Minimizing trapped energetic particle resonances in stellarators via equilibrium optimization

Energetic particle (EP) confinement is essential to stellarator power plant design to provide plasma heating from fusion and minimize heat flux on the device walls. Due to low collisionality, EP guiding center motion can be modeled as a single-particle Hamiltonian system. These systems suffer from confinement losses due to the opening of phase-space islands that occur when a rational value of the ratio between precession and bounce frequencies experiences a corresponding resonant perturbation [1]. The low-order resonances are at highest risk for opening large phase-space islands and chaotic regions that can lead to radial transport [2]. Prior stellarator optimization efforts do not include objectives for avoiding these low-order resonances. This study first characterizes trapped EP resonances for quasiaxisymmetric, quasihelical, and quasi-isodynamic equilibria using particle tracing in SIMSOPT [3] and bounce integration in DESC [4]. Equivalence between these two methods was confirmed at low EP energies. DESC was then used for stellarator equilibrium optimization with a novel objective configured to avoid low-order EP bounce motion resonances. Optimized equilibria were compared with corresponding optimizations using the γ_c objective and evaluated for performance.

[1] Imbert-Gerard, L. M., Paul, et al. SIAM 2024.

[2] Chambliss, A., Paul, E., et al. Journal of Plasma Physics 2025.

[3] M Landreman, B Medasani, et al. J. Open Source Software 2021.

[4] Dudt, D. & Kolemen, E. Physics of Plasmas 2020.