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Available energy (\AE{}), which quantifies the maximum amount of thermalenergy that may be liberated and converted into instabilities and turbulence,has shown to be a useful metric for predicting saturated energy fluxes intrapped-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 reproducesvarious trends also observed in experiments; negative shear, increasingShafranov shift, vertical elongation, and negative triangularity can all bestabilising, as indicated by a reduction in \AE{}, although it is stronglydependent on the chosen equilibrium. Comparing \AE{} with saturated energy fluxestimates 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 invertically elongated configurations with positive shear or low gradients. Wefurthermore extract a gradient threshold-like quantity from \AE{} and find thatit behaves similarly to gyrokinetic gradient thresholds: it tends to increaselinearly with magnetic shear, and negative triangularity leads to an especiallyhigh threshold. We next optimise the device geometry for minimal \AE{} and findthat the optimum is strongly dependent on equilibrium parameters, e.g. magneticshear or pressure gradient. Investigating the competing effects of increasingthe density gradient, the pressure gradient, and decreasing the shear, we findregimes that have steep gradients yet low \AE{}, and that such a regime isinaccessible in negative-triangularity tokamaks.

Available energy of trapped electrons in Miller tokamak equilibria