Analytic stability boundaries for compressional and global Alfvén eigenmodes driven by fast ions. I. Interaction via ordinary and anomalous cyclotron resonances

Lestz, J. B.; Gorelenkov, N. N.; Belova, E. V.; Tang, S. X.; Crocker, N. A.

doi:10.1063/1.5127551

Analytic stability boundaries for compressional and global Alfvén eigenmodes driven by fast ions. I. Interaction via ordinary and anomalous cyclotron resonances

Journal Article · Tue Feb 18 04:00:00 EST 2020 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.5127551· OSTI ID:1616947

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Princeton Univ., NJ (United States); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Univ. of California, Los Angeles, CA (United States)

Conditions for net fast ion drive are derived for beam-driven, sub-cyclotron compressional (CAE) and global (GAE) Alfvén eigenmodes, such as those routinely observed in spherical tokamaks such as NSTX(-U) and MAST. Both co- and counter-propagating CAEs and GAEs are investigated, driven by the ordinary and anomalous Doppler-shifted cyclotron resonance with fast ions. Whereas prior results were restricted to vanishingly narrow distributions in velocity space, broad parameter regimes are identified in this work which enable an analytic treatment for realistic fast ion distributions generated by neutral beam injection. The simple, approximate conditions derived in these regimes for beam distributions of realistic width compare well to the numerical evaluation of the full analytic expressions for fast ion drive. Additionally, previous results in the very narrow beam case are corrected and generalized to retain all terms in ω/ω_ci and |k_∥/k_⊥|, which are often assumed to be small parameters but can significantly modify the conditions of drive and damping when they are non-negligible. Lastly, favorable agreement is demonstrated between the approximate stability criterion, simulation results, and a large database of NSTX observations of cntr-GAEs.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-09CH11466; SC0011810

OSTI ID:: 1616947

Alternate ID(s):: OSTI ID: 1600047

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 2 Vol. 27; ISSN 1070-664X

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

Country of Publication:: United States

Language:: English

References (54)

