Degraders and ionization cooling

Procedures are given for minimizing the increase in phase space when a beam is degraded, with and without an axial magnetic field and in a lithium lens. Optimum focusing of the beam onto the degrader is recommended. The transverse diffusion of the beam is as important as the spread in angle, so high density, low Z materials such as diamond and boron carbide are the best. For chaotic beams, focusing by increasing axial fields is suitable and the corresponding acceptance is calculated. Ionization cooling of muon beams by various materials is compared for typical cases.