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Nonlinear velocity redistribution caused by energetic-particle-driven geodesic acoustic modes, mapped with the beam-plasma system

Part of: Professor Francesco Pegoraro

Published online by Cambridge University Press:  06 December 2018

A. Biancalani ,
N. Carlevaro ,
A. Bottino ,
G. Montani  and
Z. Qiu
A. Biancalani*
Affiliation:
Max-Planck Institute for Plasma Physics, 85748 Garching, Germany
N. Carlevaro
Affiliation:
ENEA, Fusion and Nuclear Safety Department, C. R. Frascati, Via E. Fermi 45, 00044 Frascati (Roma), Italy LTCalcoli Srl, Via Bergamo 60, 23807 Merate (LC), Italy
A. Bottino
Affiliation:
Max-Planck Institute for Plasma Physics, 85748 Garching, Germany
G. Montani
Affiliation:
ENEA, Fusion and Nuclear Safety Department, C. R. Frascati, Via E. Fermi 45, 00044 Frascati (Roma), Italy Physics Department, ‘Sapienza’ University of Rome, P.le Aldo Moro 5, 00185 Roma, Italy
Z. Qiu
Affiliation:
Institute for Fusion Theory and Simulation and Department of Physics, Zhejiang University, 310027 Hangzhou, PR China
*
†Email address for correspondence: biancalani@ipp.mpg.de
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Abstract

The nonlinear dynamics of energetic-particle (EP) driven geodesic acoustic modes (EGAM) in tokamaks is investigated, and compared with the beam-plasma system (BPS). The EGAM is studied with the global gyrokinetic (GK) particle-in-cell code ORB5, treating the thermal ions and EP (in this case, fast ions) as GK and neglecting the kinetic effects of the electrons. The wave–particle nonlinearity is only considered in the EGAM nonlinear dynamics. The BPS is studied with a one-dimensional code where the thermal plasma is treated as a linear dielectric, and the EP (in this case, fast electrons) with an N-body Hamiltonian formulation. A one-to-one mapping between the EGAM and the BPS is described. The focus is on understanding and predicting the EP redistribution in phase space. We identify here two distinct regimes for the mapping: in the low-drive regime, the BPS mapping with the EGAM is found to be complete, and in the high-drive regime, the EGAM dynamics and the BPS dynamics are found to differ. The transition is described with the presence of a non-negligible frequency chirping, which affects the EGAM but not the BPS, above the identified drive threshold. The difference can be resolved by adding an ad hoc frequency modification to the BPS model. As a main result, the formula for the prediction of the nonlinear width of the velocity redistribution around the resonance velocity is provided. This article is written as the second of a series of articles (the first being Biancalani et al. (J. Plasma Phys., vol. 83 (6), 2017, 725830602)) on the saturation of EGAMs due to wave–particle nonlinearity.

Keywords

fusion plasmaplasma instabilitiesplasma nonlinear phenomena
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 6 , December 2018 , 725840602
Copyright
© The Author(s) (2018). Published by Cambridge University Press 

