Solenoidal ionization cooling lattices

We explore a practical approach for designing ionization cooling channels with periodic solenoidal focusing. We examine the lattice characteristics in terms of the properties of the coils and the cell geometry. The peak magnetic field in the coils is an important engineering constraint in lattice design. We examine the dependence of the peak field, momentum passband locations, and the beta function on the coil parameters. We make a systematic examination of all allowed lattice configurations taking into account the symmetry properties of the current densities and the beta function. We introduce a unique classification for comparing cooling lattice configurations. While solutions with a single coil per cell illustrate most of the effects that are important for cooling channel design, the introduction of additional coils allows more flexibility in selecting the lattice properties. We look at example solutions for the problem of the initial transverse cooling stage of a neutrino factory or muon collider and compare our results with the properties of some published cooling lattice designs. Scaling laws are used to compare solutions from different symmetry classes.