Collisional alpha transport in a weakly rippled magnetic field

Abstract

To properly treat the collisional transport of alpha particles due to a weakly rippled tokamak magnetic field the tangential magnetic drift due to its gradient (the $\unicode[STIX]{x1D735}B$ drift) and pitch angle scatter must be retained. Their combination gives rise to a narrow boundary layer in which collisions are able to match the finite trapped response to the ripple to the vanishing passing response of the alphas. Away from this boundary layer collisions are ineffective. There the $\unicode[STIX]{x1D735}B$ drift of the alphas balances the small radial drift of the trapped alphas caused by the ripple. A narrow collisional boundary layer is necessary since this balance does not allow the perturbed trapped alpha distribution function to vanish at the trapped–passing boundary. The solution of this boundary layer problem allows the alpha transport fluxes to be evaluated in a self-consistent manner to obtain meaningful constraints on the ripple allowable in a tokamak fusion reactor. A key result of the analysis is that collisional alpha losses are insensitive to the ripple near the equatorial plane on the outboard side where the ripple is high. As the high field side ripple is normally very small, collisional $\sqrt{\unicode[STIX]{x1D708}}$ ripple transport is unlikely to be a serious issue.