New techniques for calculating heat and particle source rates due to neutral beam injection in axisymmetric tokamaks Goldston, R. J.; McCune, D. C.; Towner, H. H. Journal of Computational Physics, Vol. 43, Issue 1 https://doi.org/10.1016/0021-9991(81)90111-X	journal	September 1981
The tokamak Monte Carlo fast ion module NUBEAM in the National Transport Code Collaboration library Pankin, Alexei; McCune, Douglas; Andre, Robert Computer Physics Communications, Vol. 159, Issue 3 https://doi.org/10.1016/j.cpc.2003.11.002	journal	June 2004
Compressional Alfvén eigenmode dispersion in low aspect ratio plasmas Gorelenkov, N. N.; Cheng, C. Z.; Fredrickson, E. Physics of Plasmas, Vol. 9, Issue 8 https://doi.org/10.1063/1.1492803	journal	August 2002
Localization of compressional Alfvén eigenmodes in spherical tori Smith, H.; Fülöp, T.; Lisak, M. Physics of Plasmas, Vol. 10, Issue 5 https://doi.org/10.1063/1.1566441	journal	May 2003
Self-consistent equilibrium model of low aspect-ratio toroidal plasma with energetic beam ions Belova, E. V.; Gorelenkov, N. N.; Cheng, C. Z. Physics of Plasmas, Vol. 10, Issue 8 https://doi.org/10.1063/1.1592155	journal	August 2003
Destabilization of fast magnetoacoustic waves by circulating energetic ions in toroidal plasmas Belikov, V. S.; Kolesnichenko, Ya. I.; White, R. B. Physics of Plasmas, Vol. 10, Issue 12 https://doi.org/10.1063/1.1625375	journal	December 2003
Phenomenology of compressional Alfvén eigenmodes Fredrickson, E. D.; Gorelenkov, N. N.; Menard, J. Physics of Plasmas, Vol. 11, Issue 7 https://doi.org/10.1063/1.1760094	journal	July 2004
On the stabilization of fast magnetoacoustic waves by toroidally trapped energetic ions Belikov, V. S.; Kolesnichenko, Ya. I.; White, R. B. Physics of Plasmas, Vol. 11, Issue 12 https://doi.org/10.1063/1.1809121	journal	December 2004
High-frequency shear Alfvén instability driven by circulating energetic ions in NSTX Kolesnichenko, Ya. I.; White, R. B.; Yakovenko, Yu. V. Physics of Plasmas, Vol. 13, Issue 12 https://doi.org/10.1063/1.2402129	journal	December 2006
Conventional and nonconventional global Alfvén eigenmodes in stellarators Kolesnichenko, Ya. I.; Lutsenko, V. V.; Weller, A. Physics of Plasmas, Vol. 14, Issue 10 https://doi.org/10.1063/1.2789558	journal	October 2007
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
Non-linear modulation of short wavelength compressional Alfvén eigenmodes Fredrickson, E. D.; Gorelenkov, N. N.; Podesta, M. Physics of Plasmas, Vol. 20, Issue 4 https://doi.org/10.1063/1.4801663	journal	April 2013
Bi-directional Alfvén cyclotron instabilities in the mega-amp spherical tokamak Sharapov, S. E.; Lilley, M. K.; Akers, R. Physics of Plasmas, Vol. 21, Issue 8 https://doi.org/10.1063/1.4891322	journal	August 2014
Nonlinear simulations of beam-driven compressional Alfvén eigenmodes in NSTX Belova, E. V.; Gorelenkov, N. N.; Crocker, N. A. Physics of Plasmas, Vol. 24, Issue 4 https://doi.org/10.1063/1.4979278	journal	April 2017
Energetic-particle-modified global Alfvén eigenmodes Lestz, J. B.; Belova, E. V.; Gorelenkov, N. N. Physics of Plasmas, Vol. 25, Issue 4 https://doi.org/10.1063/1.4998602	journal	April 2018
Radial energy flux during destabilized Alfvén eigenmodes Kolesnichenko, Ya. I.; Tykhyy, A. V. Physics of Plasmas, Vol. 25, Issue 10 https://doi.org/10.1063/1.5048380	journal	October 2018
Mechanisms of the energy transfer across the magnetic field by Alfvén waves in toroidal plasmas Kolesnichenko, Ya. I.; Yakovenko, Yu. V.; Tyshchenko, M. H. Physics of Plasmas, Vol. 25, Issue 12 https://doi.org/10.1063/1.5049543	journal	December 2018
Numerical simulations of global Alfvén eigenmodes excitation and stabilization in NSTX-U Belova, E. V.; Fredrickson, E. D.; Lestz, J. B. Physics of Plasmas, Vol. 26, Issue 9 https://doi.org/10.1063/1.5116357	journal	September 2019
Analytic stability boundaries for compressional and global Alfvén eigenmodes driven by fast ions. II. Interaction via Landau resonance Lestz, J. B.; Gorelenkov, N. N.; Belova, E. V. Physics of Plasmas, Vol. 27, Issue 2 https://doi.org/10.1063/1.5127552	journal	February 2020
