Collisionless zonal-flow dynamics in quasisymmetric stellarators

Zhu, Hongxuan; Lin, Z.; Bhattacharjee, A.

doi:10.1017/S0022377824001739

Collisionless zonal-flow dynamics in quasisymmetric stellarators

Journal Article · Sun Jan 26 23:00:00 EST 2025 · Journal of Plasma Physics

DOI:https://doi.org/10.1017/S0022377824001739· OSTI ID:2507105

; Lin, Z.; Bhattacharjee, A.

The linear collisionless plasma response to a zonal-density perturbation in quasisymmetric stellarators is studied, including the geodesic-acoustic-mode oscillations and the Rosenbluth–Hinton residual flow. While the geodesic-acoustic-mode oscillations in quasiaxisymmetric configurations are similar to tokamaks, they become non-existent in quasi-helically symmetric configurations when the effective safety factor in helical-angle coordinates is small. Compared with concentric-circular tokamaks, the Rosenbluth–Hinton residual is also found to be multiplied by a geometric factor $$\mathcal {C}$$ that arises from the flux-surface-averaged classical polarization. Using the near-axis-expansion framework, we derive an analytic expression for $$\mathcal {C}$$ , which varies significantly among different configurations. These analytic results are compared with numerical simulation results from the global gyrokinetic particle-in-cell code GTC, and good agreement with the theoretical Rosenbluth–Hinton residual level is achieved when the quasisymmetry error is small enough.

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Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-05CH11231; SC0024548

OSTI ID:: 2507105

Journal Information:: Journal of Plasma Physics, Journal Name: Journal of Plasma Physics Journal Issue: 1 Vol. 91; ISSN 0022-3778

Publisher:: Cambridge University Press (CUP)Copyright Statement

Country of Publication:: United Kingdom

Language:: English

References (60)

