Available energy (Æ), 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 Æ in the analytical tokamak equilibria introduced by Miller et al. (Phys. Plasmas, vol. 5, issue, 4, 1998, pp. 973–978). The Æ 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 Æ, although it is strongly dependent on the chosen equilibrium. Comparing Æ with saturated energy flux estimates from the TGLF (trapped gyro-Landau fluid) model, we find fairly good correspondence, showcasing that Æ can be useful to predict trends. We go on to investigate Æ 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 Æ 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 Æ 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 Æ, and that such a regime is inaccessible in negative-triangularity tokamaks.

The magnetohydrodynamic stability of plasmas with an anisotropic pressure component is analysed for a low magnetic field configuration of the large helical device. Magnetic equilibria are calculated by the anisotropic Neumann inverse moments equilibrium code, an extension of the three-dimensional variational moments equilibrium code. A modified version of the bi-Maxwellian is used to model the anisotropic particle velocity distribution. Magnetohydrodynamic stability calculations for the $n=1$ mode family are carried out by TERPSICHORE, which has been expanded by the Kruskal–Oberman energy principle. For on-axis particle deposition, the growth rate and plasma displacement show that the parallel dominant plasmas are significantly more stable than isotropic or perpendicular dominant plasmas. For off-axis particle deposition, the growth rate and the Mercier criterion in the peripheral region $\rho =0.9$, show that low field (LF) deposition perpendicular dominant plasmas are most unstable. For the most realistic off-axis deposition profile, it is found that parallel dominant plasmas are most stable for LF deposition, while perpendicular dominant plasmas are most stable for high field deposition. We conclude that, under low magnetic field conditions in the large helical device, tangential neutral beam injection heating has a stabilising influence on the plasma.

A collisionless plasma possesses a certain amount of ‘available energy’, which is that part of the thermal energy that can be converted into kinetic energy of plasma motion and electromagnetic fluctuations. In this paper we present a calculation of the available energy carried by trapped electrons in a slender non-omnigenous flux tube of plasma. This quantity is compared with gyrokinetic simulations of the nonlinear saturated radial energy flux resulting from turbulence driven by collisionless trapped-electron modes in various stellarators and a tokamak. The numerical calculation of available energy is fast and shows a strong correlation with the turbulent energy fluxes found in the gyrokinetic simulations. Indeed, the energy flux is found to be proportional to the available energy to the power of approximately $3/2$, which is what one would expect from a simple argument. We furthermore investigate how available energy is distributed across different bounce wells, and it is found that deeply trapped electrons typically contribute most to the available energy. Finally, we investigate the dependence of available energy on gradient strength, and we find important differences between weakly and strongly driven regimes for stellarators and tokamaks.

In tokamaks and neoclassically optimised stellarators, like Wendelstein 7-X (W7-X) and the Helically Symmetric Experiment, turbulent transport is expected to be the dominant transport mechanism. Among the electrostatic instabilities that drive turbulence, the trapped-electron mode (TEM) has been shown both analytically and in simulations to be absent over large ranges of parameter space in quasi-isodynamic stellarator configurations with the maximum-$J$ property. It has been proposed that the reduction of the linear TEM growth rate in such configurations may lead to the passing-electron-driven universal instability, which is often subdominant to the TEM, becoming the fastest-growing instability over some range of parameter space. Here, we show through gyrokinetic simulations using the Gene code, that the universal instability is dominant in a variety of stellarator geometries over a range of parameter space typically occupied by the TEM, but most consequentially in devices which possess beneficial TEM stability properties like W7-X, which locally satisfies the maximum-$J$ property for deeply trapped particles in the regions of worst curvature. We find that the universal instability exists at long perpendicular wavelengths and, as a result, dominates the potential fluctuation amplitude in nonlinear simulations. In W7-X, universal modes are found to differ in parallel mode structure from trapped-particle modes, which may impact turbulence localisation in experiments.

In fusion devices, the geometry of the confining magnetic field has a significant impact on the instabilities that drive turbulent heat loss. This is especially true of stellarators, where the density-gradient-driven branch of the ‘trapped electron mode’ (TEM) is predicted to be linearly stable if the magnetic field has the maximum-J property, as is very approximately the case in certain magnetic configurations of the Wendelstein 7-X experiment (W7-X). Here we show, using both analytical theory and simulations, that the benefits of the optimisation of W7-X also serve to mitigate ion-temperature-gradient (ITG) modes as long as an electron density gradient is present. We find that the effect indeed carries over to nonlinear numerical simulations, where W7-X has low TEM-driven transport, and reduced ITG turbulence in the presence of a density gradient, giving theoretical support for the existence of enhanced confinement regimes, in the presence of strong density gradients (e.g. hydrogen pellet or neutral beam injection).