Available energy of trapped electrons in Miller tokamak equilibria

TL;DR

This paper investigates the available energy (AE{}) in Miller tokamak equilibria, demonstrating its potential to predict turbulence trends and optimize device geometry for stability, especially considering effects like triangularity and shear.

Contribution

It introduces a detailed analysis of AE{} in Miller equilibria, linking it to experimental trends, and explores how geometry and gradients influence stability and turbulence predictions.

Findings

AE{} correlates with experimental turbulence trends.

Negative triangularity stabilizes by reducing AE{} in certain configurations.

Optimal device parameters depend strongly on equilibrium conditions.

Abstract

Available energy (\AE{}), which quantifies the maximum amount of thermal energy that may be liberated and converted into instabilities and turbulence, has shown to be a useful metric for predicting saturated energy fluxes in trapped-electron-mode-driven turbulence. Here, we calculate and investigate the \AE{} in the analytical tokamak equilibria introduced by \citet{Miller1998NoncircularModel}. The \AE{} of trapped electrons reproduces various trends also observed in experiments; negative shear, increasing Shafranov shift, vertical elongation, and negative triangularity can all be stabilising, as indicated by a reduction in \AE{}, although it is strongly dependent on the chosen equilibrium. Comparing \AE{} with saturated energy flux estimates from the \textsc{tglf} model, we find fairly good correspondence, showcasing that \AE{} can be useful to predict trends. We go on to investigate \AE{} and find that negative triangularity is especially beneficial in vertically elongated configurations with positive shear or low gradients. We furthermore extract a gradient threshold-like quantity from \AE{} and find that it behaves similarly to gyrokinetic gradient thresholds: it tends to increase linearly with magnetic shear, and negative triangularity leads to an especially high threshold. We next optimise the device geometry for minimal \AE{} and find that the optimum is strongly dependent on equilibrium parameters, e.g. magnetic shear or pressure gradient. Investigating the competing effects of increasing the density gradient, the pressure gradient, and decreasing the shear, we find regimes that have steep gradients yet low \AE{}, and that such a regime is inaccessible in negative-triangularity tokamaks.