A novel objective function minimizes resonant trapped energetic particle losses in stellarators

Abstract

Near-omnigenous stellarators are susceptible to energetic particle (EP) losses due to resonances between trapped EPs and non-omnigenous perturbations to the magnetic field. Existing bounce-averaged objectives such as ${\Gamma}_c$, ${\Gamma}_{\delta}$ , and ${\Gamma}_{\alpha}$ target the non-resonant misalignment of drift and flux surfaces, but they do not capture resonant convective or diffusive motion. We develop a discrete map theory for the bounce points of trapped EPs in near-omnigenous fields, in which phase-space islands form due to resonance between the precession and bounce frequencies. We introduce ${\Delta}_{res}$, a differentiable, bounce-averaged objective function that penalizes the widths of these islands, promoting phase-space integrability. Optimizing a quasi-axisymmetric configuration using ${\Delta}_{res}$ combined with a two-term quasi-symmetry objective yields a factor-of-four improvement in EP confinement by displacing low-order resonances and forming EP transport barriers. ${\Delta}_{res}$ is a powerful tool to combat both resonant convective and diffusive losses in power plant-relevant stellarators.