Available energy of trapped electrons in Miller tokamak equilibria

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 Miller et al. (Phys. Plasmas, vol. 5, issue, 4, 1998, pp. 973–978). 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 TGLF (trapped gyro-Landau fluid) 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. Furthermore, we 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, for example, 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.