Existence and numerical convergence of stellarator equilibria with nested flux surfaces

Establish the existence of ideal MHD stellarator equilibria with integrable magnetic fields characterized by nested flux surfaces, and prove that numerical stellarator equilibrium computations converge to equilibria with vanishing force error under this assumption.

Background

The paper develops a nonlinear flux-tube model for ballooning-mode saturation in stellarators and shows that direct energy calculations are contaminated by force-balance errors in numerical stellarator equilibria. This sensitivity is tied to the fact that 3D equilibria with nested flux surfaces lack a general existence proof, in contrast to axisymmetric tokamak equilibria, and numerical solutions may not converge to zero force error.

To mitigate this, the authors introduce a variational method to compute flux-tube energy that is robust against force-balance errors. However, the broader mathematical question of the existence of stellarator equilibria with integrable magnetic fields (nested flux surfaces) and the guaranteed convergence of numerical solvers to force-balanced states remains unresolved, which directly impacts the reliability of nonlinear stability predictions.