Quasi-helically symmetric toroidal stellarators Nührenberg, J.; Zille, R. Physics Letters A, Vol. 129, Issue 2 https://doi.org/10.1016/0375-9601(88)90080-1	journal	May 1988
Stellarator symmetry Dewar, R. L.; Hudson, S. R. Physica D: Nonlinear Phenomena, Vol. 112, Issue 1-2 https://doi.org/10.1016/S0167-2789(97)00216-9	journal	January 1998
A gyrokinetic continuum code based on the numerical Lie transform (NLT) method Ye, Lei; Xu, Yingfeng; Xiao, Xiaotao Journal of Computational Physics, Vol. 316 https://doi.org/10.1016/j.jcp.2016.03.068	journal	July 2016
Collisionless damping of geodesic acoustic modes Sugama, H.; Watanabe, T. -H. Journal of Plasma Physics, Vol. 72, Issue 06 https://doi.org/10.1017/S0022377806004958	journal	December 2006
Erratum: ‘Collisionless damping of geodesic acoustic modes’ [J. Plasma Physics (2006) 72, 825] Sugama, H.; Watanabe, T. -H. Journal of Plasma Physics, Vol. 74, Issue 1 https://doi.org/10.1017/S002237780700668X	journal	February 2008
Tokamak elongation – how much is too much? Part 2. Numerical results Lee, J. P.; Cerfon, A.; Freidberg, J. P. Journal of Plasma Physics, Vol. 81, Issue 6 https://doi.org/10.1017/S0022377815001300	journal	December 2015
Trapped particle precession and sub-bounce zonal flow dynamics in tokamaks Sengupta, W.; Hassam, A. B. Journal of Plasma Physics, Vol. 84, Issue 1 https://doi.org/10.1017/S0022377818000119	journal	February 2018
Direct construction of optimized stellarator shapes. Part 1. Theory in cylindrical coordinates Landreman, Matt; Sengupta, Wrick Journal of Plasma Physics, Vol. 84, Issue 6 https://doi.org/10.1017/S0022377818001289	journal	December 2018
Direct construction of optimized stellarator shapes. Part 2. Numerical quasisymmetric solutions Landreman, Matt; Sengupta, Wrick; Plunk, Gabriel G. Journal of Plasma Physics, Vol. 85, Issue 1 https://doi.org/10.1017/S0022377818001344	journal	January 2019
Constructing stellarators with quasisymmetry to high order Landreman, Matt; Sengupta, Wrick Journal of Plasma Physics, Vol. 85, Issue 6 https://doi.org/10.1017/S0022377819000783	journal	November 2019
Magnetohydrodynamic stability and the effects of shaping: a near-axis view for tokamaks and quasisymmetric stellarators Rodríguez, Eduardo Journal of Plasma Physics, Vol. 89, Issue 2 https://doi.org/10.1017/S0022377823000211	journal	April 2023
Nonlinear drift-wave and energetic particle long-time behaviour in stellarators: solution of the kinetic problem Zocco, Alessandro; Mishchenko, Alexey; Könies, Axel Journal of Plasma Physics, Vol. 89, Issue 3 https://doi.org/10.1017/S002237782300048X	journal	June 2023
The residual flow in well-optimized stellarators Plunk, G. G.; Helander, P. Journal of Plasma Physics, Vol. 90, Issue 2 https://doi.org/10.1017/S002237782400031X	journal	March 2024
Geodesic Acoustic Waves in Hydromagnetic Systems Winsor, Niels Physics of Fluids, Vol. 11, Issue 11 https://doi.org/10.1063/1.1691835	journal	January 1968
Collisionless damping of zonal flows in helical systems Sugama, H.; Watanabe, T. -H. Physics of Plasmas, Vol. 13, Issue 1 https://doi.org/10.1063/1.2149311	journal	January 2006
Plasma shaping effects on the collisionless residual zonal flow level Xiao, Yong; Catto, Peter J. Physics of Plasmas, Vol. 13, Issue 8 https://doi.org/10.1063/1.2266892	journal	August 2006
Eigenmode analysis of geodesic acoustic modes Gao, Zhe; Itoh, K.; Sanuki, H. Physics of Plasmas, Vol. 15, Issue 7 https://doi.org/10.1063/1.2956993	journal	July 2008
Collisionless dynamics of zonal flows in stellarator geometry Mishchenko, Alexey; Helander, Per; Könies, Axel Physics of Plasmas, Vol. 15, Issue 7 https://doi.org/10.1063/1.2963085	journal	July 2008
Plasma shaping effects on the geodesic acoustic mode in the large orbit drift width limit Gao, Zhe Physics of Plasmas, Vol. 17, Issue 9 https://doi.org/10.1063/1.3481464	journal	September 2010
Energetic consistency and momentum conservation in the gyrokinetic description of tokamak plasmas Scott, B.; Smirnov, J. Physics of Plasmas, Vol. 17, Issue 11 https://doi.org/10.1063/1.3507920	journal	November 2010
Exact momentum conservation laws for the gyrokinetic Vlasov-Poisson equations Brizard, Alain J.; Tronko, Natalia Physics of Plasmas, Vol. 18, Issue 8 https://doi.org/10.1063/1.3625554	journal	August 2011
