Collisional alpha transport in a weakly non-quasisymmetric stellarator magnetic field

Abstract

Alpha particle confinement is a serious concern in stellarators and provides strong motivation for optimizing magnetic field configurations. In addition to the collisionless confinement of trapped alphas in stellarators, excessive collisional transport of the trapped alpha particles must be avoided while they tangentially drift due to the magnetic gradient (the $\unicode[STIX]{x1D735}B$ drift). The combination of pitch angle scatter off the background ions and the $\unicode[STIX]{x1D735}B$ drift gives rise to two narrow boundary layers in the trapped region. The first is at the trapped–passing boundary and enables the finite trapped response to be matched to the vanishing passing response of the alphas. The second layer is a region that encompasses the somewhat more deeply trapped alphas with vanishing tangential $\unicode[STIX]{x1D735}B$ drift. Away from (and between) these boundary layers, collisions are ineffective and the alpha $\unicode[STIX]{x1D735}B$ drift simply balances the small radial drift of the trapped alphas. As this balance does not vanish as the trapped–passing boundary is approached, the first collisional boundary layer is necessary and gives rise to $\surd \unicode[STIX]{x1D708}$ transport, with $\unicode[STIX]{x1D708}$ the collision frequency. The vanishing of the tangential drift results in a separate, somewhat wider boundary layer, and significantly stronger superbanana plateau transport that is independent of collisionality. The constraint imposed by the need to avoid significant energy depletion loss in the slowing down tail distribution function sets the allowed departure of a stellarator from an optimal quasisymmetric configuration.