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2026PJCD

Codex/ChatGPT (July 2026)

Summary

This paper applies deflation to find physically distinct stellarator equilibria and optimization minima from a common initial guess. Known solutions are excluded either by multiplying equilibrium residuals by inverse-distance barriers or by adding nonlinear distance constraints to optimization. In DESC, repeated deflation finds 25 first-order near-axis-constrained quasi-axisymmetric equilibria sharing the same magnetic axis and on-axis transform but differing in shear, outer geometry, and magnetic-well behavior. It also recovers a helical-core branch from an axisymmetric starting point without prescribing the helical perturbation. For stage-one quasi-helical optimization, 18 of 30 runs pass transform and force-balance filters, although coordinate and toroidal-shift degeneracies expose limits of coefficient-space distance. A proposed sum-reduction operator prevents multiple deflations from unintentionally shrinking earlier exclusion regions. Stage-two optimization then finds six coil sets, five satisfying the stated engineering and normal-field constraints. The results establish deflation as a practical landscape-exploration tool while motivating more invariant distance metrics and robust least-squares formulations.

Contributions

  1. Adapted residual and constraint forms of deflation to non-axisymmetric MHD equilibrium and stellarator optimization.
  2. Found 25 near-axis-constrained quasi-axisymmetric equilibria with shared core constraints but diverse global geometry and profiles.
  3. Recovered a helical-core equilibrium from an axisymmetric initial state without a prescient helical perturbation.
  4. Produced multiple attractive stage-one quasi-helical equilibria and diagnosed coordinate-representation and toroidal-shift degeneracies.
  5. Introduced sum-reduction multiple deflation and used it to obtain several distinct, mostly feasible stage-two coil sets.