Muon capture and cooling dynamics, capture in solenoidal channels

Ionization cooling is a crucial component of either a muon collider or a neutrino factory based on muon decays. It determines the number of muons, per proton on target, that fall into the acceptance of the accelerator and storage ring. Current studies of cooling channels predominantly use simulations which track many particles, an often time consuming procedure. Analytic models [K.-J. Kim and C.X. Wang, Phys. Rev. Lett. 85(4):760-763; G. Penn and J.S. Wurtele, Phys. Rev. Lett. 85(4):764-767] using equations for the beam moments have been developed. These dynamic equations, similar to the Courant-Snyder description of quadrupole focusing, incorporate the basic aspects of ionization cooling: energy loss and scattering in material, acceleration by radio frequency (RF) cavities, and focusing in solenoid magnets. The moments method is compared to simulations and shown to provide for a reasonable prediction of the percentage of muons captured within a defined lattice acceptance, which is the figure of merit that is customarily used for evaluating the performance of cooling channels in simulations. The moments method is used to evaluate the impact on channel performance of engineering constraints and beam structure