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

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