On the curvature-driven ion-temperature-gradient instability and its available energy

In this paper, we calculate the available energy, an upper bound on the thermal energy released that may in turn drive turbulence, due to an ion-temperature-gradient instability driven by curvature in the presence of adiabatic electrons. This is done by choosing an appropriate set of invariants that neglect parallel dynamics, whilst keeping the density profile fixed. Conditions for vanishing available energy are derived and are found to be qualitatively similar to conditions for stability derived from gyrokinetic theory, including strong stabilisation if the ratio of the temperature and density gradient, $\mathrm{d} \ln T / \mathrm{d} \ln n =\eta$ , falls in the range $0 \leqslant \eta \leqslant 2/3$ . To assess the utility of the available energy, a database consisting of $6 \times 10^4$ local gyrokinetic simulations in randomly sampled tokamak geometries is constructed. Using this database and a similar one sampling stellarators (Landreman et al. 2025 J. Plasma Phys. vol. 91 , E120), the available energy is shown to exhibit correlation with the ion energy flux as long as the parallel dynamics is unimportant. Overall it is found that available energy is good at predicting the energy flux variability due to the gradients in density and temperature, but performs worse when it comes to predicting its variability arising from geometry.