Six-dimensional muon beam cooling using a homogeneous absorber: Concepts, beam dynamics, cooling decrements, and equilibrium emittances in a helical dipole channel

The fast reduction of the six-dimensional phase space of muon beams is an essential requirement for muon colliders and 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 energy spread cannot be reduced by this method unless the longitudinal emittance can be transformed or exchanged into the transverse emittance. Emittance exchange plans until 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, a special magnetic channel designed such that higher momentum corresponds to a longer path length, and therefore larger ionization energy loss, provides the desired emittance exchange in a homogeneous absorber without special edge shaping. Normal-conducting rf cavities imbedded in the magnetic field regenerate the energy lost in the absorber. One very attractive example of a cooling channel based on this principle uses a series of high-gradient rf cavities filled with dense hydrogen gas, where the cavities are in a magnetic channel composed of a solenoidal field with superimposed helical transverse dipole and quadrupole fields. In this scheme, the energy loss, the rf energy regeneration, the emittance exchange, and the transverse cooling happen simultaneously. The theory of this helical channel is described in some detail to support the analytical prediction of almost a factor of 106 reduction in six-dimensional phase space volume in a channel about 56 m long. Equations describing the particle beam dynamics are derived and beam stability conditions are explored. Equations describing six-dimensional cooling in this channel are also derived, including explicit expressions for cooling decrements and equilibrium emittances.