Magnetic Fields with General Omnigenity

Omnigenity is a desirable property of toroidal magnetic fields that ensures confinement of trapped particles. All of the ideal magnetohydrodynamic equilibria previously found to approximate omnigenity have been either axisymmetric, quasi-symmetric, or have poloidally closed contours of magnetic field strength $B$. However, general omnigenous equilibria are a much larger design space than these subsets with hidden symmetries. A new model is presented and employed in the DESC stellarator optimization suite to represent and discover the full parameter space of omnigenous equilibria. Examples far from quasi-symmetry with poloidally, helically, and toroidally closed $B$ contours are shown to have low neoclassical collisional transport and fast particle losses.