Optimization of Nonlinear Turbulence in Stellarators

Turbulent transport is one of the major limiting factors on performance for stellarators as it determines the rates of heat and particle loss of the plasma. However, directly optimizing for reduced turbulence is usually very challenging due to the large computational cost of typical turbulence simulations. While there have been works minimizing linear/quasi-linear metrics of turbulence [1], [2], linear theory may not be able to correctly predict nonlinear turbulence physics [3]. In this work, we directly optimize stellarators for reduced nonlinear turbulent heat fluxes. In order to run nonlinear simulations inside the optimization loop, we use the new GPU-native gyrokinetic code GX [4], which utilizes pseudo-spectral methods in velocity space. GPU acceleration combined with flexible velocity resolution allows for nonlinear GX simulations that only take minutes to run. The optimization is performed using the stellarator equilibrium and optimization code DESC [5] and employs stochastic optimization methods to robustly handle the noisy heat fluxes from GX. We show different examples of optimized equilibria that have both reduced heat fluxes along with good quasisymmetry to also ensure low neoclassical fluxes. Finally, we study the geometric properties of each equilibria to determine which properties most strongly affect the resulting heat fluxes.

[1] G. T. Roberg-Clark, P. Xanthopoulos, and G. G. Plunk, “Reduction of electrostatic turbulence in a quasi-helically symmetric stellarator via critical gradient optimization,” 2022.

[2] R. Jorge, W. Dorland, P. Kim, et al., “Direct Microstability Optimization of Stellarator Devices,” 2023.

[3] I. J. McKinney, M. J. Pueschel, B. J. Faber, et al., “A comparison of turbulent transport in a quasi-helical and a quasi-axisymmetric stellarator,” Journal of Plasma Physics, vol. 85,

no. 5, p. 905 850 503, 2019.

[4] N. R. Mandell, W. Dorland, and M. Landreman, “Laguerre-Hermite pseudo-spectral velocity formulation of gyrokinetics,” J. Plasma Phys, vol. 84, no. 1, p. 905 840 108, 2018.

[5] D. W. Dudt and E. Kolemen, “DESC: A stellarator equilibrium solver,” Physics of Plasmas, vol. 27, no. 10, p. 102 513, 2020.