On the Effect of Beating during Nonlinear Frequency Chirping
Abstract
Spectroscopic analyses of energetic particle (EP) driven bursts of MHD fluctuations in magnetically confined plasmas often exhibit chirps that occur simultaneously in groups of two or more. While the superposition of oscillations at multiple frequencies necessarily causes beating in the signal acquired by a localized external probe, self-consistent hybrid simulations of chirping EP modes in a JT-60U tokamak plasma have demonstrated the possibility of global beating, where the mode's electromagnetic field vanishes globally between beats and reappears with opposite phase [Bierwage et al., Nucl. Fusion 57, 016036 (2017)]. This implies that there can be a single coherent field mode that oscillates at multiple frequencies simultaneously when it is resonantly driven by multiple density waves in EP phase space. Conversely, this means that the EP density waves are mutually coupled and interfere with each other via the jointly driven field, a mechanism ignored in some theories of chirping. In this thesis-style treatise, we study the role of field pulsations in general and beating in particular using the Hamiltonian guiding center orbit-following code ORBIT with a reduced wave-particle interaction model in realistic geometry. Beating is found to drive the evolution of EP phase space structures. Additionally, a key mechanism is the pulsationmore »
- Authors:
-
- National Institutes for Quantum and Radiological Science and Technology (QST), Rokkasho Fusion Inst., Aomori (Japan).; National Institutes for Quantum and Radiological Science and Technology (QST), Naka Fusion Inst., Ibaraki (Japan)
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Publication Date:
- Research Org.:
- Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1818986
- Grant/Contract Number:
- AC02-09CH11466
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Plasma and Fusion Research
- Additional Journal Information:
- Journal Volume: 16; Journal Issue: 0; Journal ID: ISSN 1880-6821
- Publisher:
- Japan Society of Plasma Science and Nuclear Fusion Research
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; tokamak; fast particles; Hamiltonian guiding center simulation; phase space dynamics; chirping
Citation Formats
Bierwage, Andreas, White, Roscoe B., and Duarte, Vinícius N. On the Effect of Beating during Nonlinear Frequency Chirping. United States: N. p., 2021.
Web. doi:10.1585/pfr.16.1403087.
Bierwage, Andreas, White, Roscoe B., & Duarte, Vinícius N. On the Effect of Beating during Nonlinear Frequency Chirping. United States. https://doi.org/10.1585/pfr.16.1403087
Bierwage, Andreas, White, Roscoe B., and Duarte, Vinícius N. Mon .
"On the Effect of Beating during Nonlinear Frequency Chirping". United States. https://doi.org/10.1585/pfr.16.1403087. https://www.osti.gov/servlets/purl/1818986.
@article{osti_1818986,
title = {On the Effect of Beating during Nonlinear Frequency Chirping},
author = {Bierwage, Andreas and White, Roscoe B. and Duarte, Vinícius N.},
abstractNote = {Spectroscopic analyses of energetic particle (EP) driven bursts of MHD fluctuations in magnetically confined plasmas often exhibit chirps that occur simultaneously in groups of two or more. While the superposition of oscillations at multiple frequencies necessarily causes beating in the signal acquired by a localized external probe, self-consistent hybrid simulations of chirping EP modes in a JT-60U tokamak plasma have demonstrated the possibility of global beating, where the mode's electromagnetic field vanishes globally between beats and reappears with opposite phase [Bierwage et al., Nucl. Fusion 57, 016036 (2017)]. This implies that there can be a single coherent field mode that oscillates at multiple frequencies simultaneously when it is resonantly driven by multiple density waves in EP phase space. Conversely, this means that the EP density waves are mutually coupled and interfere with each other via the jointly driven field, a mechanism ignored in some theories of chirping. In this thesis-style treatise, we study the role of field pulsations in general and beating in particular using the Hamiltonian guiding center orbit-following code ORBIT with a reduced wave-particle interaction model in realistic geometry. Beating is found to drive the evolution of EP phase space structures. Additionally, a key mechanism is the pulsation of effective phase space islands combined with the alternation of their effective O- and X-points due to phase jumps between each beat. Observations: (1) Beating causes density wave fronts to advance radially in a pulsed manner and the resulting chirps become staircase-like. (2) The pulsations facilitate convective transfer of material between neighboring layers of phase space density waves. On the one hand, this may inhibit the early detachment of solitary phase space vortices. On the other hand, it facilitates the accumulation of hole and clump fragments into larger structures. (3) Long-range chirping is observed when massive holes or clumps detach and drift away from the turbulent belt around the seed resonance. It is remarkable that the detached vortices remain robust and,on average, maintain their concentric nested layers while being visibly perturbed by the field's continued beating.},
doi = {10.1585/pfr.16.1403087},
journal = {Plasma and Fusion Research},
number = 0,
volume = 16,
place = {United States},
year = {Mon Jul 12 00:00:00 EDT 2021},
month = {Mon Jul 12 00:00:00 EDT 2021}
}
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Works referenced in this record:
Nonlinear dynamics of toroidal Alfvén eigenmodes in the presence of tearing modes
journal, February 2018
- Zhu, J.; Ma, Z. W.; Wang, S.
