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Parametric-Resonance Ionization Cooling and Reverse Emittance Exchange for Muon Colliders

Two new ideas are being developed to reduce the transverse emittance of muon beams in order to increase the luminosity of muon colliders. The first idea involves driving a 12‐integer parametric resonance in a beam line or ring such that particle motion becomes hyperbolic, where xx′=constant. With the proper phase of the resonance driving term, particles move to larger and larger x′ and smaller and smaller x at the position of a thin wedge absorber. The usual mechanism of ionization cooling reduces or constrains the excursion in x′ while the dynamics of the resonance reduces the spread of x. The second idea takes advantage of the large reduction of relative momentum spread with increasing momentum in going from a few hundred MeV/c where the beam is cooled to a few TeV/c for an energy frontier collider. In this case we can use thin wedge absorbers to exchange the transverse and longitudinal emittances to make the transverse emittance smaller. These two ideas depend on careful control of the lattice function...