Stellarator Confinement as Parametric Resonance

We present a novel intuitive description for how stellarators confine particles in a plasma. Typically, the magnetic field is plotted using a Poincaré section in a transverse plane, where we see nested flux surfaces. If we instead plot only the two components of the magnetic field within the transverse plane ( B_r(r,z) and B_z(r,z) ), the magnetic axis must be a saddle or degenerate because no other equilibrium satisfies ∇×B = 0 and ∇·B = 0. The nested flux surfaces are formed as a consequence of parametric resonance. As a magnetic field line transverses the stellarator toroidally, it experiences a rotating saddle, which stabilizes the otherwise unstable system. We analyze past and current stellarators to show that their magnetic fields exhibit parametric resonance. We hope that this new understanding allows us to use ideas from parametric resonance to help design better stellarators.