Nonlinear saturation of kinetic ballooning modes by zonal fields in toroidal plasmas Dong, G.; Bao, J.; Bhattacharjee, A. Physics of Plasmas, Vol. 26, Issue 1 https://doi.org/10.1063/1.5066583	journal	January 2019
Magnetic field strength of toroidal plasma equilibria Garren, D. A.; Boozer, A. H. Physics of Fluids B: Plasma Physics, Vol. 3, Issue 10 https://doi.org/10.1063/1.859915	journal	October 1991
Existence of quasihelically symmetric stellarators Garren, D. A.; Boozer, A. H. Physics of Fluids B: Plasma Physics, Vol. 3, Issue 10 https://doi.org/10.1063/1.859916	journal	October 1991
Establishment of magnetic coordinates for a given magnetic field Boozer, Allen H. Physics of Fluids, Vol. 25, Issue 3 https://doi.org/10.1063/1.863765	journal	January 1982
Transport and isomorphic equilibria Boozer, Allen H. Physics of Fluids, Vol. 26, Issue 2 https://doi.org/10.1063/1.864166	journal	January 1983
Comparisons and physics basis of tokamak transport models and turbulence simulations Dimits, A. M.; Bateman, G.; Beer, M. A. Physics of Plasmas, Vol. 7, Issue 3 https://doi.org/10.1063/1.873896	journal	March 2000
Gyrokinetic simulations in general geometry and applications to collisional damping of zonal flows Lin, Z.; Hahm, T. S.; Lee, W. W. Physics of Plasmas, Vol. 7, Issue 5 https://doi.org/10.1063/1.874008	journal	May 2000
Necessary and sufficient conditions for quasisymmetry Rodríguez, E.; Helander, P.; Bhattacharjee, A. Physics of Plasmas, Vol. 27, Issue 6 https://doi.org/10.1063/5.0008551	journal	June 2020
Global gyrokinetic particle simulations of microturbulence in W7-X and LHD stellarators Wang, H. Y.; Holod, I.; Lin, Z. Physics of Plasmas, Vol. 27, Issue 8 https://doi.org/10.1063/5.0014198	journal	August 2020
Comparison of local and global gyrokinetic calculations of collisionless zonal flow damping in quasi-symmetric stellarators Smoniewski, J.; Sánchez, E.; Calvo, I. Physics of Plasmas, Vol. 28, Issue 4 https://doi.org/10.1063/5.0038841	journal	April 2021
Global gyrokinetic simulation of neoclassical ambipolar electric field and its effects on microturbulence in W7-X stellarator Fu, J. Y.; Nicolau, J. H.; Liu, P. F. Physics of Plasmas, Vol. 28, Issue 6 https://doi.org/10.1063/5.0047291	journal	June 2021
Equilibrium and stability of a toroidal magnetohydrodynamic system in the neighbourhood of a magnetic axis Mercier, Claude Nuclear Fusion, Vol. 4, Issue 3 https://doi.org/10.1088/0029-5515/4/3/008	journal	September 1964
Experimental vertical stability studies for ITER performance and design guidance Humphreys, D. A.; Casper, T. A.; Eidietis, N. Nuclear Fusion, Vol. 49, Issue 11 https://doi.org/10.1088/0029-5515/49/11/115003	journal	September 2009
Numerical modelling of geodesic acoustic mode relaxation in a tokamak edge Dorf, M. A.; Cohen, R. H.; Dorr, M. Nuclear Fusion, Vol. 53, Issue 6 https://doi.org/10.1088/0029-5515/53/6/063015	journal	May 2013
Zonal flows in plasma—a review Diamond, P. H.; Itoh, S-I; Itoh, K. Plasma Physics and Controlled Fusion, Vol. 47, Issue 5 https://doi.org/10.1088/0741-3335/47/5/R01	journal	April 2005
Oscillations of zonal flows in stellarators Helander, P.; Mishchenko, A.; Kleiber, R. Plasma Physics and Controlled Fusion, Vol. 53, Issue 5 https://doi.org/10.1088/0741-3335/53/5/054006	journal	April 2011
Collisionless damping of flows in the TJ-II stellarator Sánchez, E.; Kleiber, R.; Hatzky, R. Plasma Physics and Controlled Fusion, Vol. 55, Issue 1 https://doi.org/10.1088/0741-3335/55/1/014015	journal	December 2012
Residual zonal flows in tokamaks and stellarators at arbitrary wavelengths Monreal, Pedro; Calvo, Iván; Sánchez, Edilberto Plasma Physics and Controlled Fusion, Vol. 58, Issue 4 https://doi.org/10.1088/0741-3335/58/4/045018	journal	February 2016
Semianalytical calculation of the zonal-flow oscillation frequency in stellarators Monreal, Pedro; Sánchez, Edilberto; Calvo, Iván Plasma Physics and Controlled Fusion, Vol. 59, Issue 6 https://doi.org/10.1088/1361-6587/aa6990	journal	April 2017
