Symmetry-agnostic stellarators for collisionless confinement

Quasisymmetry, omnigenity and piecewise omnigenity confine trapped particles by making the bounce action independent of the field-line label. Recent optimizations produce mixed-symmetry stellarators that confine alpha particles well without them. We propose a general theory for them. From Whitham modulation theory we define iso-action, which requires only that the drift surface close and allows misalignment with flux surfaces. A solvable model supplies an exact relation between trapped segments while branch actions vary. We develop a proxy $Γ_W$ for the reach that misalignment costs.