Parametric-resonance ionization cooling for muon beams in the twin helix channel

Muon colliders have been proposed for the next generation of particle accelerators that study high-energy physics at the energy and intensity frontiers. This dissertation examines muon cooling techniques, a critical aspect to the feasibility of these proposed machines. Muon cooling reduces the emittance of muon beams, a measurement of the phase space volume of the beam. Reducing emittance improves the luminosity and physics reach of these machines. Ionization cooling, the basic method for reducing muon beam emittance, is detailed, as well as various cooling channel proposals implementing this method. One particular implementation of ionization cooling is parametric-resonance ionization cooling (PIC). PIC is proposed as the final 6D cooling stage of a high-luminosity muon collider. It can also be used for final cooling in a muon-based Higgs factory. Adding the cooling methods of PIC offers the potential to reduce emittance beyond that achievable with ionization cooling alone. PIC theory is detailed and implemented in a magnetic channel based on the superposition of two helical dipole magnetic harmonics identical in gradient, period, and phase but with opposite helicities. This channel, known as the twin helix, is simulated so that the effects of PIC can be demonstrated.