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Resonance overlap and nonlinear features of the beam–plasma system

Part of: Laboratory and Astrophysical Plasmas: New Perspectives

Published online by Cambridge University Press:  27 August 2020

N. Carlevaro Open the ORCID record for N. Carlevaro [Opens in a new window] ,
G. Montani  and
M. V. Falessi Open the ORCID record for M. V. Falessi [Opens in a new window]
N. Carlevaro*
Affiliation:
Fusion and Nuclear Safety Department, ENEA, C. R. Frascati, Via E. Fermi 45, 00044Frascati (Roma), Italy Consorzio RFX, Corso Stati Uniti 4, 35127Padova, Italy
G. Montani
Affiliation:
Fusion and Nuclear Safety Department, ENEA, C. R. Frascati, Via E. Fermi 45, 00044Frascati (Roma), Italy Physics Department, ‘Sapienza’ University of Rome, P.le Aldo Moro 5, 00185Roma, Italy
M. V. Falessi
Affiliation:
Fusion and Nuclear Safety Department, ENEA, C. R. Frascati, Via E. Fermi 45, 00044Frascati (Roma), Italy INFN – Rome Section, P.le Aldo Moro 2, 00185Roma, Italy
*
†Email address for correspondence: nakia.carlevaro@enea.it
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Abstract

The beam–plasma instability can be addressed as a reduced model in several contexts of plasma physics, from space to fusion plasma. In this paper, we review and refine some nonlinear features of this model. Specifically, by analysing the dependence of the nonlinear velocity spread as a function of the linear growth rate, we discuss the effective size of the resonance in view of its role in the spectral overlap at saturation. The relevance of this characterization relies on the necessity of a quantitative determination of the overlap degree to discriminate among different transport regimes of the self-consistent dynamics. The analysis is enriched with a study of the phase-space dynamics by means of the Lagrangian coherent structure technique, in order to define the transport barriers of the system describing the relevant features of the overlap process. Finally, we discuss relevant features related to the mode saturation levels.

