Theory of the Tertiary Instability and the Dimits Shift from Reduced Drift-Wave Models

Zhu, Hongxuan; Zhou, Yao; Dodin, I. Y.

doi:10.1103/PhysRevLett.124.055002

Theory of the Tertiary Instability and the Dimits Shift from Reduced Drift-Wave Models

Journal Article · Mon Feb 03 23:00:00 EST 2020 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.124.055002· OSTI ID:1616941

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Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

Tertiary modes in electrostatic drift-wave turbulence are localized near extrema of the zonal velocity U(x) with respect to the radial coordinate x. We argue that these modes can be described as quantum harmonic oscillators with complex frequencies, so their spectrum can be readily calculated. The corresponding growth rate $$γ$$_TI is derived within the modified Hasegawa-Wakatani model. We show that $$γ$$TI equals the primary-instability growth rate plus a term that depends on the local U''; hence, the instability threshold is shifted compared to that in homogeneous turbulence. This provides a generic explanation of the well-known yet elusive Dimits shift, which we find explicitly in the Terry-Horton limit. Linearly unstable tertiary modes either saturate due to the evolution of the zonal density or generate radially propagating structures when the shear |U'| is sufficiently weakened by viscosity. The Dimits regime ends when such structures are generated continuously.

View Accepted Manuscript (DOE)

Research Organization:: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-09CH11466

OSTI ID:: 1616941

Alternate ID(s):: OSTI ID: 1599479

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 5 Vol. 124; ISSN 0031-9007; ISSN PRLTAO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (42)

