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