Keywords

plasma instabilitiesplasma nonlinear phenomenaplasma waves
Type
Research Article
Information
Journal of Plasma Physics , Volume 86 , Issue 4 , August 2020 , 845860401
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Al'Tshul, L. M. & Karpman, V. I. 1966 Theory of nonlinear oscillations in a collisionless plasma. Sov. Phys. JETP 22 (2), 361–369.Google Scholar
Berk, H. L. & Breizman, B. N. 1990 a Saturation of a single mode driven by an energetic injected beam. I. Plasma wave problem. Phys. Fluids B 2 (9), 2226–2234.CrossRefGoogle Scholar
Berk, H. L. & Breizman, B. N. 1990 b Saturation of a single mode driven by an energetic injected beam. II. Electrostatic “universal” destabilization mechanism. Phys. Fluids B 2 (9), 2235–2245.CrossRefGoogle Scholar
Berk, H. L. & Breizman, B. N. 1990 c Saturation of a single mode driven by an energetic injected beam. III. Alfvén wave problem. Phys. Fluids B 2 (9), 2246–2252.CrossRefGoogle Scholar
Berk, H. L. & Breizman, B. N. 1994 Scenarios for the nonlinear evolution of beam-driven instability with a weak source, AIP Conf. Ser. 314, 140–155.CrossRefGoogle Scholar
Berk, H. L., Breizman, B. N., Fitzpatrick, J. & Wong, H. V. 1995 a Line broadened quasi-linear burst model [fusion plasma]. Nucl. Fusion 35 (12), 1661–1668.CrossRefGoogle Scholar
Berk, H. L., Breizman, B. N. & Pekker, M. 1994 Basic principles approach for studying nonlinear Alfvén wave-alpha particle dynamics. AIP Conf. Ser. 311, 18–31.CrossRefGoogle Scholar
Berk, H. L., Breizman, B. N. & Pekker, M. 1995 b Numerical simulation of bump-on-tail instability with source and sink. Phys. Plasmas 2 (8), 3007–1259.CrossRefGoogle Scholar
Berk, H. L., Breizman, B. N. & Ye, H. 1992 Scenarios for the nonlinear evolution of alpha-particle-induced Alfvén wave instability. Phys. Rev. Lett. 68 (24), 3563–3566.CrossRefGoogle ScholarPubMed
Breizman, B. N., Berk, H. L. & Ye, H. 1993 Collective transport of alpha particles due to Alfvén wave instability. Phys. Fluids B 5 (9), 3217–3226.CrossRefGoogle Scholar
Breizman, B. N. & Sharapov, S. E. 2011 Major minority: energetic particles in fusion plasmas. Plasma Phys. Control. Fusion 53 (5), 054001.CrossRefGoogle 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.CrossRefGoogle Scholar
Carlevaro, N., Fanelli, D., Garbet, X., Ghendrih, P., Montani, G. & Pettini, M. 2014 Beam-plasma instability and fast particles: the Lynden–Bell approach. Plasma Phys. Control. Fusion 56 (3), 035013.CrossRefGoogle Scholar
Carlevaro, N., Finelli, F. & Montani, G. 2019 a Reanalysis of the beam-plasma instability using the Dyson-like equation formalism. Europhys. Lett. 127, 25002.CrossRefGoogle Scholar
Carlevaro, N., Milovanov, A. V., Falessi, M. V., Montani, G., Terzani, D. & Zonca, F. 2016 a Mixed diffusive-convective relaxation of a warm beam of energetic particles in cold plasma. Entropy 18 (4), 143.CrossRefGoogle Scholar
Carlevaro, N., Montani, G., Wang, X. & Zonca, F. 2016 b Hamiltonian bump-on-tail model: interpretation of EP/AE interaction. In 43rd EPS Conference on Plasma Physics, vol. 40A, p. P5.018. http://ocs.ciemat.es/EPS2016PAP/html/author.html.Google Scholar
Carlevaro, N., Montani, G. & Zonca, F. 2018 Resonance overlap and non-linear velocity spread in Hamiltonian beam-plasma systems. In 45th EPS Conference on Plasma Physics, vol. 42A, p. P5.1067. http://ocs.ciemat.es/EPS2018PAP/html/author.html.Google Scholar
Carlevaro, N., Montani, G., Zonca, F., Lauber, P. & Hayward-Schneider, T. 2019 b Beam-plasma system as reduced model for ITER relevant energetic particle transport. In 46th EPS Conference on Plasma Physics, vol. 43C, p. P5.1014. http://ocs.ciemat.es/EPS2019PAP/html/author.html.Google Scholar
Chen, L. & Zonca, F. 2016 Physics of Alfvén waves and energetic particles in burning plasmas. Rev. Mod. Phys. 88 (1), 015008.CrossRefGoogle Scholar
Chirikov, B. V. 1960 Resonance processes in magnetic traps. J. Nucl. Energy 1, 263–260.Google Scholar
Chirikov, B. V. 1979 A universal instability of many-dimensional oscillator systems. Phys. Rep. 52 (5), 263–379.CrossRefGoogle Scholar
Di Giannatale, G., Falessi, M. V., Grasso, D., Pegoraro, F. & Schep, T. J. 2018 a Coherent transport structures in magnetized plasmas. I. Theory. Phys. Plasmas 25 (5), 052306.CrossRefGoogle Scholar
Di Giannatale, G., Falessi, M. V., Grasso, D., Pegoraro, F. & Schep, T. J. 2018 b Coherent transport structures in magnetized plasmas. II. Numerical results. Phys. Plasmas 25 (5), 052307.CrossRefGoogle Scholar
Drummond, W. E. & Pines, D. 1962 Non-linear stability of plasma oscillations. Nucl. Fusion Suppl. Part. 3, 1049–1057.Google Scholar
