Transition of a network of nonlinear interactions into a regime of strong nonlinear fluctuations: A paradigm for the edge localized mode onset

Dominski, J.; Diallo, A.

doi:10.1063/5.0050543

Title: Transition of a network of nonlinear interactions into a regime of strong nonlinear fluctuations: A paradigm for the edge localized mode onset

Journal Article · 16 September 2021 · Physics of Plasmas

DOI: https://doi.org/10.1063/5.0050543 · OSTI ID:1822212

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Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

We study how a network of nonlinear oscillators transits into a regime of strong nonlinear fluctuations when perturbed by a triad. In this regime, most of the potential energy contained in the waves is made available to the system through strong nonlinear fluctuations. This analysis is motivated by recent experimental observations [Dominski and Diallo, Plasma Phys. Control. Fusion 62, 095011 (2020)] where it was found that magnetic fluctuations trigger the onset of edge localized modes by suddenly exciting a network of nonlinear interactions. In our study, we consider the simplest system of many harmonic oscillators that are organized in a network of nonlinear triads. We model and simulate the sudden transition of this network of triads into a regime of strong nonlinear fluctuations—reminiscent of the onset of edge localized modes in tokamaks. This transition is triggered by the activation of a nonlinear perturbation. An abrupt rise of the system's disorder (an entropy-like quantity) is measured during the transition. This transition from weak to strong nonlinear fluctuations is even more abrupt when these fluctuations are chaotic, i.e., when the timescale of the nonlinear interaction is comparable to the timescale of the wave oscillations.

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

Sponsoring Organization:: USDOE Office of Science (SC), Fusion Energy Sciences (FES)

Grant/Contract Number:: AC02-09CH11466; FC02-04ER54698

OSTI ID:: 1822212

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 9 Vol. 28; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (33)

