  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.
