The maximum-J property in quasi-isodynamic stellarators

Quasi-isodynamic stellarators, one of the leading concepts of optimised stellarators, tend to exhibit a favourable average magnetic curvature for trapped-particles when the plasma pressure is sufficiently high. This so-called maximum-J-property has several positive implications for plasma performance, such as good fast-particle confinement and suppression of trapped-particle instabilities, which make this concept highly attractive. We show that the maximum-J-property can be achieved to arbitrary accuracy (but not exactly) in quasi-isodynamic stellarators, even at zero plasma pressure, unlike in quasisymmetric stellarators (or tokamaks). This requires of a carefully curated field, whose properties we study through a new asymptotic expansion around the magnetic axis.