Beam Envelope Equations for Cooling of Muons in Solenoid Fields

Muon cooling is a critical component of the proposed muon collider and neutrino factory. Previous studies of cooling channels have tracked single muons through the channel, which requires many particles for good statistics and does not lend itself to an understanding of channel dynamics. In this paper, a system of moment equations are derived which captures the major aspects of cooling: interactions with material and acceleration by radio frequency (rf) cavities. A general analysis of solenoid lattice types compares well with prior simulations and indicates new directions for study.