Six-dimensional muon beam cooling in a continuous, homogeneous, gaseous hydrogen absorber

The fast reduction of the six-dimensional phase space of muon beams is required for muon colliders and is also of great importance for neutrino factories based on accelerated muon beams. Ionization cooling, where all momentum components are degraded by an energy absorbing material and only the longitudinal momentum is restored by RF cavities, provides a means to quickly reduce transverse beam sizes. However, the beam momentum spread cannot be reduced by this method unless the longitudinal emittance can be transformed or exchanged into the transverse emittance. The best emittance exchange plans up to now have been accomplished by using magnets to disperse the beam along the face of a wedge-shaped absorber such that higher momentum particles pass through thicker parts of the absorber and thus suffer larger ionization energy loss. In the scheme advocated in this paper, it is noted that one can generate a magnetic channel filled with absorber where higher momentum corresponds to a longer path length and therefore larger ionization energy loss. Thus a homogeneous absorber, without any special edge shaping, can provide the desired emittance exchange. An attractive example of a cooling channel based on this principle involves the use of RF cavities filled with a continuous gaseous hydrogen absorber in a magnetic channel composed of a solenoidal field with superimposed helical transverse dipole, quadrupole, and octupole fields. The theory of this helical channel is described to support the analytical prediction of a million-fold reduction in phase space volume in a channel 150 m long.