Longitudinal ionization cooling without wedges

The emittance of a muon beam must be reduced very rapidly due to the finite lifetime of the muons. The most effective known way to accomplish this is ionization cooling. It is straightforward to reduce transverse emittance through ionization cooling, but the reducing the longitudinal emittance is more challenging. Longitudinal cooling is necessary for a muon collider, and would be helpful for a neutrino factory. The method traditionally proposed for longitudinal cooling is emittance exchange involving wedges of absorber material: the longitudinal emittance is reduced at the cost of increased transverse emittance. The larger transverse emittance can then be reduced straightforwardly. An alternative method is proposed here, which does not require wedges of material but instead makes slight modifications to the standard transverse cooling lattice. We demonstrate a lattice which is a slight modification to a standard "Super FOFO" transverse cooling lattice, which has linear eigenvalues all of which have magnitude less than one