Stability of the global Alfvén eigenmode in the presence of fusion alpha particles in an ignited tokamak plasma Fu, G. Y.; Van Dam, J. W. Physics of Fluids B: Plasma Physics, Vol. 1, Issue 12 https://doi.org/10.1063/1.859175	journal	December 1989
Discrete Alfvén eigenmode spectrum in magnetohydrodynamics Mahajan, S. M. Physics of Fluids, Vol. 26, Issue 8 https://doi.org/10.1063/1.864404	journal	January 1983
Spectrum of compressional Alfvén waves Mahajan, S. M. Physics of Fluids, Vol. 26, Issue 9 https://doi.org/10.1063/1.864445	journal	January 1983
Kinetic theory of shear Alfvén waves Mahajan, S. M. Physics of Fluids, Vol. 27, Issue 9 https://doi.org/10.1063/1.864878	journal	January 1984
Destabilization of global Alfvén eigenmodes and kinetic Alfvén waves by alpha particles in a tokamak plasma Li, Yan Ming; Mahajan, Swadesh M.; Ross, David W. Physics of Fluids, Vol. 30, Issue 5 https://doi.org/10.1063/1.866260	journal	January 1987
Excitation of Alfvén cyclotron instability by charged fusion products in tokamaks Gorelenkov, N. N.; Cheng, C. Z. Physics of Plasmas, Vol. 2, Issue 6 https://doi.org/10.1063/1.871281	journal	June 1995
Magnetosonic eigenmodes near the magnetic field well in a spherical torus Gorelenkova, M. V.; Gorelenkov, N. N. Physics of Plasmas, Vol. 5, Issue 11 https://doi.org/10.1063/1.873133	journal	November 1998
Fast-wave heating of a two-component plasma Stix, T. H. Nuclear Fusion, Vol. 15, Issue 5 https://doi.org/10.1088/0029-5515/15/5/003	journal	October 1975
Alfven cyclotron instability and ion cyclotron emission Gorelenkov, N. N.; Cheng, C. Z. Nuclear Fusion, Vol. 35, Issue 12 https://doi.org/10.1088/0029-5515/35/12/I39	journal	December 1995
Localized fast magnetoacoustic eigenmodes in tokamak plasmas Kolesnichenko, Ya. I.; Fülöp, T.; Lisak, M. Nuclear Fusion, Vol. 38, Issue 12 https://doi.org/10.1088/0029-5515/38/12/311	journal	December 1998
On properties of compressional Alfv n eigenmode instability driven by superAlfv nic ions Gorelenkov, N. N.; Cheng, C. Z. Nuclear Fusion, Vol. 42, Issue 10 https://doi.org/10.1088/0029-5515/42/10/307	journal	September 2002
Compressional Alfvén eigenmode instability in NSTX Gorelenkov, N. N.; Cheng, C. Z.; Fredrickson, E. Nuclear Fusion, Vol. 42, Issue 8 https://doi.org/10.1088/0029-5515/42/8/306	journal	August 2002
Theory and observations of high frequency Alfv n eigenmodes in low aspect ratio plasmas Gorelenkov, N. N.; Fredrickson, E.; Belova, E. Nuclear Fusion, Vol. 43, Issue 4 https://doi.org/10.1088/0029-5515/43/4/302	journal	March 2003
Discrete compressional Alfvén eigenmode spectrum in tokamaks Gorelenkov, N. N.; Fredrickson, E. D.; Heidbrink, W. W. Nuclear Fusion, Vol. 46, Issue 10 https://doi.org/10.1088/0029-5515/46/10/S10	journal	September 2006
Observation of compressional Alfvén eigenmodes (CAE) in a conventional tokamak Heidbrink, W. W.; Fredrickson, E. D.; Gorelenkov, N. N. Nuclear Fusion, Vol. 46, Issue 2 https://doi.org/10.1088/0029-5515/46/2/016	journal	January 2006
Effects of energetic-ion-driven instabilities on plasma heating, transport and rotation in toroidal systems Kolesnichenko, Ya. I.; Yakovenko, Yu. V.; Lutsenko, V. V. Nuclear Fusion, Vol. 50, Issue 8 https://doi.org/10.1088/0029-5515/50/8/084011	journal	July 2010
Anomalous electron transport due to multiple high frequency beam ion driven Alfvén eigenmodes Gorelenkov, N. N.; Stutman, D.; Tritz, K. Nuclear Fusion, Vol. 50, Issue 8 https://doi.org/10.1088/0029-5515/50/8/084012	journal	July 2010
Internal amplitude, structure and identification of compressional and global Alfvén eigenmodes in NSTX Crocker, N. A.; Fredrickson, E. D.; Gorelenkov, N. N. Nuclear Fusion, Vol. 53, Issue 4 https://doi.org/10.1088/0029-5515/53/4/043017	journal	March 2013
Excitation of global eigenmodes of the Alfven wave in Tokamaks Appert, K.; Gruber, R.; Troyuon, F. Plasma Physics, Vol. 24, Issue 9 https://doi.org/10.1088/0032-1028/24/9/010	journal	September 1982
Compressional Alfvén Eigenmodes on MAST Appel, L. C.; Fülöp, T.; Hole, M. J. Plasma Physics and Controlled Fusion, Vol. 50, Issue 11 https://doi.org/10.1088/0741-3335/50/11/115011	journal	October 2008