Kolmogorov Spectra of Turbulence I: Wave Turbulence Zakharov, Vladimir E.; L’vov, Victor S.; Falkovich, Gregory Springer Series in Nonlinear Dynamics https://doi.org/10.1007/978-3-642-50052-7	book	January 1992
A symplectic integration algorithm for separable Hamiltonian functions Candy, J.; Rozmus, W. Journal of Computational Physics, Vol. 92, Issue 1 https://doi.org/10.1016/0021-9991(91)90299-Z	journal	January 1991
Explosive instabilities and detonation in magnetohydrodynamics Cowley, Steven C.; Artun, Mehmet Physics Reports, Vol. 283, Issue 1-4 https://doi.org/10.1016/S0370-1573(96)00060-9	journal	April 1997
Modern Plasma Physics Diamond, Patrick H.; Itoh, Sanae-I.; Itoh, Kimitaka https://doi.org/10.1017/CBO9780511780875	book	October 2010
Explosive transitions to synchronization in networks of phase oscillators Leyva, I.; Navas, A.; Sendiña-Nadal, I. Scientific Reports, Vol. 3, Issue 1 https://doi.org/10.1038/srep01281	journal	February 2013
Edge localized modes and the pedestal: A model based on coupled peeling–ballooning modes Snyder, P. B.; Wilson, H. R.; Ferron, J. R. Physics of Plasmas, Vol. 9, Issue 5 https://doi.org/10.1063/1.1449463	journal	May 2002
Progress in the peeling-ballooning model of edge localized modes: Numerical studies of nonlinear dynamics Snyder, P. B.; Wilson, H. R.; Xu, X. Q. Physics of Plasmas, Vol. 12, Issue 5 https://doi.org/10.1063/1.1873792	journal	May 2005
Nonlinear gyrofluid computation of edge localized ideal ballooning modes Kendl, Alexander; Scott, Bruce D.; Ribeiro, Tiago T. Physics of Plasmas, Vol. 17, Issue 7 https://doi.org/10.1063/1.3449807	journal	July 2010
A self-consistent three-wave coupling model with complex linear frequencies Kim, J. -H.; Terry, P. W. Physics of Plasmas, Vol. 18, Issue 9 https://doi.org/10.1063/1.3640807	journal	September 2011
Nonlinear excitation of low-n harmonics in reduced magnetohydrodynamic simulations of edge-localized modes Krebs, I.; Hölzl, M.; Lackner, K. Physics of Plasmas, Vol. 20, Issue 8 https://doi.org/10.1063/1.4817953	journal	August 2013
The impact of pedestal turbulence and electron inertia on edge-localized-mode crashes Xi, P. W.; Xu, X. Q.; Diamond, P. H. Physics of Plasmas, Vol. 21, Issue 5 https://doi.org/10.1063/1.4875332	journal	May 2014
Edge-localized-modes in tokamaks Leonard, A. W. Physics of Plasmas, Vol. 21, Issue 9 https://doi.org/10.1063/1.4894742	journal	September 2014
Correlations between quasi-coherent fluctuations and the pedestal evolution during the inter-edge localized modes phase on DIII-Da) Diallo, A.; Groebner, R. J.; Rhodes, T. L. Physics of Plasmas, Vol. 22, Issue 5 https://doi.org/10.1063/1.4921148	journal	May 2015
Explosive synchronization coexists with classical synchronization in the Kuramoto model Danziger, Michael M.; Moskalenko, Olga I.; Kurkin, Semen A. Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 26, Issue 6 https://doi.org/10.1063/1.4953345	journal	June 2016
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
The direct-interaction approximation and statistically steady states of three nonlinearly coupled modes Krommes, John A. Physics of Fluids, Vol. 25, Issue 8 https://doi.org/10.1063/1.863905	journal	January 1982
Nonlinear magnetohydrodynamic detonation: Part I Hurricane, O. A.; Fong, B. H.; Cowley, S. C. Physics of Plasmas, Vol. 4, Issue 10 https://doi.org/10.1063/1.872252	journal	October 1997
Edge localized modes (ELMs) Zohm, H. Plasma Physics and Controlled Fusion, Vol. 38, Issue 2 https://doi.org/10.1088/0741-3335/38/2/001	journal	February 1996
Edge-localized modes - physics and theory Connor, J. W. Plasma Physics and Controlled Fusion, Vol. 40, Issue 5 https://doi.org/10.1088/0741-3335/40/5/002	journal	May 1998
The physics of large and small edge localized modes Suttrop, W. Plasma Physics and Controlled Fusion, Vol. 42, Issue 5A https://doi.org/10.1088/0741-3335/42/5A/301	journal	May 2000
Washboard modes as ELM-related events in JET Perez, C. P.; Koslowski, H. R.; Hender, T. C. Plasma Physics and Controlled Fusion, Vol. 46, Issue 1 https://doi.org/10.1088/0741-3335/46/1/005	journal	November 2003
Inter-ELM behaviour of the electron density and temperature pedestal in ASDEX Upgrade Burckhart, A.; Wolfrum, E.; Fischer, R. Plasma Physics and Controlled Fusion, Vol. 52, Issue 10 https://doi.org/10.1088/0741-3335/52/10/105010	journal	September 2010
Nonlinear MHD simulations of edge-localized-modes in JET Pamela, S. J. P.; Huysmans, G. T. A.; Beurskens, M. N. A. Plasma Physics and Controlled Fusion, Vol. 53, Issue 5 https://doi.org/10.1088/0741-3335/53/5/054014	journal	April 2011
High frequency magnetic fluctuations correlated with the inter-ELM pedestal evolution in ASDEX Upgrade Laggner, F. M.; Wolfrum, E.; Cavedon, M. Plasma Physics and Controlled Fusion, Vol. 58, Issue 6 https://doi.org/10.1088/0741-3335/58/6/065005	journal	May 2016
Identification of a network of nonlinear interactions as a mechanism triggering the onset of edge localized modes Dominski, J.; Diallo, A. Plasma Physics and Controlled Fusion, Vol. 62, Issue 9 https://doi.org/10.1088/1361-6587/ab9c48	journal	July 2020
Role of the pedestal position on the pedestal performance in AUG, JET-ILW and TCV and implications for ITER Frassinetti, L.; Dunne, M. G.; Sheikh, U. Nuclear Fusion, Vol. 59, Issue 7 https://doi.org/10.1088/1741-4326/ab1eb9	journal	June 2019
Nonlinear energy transfer from low frequency electromagnetic fluctuations to broadband turbulence during edge localized mode crashes Kim, Jaewook; Choi, M. J.; Nam, Y. U. Nuclear Fusion, Vol. 60, Issue 12 https://doi.org/10.1088/1741-4326/abb2d6	journal	October 2020
Non-linear extended MHD simulations of type-I edge localised mode cycles in ASDEX Upgrade and their underlying triggering mechanism Cathey, A.; Hoelzl, M.; Lackner, K. Nuclear Fusion, Vol. 60, Issue 12 https://doi.org/10.1088/1741-4326/abbc87	journal	November 2020
Microtearing modes as the source of magnetic fluctuations in the JET pedestal Hatch, D. R.; Kotschenreuther, M.; Mahajan, S. M. Nuclear Fusion, Vol. 61, Issue 3 https://doi.org/10.1088/1741-4326/abd21a	journal	February 2021
Statistical assessment of ELM triggering by pellets on JET Lennholm, M.; McKean, R.; Mooney, R. Nuclear Fusion, Vol. 61, Issue 3 https://doi.org/10.1088/1741-4326/abd861	journal	February 2021
Explosive Synchronization Transitions in Scale-Free Networks Gómez-Gardeñes, Jesús; Gómez, Sergio; Arenas, Alex Physical Review Letters, Vol. 106, Issue 12 https://doi.org/10.1103/PhysRevLett.106.128701	journal	March 2011
Direct Observation of Nonlinear Coupling between Pedestal Modes Leading to the Onset of Edge Localized Modes Diallo, A.; Dominski, J.; Barada, K. Physical Review Letters, Vol. 121, Issue 23 https://doi.org/10.1103/PhysRevLett.121.235001	journal	December 2018
Theory for Explosive Ideal Magnetohydrodynamic Instabilities in Plasmas Wilson, H.; Cowley, S. Physical Review Letters, Vol. 92, Issue 17 https://doi.org/10.1103/PhysRevLett.92.175006	journal	April 2004