Direct construction of optimized stellarator shapes. Part 3. Omnigenity near the magnetic axis

Abstract

The condition of omnigenity is investigated, and applied to the near-axis expansion of Garren & Boozer ( Phys. Fluids B, vol. 3 (10), 1991 a , pp. 2805–2821). Due in part to the particular analyticity requirements of the near-axis expansion, we find that, excluding quasi-symmetric solutions, only one type of omnigenity, namely quasi-isodynamicity, can be satisfied at first order in the distance from the magnetic axis. Our construction provides a parameterization of the space of such solutions, and the cylindrical reformulation and numerical method of Landreman & Sengupta ( J. Plasma Phys. , vol. 84 (6), 2018, 905840616); Landreman et al.  ( J. Plasma Phys. , vol. 85 (1), 2019, 905850103), enables their efficient numerical construction.