A stellarator is said to be omnigeneous if all particles have vanishing average radial drifts. In omnigeneous stellarators, particles are perfectly confined in the absence of turbulence and collisions, whereas in non-omnigeneous configurations, particle can drift large radial distances. One of the consequences of omnigeneity is that the unfavourable inverse scaling with collisionality of the stellarator neoclassical fluxes disappears. In the pioneering and influential article by Cary and Shasharina (1997 Phys. Plasmas4 3323), the conditions that the magnetic field of a stellarator must satisfy to be omnigeneous are derived. However, Cary and Shasharina (1997 Phys. Plasmas4 3323) only considered omnigeneous stellarators in which all the minima of the magnetic field strength on a flux surface must have the same value. The same is assumed for the maxima. We show that omnigeneous magnetic fields can have local minima and maxima with different values. Thus, the parameter space in which omnigeneous stellarators are possible is larger than previously expected. The analysis presented in this article is only valid for orbits with vanishing radial width, and in principle it is not applicable to energetic particles. However, one would expect that improving neoclassical confinement would improve energetic particle confinement.
Piecewise Omnigenous Stellarators