Three-wave interactions in magnetized warm-fluid plasmas: General theory with evaluable coupling coefficient

Shi, Yuan

doi:10.1103/PhysRevE.99.063212

Title: Three-wave interactions in magnetized warm-fluid plasmas: General theory with evaluable coupling coefficient

Journal Article · Fri Jun 28 00:00:00 EDT 2019 · Physical Review E

DOI:https://doi.org/10.1103/PhysRevE.99.063212· OSTI ID:1543082

Shi, Yuan ^[1]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

We report that resonant three-wave coupling is an important mechanism via which waves interact in a nonlinear medium. When the medium is a magnetized warm-fluid plasma, a previously unknown formula for the coupling coefficients is derived by solving the fluid-Maxwell's equations to second order using multiscale perturbative expansions. The formula is not only general but also evaluable, whereby numerical values of the coupling coefficient can be determined for any three resonantly interacting waves propagating at arbitrary angles. To illustrate how the general formula can be applied, coupling coefficient governing laser scattering is evaluated as one example. In conditions relevant to magnetized inertial confinement fusion, Raman and Brillouin instabilities are replaced by scattering from magnetized plasma waves when lasers propagate at oblique angles. As another example, coupling coefficient between two Alfvén waves via a sound wave is evaluated. Lastly, in conditions relevant to solar corona, the decay of a parallel Alfvén wave only slightly prefers exact backward geometry.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344; 19-ERD-038

OSTI ID:: 1543082

Alternate ID(s):: OSTI ID: 1546262

Report Number(s):: LLNL-JRNL-768920; PLEEE8; 959410

Journal Information:: Physical Review E, Vol. 99, Issue 6; ISSN 2470-0045

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 6 works

Citation information provided by
Web of Science

References (80)

