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

TL;DR

This work addresses predicting the H-mode separatrix density $n_{e,\mathrm{sep}}$ to aid core–edge integration in tokamaks. By assembling a cross-machine database from C-Mod, AUG, and JET with a uniform analysis, the authors derive a regression-based scaling and compare it to a physics-grounded two-point model, finding strikingly similar parameter dependencies and device-specific constants. Building on this agreement, they formulate a fully predictive expression that combines regression-like dependencies with the two-point constant, achieving predictions within a factor of $1.5$ for three devices and aligning with SOLPS-ITER simulations for ITER, SPARC, DTT, and JT60-SA. The study also outlines limitations related to divertor geometry and impurity seeding, and suggests future work to extend the approach to more complex physics while preserving the simplicity of reduced models.

Abstract

The electron density at the separatrix ($n_{e,\mathrm{sep}}$) plays a central role in balancing energy confinement, detachment achievement, and ELM suppression in tokamaks, thereby influencing core-edge integration. To study what determines this key parameter, a database of H-mode separatrix density measurements from Alcator C-Mod, ASDEX Upgrade, and JET tokamaks has been assembled using a consistent analysis method across all devices. This dataset is used to derive a regression scaling expression based solely on engineering parameters, and the results are compared to predictions from the two-point model. The agreement found is remarkable: both the regression and model provide similar parameter dependencies and tokamak-specific multiplicative constants. Building on this agreement, a fully predictive formula that combines the regression dependencies and the two-point model multiplicative constant is proposed. This formula is able to estimate $n_{e,\mathrm{sep}}$ across the three machines within a factor of 1.5, and provides projections to next-step devices (ITER, SPARC, DTT, JT-60SA and COMPASS-U) that are in agreement with available SOLPS simulations.

Figures (7)

• Figure 1: On-axis toroidal magnetic field vs. plasma current (a) and power crossing the separatrix vs. edge safety factor (b) for the analyzed C-Mod (circles), AUG (squares) and JET (crosses) datasets.
• Figure 2: Correlation matrix of the variables used for the regression analysis.
• Figure 3: Experimental $n_{e,\mathrm{sep}}$ values against those predicted by Eq. \ref{['eq:nsepsc']} for C-Mod (gray circles), AUG (red squares) and JET (blue crosses).
• Figure 4: Experimental $n_{e,\mathrm{sep}}$ values normalized by the scaling expression in Eq. \ref{['eq:nsepsc']}, excluding the dependence on the parameter shown on the x-axis: $p_{0,\mathrm{div}}$ in (a) and $a_{\mathrm{geo}}$ in (b). The residual scaling dependence on $p_{0,\mathrm{div}}$ and $a_{\mathrm{geo}}$ is plotted as a dashed line. Results from SOLPS gas scan simulations of an AUG H-mode plasma are shown in light red diamonds in panel (a).
• Figure 5: Experimental $n_{e,\mathrm{sep}}$ values against those given by the predictive formula (Eq. \ref{['eq:nsep_mod']}) for C-Mod (gray circles), AUG (red squares) and JET (blue crosses).