- Nuclear Fusion, Vol. 58, Issue 4
The Synchrotron—A Proposed High Energy Particle Accelerator
journal, September 1945
- McMillan, Edwin M.
- Physical Review, Vol. 68, Issue 5-6
Physics of Alfvén waves and energetic particles in burning plasmas
journal, March 2016
- Chen, Liu; Zonca, Fulvio
- Reviews of Modern Physics, Vol. 88, Issue 1
Fast ion profile stiffness due to the resonance overlap of multiple Alfvén eigenmodes
journal, July 2016
- Todo, Y.; Van Zeeland, M. A.; Heidbrink, W. W.
- Nuclear Fusion, Vol. 56, Issue 11
Validation of comprehensive magnetohydrodynamic hybrid simulations for Alfvén eigenmode induced energetic particle transport in DIII-D plasmas
journal, June 2015
- Todo, Y.; Van Zeeland, M. A.; Bierwage, A.
- Nuclear Fusion, Vol. 55, Issue 7
Hamiltonian guiding center drift orbit calculation for plasmas of arbitrary cross section
journal, January 1984
- White, R. B.; Chance, M. S.
- Physics of Fluids, Vol. 27, Issue 10
Orbit-based analysis of resonant excitations of Alfvén waves in tokamaks
journal, November 2014
- Bierwage, Andreas; Shinohara, Kouji
- Physics of Plasmas, Vol. 21, Issue 11
Nonlinear travelling waves in energetic particle phase space
journal, July 2010
- Breizman, Boris N.
- Nuclear Fusion, Vol. 50, Issue 8
Spontaneous hole-clump pair creation in weakly unstable plasmas
journal, September 1997
- Berk, H. L.; Breizman, B. N.; Petviashvili, N. V.
- Physics Letters A, Vol. 234, Issue 3
Existence of discrete modes in an unstable shear Alfvén continuous spectrum
journal, December 1998
- Zonca, Fulvio; Chen, Liu; Santoro, Robert A.
- Plasma Physics and Controlled Fusion, Vol. 40, Issue 12
Saturation of kinetic plasma instabilities by particle trapping
journal, January 1973
- Dewar, R. L.
- Physics of Fluids, Vol. 16, Issue 3
Effects of the non-perturbative mode structure on energetic particle transport
journal, April 2020
- Meng, G.; Lauber, Ph.; Lu, Z.
- Nuclear Fusion, Vol. 60, Issue 5
Modeling of long range frequency sweeping for energetic particle modes
journal, April 2013
- Nyqvist, R. M.; Breizman, B. N.
- Physics of Plasmas, Vol. 20, Issue 4
Mechanisms of energetic-particle transport in magnetically confined plasmas
journal, March 2020
- Heidbrink, W. W.; White, R. B.
- Physics of Plasmas, Vol. 27, Issue 3
Particle resonances in toroidal fusion devices
journal, March 2021
- White, Roscoe; Bierwage, Andreas
- Physics of Plasmas, Vol. 28, Issue 3
Nonlinear Splitting of Fast Particle Driven Waves in a Plasma: Observation and Theory
journal, December 1998
- Fasoli, A.; Breizman, B. N.; Borba, D.
