Helicity of the magnetic axes of quasi-isodynamic stellarators

In this study, we explore the influence of the helicity of the magnetic axis – defined as the self-linking number of the curve – on the quality of quasi-isodynamic stellarator-symmetric configurations constructed using the near-axis expansion method (Plunk et al., J. Plasma Phys., vol. 85, 2019, 905850602; Camacho Mata et al., J. Plasma Phys., vol. 88, 2022, 905880503). A class of magnetic axes previously unexplored within this formalism is identified when analysing the axis shape of the QIPC configuration (Subbotin et al., Nucl. Fusion, vol. 46, 2006, p. 921): the case of half-helicity (per field period). We show that these shapes are compatible with the near-axis formalism and how they can be used to construct near-axis stellarators with up to five field periods, $\def\iotaslash{{\require{HTML} \style{display: inline-block; transform: rotate(-13deg)}{\iota}}\kern-7pt{\require{HTML} \style{display: inline-block; transform: rotate(-25deg)}{-}}}{\epsilon _{\mathrm {eff}}} \approx 1.3\,\%$, and similar rotational transform to existing conventionally optimized designs, without the need of a plasma boundary optimization.