Stochastic effects on phase-space holes and clumps in kinetic systems near marginal stability

Woods, Benjamin J. Q.; Duarte, Vinicius N.; De-Gol, Anthony J.; Gorelenkov, Nikolai N.; Vann, Roddy G. L.

doi:10.1088/1741-4326/aaa9fd

Title: Stochastic effects on phase-space holes and clumps in kinetic systems near marginal stability

Journal Article · Tue Jan 23 00:00:00 EST 2018 · Nuclear Fusion

DOI:https://doi.org/10.1088/1741-4326/aaa9fd· OSTI ID:1425202

^[1];

^[2]; De-Gol, Anthony J. ^[1]; Gorelenkov, Nikolai N. ^[3]; Vann, Roddy G. L. ^[1]

Univ. of York (United Kingdom). York Plasma Inst., Dept. of Physics
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Univ. of Sao Paulo (Brazil). Inst. of Physics
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

The creation and subsequent evolution of marginally-unstable modes have been observed in a wide range of fusion devices. This behaviour has been successfully explained, for a single frequency shifting mode, in terms of phase-space structures known as a 'hole' and 'clump'. Here in this paper, we introduce stochasticity into a 1D kinetic model, affecting the formation and evolution of resonant modes in the system. We find that noise in the fast particle distribution or electric field leads to a shift in the asymptotic behaviour of a chirping resonant mode; this noise heuristically maps onto radial microturbulence via canonical toroidal momentum scattering, affecting hole and clump formation. While the mechanism allowing for the formation of the hole and clump is coherent, the lifetime of a hole and clump is shown to be highly sensitive to initial conditions, affecting the temporal profile of a single bursting event in mode amplitude.

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

Sponsoring Organization:: USDOE; So Paulo Research Foundation

Grant/Contract Number:: AC02-09CH11466; EP/K000225; EP/L01663X; 2012/22830-2

OSTI ID:: 1425202

Journal Information:: Nuclear Fusion, Vol. 58, Issue 8; ISSN 0029-5515

Publisher:: IOP ScienceCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 5 works

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References (29)