- Physical Review Letters, Vol. 81, Issue 25
A modulation model for mode splitting of magnetic perturbations in the Mega Ampere Spherical Tokamak
journal, January 2009
- Hole, M. J.; Appel, L. C.
- Plasma Physics and Controlled Fusion, Vol. 51, Issue 4
The HAGIS self-consistent nonlinear wave-particle interaction model
journal, June 1998
- Pinches, S. D.; Appel, L. C.; Candy, J.
- Computer Physics Communications, Vol. 111, Issue 1-3
Experimental observation of multi-scale interactions among kink /tearing modes and high-frequency fluctuations in the HL-2A core NBI plasmas
journal, August 2017
- Chen, W.; Jiang, M.; Xu, Y.
- Nuclear Fusion, Vol. 57, Issue 11
Modeling of chirping toroidal Alfvén eigenmodes in NSTX
journal, September 2019
- White, R. B.; Duarte, V. N.; Gorelenkov, N. N.
- Physics of Plasmas, Vol. 26, Issue 9
Nonlinear wave interactions generate high-harmonic cyclotron emission from fusion-born protons during a KSTAR ELM crash
journal, July 2018
- Chapman, B.; Dendy, R. O.; Chapman, S. C.
- Nuclear Fusion, Vol. 58, Issue 9
Gyrokinetic analysis of low-n shear Alfvén and ion sound wave spectra in a high-beta tokamak plasma
journal, September 2017
- Bierwage, Andreas; Lauber, Philipp
- Nuclear Fusion, Vol. 57, Issue 11
Exact Nonlinear Plasma Oscillations
journal, November 1957
- Bernstein, Ira B.; Greene, John M.; Kruskal, Martin D.
- Physical Review, Vol. 108, Issue 3
Enhanced radial energy transport induced by radially curved Alfvén eigenmode wavefronts
journal, July 2019
- Kramer, G. J.; Tobias, B. J.; Turnbull, A.
- Nuclear Fusion, Vol. 59, Issue 9
Resonance frequency broadening of wave-particle interaction in tokamaks due to Alfvénic eigenmode
journal, June 2018
- Meng, G.; Gorelenkov, N. N.; Duarte, V. N.
- Nuclear Fusion, Vol. 58, Issue 8
LIGKA: A linear gyrokinetic code for the description of background kinetic and fast particle effects on the MHD stability in tokamaks
journal, September 2007
- Lauber, Ph.; Günter, S.; Könies, A.
- Journal of Computational Physics, Vol. 226, Issue 1
Numerical Studies of the Nonlinear Vlasov Equation
journal, January 1967
- Armstrong, Thomas P.
- Physics of Fluids, Vol. 10, Issue 6
Theory of magnetohydrodynamic instabilities excited by energetic particles in tokamaks*
journal, May 1994
- Chen, Liu
- Physics of Plasmas, Vol. 1, Issue 5
Phase-space dynamics of Alfvén mode chirping
journal, May 2020
- White, R. B.; Duarte, V. N.; Gorelenkov, N. N.
- Physics of Plasmas, Vol. 27, Issue 5
Simulation of intermittent beam ion loss in a Tokamak Fusion Test Reactor experiment
journal, July 2003
- Todo, Y.; Berk, H. L.; Breizman, B. N.
- Physics of Plasmas, Vol. 10, Issue 7
Adiabatic description of long range frequency sweeping
journal, September 2012
- Nyqvist, R. M.; Lilley, M. K.; Breizman, B. N.
- Nuclear Fusion, Vol. 52, Issue 9
Simulation Study of Alfvén-Eigenmode-Induced Energetic Ion Transport in LHD
journal, January 2013
- Nishimura, Seiya; Todo, Yasushi; Spong, Donald A.
- Plasma and Fusion Research, Vol. 8, Issue 0
Orbit-based representation of equilibrium distribution functions for low-noise initialization of kinetic simulations of toroidal plasmas
journal, May 2012
- Bierwage, A.; Di Troia, C.; Briguglio, S.
