| Summary: | In the past few years, the concept of a high intensity muon storage ring has been pursued as an option for the next generation neutrino source. To produce the high intensity muon beam needed for the successful operation of a neutrino source, on the order of 10^{20} muon decays per year, the phase space occupied by the muon beam must be significantly reduced before the beam is accelerated. The initial transverse emittance of the muon beam before acceleration is assumed to be 9π mm rad. Because of the time limitation imposed by the muon lifetime, the technique employed to accomplish the desired emittance reduction is ionization cooling. In this paper we present two ionization cooling lattice designs, which use solenoidal focusing elements and liquid hydrogen absorbers to reduce the muon beam phase space. We discuss the design concepts and engineering constraints for these lattices and present simulation results obtained using a detailed tracing code with a complete model of muon-matter interactions. The reduction in transverse emittance is approximately a factor of 5. This result is within a factor of 2 of the total cooling requirements for a successful neutrino factory design and within a factor of 1.4 of the requirements for the main cooling section specified in the conceptual design of this machine.
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