Elskens, Y. & Escande, D. F. 2003 Microscopic Dynamics of Plasmas Chaos. Taylor Francis Ltd.CrossRefGoogle Scholar
Esarey, E., Sprangle, P., Krall, J. & Ting, A. 1996 Overview of plasma-based accelerator concepts. IEEE Trans. Plasma Sci. 24 (2), 252–288.CrossRefGoogle Scholar
Escande, D. F., Bènisti, D., Elskens, Y., Zarzoso, D. & Doveil, D. 2018 Basic microscopic plasma physics from $N$-body mechanics. Rev. Mod. Plasma Phys. 2, 9.CrossRefGoogle 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 (2), 257–284.CrossRefGoogle Scholar
Falessi, M. V., Pegoraro, F. & Schep, T. J. 2015 Lagrangian coherent structures and plasma transport processes. J. Plasma Phys. 81 (5), 495810505.CrossRefGoogle Scholar
Fried, B. D., Liu, C. S., Means, R. W. & Sagdeev, R. Z. 1971 Nonlinear evolution and saturation of an ustable electrostatic wave. UCLA Report PPG-93.Google Scholar
Greene, J. M. 1968 Two-dimensional measure-preserving mappings. J. Math. Phys. 9 (5), 760–768.CrossRefGoogle Scholar
Haller, G. 2015 Lagrangian coherent structures. Annu. Rev. Fluid Mech. 47 (1), 137–162.CrossRefGoogle Scholar
Jaeger, E. F. & Lichtenberg, A. J. 1972 Resonant modification and destruction of adiabatic invariants. Ann. Phys. 71 (2), 319–356.CrossRefGoogle Scholar
Keinigs, R. & Jones, M. E. 1987 Two-dimensional dynamics of the plasma wakefield accelerator. Phys. Fluids 30 (1), 252–263.CrossRefGoogle Scholar
Levin, M. B., Lyubarski, 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. Phys. JETP 35 (5), 898–901.Google Scholar
Lichtenberg, A. J. & Lieberman, M. A. 2010 Regular and Chaotic Dynamics, 2nd edn.Springer.Google Scholar
Lifshitz, E. M. & Pitaevskii, L. P. 1976 Physical kinetics. Course of Theoretical Physics, vol. 10. Butterworth-Heinemann.Google Scholar
Litos, M., Adli, E., An, W., Clarke, C. I., Clayton, C. E., Corde, S., Delahaye, J. P., England, R. J., Fisher, A. S., Frederico, J., et al. 2014 High-efficiency acceleration of an electron beam in a plasma wakefield accelerator. Nature 515 (7525), 92–95.CrossRefGoogle Scholar
Mynick, H. E. & Kaufman, A. N. 1978 Soluble theory of nonlinear beam-plasma interaction. Phys. Fluids 21, 653–663.CrossRefGoogle Scholar
O'Neil, T. M. & Malmberg, J. H. 1968 Transition of the dispersion roots from beam-type to Landau-type solutions. Phys. Fluids 11 (8), 1754–1760.CrossRefGoogle Scholar
O'Neil, T. M., Winfrey, J. H. & Malmberg, J. H. 1971 Nonlinear interaction of a small cold beam and a plasma. Phys. Fluids 14 (6), 1204–1212.CrossRefGoogle Scholar
Pegoraro, F., Bonfiglio, D., Cappello, S., Di Giannatale, G., Falessi, M. V., Grasso, D. & Veranda, M. 2019 Coherent magnetic structures in self-organized plasmas. Plasma Phys. Control. Fusion 61 (4), 044003.CrossRefGoogle Scholar
Pommois, K., Valentini, F., Pezzi, O. & Veltri, P. 2017 Slow electrostatic fluctuations generated by beam-plasma interaction. Phys. Plasmas 24 (1), 012105.CrossRefGoogle Scholar
Schneller, M., Lauber, P. & Briguglio, S. 2016 Nonlinear energetic particle transport in the presence of multiple Alfvénic waves in ITER. Plasma Phys. Control. Fusion 58, 014019.CrossRefGoogle Scholar
Shalaby, M., Broderick, A. E., Chang, P., Pfrommer, C., Lamberts, A. & Puchwein, E. 2017 Importance of resolving the spectral support of beam-plasma instabilities in simulations. Astrophys. J. 848, 81.CrossRefGoogle Scholar
Tao, X., Zonca, F. & Chen, L. 2017 Identify the nonlinear wave-particle interaction regime in rising tone chorus generation. Geophys. Res. Lett. 44 (8), 3441–3446.CrossRefGoogle Scholar
Tennyson, J. L., Meiss, J. D. & Morrison, P. J. 1994 Self-consistent chaos in the beam-plasma instability. Physica D 71 (1–2), 1–17.CrossRefGoogle Scholar
Tobita, M. & Omura, Y. 2018 Nonlinear dynamics of resonant electrons interacting with coherent Langmuir waves. Phys. Plasmas 25 (3), 032105.CrossRefGoogle Scholar
Vedenov, A. A., Velikhov, E. P. & Sagdeev, R. Z. 1961 Nonlinear oscillations of rarified plasma. Nucl. Fusion 1, 82–100.CrossRefGoogle Scholar
Vlad, G., Briguglio, S., Fogaccia, G., Fusco, V., Di Troia, C., Giovannozzi, E., Wang, X. & Zonca, F. 2018 Single-n versus multiple-n simulations of Alfvénic modes. Nucl. Fusion 58 (8), 082020.CrossRefGoogle Scholar
Volokitin, A. & Krafft, C. 2012 Velocity diffusion in plasma waves excited by electron beams. Plasma Phys. Control. Fusion 54 (8), 085002.CrossRefGoogle Scholar
Wu, Y., Cheng, C. Z. & White, R. B. 1994 Alpha particle effects on the internal kink and fishbone modes. Phys. Plasmas 1, 3369–3377.CrossRefGoogle 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.CrossRefGoogle Scholar