- Computer Physics Communications, Vol. 183, Issue 5
Long range frequency chirping of Alfvén eigenmodes
journal, April 2020
- Hezaveh, H.; Qu, Z. S.; Breizman, B. N.
- Nuclear Fusion, Vol. 60, Issue 5
Stability of beta-induced Alfvén eigenmodes (BAE) in DIII-D
journal, May 2021
- Heidbrink, W. W.; Van Zeeland, M. A.; Austin, M. E.
- Nuclear Fusion, Vol. 61, Issue 6
A high-resolution technique for multidimensional NMR spectroscopy
journal, January 1998
- Li, Y.; Razavilar, J.; Liu, K. J. Ray
- IEEE Transactions on Biomedical Engineering, Vol. 45, Issue 1
Self-consistent long-time simulation of chirping and beating energetic particle modes in JT-60U plasmas
journal, December 2016
- Bierwage, A.; Shinohara, K.; Todo, Y.
- Nuclear Fusion, Vol. 57, Issue 1
Kinetic theory of low-frequency Alfvén modes in tokamaks
journal, November 1996
- Zonca, Fulvio; Chen, Liu; Santoro, Robert A.
- Plasma Physics and Controlled Fusion, Vol. 38, Issue 11
The MHD continuum with a radial electric field
journal, December 2020
- Könies, Axel; Slaby, Christoph; Kleiber, Ralf
- Physics of Plasmas, Vol. 27, Issue 12
Theory of mode-induced beam particle loss in tokamaks
journal, January 1983
- White, R. B.
- Physics of Fluids, Vol. 26, Issue 10
A water bag theory of autoresonant Bernstein-Greene-Kruskal modes
journal, August 2007
- Khain, P.; Friedland, L.
- Physics of Plasmas, Vol. 14, Issue 8
Theoretical description of chirping waves using phase-space waterbags
journal, April 2021
- Hezaveh, H.; Qu, Z. S.; Hole, M. J.
- Plasma Physics and Controlled Fusion, Vol. 63, Issue 6
Alpha‐particle losses from toroidicity‐induced Alfvén eigenmodes. Part I: Phase‐space topology of energetic particle orbits in tokamak plasma
journal, June 1992
- Hsu, C. T.; Sigmar, D. J.
- Physics of Fluids B: Plasma Physics, Vol. 4, Issue 6
Spectroscopic determination of the internal amplitude of frequency sweeping TAE
journal, May 2004
- Pinches, S. D.; Berk, H. L.; Gryaznevich, M. P.
- Plasma Physics and Controlled Fusion, Vol. 46, Issue 7
Dynamics of reversed shear Alfvén eigenmode and energetic particles during current ramp-up
journal, October 2020
- Wang, Tao; Qiu, Zhiyong; Zonca, Fulvio
- Nuclear Fusion, Vol. 60, Issue 12
Frequency chirping in the Alfvén continuum
journal, June 2018
- Wang, G.; Berk, H. L.; Breizman, B. N.
- Nuclear Fusion, Vol. 58, Issue 8
Chaotic Regime of Alfvén Eigenmode Wave-Particle Interaction
journal, October 2000
- Heeter, R. F.; Fasoli, A. F.; Sharapov, S. E.
- Physical Review Letters, Vol. 85, Issue 15
Orbit-based analysis of nonlinear energetic ion dynamics in tokamaks. II. Mechanisms for rapid chirping and convective amplification
journal, April 2016
- Bierwage, Andreas; Shinohara, Kouji
- Physics of Plasmas, Vol. 23, Issue 4
Orbit-based analysis of nonlinear energetic ion dynamics in tokamaks. I. Effective mode number profile and resonant frequency tracking
journal, April 2016
- Bierwage, Andreas; Shinohara, Kouji
- Physics of Plasmas, Vol. 23, Issue 4
Simulations tackle abrupt massive migrations of energetic beam ions in a tokamak plasma
journal, August 2018
- Bierwage, Andreas; Shinohara, Kouji; Todo, Yasushi
- Nature Communications, Vol. 9, Issue 1
Formation of Phase Space Holes and Clumps
journal, April 2014
- Lilley, M. K.; Nyqvist, R. M.
