Near-axis measures of quasi-isodynamic configurations

Abstract: We present a number of measures and techniques to characterise and effectively construct quasi-isodynamic stellarators within the near-axis framework, without the need to resort to the computation of global equilibria. These include measures of the reliability of the model (including aspect-ratio limits and the appearance of ripple wells), quantification of omnigeneity through $\epsilon_\mathrm{eff}$, measure and construction of MHD stabilised fields, and the sensitivity of the field to the pressure gradient. The paper presents, discusses and gives examples of all of these, for which expansions to second order are crucial. This opens the door to the exploration of how key underlying choices of the field design govern the interaction of desired properties (``trade-offs''), and provides a practical toolkit to perform efficient optimisation directly within the space of near-axis QI configurations.