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Introducing up-down asymmetry into the tokamak magnetic equilibria appears tobe a feasible method to drive fast intrinsic toroidal rotation in future largedevices. In this paper we investigate how the intrinsic momentum transportgenerated by up-down asymmetric shaping scales with the mode number of theshaping effects. Making use the gyrokinetic tilting symmetry (Ball et al (2016)Plasma Phys. Control. Fusion 58 045023), we study the effect of envelopescreated by the beating of different high-order shaping effects. This revealsthat the presence of an envelope can change the scaling of the momentum fluxfrom exponentially small in the limit of large shaping mode number to justpolynomially small. This enhancement of the momentum transport requires theenvelope to be both up-down asymmetric and have a spatial scale on the order ofthe minor radius.

Turbulent momentum transport due to the beating between different tokamak flux surface shaping effects