- Physical Review Letters, Vol. 112, Issue 15
Investigation of mode activity in NBI-heated experiments of Wendelstein 7-X
journal, August 2020
- Slaby, C.; Äkäslompolo, S.; Borchardt, M.
- Nuclear Fusion, Vol. 60, Issue 11
Quantum Phenomena in a Chirped Parametric Anharmonic Oscillator
journal, July 2014
- Barth, I.; Friedland, L.
- Physical Review Letters, Vol. 113, Issue 4
Numerical study of the nonlinear evolution of toroidicity-induced Alfvén eigenmodes
journal, January 1999
- Chen, Yang; White, Roscoe B.; Fu, Guo-yong
- Physics of Plasmas, Vol. 6, Issue 1
Spontaneous hole–clump pair creation
journal, August 1999
- Berk, H. L.; Breizman, B. N.; Candy, J.
- Physics of Plasmas, Vol. 6, Issue 8
Impact of energetic particle orbits on long range frequency chirping of BGK modes
journal, September 2017
- Hezaveh, H.; Qu, Z. S.; Layden, B.
- Nuclear Fusion, Vol. 57, Issue 12
Particle dynamics in chirped-frequency fluctations
journal, April 1994
- Hsu, C. T.; Cheng, C. Z.; Helander, P.
- Physical Review Letters, Vol. 72, Issue 16
Introduction to the interaction between energetic particles and Alfven eigenmodes in toroidal plasmas
journal, December 2018
- Todo, Y.
- Reviews of Modern Plasma Physics, Vol. 3, Issue 1
Nonlinear dynamics of phase space zonal structures and energetic particle physics in fusion plasmas
journal, January 2015
- Zonca, F.; Chen, L.; Briguglio, S.
- New Journal of Physics, Vol. 17, Issue 1
Nonlinear Study of Vlasov's Equation for a Special Class of Distribution Functions
journal, January 1967
- Berk, H. L.
- Physics of Fluids, Vol. 10, Issue 7
Orbit-based representation of equilibrium distribution functions for low-noise initialization of kinetic simulations of toroidal plasmas
journal, May 2012
- Bierwage, A.; Di Troia, C.; Briguglio, S.
- Computer Physics Communications, Vol. 183, Issue 5
Simulation of intermittent beam ion loss in a Tokamak Fusion Test Reactor experiment
journal, July 2003
- Todo, Y.; Berk, H. L.; Breizman, B. N.
- Physics of Plasmas, Vol. 10, Issue 7
Orbit-based analysis of resonant excitations of Alfvén waves in tokamaks
journal, November 2014
- Bierwage, Andreas; Shinohara, Kouji
- Physics of Plasmas, Vol. 21, Issue 11
Orbit-based analysis of nonlinear energetic ion dynamics in tokamaks. I. Effective mode number profile and resonant frequency tracking
journal, April 2016
- Bierwage, Andreas; Shinohara, Kouji
- Physics of Plasmas, Vol. 23, Issue 4
Orbit-based analysis of nonlinear energetic ion dynamics in tokamaks. II. Mechanisms for rapid chirping and convective amplification
journal, April 2016
- Bierwage, Andreas; Shinohara, Kouji
- Physics of Plasmas, Vol. 23, Issue 4
Nonlinear travelling waves in energetic particle phase space
journal, July 2010
- Breizman, Boris N.
- Nuclear Fusion, Vol. 50, Issue 8
Impact of energetic particle orbits on long range frequency chirping of BGK modes
journal, September 2017
- Hezaveh, H.; Qu, Z. S.; Layden, B.
- Nuclear Fusion, Vol. 57, Issue 12
Below-the-Knee Amputation With Targeted Muscle Reinnervation: Operative Technique and Technical Pearls of an Interfascicular Superficial Peroneal Nerve Targeted Muscle Reinnervation
journal, October 2020
- Chang, Brian L.; Kleiber, Grant M.
- Plastic and Reconstructive Surgery - Global Open, Vol. 8, Issue 9S