Compressional Alfvén eigenmode structure in spherical tokamaks Smith, H. M.; Verwichte, E. Plasma Physics and Controlled Fusion, Vol. 51, Issue 7 https://doi.org/10.1088/0741-3335/51/7/075001	journal	May 2009
Compressional Alfvén eigenmodes in rotating spherical tokamak plasmas Smith, H. M.; Fredrickson, E. D. Plasma Physics and Controlled Fusion, Vol. 59, Issue 3 https://doi.org/10.1088/1361-6587/aa58fd	journal	February 2017
Energetic particles in spherical tokamak plasmas McClements, K. G.; Fredrickson, E. D. Plasma Physics and Controlled Fusion, Vol. 59, Issue 5 https://doi.org/10.1088/1361-6587/aa626e	journal	March 2017
Recent progress in understanding electron thermal transport in NSTX Ren, Y.; Belova, E.; Gorelenkov, N. Nuclear Fusion, Vol. 57, Issue 7 https://doi.org/10.1088/1741-4326/aa4fba	journal	March 2017
Density perturbation mode structure of high frequency compressional and global Alfvén eigenmodes in the National Spherical Torus Experiment using a novel reflectometer analysis technique Crocker, N. A.; Kubota, S.; Peebles, W. A. Nuclear Fusion, Vol. 58, Issue 1 https://doi.org/10.1088/1741-4326/aa953e	journal	December 2017
Global Alfvén eigenmode scaling and suppression: experiment and theory Fredrickson, E. D.; Belova, E. V.; Gorelenkov, N. N. Nuclear Fusion, Vol. 58, Issue 8 https://doi.org/10.1088/1741-4326/aac64c	journal	June 2018
NSTX/NSTX-U theory, modeling and analysis results Kaye, S. M.; Battaglia, D. J.; Baver, D. Nuclear Fusion, Vol. 59, Issue 11 https://doi.org/10.1088/1741-4326/ab023a	journal	June 2019
Correlation between Electron Transport and Shear Alfvén Activity in the National Spherical Torus Experiment Stutman, D.; Delgado-Aparicio, L.; Gorelenkov, N. Physical Review Letters, Vol. 102, Issue 11 https://doi.org/10.1103/PhysRevLett.102.115002	journal	March 2009
Channeling of the Energy and Momentum during Energetic-Ion-Driven Instabilities in Fusion Plasmas Kolesnichenko, Ya. I.; Yakovenko, Yu. V.; Lutsenko, V. V. Physical Review Letters, Vol. 104, Issue 7 https://doi.org/10.1103/PhysRevLett.104.075001	journal	February 2010
Coupling of Neutral-Beam-Driven Compressional Alfvén Eigenmodes to Kinetic Alfvén Waves in NSTX Tokamak and Energy Channeling Belova, E. V.; Gorelenkov, N. N.; Fredrickson, E. D. Physical Review Letters, Vol. 115, Issue 1 https://doi.org/10.1103/PhysRevLett.115.015001	journal	June 2015
Suppression of Alfvén Modes on the National Spherical Torus Experiment Upgrade with Outboard Beam Injection Fredrickson, E. D.; Belova, E. V.; Battaglia, D. J. Physical Review Letters, Vol. 118, Issue 26 https://doi.org/10.1103/PhysRevLett.118.265001	journal	June 2017
Observation of Compressional Alfvén Modes During Neutral-Beam Heating on the National Spherical Torus Experiment Fredrickson, E. D.; Gorelenkov, N.; Cheng, C. Z. Physical Review Letters, Vol. 87, Issue 14 https://doi.org/10.1103/PhysRevLett.87.145001	journal	September 2001
Thermonuclear Instability of Global-Type Shear Alfvén Modes van Dam, James W.; Fu, Guo-Yong; Cheng, C. Z. Fusion Technology, Vol. 18, Issue 3 https://doi.org/10.13182/FST90-A29282	journal	November 1990
Observation of Compressional Alfvén Modes During Neutral-Beam Heating on the National Spherical Torus Experiment Bell, R.; Cheng, C. Z.; Darrow, D. The American Physical Society https://doi.org/10.17877/de290r-11033	text	January 2001
Analytic stability boundaries for compressional and global Alfvén eigenmodes driven by fast ions. II. Interaction via Landau resonance Lestz, J. B.; Gorelenkov, N. N.; Belova, E. V. arXiv https://doi.org/10.48550/arxiv.1909.05465	text	January 2019

Cited By (2)

Analytic stability boundaries for compressional and global Alfvén eigenmodes driven by fast ions. II. Interaction via Landau resonance Lestz, J. B.; Gorelenkov, N. N.; Belova, E. V. Physics of Plasmas, Vol. 27, Issue 2 https://doi.org/10.1063/1.5127552	journal	February 2020
Analytic stability boundaries for compressional and global Alfvén eigenmodes driven by fast ions. II. Interaction via Landau resonance Lestz, J. B.; Gorelenkov, N. N.; Belova, E. V. arXiv https://doi.org/10.48550/arxiv.1909.05465	text	January 2019

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