Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-13T02:12:55.997Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear dispersion relation of geodesic acoustic modes driven by trapped and circulating energetic particles

Part of: Focus on Fusion

Published online by Cambridge University Press:  28 July 2021

I. Chavdarovski Open the ORCID record for I. Chavdarovski [Opens in a new window] ,
M. Schneller  and
A. Biancalani Open the ORCID record for A. Biancalani [Opens in a new window]
I. Chavdarovski*
Affiliation:
Korea Institute of Fusion Energy, 34133 Daejeon, South Korea
M. Schneller
Affiliation:
Princeton Plasma Physics Laboratory, 100 Stellarator Rd, Princeton, NJ 08540, USA
A. Biancalani
Affiliation:
Max-Planck Institute for Plasma Physics, 85748 Garching, Germany
*
†Email address for correspondence: chavdarovski@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

We derive the local dispersion relation of energetic-particle-induced geodesic acoustic modes (EGAMs) for both trapped and circulating ion beams with single pitch angle slowing-down and Maxwellian distributions, as well as a bump-on-tail distribution in tokamak plasmas. For slowing-down and Maxwellian particles, the solutions of the local dispersion relation give the spectrum, growth rate and thresholds of excitation as functions of the pitch angle, beam density and frequency of the energetic particles bounce motion. For circulating ions there is only one unstable branch with frequency below the GAM continuum and a threshold of excitation in the pitch angle, for both the slowing-down and single pitch Maxwellian distributions. Trapped particles cause no excitation of a mode for neither slowing-down nor Maxwellian ion beams, but they can excite a mode with a bump-on-tail distribution when the mean velocity of the beam is larger than the threshold and the energetic particle bounce frequency is high enough.

