Contour Optimization of High-Temperature Superconducting Toroidal Field Coils for Spherical Tokamaks

High-temperature superconducting (HTS) spherical tokamaks face stringent space constraints, particularly at the inboard side, where excessive toroidal field (TF) coil inner-leg thickness limits space for other components like the central solenoid (CS) and shielding. To resolve this conflict, this study develops a genetic algorithm (GA) framework to optimize TF coil contours, minimizing their inner-leg thickness. Rigorous enforcement of TF coil safety constraints—electromagnetic, thermal, and mechanical—and plasma performance requirements is maintained throughout. Integrated rapid semi-analytical models evaluate key parameters during optimization: magnetic fields, quench temperature rise, and Tresca stress. Applied to the Compact Tokamak Based Repetitive Fusion Reactor-1 (CTRFR-1) HTS spherical tokamak, the GA optimization reduced TF coil inner-leg thickness by 18 mm. This space reclamation enables a 26% increase in CS flux generation capacity at a engineering current density of 100 A/mm2. Crucially, finite element analysis (FEA) validated that critical thresholds were maintained: toroidal field ripple below 1%, peak loading factor (J/Jc) below 0.6, maximum quench temperature under 150 K, and peak von Mises stress under 600 MPa. This approach successfully resolves the space-performance conflict in spherical tokamaks, achieving significant CS enhancement while fully preserving TF operational safety and plasma performance. The work establishes an efficient multiphysics optimization framework for designing next-generation spherical tokamaks that fully leverage HTS capabilities within their unique geometry.