Using Turbulent Saturation Physics to Optimize Stellarator Confinement*

The goal of this work is to find mechanisms to improve stellarator confinement by optimally using 3D shaping to affect turbulent saturation levels.   An analytic theory for saturation of ion temperature gradient driven turbulence is developed for general 3D equilibrium [1].  The theory relies on the premise that coupling of linear instabilities to damped eigenmodes at comparable wave number is the dominant saturation process.  The dominant nonlinear energy transfer from unstable to damped modes is enabled by a three-wave interaction, where the third mode depends upon the properties of the 3D shaping.  The theory identifies an important metric, the produce of a turbulent correlation lifetime and a geometric coupling coefficient, which quantifies nonlinear energy transfer.  Large values of this metric correspond to small values of ITG-induced turbulent transport.  

As an application of the theory, the nonlinear transfer metrics are quantified for two classes of quasi-symmetric stellarator configurations.  While nonlinear transfer physics in quasi-axisymmetry is largely determined by three-wave interactions involving zonal flows, in quasi-helically symmetry (QHS) there are additional nonlinear energy transfer channels involving nearly marginally stable eigenmodes.   The reason for this difference is primarily geometric. QHS has relatively short connection lengths which enables vigorous non-zonal energy transfer.   This suggests that QHS has an inherent advantage with regard to turbulent saturation physics.  The nonlinear energy transfer metric is being incorporated into the stellarator optimization schemes to produce configurations with reduced turbulent transport.    Quantification of the turbulent transport improvement for the optimized configurations is provided by nonlinear gyrokinetic simulations using GENE.

[1] C. C. Hegna et al, Phys. Plasm 25, 022511 (2018).