Linear design of combined-function ionization cooling lattices

Ionization cooling lattices simultaneously require small beta-functions at the absorber and large energy acceptances to be effective. Simultaneously achieving these goals as well as having a good dynamic aperture requires that the lattice be relatively compact. If one wishes to avoid solenoids, one choice for creating such a lattice is to use combined-function magnets. These magnets can simultaneously focus in both planes, allowing one to achieve a low beta in both planes with a minimum number of magnets. In this paper we explore the design of lattices which contain only combined-function bending magnets using a thin-lens approximation, showing how to optimally achieve the requirements for muon cooling.