ionisation-cooling and the first stage of the muon acceleration. Different schemes, their performance and the technical challenges are compared. 
G. Franchetti, S. Gilardoni, P. Gruber, K. Hanke, H. Haseroth, E. B.   Holzer, D. Kuechler, A. M. Lombardi, R. Scrivens