Fast particle trajectories and integrability in quasiaxisymmetric and quasihelical stellarators

Even if the magnetic field in a stellarator is integrable, phase-space integrability for energetic particle guiding-center trajectories is not guaranteed. Both trapped and passing particle trajectories can experience convective losses, caused by wide phase-space island formation, and diffusive losses, caused by phase-space island overlap. By locating trajectories that are closed in the angle coordinate but not necessarily closed in the radial coordinate, we can quantify the magnitude of the perturbation that results in island formation. We characterize island width and island overlap in quasihelical (QH) and quasiaxisymmetric (QA) equilibria with finite plasma pressure $\beta$ for both trapped and passing energetic particles. For trapped particles in QH, low-shear toroidal precession frequency profiles near zero result in wide island formation. While QA transit frequencies do not cross through the zero resonance, we observe that island overlap is more likely since higher shear results in the crossing of more low-order resonances.