Keywords

fusion plasmaplasma confinementplasma simulation
Type
Research Article
Information
Journal of Plasma Physics , Volume 87 , Issue 4 , August 2021 , 905870408
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Berk, H. L., Boswell, C. J., Borba, D., Figueiredo, A. C. A., Johnson, T., Nave, M. F. F., Pinches, S. D., Sharapov, S. E. & JET EFDA contributors 2006 Explanation of the JET $n = 0$ chirping mode. Nucl. Fusion 46 (10), S888.CrossRefGoogle Scholar
Biancalani, A., Chavdarovski, I., Qiu, Z., Bottino, A., Del Sarto, D., Ghizzo, A., Gürcan, O., Morel, P. & Novikau, I. 2017 a Saturation of energetic-particle-driven geodesic acoustic modes due to wave particle nonlinearity. J. Plasma Phys. 83 (6).CrossRefGoogle Scholar
Biancalani, A., Chavdarovski, I., Qiu, Z., Di Siena, A., Gürcan, O., Jenko, F., Morel, P., Novikau, I. & Zonca, F. 2017 b Nonlinear gyrokinetic investigation of energetic particle-driven geodesic acoustic modes. In 17th European Fusion Theory Conference, Athens, R. Greece.CrossRefGoogle Scholar
Cao, J., Qiu, Z. & Zonca, F. 2008 Fast excitation of geodesic acoustic mode by energetic particle beams. Phys. Plasmas 22, 124505.CrossRefGoogle Scholar
Chavdarovski, I. 2009 Kinetic theory of low frequency Alfvén waves in burning plasmas. PhD thesis. University of Tor vergata, Rome, Italy.Google Scholar
Chavdarovski, I., Schneller, M., Qiu, Z. & Biancalani, A. 2017 Excitation of energetic particle driven Geodesic Acoustic Modes (EGAMs) by the velocity anisotropy of ion beam with slowing down and Maxwellian distribution. In 15th IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems, 5–8 September 2017, Princeton, NJ, USA P-3, p. 54.Google Scholar
Chavdarovski, I. & Zonca, F. 2009 Effects of trapped particle dynamics on the structures of a low-frequency shear Alfvén continuous spectrum. Plasma Phys. Control. Fusion 51, 115001.CrossRefGoogle Scholar
Chavdarovski, I. & Zonca, F. 2014 Analytic studies of dispersive properties of shear Alfvén and acoustic wave spectra in tokamaks. Phys. Plasmas 21, 052506.CrossRefGoogle Scholar
Chen, L. 1994 Theory of magnetohydrodynamic instabilities excited by energetic particles in tokamaks. Phys. Plasmas 1, 1519.CrossRefGoogle Scholar
Chen, L. & Hasegawa, A. 1974 Plasma heating by spatial resonance of Alfvén wave. Phys. Fluids 17, 1399.CrossRefGoogle Scholar
Chen, L., Qiu, Z. & Zonca, F. 2014 Fine structure zonal flow excitation by beta-induced Alfvén eigenmode. Europhys. Lett. 107, 15003.CrossRefGoogle Scholar
Dannert, T., Günter, S., Hauff, T., Jenko, F., Lapillonne, X. & Lauber, P. 2008 Turbulent transport of beam ions. Phys. Plasmas 15, 062508.CrossRefGoogle Scholar
Dumont, R. J., et al. 2013 Interplay between fast ions and turbulence in magnetic fusion plasmas. Plasma Phys. Control. Fusion 55 (12), 124012.CrossRefGoogle Scholar
Fu, G. Y. 2008 Energetic-particle-induced geodesic acoustic mode. Phys. Rev. Lett. 101, 185002.CrossRefGoogle ScholarPubMed
Fu, G. Y. 2011 On nonlinear self-interaction of geodesic acoustic mode driven by energetic particles. J. Plasma Phys. 77 (4), 457.CrossRefGoogle Scholar
Garbet, X., Falchetto, G., Ottaviani, M., Sabot, R., Sirinelli, A. & Smolyakov, A. 2006 Coherent modes in the acoustic frequency range in tokamaks. AIP Conf. Proc. 871 (1), 342–349.CrossRefGoogle Scholar
Grad, H. 1969 Plasmas. Phys. Today 22, 34.CrossRefGoogle Scholar
Grandgirard, V., et al. 2008 Computing ITG turbulence with a full-f semi-Lagrangian code. Commun. Nonlinear Sci. Numer. Simul. 13 (1), 81–87.CrossRefGoogle Scholar
Hasegawa, A. & Chen, L. 1974 Plasma heating by Alfvén-wave phase mixing. Phys. Rev. Lett. 32, 454.CrossRefGoogle Scholar
Heidbrink, W. W., Strait, E. J., Chu, M. S. & Turnbull, A.D. 1993 Observation of beta-induced Alfvén eigenmodes in the DIII-D tokamak. Phys. Rev. Lett. 71, 855.CrossRefGoogle ScholarPubMed
Ido, T., et al. 2015 Identification of the energetic-particle driven GAM in the LHD. Nucl. Fusion 55, 080324.CrossRefGoogle Scholar
Ma, R., Chavdarovski, I., Ye, G. & Wang, X. 2014 Linear dispersion relation of beta-induced Alfvén eigenmodes in presence of anisotropic energetic ions. Plasma Phys 21, 062120.CrossRefGoogle Scholar
McKee, G. R., Gupta, D. K., Fonck, R. J., Schlossberg, D. J., Shafer, M. W. & Gohil, P. 2006 Structure and scaling properties of the geodesic acoustic mode. Plasma Phys. Control. Fusion 48, S123–S136.CrossRefGoogle Scholar
Nazikian, R., et al. 2008 Intense geodesic acousticlike modes driven by suprathermal ions in a tokamak plasma. Phys. Rev. Lett. 101, 185001.CrossRefGoogle Scholar
