Optimization of the HEQ equilibrium reconstruction code for the EXL-50U and its application to plasma boundary reconstruction

This study validates the reliability and efficacy of HEQ, a lightweight, open-source Python-based free-boundary equilibrium reconstruction code, for the EXL-50U spherical tokamak (ST). To address the compact geometry of STs, the paper presents HEQ's physical models and numerical algorithms. HEQ's performance is systematically evaluated using both simulated and experimental data from EXL-50U. The results demonstrate self-consistency, robustness, and reconstruction accuracy. Comparative analyses and error tests show that HEQ stably and precisely reconstructs complex limiter and divertor configurations, confining boundary errors to within centimeters (typically 1cm). This work verifies HEQ's effectiveness as a tool for equilibrium reconstruction in spherical tokamaks and lays a foundation for its future integration into real-time control systems. These findings have important implications for both the physics analysis and engineering applications of the EXL-50U device.