Transition to subcritical turbulence in a tokamak plasma van Wyk, F.; Highcock, E. G.; Schekochihin, A. A. Journal of Plasma Physics, Vol. 82, Issue 6 https://doi.org/10.1017/S0022377816001148	journal	December 2016
On non-local energy transfer via zonal flow in the Dimits shift St-Onge, Denis A. Journal of Plasma Physics, Vol. 83, Issue 5 https://doi.org/10.1017/S0022377817000708	journal	October 2017
Simple advecting structures and the edge of chaos in subcritical tokamak plasmas McMillan, Ben F.; Pringle, Chris C. T.; Teaca, Bogdan Journal of Plasma Physics, Vol. 84, Issue 6 https://doi.org/10.1017/S0022377818001216	journal	December 2018
Dynamics of zonal flow saturation in strong collisionless drift wave turbulence Kim, Eun-jin; Diamond, P. H. Physics of Plasmas, Vol. 9, Issue 11 https://doi.org/10.1063/1.1514641	journal	November 2002
Noncurvature-driven modes in a transport barrier Rogers, B. N.; Dorland, W. Physics of Plasmas, Vol. 12, Issue 6 https://doi.org/10.1063/1.1928250	journal	June 2005
Bifurcation in electrostatic resistive drift wave turbulence Numata, Ryusuke; Ball, Rowena; Dewar, Robert L. Physics of Plasmas, Vol. 14, Issue 10 https://doi.org/10.1063/1.2796106	journal	October 2007
Linearized model Fokker–Planck collision operators for gyrokinetic simulations. I. Theory Abel, I. G.; Barnes, M.; Cowley, S. C. Physics of Plasmas, Vol. 15, Issue 12 https://doi.org/10.1063/1.3046067	journal	December 2008
Linearized model Fokker–Planck collision operators for gyrokinetic simulations. II. Numerical implementation and tests Barnes, M.; Abel, I. G.; Dorland, W. Physics of Plasmas, Vol. 16, Issue 7 https://doi.org/10.1063/1.3155085	journal	July 2009
The quench rule, Dimits shift, and eigenmode localization by small-scale zonal flows Kobayashi, Sumire; Rogers, Barrett N. Physics of Plasmas, Vol. 19, Issue 1 https://doi.org/10.1063/1.3677355	journal	January 2012
Zonal-flow dynamics from a phase-space perspective Ruiz, D. E.; Parker, J. B.; Shi, E. L. Physics of Plasmas, Vol. 23, Issue 12 https://doi.org/10.1063/1.4971813	journal	December 2016
On the tertiary instability formalism of zonal flows in magnetized plasmas Rath, F.; Peeters, A. G.; Buchholz, R. Physics of Plasmas, Vol. 25, Issue 5 https://doi.org/10.1063/1.5026670	journal	May 2018
On the Rayleigh–Kuo criterion for the tertiary instability of zonal flows Zhu, Hongxuan; Zhou, Yao; Dodin, I. Y. Physics of Plasmas, Vol. 25, Issue 8 https://doi.org/10.1063/1.5038859	journal	August 2018
On the structure of the drifton phase space and its relation to the Rayleigh–Kuo criterion of the zonal-flow stability Zhu, Hongxuan; Zhou, Yao; Dodin, I. Y. Physics of Plasmas, Vol. 25, Issue 7 https://doi.org/10.1063/1.5039652	journal	July 2018
Localization of the eigenmode of the drift-resistive plasma by zonal flow Kim, Chang-Bae; Min, Byunghoon; An, Chan-Yong Physics of Plasmas, Vol. 25, Issue 10 https://doi.org/10.1063/1.5048952	journal	October 2018
A flux-balanced fluid model for collisional plasma edge turbulence: Model derivation and basic physical features Majda, Andrew J.; Qi, Di; Cerfon, Antoine J. Physics of Plasmas, Vol. 25, Issue 10 https://doi.org/10.1063/1.5049389	journal	October 2018
A flux-balanced fluid model for collisional plasma edge turbulence: Numerical simulations with different aspect ratios Qi, Di; Majda, Andrew J.; Cerfon, Antoine J. Physics of Plasmas, Vol. 26, Issue 8 https://doi.org/10.1063/1.5083845	journal	August 2019
Quasioptical modeling of wave beams with and without mode conversion. I. Basic theory Dodin, I. Y.; Ruiz, D. E.; Yanagihara, K. Physics of Plasmas, Vol. 26, Issue 7 https://doi.org/10.1063/1.5095076	journal	July 2019
Influence of sheared poloidal rotation on edge turbulence Biglari, H.; Diamond, P. H.; Terry, P. W. Physics of Fluids B: Plasma Physics, Vol. 2, Issue 1 https://doi.org/10.1063/1.859529	journal	January 1990
Stochasticity and the random phase approximation for three electron drift waves Terry, Paul Physics of Fluids, Vol. 25, Issue 3 https://doi.org/10.1063/1.863761	journal	January 1982
Generalized action invariants for drift waves-zonal flow systems Smolyakov, A. I.; Diamond, P. H. Physics of Plasmas, Vol. 6, Issue 12 https://doi.org/10.1063/1.873725	journal	December 1999
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
Electron temperature gradient driven turbulence Jenko, F.; Dorland, W.; Kotschenreuther, M. Physics of Plasmas, Vol. 7, Issue 5 https://doi.org/10.1063/1.874014	journal	May 2000
Secondary instability in drift wave turbulence as a mechanism for zonal flow and avalanche formation Diamond, P. H.; Champeaux, S.; Malkov, M. Nuclear Fusion, Vol. 41, Issue 8 https://doi.org/10.1088/0029-5515/41/8/310	journal	August 2001
Developments in the gyrofluid approach to Tokamak turbulence simulations Hammett, G. W.; Beer, M. A.; Dorland, W. Plasma Physics and Controlled Fusion, Vol. 35, Issue 8 https://doi.org/10.1088/0741-3335/35/8/006	journal	August 1993
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
On the effects of nonuniform zonal flow in the resistive-drift plasma Kim, Chang-Bae; Min, Byunghoon; An, Chan-Yong Plasma Physics and Controlled Fusion, Vol. 61, Issue 3 https://doi.org/10.1088/1361-6587/aaf622	journal	January 2019
Formation of solitary zonal structures via the modulational instability of drift waves Zhou, Yao; Zhu, Hongxuan; Dodin, I. Y. Plasma Physics and Controlled Fusion, Vol. 61, Issue 7 https://doi.org/10.1088/1361-6587/ab16a8	journal	May 2019
Effects of zonal flows on transport crossphase in dissipative trapped-electron mode turbulence in edge plasmas Leconte, M.; Singh, R. Plasma Physics and Controlled Fusion, Vol. 61, Issue 9 https://doi.org/10.1088/1361-6587/ab2e7b	journal	July 2019
Generation of zonal flows through symmetry breaking of statistical homogeneity Parker, Jeffrey B.; Krommes, John A. New Journal of Physics, Vol. 16, Issue 3 https://doi.org/10.1088/1367-2630/16/3/035006	journal	March 2014
Nonlinear saturation and oscillations of collisionless zonal flows Zhu, Hongxuan; Zhou, Yao; Dodin, I. Y. New Journal of Physics, Vol. 21, Issue 6 https://doi.org/10.1088/1367-2630/ab2251	journal	June 2019
Avalanches triggered by Kelvin-Helmholtz instability in a cylindrical plasma device Lang, Y.; Guo, Z. B.; Wang, X. G. Physical Review E, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevE.100.033212	journal	September 2019
Interactions of disparate scales in drift-wave turbulence Krommes, John A.; Kim, Chang-Bae Physical Review E, Vol. 62, Issue 6 https://doi.org/10.1103/PhysRevE.62.8508	journal	December 2000
Wave kinetics of drift-wave turbulence and zonal flows beyond the ray approximation Zhu, Hongxuan; Zhou, Yao; Ruiz, D. E. Physical Review E, Vol. 97, Issue 5 https://doi.org/10.1103/PhysRevE.97.053210	journal	May 2018
Dimits Shift in Realistic Gyrokinetic Plasma-Turbulence Simulations Mikkelsen, D. R.; Dorland, W. Physical Review Letters, Vol. 101, Issue 13 https://doi.org/10.1103/PhysRevLett.101.135003	journal	September 2008
Stationary Spectrum of Strong Turbulence in Magnetized Nonuniform Plasma Hasegawa, Akira; Mima, Kunioki Physical Review Letters, Vol. 39, Issue 4 https://doi.org/10.1103/PhysRevLett.39.205	journal	July 1977
Plasma Edge Turbulence Hasegawa, Akira; Wakatani, Masahiro Physical Review Letters, Vol. 50, Issue 9 https://doi.org/10.1103/PhysRevLett.50.682	journal	February 1983
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
Generation and Stability of Zonal Flows in Ion-Temperature-Gradient Mode Turbulence Rogers, B. N.; Dorland, W.; Kotschenreuther, M. Physical Review Letters, Vol. 85, Issue 25 https://doi.org/10.1103/PhysRevLett.85.5336	journal	December 2000
Transition to Collisionless Ion-Temperature-Gradient-Driven Plasma Turbulence: A Dynamical Systems Approach Kolesnikov, R. A.; Krommes, J. A. Physical Review Letters, Vol. 94, Issue 23 https://doi.org/10.1103/PhysRevLett.94.235002	journal	June 2005
Small-Scale Turbulence in a Closed-Field-Line Geometry Ricci, Paolo; Rogers, B. N.; Dorland, W. Physical Review Letters, Vol. 97, Issue 24 https://doi.org/10.1103/PhysRevLett.97.245001	journal	December 2006
Drift waves and transport Horton, W. Reviews of Modern Physics, Vol. 71, Issue 3 https://doi.org/10.1103/RevModPhys.71.735	journal	April 1999
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

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