README.md

2026KLJH

Codex/ChatGPT (July 2026)

Summary

The study tests whether the minimum magnetic-gradient scale length $\min(L_{\nabla B})$ on a stellarator's last closed flux surface predicts engineering difficulty for discrete filamentary coils. Across 3,027 single-stage QUASR configurations, $\min(L_{\nabla B})$ correlates with minimum coil--surface distance, and its location is usually near the closest coil point; the second-gradient metric $L_{\nabla\nabla B}$ is even more spatially correlated. The authors then optimize 42 quasihelically symmetric equilibria over $\min(L_{\nabla B})$ and use continuation to design progressively longer coils. Larger scale length generally permits greater coil--surface and coil--coil separation and lower normal-field error, provided enough coil length is available. At short coil lengths the relationship breaks down in a high-ripple regime. Alpha-particle tracing exposes a trade-off: increasing $\min(L_{\nabla B})$ reduces coil-ripple loss but worsens quasisymmetry, producing an intermediate optimum. A third ensemble of finite-$\beta$ random-boundary equilibria retains moderate correlations, showing robustness but also that scale length alone cannot determine coil distance; its location and global boundary shape matter.

Contributions

1. Established filament-coil correlations between $\min(L_{\nabla B})$ and coil--plasma spacing across three datasets.
2. Quantified spatial coincidence between magnetic-scale-length minima and closest coil locations in QUASR.
3. Demonstrated improvement through staged equilibrium optimization and continuation-based coil design.
4. Identified insufficient coil length and high ripple as a regime where the proxy fails.
5. Exposed the confinement trade-off between quasisymmetry error and coil-ripple reduction.