References

[FC82]

E. A. Frieman and L. Chen, “Nonlinear gyrokinetic equations for low- frequency electromagnetic waves in general plasma equilibria,” Physics of Fluids 25, 502 (1982). DOI.

[AL80]

T. M. Antonsen Jr. and B. Lane, “Kinetic equations for low frequency instabilities in inhomogeneous plasmas,” Physics of Fluids 23, 1205 (1980). DOI.

[MDL17]

N. R. Mandell, W. Dorland, and M. Landreman, “Laguerre-Hermite Pseudo-Spectral Velocity Formulation of Gyrokinetics,” arXiv:1708.04029 (2017). arXiv.

[Dimits00]

A. M. Dimits et al., “Comparisons and physics basis of tokamak transport models and turbulence simulations,” Physics of Plasmas 7, 969 (2000). DOI.

[Lin99]

Z. Lin et al., Phys. Rev. Lett. 83, 3645 (1999). DOI.

[Dorland00]

W. Dorland et al., Phys. Rev. Lett. 85, 5579 (2000). DOI.

[Jenko00]

F. Jenko et al., Physics of Plasmas 7, 1904 (2000). DOI.

[GX]

N. R. Mandell et al., “GX: a GPU-native gyrokinetic turbulence code for tokamak and stellarator design,” Journal of Plasma Physics (2022). DOI.

[GonzalezJerez22]

A. González-Jerez et al., “Electrostatic gyrokinetic simulations in Wendelstein 7-X geometry: benchmark between the codes stella and GENE,” Journal of Plasma Physics 88, 905880310 (2022). Cambridge Core, arXiv, DOI.

[Sanchez21]

E. Sánchez et al., “Gyrokinetic simulations in stellarators using different computational domains,” Nuclear Fusion 61, 116074 (2021). arXiv, DOI.

[Papadopoulos23]

A. D. Papadopoulos, J. Anderson, E.-j. Kim, M. Mavridis, and H. Isliker, “Statistical Analysis of Plasma Dynamics in Gyrokinetic Simulations of Stellarator Turbulence,” Entropy 25, 942 (2023). article, DOI.

[Hoffmann23]

A. C. D. Hoffmann, B. J. Frei, and P. Ricci, “Gyrokinetic moment-based simulations of the Dimits shift,” Journal of Plasma Physics 89, 905890616 (2023). arXiv, Cambridge Core.

[Oberparleiter16]

M. Oberparleiter, H. Nordman, G. Verdoolaege, and F. Jenko, “Uncertainty estimation and a stopping rule in nonlinear gyrokinetic simulations,” Journal of Physics: Conference Series 775, 012009 (2016). DOI.

[GENE]

F. Jenko et al., “The GENE code,” Journal of Computational Physics 230, 6979 (2011). DOI.

[Stephens21]

C. D. Stephens et al., “Quasilinear gyrokinetic theory: A derivation of QuaLiKiz,” Journal of Plasma Physics 87, 905870409 (2021). arXiv, DOI.

[Parker23]

J. B. Parker et al., “Comparison of Saturation Rules Used for Gyrokinetic Quasilinear Transport Modeling,” Plasma 6, 611 (2023). article, DOI.

[Citrin17]

J. Citrin et al., “Tractable flux-driven temperature, density, and rotation profile evolution with the quasilinear gyrokinetic transport model QuaLiKiz,” Plasma Physics and Controlled Fusion 59, 124005 (2017). arXiv, DOI.

[Waltz09]

R. E. Waltz, A. Casati, and G. M. Staebler, “Gyrokinetic simulation tests of quasilinear and tracer transport,” Physics of Plasmas 16, 072303 (2009). ORNL record, DOI.

[Biglari90]

H. Biglari, P. H. Diamond, and P. W. Terry, “Influence of sheared poloidal rotation on edge turbulence,” Physics of Fluids B 2, 1 (1990). DOI.

[Waltz95]

R. E. Waltz, G. D. Kerbel, J. Milovich, and G. W. Hammett, “Advances in the simulation of toroidal gyro-Landau fluid model turbulence,” Physics of Plasmas 2, 2408 (1995). DOI.

[Schekochihin12]

A. A. Schekochihin, E. G. Highcock, and S. C. Cowley, “Subcritical fluctuations and suppression of turbulence in differentially rotating gyrokinetic plasmas,” Plasma Physics and Controlled Fusion 54, 055011 (2012). arXiv, DOI.

[McMillan19]

B. F. McMillan, J. Ball, and S. Brunner, “Simulating background shear flow in local gyrokinetic simulations,” Plasma Physics and Controlled Fusion 61, 055006 (2019). arXiv, DOI.

[Ball19]

J. Ball, S. Brunner, and B. F. McMillan, “The effect of background flow shear on gyrokinetic turbulence in the cold ion limit,” Plasma Physics and Controlled Fusion 61, 064004 (2019). arXiv, DOI.

[Staebler24]

G. Staebler, C. Bourdelle, J. Citrin, and R. Waltz, “Quasilinear theory and modelling of gyrokinetic turbulent transport in tokamaks,” Nuclear Fusion 64, 103001 (2024). ORNL record, DOI.

[Dudding22]

H. G. Dudding et al., “A new quasilinear saturation rule for tokamak turbulence with application to the isotope scaling of transport,” Nuclear Fusion 62, 096005 (2022). accepted PDF, DOI.

[Sar26]

P. Sar, S. De Pascuale, H. Dudding, and G. Staebler, “A machine learning framework for developing quasilinear saturation rules of turbulent transport from linear gyrokinetic data,” arXiv:2604.00462 (2026). arXiv.

[Jorge24]

R. Jorge et al., “Direct microstability optimization of stellarator devices,” Physical Review E 110, 035201 (2024). arXiv, DOI.

[Kim24]

P. Kim et al., “Optimization of nonlinear turbulence in stellarators,” Journal of Plasma Physics 90, 905900210 (2024). Cambridge Core, arXiv, DOI.

[Pueschel16]

M. J. Pueschel, B. J. Faber, J. Citrin, C. C. Hegna, P. W. Terry, and D. R. Hatch, “Stellarator Turbulence: Subdominant Eigenmodes and Quasilinear Modeling,” Physical Review Letters 116, 085001 (2016). DIFFER record, DOI.

[Hegna18]

C. C. Hegna, P. W. Terry, and B. J. Faber, “Theory of ITG turbulent saturation in stellarators: identifying mechanisms to reduce turbulent transport,” Physics of Plasmas 25, 022511 (2018). OSTI record, DOI.

[McKinney19]

I. J. McKinney et al., “A comparison of turbulent transport in a quasi-helical and a quasi-axisymmetric stellarator,” Journal of Plasma Physics 85, 905850503 (2019). OSTI record, DOI.

[Tiwari25]

A. Tiwari et al., “Zonal flow suppression of turbulent transport in the optimized stellarators W7-X and QSTK,” arXiv:2501.12722 (2025). arXiv.

[HirshmanWhitson83]

S. P. Hirshman and J. C. Whitson, “Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria,” Physics of Fluids 26, 3553 (1983). DOI.

[LandremanPaul22]

M. Landreman and E. Paul, “Magnetic Fields with Precise Quasisymmetry for Plasma Confinement,” Physical Review Letters 128, 035001 (2022). DOI.