Abstract
Muon collider luminosity depends on the number of muons in the storage ring and on the transverse size of the beams in collision. Ionization cooling as it is presently envisioned will not cool the beam sizes sufficiently well to provide adequate luminosity without large muon intensities. A new idea to combine ionization cooling with parametric resonances has been developed that will lead to beams with much smaller sizes so that high luminosity in a muon collider can be achieved with fewer muons. In the linear channel described here, 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' as they pass down the channel. 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 discuss the elementary theory of Parametric-resonance Ionization Cooling (PIC), including the need to start with a beam that has already been cooled adequately.
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