Nonlinear dynamical models and jerky motion Linz, Stefan J. American Journal of Physics, Vol. 65, Issue 6 https://doi.org/10.1119/1.18594	journal	June 1997
Nonlinear simulation of toroidal Alfvén eigenmode with microturbulence-induced radial diffusion Lang, Jianying; Fu, Guo-Yong Physics of Plasmas, Vol. 18, Issue 5 https://doi.org/10.1063/1.3574503	journal	May 2011
Prediction of nonlinear evolution character of energetic-particle-driven instabilities Duarte, V. N.; Berk, H. L.; Gorelenkov, N. N. Nuclear Fusion, Vol. 57, Issue 5 https://doi.org/10.1088/1741-4326/aa6232	journal	March 2017
Numerical simulation of bump‐on‐tail instability with source and sink Berk, H. L.; Breizman, B. N.; Pekker, M. Physics of Plasmas, Vol. 2, Issue 8 https://doi.org/10.1063/1.871198	journal	August 1995
Nonlinear categorization of the energetic-beam-driven instability with drag and diffusion Lesur, M.; Idomura, Y. Nuclear Fusion, Vol. 52, Issue 9 https://doi.org/10.1088/0029-5515/52/9/094004	journal	September 2012
Nonlinear travelling waves in energetic particle phase space Breizman, Boris N. Nuclear Fusion, Vol. 50, Issue 8 https://doi.org/10.1088/0029-5515/50/8/084014	journal	July 2010
Nonlinear simulation of toroidal Alfvén eigenmode with source and sink Lang, Jianying; Fu, Guo-Yong; Chen, Yang Physics of Plasmas, Vol. 17, Issue 4 https://doi.org/10.1063/1.3394702	journal	April 2010
Chaotic hyperjerk systems Chlouverakis, Konstantinos E.; Sprott, J. C. Chaos, Solitons & Fractals, Vol. 28, Issue 3 https://doi.org/10.1016/j.chaos.2005.08.019	journal	May 2006
Theory and observation of the onset of nonlinear structures due to eigenmode destabilization by fast ions in tokamaks Duarte, V. N.; Berk, H. L.; Gorelenkov, N. N. Physics of Plasmas, Vol. 24, Issue 12 https://doi.org/10.1063/1.5007811	journal	December 2017
Energetic particle physics in fusion research in preparation for burning plasma experiments Gorelenkov, N. N.; Pinches, S. D.; Toi, K. Nuclear Fusion, Vol. 54, Issue 12 https://doi.org/10.1088/0029-5515/54/12/125001	journal	November 2014
Nonlinear excitation of subcritical fast ion-driven modes Lesur, M.; Itoh, K.; Ido, T. Nuclear Fusion, Vol. 56, Issue 5 https://doi.org/10.1088/0029-5515/56/5/056009	journal	April 2016
On the Construction and Comparison of Difference Schemes Strang, Gilbert SIAM Journal on Numerical Analysis, Vol. 5, Issue 3 https://doi.org/10.1137/0705041	journal	September 1968
The Piecewise Parabolic Method (PPM) for gas-dynamical simulations Colella, Phillip; Woodward, Paul R. Journal of Computational Physics, Vol. 54, Issue 1 https://doi.org/10.1016/0021-9991(84)90143-8	journal	April 1984
Basic physics of Alfvén instabilities driven by energetic particles in toroidally confined plasmas Heidbrink, W. W. Physics of Plasmas, Vol. 15, Issue 5 https://doi.org/10.1063/1.2838239	journal	May 2008
Critical nonlinear phenomena for kinetic instabilities near threshold Breizman, B. N.; Berk, H. L.; Pekker, M. S. Physics of Plasmas, Vol. 4, Issue 5 https://doi.org/10.1063/1.872286	journal	May 1997
Fully nonlinear phenomenology of the Berk–Breizman augmentation of the Vlasov–Maxwell system Vann, R. G. L.; Dendy, R. O.; Rowlands, G. Physics of Plasmas, Vol. 10, Issue 3 https://doi.org/10.1063/1.1539854	journal	March 2003
A Critical Comparison of Eulerian-Grid-Based Vlasov Solvers Arber, T. D.; Vann, R. G. L. Journal of Computational Physics, Vol. 180, Issue 1 https://doi.org/10.1006/jcph.2002.7098	journal	July 2002
The role of energetic particles in fusion plasmas Pinches, S. D.; Berk, H. L.; Borba, D. N. Plasma Physics and Controlled Fusion, Vol. 46, Issue 12B https://doi.org/10.1088/0741-3335/46/12B/017	journal	November 2004
Fast ion loss in a ‘sea-of-TAE’ Fredrickson, E. D.; Gorelenkov, N. N.; Bell, R. E. Nuclear Fusion, Vol. 46, Issue 10 https://doi.org/10.1088/0029-5515/46/10/S09	journal	September 2006
Spontaneous hole-clump pair creation in weakly unstable plasmas Berk, H. L.; Breizman, B. N.; Petviashvili, N. V. Physics Letters A, Vol. 234, Issue 3 https://doi.org/10.1016/S0375-9601(97)00523-9	journal	September 1997
Hole-Clump Pair Creation in the Evolution of Energetic-Particle-Driven Geodesic Acoustic Modes Wang, Hao; Todo, Yasushi; Kim, Charlson C. Physical Review Letters, Vol. 110, Issue 15 https://doi.org/10.1103/PhysRevLett.110.155006	journal	April 2013
Sur les courbes définies par des équations différentielles Bendixson, Ivar Acta Mathematica, Vol. 24, Issue 0 https://doi.org/10.1007/BF02403068	journal	January 1901
Radial Localization of Toroidicity-Induced Alfvén Eigenmodes Wang, Zhixuan; Lin, Zhihong; Holod, Ihor Physical Review Letters, Vol. 111, Issue 14 https://doi.org/10.1103/PhysRevLett.111.145003	journal	October 2013
Physics of Alfvén waves and energetic particles in burning plasmas Chen, Liu; Zonca, Fulvio Reviews of Modern Physics, Vol. 88, Issue 1 https://doi.org/10.1103/RevModPhys.88.015008	journal	March 2016
The Design and Implementation of FFTW3 Frigo, M.; Johnson, S. G. Proceedings of the IEEE, Vol. 93, Issue 2 https://doi.org/10.1109/JPROC.2004.840301	journal	February 2005
�ber die partiellen Differenzengleichungen der mathematischen Physik Courant, R.; Friedrichs, K.; Lewy, H. Mathematische Annalen, Vol. 100, Issue 1 https://doi.org/10.1007/BF01448839	journal	December 1928
Neue Begr�ndung der Theorie der endlichen Transformationsgruppen Schur, Friedrich Mathematische Annalen, Vol. 35, Issue 1-2 https://doi.org/10.1007/BF01443876	journal	March 1889
The integration of the vlasov equation in configuration space Cheng, C. Z.; Knorr, Georg Journal of Computational Physics, Vol. 22, Issue 3 https://doi.org/10.1016/0021-9991(76)90053-X	journal	November 1976
Prediction of Nonlinear Evolution Character of Energetic-Particle-Driven Instabilities Duarte, Vinicius; Berk, Herbert; Gorelenkov, Nikolai arXiv https://doi.org/10.48550/arxiv.1610.05059	text	January 2016

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Analytical solutions for nonlinear plasma waves with time-varying complex frequency Woods, Benjamin J. Q. arXiv https://doi.org/10.48550/arxiv.1905.03104	preprint	January 2019