Poloidal tilting symmetry of high order tokamak flux surface shaping in gyrokinetics

TL;DR

This paper demonstrates a poloidal tilting symmetry in high order flux surface shaping within gyrokinetics, showing that tilting high mode number effects minimally impacts tokamak transport, with implications for rotation control.

Contribution

It analytically and numerically establishes a symmetry allowing flux calculations in tilted configurations based on a single reference, advancing understanding of flux surface shaping effects.

Findings

Poloidal tilting symmetry reduces impact of high mode number shaping on transport.

Fluxes in tilted configurations can be derived from a single baseline configuration.

Symmetry distinguishes mirror symmetric and non-symmetric flux surfaces with implications for rotation.

Abstract

A poloidal tilting symmetry of the local nonlinear $\delta f$ gyrokinetic model is demonstrated analytically and verified numerically. This symmetry shows that poloidally rotating all the flux surface shaping effects with large poloidal mode number by a single tilt angle has an exponentially small effect on the transport properties of a tokamak. This is shown using a generalization of the Miller local equilibrium model to specify an arbitrary flux surface geometry. With this geometry specification we find that, when performing an expansion in large flux surface shaping mode number, the governing equations of gyrokinetics are symmetric in the poloidal tilt of the high order shaping effects. This allows us to take the fluxes from a single configuration and calculate the fluxes in any configuration that can be produced by tilting the large mode number shaping effects. This creates a distinction between tokamaks with mirror symmetric flux surfaces and tokamaks without mirror symmetry, which is expected to have important consequences for generating toroidal rotation using up-down asymmetry.