Parametric-resonance Ionization Cooling of Muon Beams
  Cooling of muon beams for the next-generation lepton collider is necessary to achieve its higher luminosity with fewer muons. In this paper we present an idea to combine ionization cooling with parametric resonances that is expected to lead to muon beams with much smaller transverse sizes. We describe a linear magnetic transport channel where a half integer resonance is induced such that the normal elliptical motion of particles in x-x' phase space becomes hyperbolic, with particles moving to smaller x and larger x' at the channel focal points. Thin absorbers placed at the focal points of the channel then cool the angular divergence of the beam by the usual ionization cooling mechanism where each absorber is followed by RF cavities. We present a theory of Parametric-resonance Ionization Cooling (PIC), starting with the basic principles in the context of a simple quadrupole-focused beam line. Then we discuss detuning caused by chromatic, spherical, and non-linear field aberrations and the techniques needed to reduce the detuning. We discuss the requirement that PIC be accompanied by emittance exchange in order to keep the momentum spread sufficiently small. Examples of PIC channel are presented, along with computer simulations aimed at practical implementation of the described theoretical concept. 
Ya.S. Derbenev, V.S. Morozov, A. Afanasev, K.B. Beard, R. Johnson, B.   Erdelyi, J.A. Maloney
physics.acc-ph hep-ex