Novikau, I., et al. 2020 Nonlinear dynamics of energetic-particle driven geodesic acoustic modes in ASDEX upgrade. Phys. Plasmas 27, 042512.CrossRefGoogle Scholar
Qiu, Z., Chavdarovski, I., Biancalani, A. & Cao, J. 2017 On zero frequency zonal flow and second harmonic generation by finite amplitude energetic particle induced geodesic acoustic mode. Phys. Plasmas 24, 072509.CrossRefGoogle Scholar
Qiu, Z., Chen, L. & Zonca, F. 2009 Collisionless damping of short wavelength geodesic acoustic modes. Plasma Phys. Control. Fusion 51, 012001.CrossRefGoogle Scholar
Qiu, Z., Chen, L. & Zonca, F. 2018 Kinetic theory of geodesic acoustic modes in toroidal plasmas: a brief review. Plasma Sci. Technol. 20, 094004.CrossRefGoogle Scholar
Qiu, Z., Zonca, F. & Chen, L. 2010 Nonlocal theory of energetic-particle-induced geodesic acoustic mode. Plasma Phys. Control. Fusion 52, 095003.CrossRefGoogle Scholar
Rutherford, P. H. & Frieman, E. A. 1968 Drift instabilities in general magnetic field configurations. Phys. Fluids 11, 569.CrossRefGoogle Scholar
Sasaki, M., Itoh, K. & Itoh, S.-I. 2011 Energy channeling from energetic particles to bulk ions via beam-driven geodesic acoustic modes-GAM channeling. Plasma Phys. Control. Fusion 53 (8), 085017.CrossRefGoogle Scholar
Schneller, M., Fu, G. Y., Chavdarovski, I., Wang, W. X., Lauber, Ph. & Lu, Z. X. 2017 What shapes the radial structure of energetic particle induced geodesic acoustic modes? In 15th IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems, 5–8 September 2017, Princeton, NJ, USA.Google Scholar
Schneller, M., Fu, G. Y., Wang, W. X., Chavdarovski, I. & Lauber, Ph. 2016 The effect of energetic particle induced geodesic acoustic modes on microturbulence. APS 2016 TP10. 024.Google Scholar
Taylor, J. B. & Hastie, R. J. 1968 Stability of general plasma equilibria-I, formal theory. Plasma Phys. 10, 479.CrossRefGoogle Scholar
Tsai, S. T. & Chen, L. 1993 Theory of kinetic ballooning modes excited by energetic particles in tokamaks. Phys. Fluids B 5, 3284.CrossRefGoogle Scholar
Turnbull, A. D., Strait, E. J., Heidbrink, W. W., Chu, M. S., Duong, H. H., Greene, J. M., Lao, L. L., Taylor, T. S. & Tompson, S. J. 1993 Global Alfvén modes: theory and experiment. Phys. Fluids B 5, 2546.CrossRefGoogle Scholar
Wang, W. X., Lin, Z., Tang, W. M., Lee, W. W., Ethier, S., Lewandowski, J. L. V., Rewoldt, G., Hahm, T. S. & Manickam, J. 2006 Gyro-kinetic simulation of global turbulent transport properties in tokamak experiments. Phys. Plasmas 13, 092505.CrossRefGoogle Scholar
Winsor, N., Johnson, J. & Dawson, J. M. 1968 Geodesic acoustic waves in hydromagnetic systems. Phys. Fluids 11, 2448.CrossRefGoogle Scholar
Zarzoso, D., Garbet, X., Sarazin, Y., Dumont, R. & Grandgirard, V. 2012 Fully kinetic description of the linear excitation and nonlinear saturation of fast-ion-driven geodesic acoustic mode instability. Phys. Plasmas 19, 022102.CrossRefGoogle Scholar
Zarzoso, D., Sarazin, Y., Garbet, X., Strugarek, A., Abiteboul, J., Cartier-Michaud, T., Dif-Pradalier, G., Ghendrih, Ph., Grandgirard, V., Latu, G., et al. 2013 Impact of energetic particle driven geodesic acoustic modes on turbulence. Phys. Rev. Lett. 110, 125002.CrossRefGoogle ScholarPubMed
Zhang, H., Qiu, Z., Chen, L. & Lin, Z. 2009 The importance of parallel nonlinearity in the self-interaction of geodesic acoustic mode. Nucl. Fusion 49, 125009.CrossRefGoogle Scholar
Zhang, H. S. & Lin, Z. 2010 Trapped electron damping of geodesic acoustic mode. Phys. Plasmas 17, 072502.CrossRefGoogle Scholar
Zonca, F. & Chavdarovski, I. 2009 Effects of trapped particle dynamics on the structures of a low-frequency shear Alfvén continuous spectrum. In 36th EPS Conference on Plasma Physics Sofia, June 29–July 3, 2009 ECA 33E, P-1.133.Google Scholar
Zonca, F. & Chen, L. 1992 Resonant damping of toroidicity-induced shear-Alfvén eigenmodes in tokamaks. Phys. Rev. Lett. 68, 592.CrossRefGoogle ScholarPubMed
Zonca, F. & Chen, L. 2008 Radial structures and nonlinear excitation of geodesic acoustic modes. Europhys. Lett. 83, 35001.CrossRefGoogle Scholar
Zonca, F. & Chen, L. 2016 Destabilization of energetic particle modes by localized particle sources. J. Plasma Phys. 7 (11), 4600–4608.CrossRefGoogle Scholar
Zonca, F., Chen, L. & Qiu, Z. 2008 Kinetic theory of Geodesic Acoustic Modes: radial structures and nonlinear excitations. In Proceedings of the 22nd International Fusion Energy Conference (Geneva, 2008) (Vienna: IAEA) CD-ROM file TH/P 3-7.Google Scholar
Zonca, F., Chen, L. & Santoro, R. A. 1996 Kinetic theory of low-frequency Alfvén modes in tokamaks. Plasma Phys. Control. Fusion 38, 2011.CrossRefGoogle Scholar