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Breaking the up-down symmetry of tokamaks removes a constraint limitingintrinsic momentum transport, and hence toroidal rotation, to be small. Usinggyrokinetic theory, we study the effect of different up-down asymmetric fluxsurface shapes on the turbulent transport of momentum. This is done byperturbatively expanding the gyrokinetic equation in large flux surface shapingmode number. It is found that the momentum flux generated by shaping that lacksmirror symmetry (which is necessarily up-down asymmetric) has a power lawscaling with the shaping mode number. However, the momentum flux generated bymirror symmetric flux surface shaping (even if it is up-down asymmetric) decaysexponentially with large shaping mode number. These scalings are consistentwith nonlinear local gyrokinetic simulations and indicate that low mode numbershaping effects (e.g. elongation, triangularity) are optimal for creatingrotation. Additionally it suggests that breaking the mirror symmetry of fluxsurfaces may generate significantly more toroidal rotation.

Scaling of up-down asymmetric turbulent momentum flux with poloidal shaping mode number in tokamaks