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Standing autoresonant plasma waves

Part of: The Many Facets of the Vlasov Equation

Published online by Cambridge University Press:  11 May 2020

L. Friedland Open the ORCID record for L. Friedland [Opens in a new window]  and
A. G. Shagalov
L. Friedland*
Affiliation:
Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem91904, Israel
A. G. Shagalov
Affiliation:
Institute of Metal Physics, Ekaterinburg620990, Russian Federation Ural Federal University, Mira 19, Ekaterinburg620002, Russian Federation
*
†Email address for correspondence: lazar@mail.huji.ac.il
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Abstract

The formation and control of strongly nonlinear standing plasma waves (SPWs) from a trivial equilibrium by a chirped frequency drive are discussed. If the drive amplitude exceeds a threshold, after passage through the linear resonance in this system, the excited wave preserves the phase locking with the drive, yielding a controlled growth of the wave amplitude. We illustrate these autoresonant waves via Vlasov–Poisson simulations, showing the formation of sharply peaked excitations with local electron density maxima significantly exceeding the unperturbed plasma density. The Whitham averaged variational approach applied to a simplified water bag model yields the weakly nonlinear evolution of the autoresonant SPWs and the autoresonance threshold. If the chirped driving frequency approaches some constant level, the driven SPW saturates at a target amplitude, avoiding the kinetic wave breaking.

Keywords

plasma nonlinear phenomenaplasma wavesplasma simulation
Type
Research Article
Information
Journal of Plasma Physics , Volume 86 , Issue 3 , June 2020 , 825860301
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Berk, H. L., Nielsen, C. E. & Roberts, K. V. 1970 Phase space hydrodynamics of equivalent nonlinear systems: experimental and computational observations. Phys. Fluids 13, 980–995.CrossRefGoogle Scholar
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1988 Spectral Methods in Fluid Dynamics, Springer.CrossRefGoogle Scholar
DePackh, D. C. 1962 The water-bag model of a sheet electron beamy. J. Electron. Control 13, 417–424.CrossRefGoogle Scholar
Dubin, D. H. E. & Ashourvan, A. 2015 Trivelpiece-gould waves: frequency, functional form, and stability. Phys. Plasmas 22, 102102.CrossRefGoogle Scholar
Fajans, J. & Friedland, L. 2001 Autoresonant (nonstationary) excitation of pendulums, plutinos, plasmas, and other nonlinear oscillators. Am. J. Phys. 69, 1096–1102.CrossRefGoogle Scholar
Feix, M. R., Hohl, F. & Staton, L. D. 1969 Nonlinear Effects in Plasmas, Gordon and Breach.Google Scholar
Friedland, L. 2009 Autoresonance in nonlinear systems. Scholarpedia 4, 5473.CrossRefGoogle Scholar
Friedland, L., Khain, P. & Shagalov, A. G. 2006 Autoresonant phase-space holes in plasmas. Phys. Rev. Lett. 96, 225001.CrossRefGoogle ScholarPubMed
Friedland, L., Marcus, G., Wurtele, J. S. & Michel, P. 2019 Excitation and control of large amplitude standing ion acoustic waves. Phys. Plasmas 26, 092109.CrossRefGoogle Scholar
Friedland, L. & Shagalov, A. G. 2014 Excitation and control of chirped nonlinear ion-acoustic waves. Phys. Rev. E 97, 063201.Google Scholar
Friedland, L. & Shagalov, A. G. 2017 Extreme driven ion acoustic wavess. Phys. Plasmas 24, 082106.CrossRefGoogle Scholar
Hohl, F. 1969 Minimum energy property of a bounded onedimensional plasma. Phys. Fluids 12, 230–234.CrossRefGoogle Scholar
Lehmann, G. & Spatschek, K. H. 2016 Transient plasma photonic crystals for high-power lasers. Phys. Rev. Lett. 116, 225002.CrossRefGoogle ScholarPubMed
Lehmann, G. & Spatschek, K. H. 2018 Hamiltonian stochastic processes induced by succesive wave–particle interactions in stimulated Raman scattering. Phys. Rev. E 79, 046404.Google Scholar
Malkin, V. M., Shvets, G. & Fisch, N. J. 1999 Fast compression of laser beams to highly overcritical power. Phys. Rev. Lett. 82, 4448–4451.CrossRefGoogle Scholar
Michel, P., Divol, L., Turnbull, D. & Moody, J. D. 2014 Dynamic control of the polarization of intense laser beams via optical wave mixing in plasmas. Phys. Rev. Lett. 113, 205001.CrossRefGoogle ScholarPubMed
Michel, P., Divol, L., Williams, E. A., Weber, S., Thomas, C. A., Callahan, D. A., Haan, S. W., Salmonson, J. D., Dixit, S., Hinkel, D. E. et al. 2009 Tuning the implosion symmetry of icf targets via controlled crossed-beam energy transfer. Phys. Rev. Lett. 102, 025004.CrossRefGoogle ScholarPubMed
Novikov, S., Manakov, S. V., Pitaevskii, L. P. & Zakharov, V. E. 1984 Theory of Solitons, Plenum Publishing.Google Scholar
Turnbull, D., Goyon, C., Kemp, G. E., Pollock, B. B., Mariscal, D., Divol, L., Ross, J. S., Patankar, S., Moody, J. D. & Michel, P. 2017 Refractive index seen by a probe beam interacting with a laser-plasma system. Phys. Rev. Lett. 118, 015001.CrossRefGoogle ScholarPubMed
Turnbull, D., Michel, P., Chapman, T., Tubman, E., Pollock, B., Chen, C., Goyon, C., Ross, J.., Divol, L., Woolsey, N. et al. 2016 High power dynamic polarization control using plasma photonics. Phys. Rev. Lett. 116, 205001.CrossRefGoogle ScholarPubMed
Whitham, G. B. 1974 Linear and Nonlinear Waves, John Wiley & Sons.Google Scholar
Wolfram Research Inc. 2017 Mathematica; Version 11.1.Google Scholar