Direct Optimization of Stellarator Omnigenity from the Second Adiabatic Invariant

Stellarators offer a steady-state, disruption-free path to fusion energy but suffer from enhanced particle losses due to their three-dimensional geometry. Existing optimization methods rely on geometric proxies rather than the actual trapped-particle orbit condition. We present a differentiable framework that directly optimizes the fundamental orbit action governing particle confinement. The approach yields compact stellarator designs with excellent fast-ion confinement, finite-pressure stability, and coil compatibility, demonstrating that first-principles orbit optimization can be integrated with engineering constraints in a single computational workflow for fusion reactor design.