Professor Felix Parra Diaz

Abstract:

© 2016 IOP Publishing Ltd Printed in the UK.Tokamaks with up-down asymmetric poloidal cross-sections spontaneously rotate due to turbulent transport of momentum. In this work, we investigate the effect of the Shafranov shift on this intrinsic rotation, primarily by analyzing tokamaks with tilted elliptical flux surfaces. By expanding the Grad-Shafranov equation in the large aspect ratio limit we calculate the magnitude and direction of the Shafranov shift in tilted elliptical tokamaks. The results show that, while the Shafranov shift becomes updown asymmetric and depends strongly on the tilt angle of the flux surfaces, it is insensitive to the shape of the current and pressure profiles (when the geometry, total plasma current, and average pressure gradient are kept fixed). Next, local nonlinear gyrokinetic simulations of these MHD equilibria are performed with GS2, which reveal that the Shafranov shift can significantly enhance the momentum transport. However, to be consistent, the effect of β′ (i.e. the radial gradient of β) on the magnetic equilibrium was also included, which was found to significantly reduce momentum transport. Including these two competing effects broadens the rotation profile, but leaves the on-axis value of the rotation roughly unchanged. Consequently, the shape of the β profile has a significant effect on the rotation profile of an up-down asymmetric tokamak.

Abstract:

Tokamaks with up–down asymmetric poloidal cross-sections spontaneously rotate due to turbulent transport of momentum. In this work, we investigate the effect of the Shafranov shift on this intrinsic rotation, primarily by analyzing tokamaks with tilted elliptical flux surfaces. By expanding the Grad–Shafranov equation in the large aspect ratio limit we calculate the magnitude and direction of the Shafranov shift in tilted elliptical tokamaks. The results show that, while the Shafranov shift becomes up–down asymmetric and depends strongly on the tilt angle of the flux surfaces, it is insensitive to the shape of the current and pressure profiles (when the geometry, total plasma current, and average pressure gradient are kept fixed). Next, local nonlinear gyrokinetic simulations of these MHD equilibria are performed with GS2, which reveal that the Shafranov shift can significantly enhance the momentum transport. However, to be consistent, the effect of ${{\beta}^{\prime}}$ (i.e. the radial gradient of β) on the magnetic equilibrium was also included, which was found to significantly reduce momentum transport. Including these two competing effects broadens the rotation profile, but leaves the on-axis value of the rotation roughly unchanged. Consequently, the shape of the β profile has a significant effect on the rotation profile of an up–down asymmetric tokamak.

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.

Abstract:

A poloidal tilting symmetry of the local nonlinear 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.