A family of quasi-axisymmetric stellarators with varied rotational transform

Abstract: We apply a continuation method to recently optimized stellarator equilibria with excellent quasi-axisymmetry (QA) 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 (ITG) simulations, and the ion heat flux in corresponding nonlinear simulations. We find values of two-term quasisymmetry error comparable to or lower than the similar Landreman-Paul (Phys. Rev. Lett. 128, 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 quasisymmetry 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 $2.8\,\mathrm{m}$ to $3.3\,\mathrm{m}$ when the configuration is scaled up to reactor size. 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 $\iota$, 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 $\iota$. Sufficiently large positive shear is destabilizing. This is reflected both in linear growth rates and nonlinear heat fluxes.