Ion-temperature-gradient stability near the magnetic axis of quasisymmetric stellarators Jorge, R.; Landreman, M. Plasma Physics and Controlled Fusion, Vol. 63, Issue 7, p. 074002 https://doi.org/10.1088/1361-6587/abfdd4	journal	June 2021
Phases and phase-transitions in quasisymmetric configuration space Rodríguez, E.; Sengupta, W.; Bhattacharjee, A. Plasma Physics and Controlled Fusion, Vol. 64, Issue 10 https://doi.org/10.1088/1361-6587/ac89af	journal	August 2022
Constructing the space of quasisymmetric stellarators through near-axis expansion Rodríguez, E.; Sengupta, W.; Bhattacharjee, A. Plasma Physics and Controlled Fusion, Vol. 65, Issue 9 https://doi.org/10.1088/1361-6587/ace739	journal	July 2023
Nonlinear dynamics of phase space zonal structures and energetic particle physics in fusion plasmas Zonca, F.; Chen, L.; Briguglio, S. New Journal of Physics, Vol. 17, Issue 1 https://doi.org/10.1088/1367-2630/17/1/013052	journal	January 2015
Momentum flux parasitic to free-energy transfer Stoltzfus-Dueck, T.; Scott, B. Nuclear Fusion, Vol. 57, Issue 8 https://doi.org/10.1088/1741-4326/aa7289	journal	July 2017
Construction of quasisymmetric stellarators using a direct coordinate approach Jorge, R.; Sengupta, W.; Landreman, M. Nuclear Fusion, Vol. 60, Issue 7 https://doi.org/10.1088/1741-4326/ab90ca	journal	June 2020
Geodesic acoustic modes in magnetic confinement devices Conway, G. D.; Smolyakov, A. I.; Ido, T. Nuclear Fusion, Vol. 62, Issue 1 https://doi.org/10.1088/1741-4326/ac0dd1	journal	December 2021
Ion temperature clamping in Wendelstein 7-X electron cyclotron heated plasmas Beurskens, M. N. A.; Bozhenkov, S. A.; Ford, O. Nuclear Fusion, Vol. 61, Issue 11 https://doi.org/10.1088/1741-4326/ac1653	journal	October 2021
Gyrokinetic simulations in stellarators using different computational domains Sánchez, E.; García-Regaña, J. M.; Bañón Navarro, A. Nuclear Fusion, Vol. 61, Issue 11 https://doi.org/10.1088/1741-4326/ac2a87	journal	October 2021
Global gyrokinetic simulation with kinetic electron for collisionless damping of zonal flow in stellarators Nicolau, Javier H.; Choi, Gyungjin; Fu, Jingyuan Nuclear Fusion, Vol. 61, Issue 12 https://doi.org/10.1088/1741-4326/ac31da	journal	November 2021
Global gyrokinetic simulations of electrostatic microturbulent transport in LHD stellarator with boron impurity Singh, Tajinder; Nicolau, Javier H.; Nespoli, Federico Nuclear Fusion, Vol. 64, Issue 1 https://doi.org/10.1088/1741-4326/ad0aca	journal	November 2023
Effect of Quasihelical Symmetry on Trapped-Electron Mode Transport in the HSX Stellarator Guttenfelder, W.; Lore, J.; Anderson, D. T. Physical Review Letters, Vol. 101, Issue 21 https://doi.org/10.1103/PhysRevLett.101.215002	journal	November 2008
Zonal Flow Dynamics and Control of Turbulent Transport in Stellarators Xanthopoulos, P.; Mischchenko, A.; Helander, P. Physical Review Letters, Vol. 107, Issue 24 https://doi.org/10.1103/PhysRevLett.107.245002	journal	December 2011
Magnetic Fields with Precise Quasisymmetry for Plasma Confinement Landreman, Matt; Paul, Elizabeth Physical Review Letters, Vol. 128, Issue 3 https://doi.org/10.1103/PhysRevLett.128.035001	journal	January 2022
Poloidal Flow Driven by Ion-Temperature-Gradient Turbulence in Tokamaks Rosenbluth, M. N.; Hinton, F. L. Physical Review Letters, Vol. 80, Issue 4 https://doi.org/10.1103/PhysRevLett.80.724	journal	January 1998
Turbulent Transport Reduction by Zonal Flows: Massively Parallel Simulations Lin, Z. Science, Vol. 281, Issue 5384 https://doi.org/10.1126/science.281.5384.1835	journal	September 1998
Development of a Gyrokinetic Particle-in-Cell Code for Whole-Volume Modeling of Stellarators Moritaka, Toseo; Hager, Robert; Cole, Michael Plasma, Vol. 2, Issue 2 https://doi.org/10.3390/plasma2020014	journal	May 2019
hiddenSymmetries/simsopt: v1.6.4 Medasani, Bharat; Landreman, Matt; Wechsung, Florian https://doi.org/10.5281/zenodo.12794607	software	July 2024
Data for the paper "Collisionless zonal-flow dynamics in quasisymmetric stellarators" Zhu, Hongxuan Zenodo https://doi.org/10.5281/zenodo.13218496	dataset	January 2025
Data for the paper "Magnetic fields with precise quasisymmetry" Landreman, Matt Zenodo https://doi.org/10.5281/zenodo.5645413	dataset	January 2021

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