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

TL;DR

This paper investigates how up-down asymmetric flux surface shaping in tokamaks influences turbulent momentum transport, revealing that mirror symmetry breaking can significantly enhance intrinsic rotation, with effects scaling differently depending on the shaping mode number.

Contribution

It introduces a gyrokinetic theory analysis showing power law scaling of momentum flux with shaping mode number for mirror asymmetric shapes, and exponential decay for mirror symmetric shapes, highlighting the importance of symmetry breaking.

Findings

Mirror asymmetric shaping induces momentum flux with power law scaling.

Mirror symmetric shaping causes exponential decay of momentum flux at large mode numbers.

Low mode number shaping like elongation optimally generates rotation.

Abstract

Breaking the up-down symmetry of tokamaks removes a constraint limiting intrinsic momentum transport, and hence toroidal rotation, to be small. Using gyrokinetic theory, we study the effect of different up-down asymmetric flux surface shapes on the turbulent transport of momentum. This is done by perturbatively expanding the gyrokinetic equation in large flux surface shaping mode number. It is found that the momentum flux generated by shaping that lacks mirror symmetry (which is necessarily up-down asymmetric) has a power law scaling with the shaping mode number. However, the momentum flux generated by mirror symmetric flux surface shaping (even if it is up-down asymmetric) decays exponentially with large shaping mode number. These scalings are consistent with nonlinear local gyrokinetic simulations and indicate that low mode number shaping effects (e.g. elongation, triangularity) are optimal for creating rotation. Additionally it suggests that breaking the mirror symmetry of flux surfaces may generate significantly more toroidal rotation.