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 paper develops a predictive formula for the electron separatrix density in tokamaks by combining regression analysis and physics-based models, validated across multiple devices and applicable to future reactors.

Contribution

It introduces a unified, predictive formula for $n_{e, ext{sep}}$ that bridges empirical regression and the two-point model, validated on data from C-Mod, AUG, and JET.

Findings

The formula estimates $n_{e, ext{sep}}$ within a factor of 1.5 across devices.

Regression and two-point model predictions show remarkable agreement.

Projections for future devices align with SOLPS simulations.

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.