High-order map treatment of superimposed cavities, absorbers, and magnetic multipole and solenoid fields

Various modern systems for the transport and manipulation of large acceptance beams of rare and short-lived particles require the treatment of nonlinear optics of acceleration, absorption, and focusing in a combined approach. We describe a differential algebraic method for the treatment of such nonlinear dynamics via high-order transfer maps. We include the processes of scattering and straggling through absorbing material, which are inherently non-deterministic and hence not representable in the map formalism, in a split operator approach. Some examples of simulations of muon beam ionization cooling channels are provided.