Abstract
The condition of quasi-isodynamicity is derived to second order in the distance from the magnetic axis. We do so using a formulation of omnigenity that explicitly requires the balance between radial particle drifts at opposite bounce points of a magnetic well. This is a physically intuitive alternative to the integrated condition involving distances between bounce points, used in previous works. We investigate the appearance of topological defects in the magnetic field strength (puddles). A hallmark of quasi-isodynamic fields, the curved contour of minimum field strength, is found to be inextricably linked to these defects. Our results pave the way to construct solutions that satisfy omnigenity to a higher degree of precision and also to simultaneously consider other physical properties, like shaping and stability.
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