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References

Biancalani, A., Bottino, A., Lauber, P. & Zarzoso, D. 2014 Numerical validation of the electromagnetic gyrokinetic code NEMORB on global axisymmetric modes. Nucl. Fusion 54 (10), 104004.Google Scholar
Biancalani, A., Chavdarovski, I., Qiu, Z., Bottino, A., Del Sarto, D., Ghizzo, A., Gürcan, Ö., Morel, P. & Novikau, I. 2017 Saturation of energetic-particle-driven geodesic acoustic modes due to wave-particle nonlinearity. J. Plasma Phys. 83 (6), 725830602.Google Scholar
Bottino, A. & Sonnendrücker, E. 2015 Monte Carlo particle-in-cell methods for the simulation of the Vlasov–Maxwell gyrokinetic equations. J. Plasma Phys. 81 (5), 435810501.Google Scholar
Bottino, A., Vernay, T., Scott, B., Brunner, S., Hatzky, R., Jolliet, S., McMillan, B. F., Tran, T. M. & Villard, L. 2011 Global simulations of tokamak microturbulence: finite- $\unicode[STIX]{x1D6FD}$ effects and collisions. Plasma Phys. Control. Fusion 53 (12), 124027.Google Scholar
Carlevaro, N., Falessi, M. V., Montani, G. & Zonca, F. 2015 Nonlinear physics and energetic particle transport features of the beam-plasma instability. J. Plasma Phys. 81 (5), 495810515.Google Scholar
Carlevaro, N., Milovanov, A., Falessi, M., Montani, G., Terzani, D. & Zonca, F. 2016 Mixed diffusive-convective relaxation of a warm beam of energetic particles in cold plasma. Entropy 18, 143.Google Scholar
Carlevaro, N., Montani, G. & Zonca, F.2018 Resonance overlap and non-linear velocity spread in Hamiltonian beam-plasma systems. 45th EPS Conference on Plasma Physics. P5.1067.Google Scholar
Chen, L. & Zonca, F. 2016 Physics of Alfvén waves and energetic particles in burning plasmas. Rev. Mod. Phys. 88 (1), 015008.Google Scholar
Di Siena, A., Biancalani, A., Görler, T., Doerk, H., Novikau, I., Lauber, P., Bottino, A., Poli, E.& the ASDEX Upgrade Team 2018 Effect of elongation on energetic particle-induced geodesic acoustic mode. Nucl. Fusion 58, 106014.Google Scholar
Diamond, P. H., Itoh, S.-I., Itoh, K. & Hahm, T. S. 2005 TOPICAL REVIEW: Zonal flows in plasma – a review. Plasma Phys. Control. Fusion 47, R35–R161.Google Scholar
Escande, D. & Elskens, Y. 2002 Microscopic Dynamics of Plasmas and Chaos, Series in Plasma Physics, vol. 12. ISBN: 978-0-7503-0612-6.Google Scholar
Escande, D. F. & Doveil, F. 1981 Renormalization method for computing the threshold of the large-scale stochastic instability in two degrees of freedom Hamiltonian systems. J. Stat. Phys. 26, 257–284; doi:10.1007/BF01013171.Google Scholar
Fu, G. Y. 2008 Energetic-particle-induced geodesic acoustic mode. Phys. Rev. Lett. 101 (18), 185002.Google Scholar
Hasegawa, A., Maclennan, C. G. & Kodama, Y. 1979 Nonlinear behavior and turbulence spectra of drift waves and Rossby waves. Phys. Fluids 22, 2122–2129.Google Scholar
Horváth, L., Papp, G., Lauber, P., Por, G., Gude, A., Igochine, V., Geiger, B., Maraschek, M., Guimarais, L., Nikolaeva, V. et al. 2016 Experimental investigation of the radial structure of energetic particle driven modes. Nucl. Fusion 56 (11), 112003.Google Scholar
Jolliet, S., Bottino, A., Angelino, P., Hatzky, R., Tran, T. M., Mcmillan, B. F., Sauter, O., Appert, K., Idomura, Y. & Villard, L. 2007 A global collisionless PIC code in magnetic coordinates. Comput. Phys. Commun. 177, 409–425.Google Scholar
Lesur, M., Itoh, K., Ido, T., Osakabe, M., Ogawa, K., Shimizu, A., Sasaki, M., Ida, K., Inagaki, S., Itoh, S.-I. et al. 2016 Nonlinear excitation of subcritical instabilities in a toroidal plasma. Phys. Rev. Lett. 116 (1), 015003.Google Scholar
Levin, M. B., Lyubarskiǐ, M. G., Onishchenko, I. N., Shapiro, V. D. & Shevchenko, V. I. 1972 Contribution to the nonlinear theory of kinetic instability of an electron beam in plasma. Sov. J. Exp. Theor. Phys. 35, 898.Google Scholar
