Stored energy and beta measurements by diamagnetic flux in the HL-3 tokamak

The beta limit is a critical constraint for advanced high-performance operation in the HL-3 tokamak. Diamagnetic flux measurements provide essential information for beta (β) and plasma stored energy (W_dia). A diamagnetic concentric loop system has been designed and developed on the HL-3 tokamak to measure these parameters. The system consists of two concentric poloidal loops enclosing the plasma column, with a 5% area difference, and an integrator with a constant time of 0.5 ms. By employing a bridge circuit, the design simplifies the integration scheme and effectively suppresses drift, achieving an average measurement accuracy of ±3.5% for the diamagnetic flux (Φ_dia). For non-circular cross-section plasmas, W_dia is calculated using standard expressions that incorporate plasma elongation ratio ( \kappa ), volume (V), and poloidal cross-sectional circumference (L_c). When real-time data for these parameters are unavailable, an appropriate \kappa must be selected, especially for normalized beta (β_N). Experimental comparisons between W_dia and β_N obtained from diamagnetic measurements and equilibrium reconstructions show consistent temporal evolution. Analysis further indicates that the beta limit in HL-3 exceeds four times the internal inductance (\ell _\texti). This system enables detailed studies of rapid variations in stored energy and beta, including those associated with edge-localized modes and neoclassical tearing modes.