  Muon colliders have been proposed for the next generation of particle
accelerators that study high-energy physics at the energy and intensity
frontiers. In this paper we study a possible implementation of muon ionization
cooling, Parametric-resonance Ionization Cooling (PIC), in the twin helix
channel. The resonant cooling method of PIC offers the potential to reduce
emittance beyond that achievable with ionization cooling with ordinary magnetic
focusing. We examine optimization of a variety of parameters, study the
nonlinear dynamics in the twin helix channel and consider possible methods of
aberration correction.