Lichtenberg, A. J. & Lieberman, M. A. 2010 Regular and Chaotic Dynamics, 2nd edn. Springer.Google Scholar
Miki, K. & Idomura, Y. 2015 Finite-orbit-width effects on energetic-particle-induced geodesic acoustic mode. Plasma Fusion Res. 10, 3403068.Google Scholar
Nazikian, R. et al. 2008 Intense geodesic acousticlike modes driven by suprathermal ions in a tokamak plasma. Phys. Rev. Lett. 101 (18), doi:10.1103/PhysRevLett.101.185001.Google Scholar
Novikau, I., Biancalani, A., Bottino, A., Conway, G. D., Gürcan, Ö. D., Manz, P., Morel, P., Poli, E., di Siena, A.& ASDEX Upgrade Team 2017 Linear gyrokinetic investigation of the geodesic acoustic modes in realistic tokamak configurations. Phys. Plasmas 24 (12), 122117.Google Scholar
O’Neil, T. 1965 Collisionless damping of nonlinear plasma oscillations. Phys. Fluids 8, 2255–2262.Google Scholar
O’Neil, T. M. & Malmberg, J. H. 1968 Transition of the dispersion roots from beam-type to landau-type solutions. Phys. Fluids 11, 1754–1760.Google 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.Google Scholar
Qiu, Z., Zonca, F. & Chen, L. 2010 Nonlocal theory of energetic-particle-induced geodesic acoustic mode. Plasma Phys. Control. Fusion 52 (9), 095003.Google Scholar
Qiu, Z., Zonca, F. & Chen, L. 2011 Kinetic theories of geodesic acoustic modes: Radial structure, linear excitation by energetic particles and nonlinear saturation. Plasma Sci. Technol. 13 (3), 257.Google Scholar
Rosenbluth, M. N. & Hinton, F. L. 1998 Poloidal flow driven by ion-temperature-gradient turbulence in tokamaks. Phys. Rev. Lett. 80, 724–727.Google Scholar
Sasaki, M., Itoh, K., Hallatschek, K., Kasuya, N., Lesur, M., Kosuga, Y. & Itoh, S.-I. 2017 Enhancement and suppression of turbulence by energetic-particle driven geodesic acoustic modes. Scientific Rep. 7, 16767.Google Scholar
Tronko, N., Bottino, A. & Sonnendrücker, E. 2016 Second order gyrokinetic theory for particle-in-cell codes. Phys. Plasmas 23 (8), 082505.Google Scholar
Wang, H., Todo, Y. & Kim, C. C. 2013 Hole-clump pair creation in the evolution of energetic-particle-driven geodesic acoustic modes. Phys. Rev. Lett. 110 (15), 155006.Google Scholar
Winsor, N., Johnson, J. L. & Dawson, J. M. 1968 Geodesic acoustic waves in hydromagnetic systems. Phys. Fluids 11, 2448–2450.Google Scholar
Wu, Y., White, R. B., Chen, Y. & Rosenbluth, M. N. 1995 Nonlinear evolution of the alpha-particle-driven toroidicity-induced Alfvén eigenmode. Phys. Plasmas 2, 4555–4562.Google Scholar
Zarzoso, D., Biancalani, A., Bottino, A., Lauber, P., Poli, E., Girardo, J.-B., Garbet, X. & Dumont, R. J. 2014 Analytic dispersion relation of energetic particle driven geodesic acoustic modes and simulations with NEMORB. Nucl. Fusion 54 (10), 103006.Google Scholar
Zarzoso, D., Del-Castillo-Negrete, D., Escande, D. F., Sarazin, Y., Garbet, X., Grandgirard, V., Passeron, C., Latu, G. & Benkadda, S. 2018 Nucl. Fusion; doi:10.1088/1741-4326/aad785.Google Scholar
Zarzoso, D., Migliano, P., Grandgirard, V., Latu, G. & Passeron, C. 2017 Nonlinear interaction between energetic particles and turbulence in gyro-kinetic simulations and impact on turbulence properties. Nucl. Fusion 57 (7), 072011.Google Scholar
Zarzoso, D., Sarazin, Y., Garbet, X., Dumont, R., Strugarek, A., Abiteboul, J., Cartier-Michaud, T., Dif-Pradalier, G., Ghendrih, P., Grandgirard, V. et al. 2013 Impact of energetic-particle-driven geodesic acoustic modes on turbulence. Phys. Rev. Lett. 110 (12), 125002.Google Scholar
Zhang, H. S. & Lin, Z. 2010 Trapped electron damping of geodesic acoustic mode. Phys. Plasmas 17 (7), 072502.Google Scholar
Zonca, F. & Chen, L. 2008 Radial structures and nonlinear excitation of geodesic acoustic modes. Eur. Phys. Lett. 83, 35001.Google Scholar