A predictive formula for the H-Mode separatrix density: Bridging regression and physics-based models across C-Mod, AUG and JET tokamaks

Understanding and predicting a core-edge integrated scenario is a major challenge on the path to building fusion power plants. A critical aspect of this challenge is predicting the electron density at the separatrix (n_e,sep​), which plays a central role in balancing energy confinement, detachment achievement, and ELM suppression.

To address this, a database of H-mode separatrix density measurements from Alcator C-Mod, ASDEX Upgrade, and JET tokamaks was assembled using a consistent analysis method across all devices. This dataset was used to derive a regression scaling law based solely on engineering parameters, and the results were compared to predictions from the two-point model. The agreement found is notable: both the regression and model provide similar parameter dependencies and tokamak-specific multiplicative constants. In particular, regression analysis reveals that n_e,sep ∝ p_0,div^0.2 a_geo^-0.5 I_p^0.0. Thus, increasing the divertor neutral pressure (p_0,div) leads to higher n_e,sep​, while a larger plasma minor radius (a_geo) reduces it. Notably, the plasma current (I_p) has a negligible impact on n_e,sep​.

Building on this agreement, a predictive formula that combines the regression dependencies and the two-point model multiplicative constant is proposed. This formula is able to estimate n_e,sep​ across the three machines within a factor of 1.5—a level of fidelity previously unmatched in the literature—paving the way for core-edge integrated scenario prediction.