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

TL;DR

This paper investigates omnigenity conditions near the magnetic axis in stellarators, revealing that only quasi-isodynamic solutions satisfy these conditions at first order, and provides a method for their efficient numerical construction.

Contribution

It characterizes the space of omnigenous stellarator solutions near the magnetic axis and introduces a numerical method for constructing quasi-isodynamic configurations.

Findings

Only quasi-isodynamic solutions satisfy omnigenity near the axis at first order.

Provides a parameterization of omnigenous solutions near the magnetic axis.

Enables efficient numerical construction of these solutions.

Abstract

The condition of omnigenity is investigated, and applied to the near-axis expansion of Garren and Boozer (1991a). 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 and Sengupta (2018); Landreman et al. (2019), enables their efficient numerical construction.