A family of quasi-axisymmetric stellarators with varied rotational transform

We apply a continuation method to recently optimized stellarator equilibria with excellent quasi-axisymmetry to generate new equilibria with a wide range of rotational transform profiles. Using these equilibria, we investigate how the rotational transform affects fast-particle confinement, the maximum coil–plasma distance, the maximum growth rate in linear gyrokinetic ion-temperature gradient simulations and the ion heat flux in corresponding nonlinear simulations. We find values of two-term quasi-symmetry error comparable to or lower than those of the similar Landreman–Paul ( Phys. Rev. Lett. , vol. 128, 2022, 035001) configuration for values of the mean rotational transform $\bar {\iota }$ between $0.12$ and $0.75$ . The fast-particle confinement improves with $\bar {\iota }$ until $\bar {\iota } = 0.73$ , at which point the degradation in quasi-symmetry outweighs the benefits of further increasing $\bar {\iota }$ . The required coil–plasma distance only varies by about ${\pm }10\,\%$ for the configurations under consideration, and is between $2.8$ and $3.3\ \mathrm {m}$ when the configuration is scaled up to reactor size (minor radius $a=1.7\ \mathrm {m}$ and volume-averaged magnetic field strength of $5.86\ \mathrm {T}$ ). The maximum growth rate from linear gyrokinetic simulations increases with $\bar {\iota }$ , but also shifts towards higher $k_y$ values. The maximum linear growth rate is sensitive to the choice of flux tube at rational $\bar {\iota }$ , but this can be compensated for by taking the maximum over several flux tubes. The corresponding ion heat fluxes from nonlinear simulations display a non-monotonic relation to $\bar {\iota }$ . Sufficiently large positive shear is destabilizing. This is reflected in both linear growth rates and nonlinear heat fluxes.