Nonlinear Optics Bloembergen, Nicolaas https://doi.org/10.1142/3046	book	January 1996
Toward a theory of interstellar turbulence. 1: Weak Alfvenic turbulence Sridhar, S.; Goldreich, P. The Astrophysical Journal, Vol. 432 https://doi.org/10.1086/174600	journal	September 1994
Interaction of Shear-Alfven Wave Packets: Implication for Weak Magnetohydrodynamic Turbulence in Astrophysical Plasmas Ng, C. S.; Bhattacharjee, A. The Astrophysical Journal, Vol. 465 https://doi.org/10.1086/177468	journal	July 1996
Magnetohydrodynamic Turbulence Revisited Goldreich, P.; Sridhar, S. The Astrophysical Journal, Vol. 485, Issue 2 https://doi.org/10.1086/304442	journal	August 1997
Weakly Turbulent Magnetohydrodynamic Waves in Compressible Low- $β$ Plasmas Chandran, Benjamin D. G. Physical Review Letters, Vol. 101, Issue 23 https://doi.org/10.1103/PhysRevLett.101.235004	journal	December 2008
The Turbulent Alfvénic Aurora Chaston, C. C.; Salem, C.; Bonnell, J. W. Physical Review Letters, Vol. 100, Issue 17 https://doi.org/10.1103/PhysRevLett.100.175003	journal	April 2008
On the nature of incompressible magnetohydrodynamic turbulence Gogoberidze, G. Physics of Plasmas, Vol. 14, Issue 2 https://doi.org/10.1063/1.2437753	journal	February 2007
Weak Alfvén-wave turbulence revisited Schekochihin, Alexander A.; Nazarenko, Sergey V.; Yousef, Tarek A. Physical Review E, Vol. 85, Issue 3 https://doi.org/10.1103/PhysRevE.85.036406	journal	March 2012
Cross-Scale Nonlinear Coupling and Plasma Energization by Alfvén Waves Voitenko, Y.; Goossens, M. Physical Review Letters, Vol. 94, Issue 13 https://doi.org/10.1103/PhysRevLett.94.135003	journal	April 2005
Proton Core Heating and Beam Formation via Parametrically Unstable Alfvén-Cyclotron Waves Araneda, Jaime A.; Marsch, Eckart; F. -Viñas, Adolfo Physical Review Letters, Vol. 100, Issue 12 https://doi.org/10.1103/PhysRevLett.100.125003	journal	March 2008
Light Scattering from a Plasma in a Magnetic Field Platzman, P. M.; Wolff, P. A.; Tzoar, N. Physical Review, Vol. 174, Issue 2 https://doi.org/10.1103/PhysRev.174.489	journal	October 1968
Kinetic theory of three-wave interaction in a magnetized plasma Stenflo, L. Journal of Plasma Physics, Vol. 7, Issue 1 https://doi.org/10.1017/S0022377800006449	journal	February 1972
Brillouin and Raman scattering of an extraordinary mode in a magnetized plasma Grebogi, Celso; Liu, C. S. Physics of Fluids, Vol. 23, Issue 7 https://doi.org/10.1063/1.863146	journal	January 1980
Parametric decay of extraordinary electromagnetic waves into two upper hybrid plasmons Grebogi, Celso; Liu, C. S. Journal of Plasma Physics, Vol. 23, Issue 1 https://doi.org/10.1017/S0022377800022212	journal	February 1980
Raman and two-plasmon decay instabilities in a magnetized plasma Barr, H. C.; Boyd, T. J. M.; Gardner, L. R. T. Physics of Fluids, Vol. 27, Issue 11 https://doi.org/10.1063/1.864577	journal	January 1984
Kinetic theory of stimulated Raman scattering from a magnetized plasma Boyd, T. J. M.; Rankin, R. Journal of Plasma Physics, Vol. 33, Issue 2 https://doi.org/10.1017/S002237780000252X	journal	April 1985
Parametric excitation of Bernstein modes in laser‐produced plasma Simon, Albert Physics of Plasmas, Vol. 2, Issue 10 https://doi.org/10.1063/1.871082	journal	October 1995
Comment on ‘‘Parametric excitation of Bernstein modes in laser‐produced plasma’’ [Phys. Plasmas 2 , 3832 (1995)] Mourenas, D. Physics of Plasmas, Vol. 3, Issue 8 https://doi.org/10.1063/1.871625	journal	August 1996
Effect of the magnetic field on coexisting stimulated Raman and Brillouin backscattering of an extraordinary mode Vyas, Ashish; Singh, Ram Kishor; Sharma, R. P. Physics of Plasmas, Vol. 23, Issue 1 https://doi.org/10.1063/1.4939886	journal	January 2016
Parametric decay of plasma waves near the upper-hybrid resonance Dodin, I. Y.; Arefiev, A. V. Physics of Plasmas, Vol. 24, Issue 3 https://doi.org/10.1063/1.4979168	journal	March 2017
Excitation of an upper hybrid wave by two intense laser beams and particle acceleration Purohit, Gunjan; Sharma, Prerana; Sharma, R. P. Physics Letters A, Vol. 374, Issue 6 https://doi.org/10.1016/j.physleta.2009.12.007	journal	January 2010
Laser-pulse compression using magnetized plasmas Shi, Yuan; Qin, Hong; Fisch, Nathaniel J. Physical Review E, Vol. 95, Issue 2 https://doi.org/10.1103/PhysRevE.95.023211	journal	February 2017
Nonlinear scattering from electron Bernstein modes in a plasma Ram, S. Plasma Physics, Vol. 24, Issue 8 https://doi.org/10.1088/0032-1028/24/8/002	journal	August 1982
Parametric Instabilities in Magnetized Plasma Sanuki, Heiji; Schmidt, George Journal of the Physical Society of Japan, Vol. 42, Issue 2 https://doi.org/10.1143/JPSJ.42.664	journal	February 1977
Non-linear coupling in a magnetized plasma Sjölund, Anders; Stenflo, Lennart Zeitschrift für Physik A Hadrons and nuclei, Vol. 204, Issue 3 https://doi.org/10.1007/BF01326195	journal	June 1967
Kinetic theory of three-wave interaction in a magnetied plasma Stenflo, L. Journal of Plasma Physics, Vol. 4, Issue 3 https://doi.org/10.1017/S0022377800005250	journal	September 1970
Kinetic Theory of Three-Wave Interaction in a Magnetised, Inhomogeneous Plasma Shivamoggi, Bhimsen K. Physica Scripta, Vol. 25, Issue 5 https://doi.org/10.1088/0031-8949/25/5/011	journal	May 1982
Effects of Axial Magnetic Fields on Backward Raman Scattering in Inhomogeneous Plasmas Laham, Nabil M.; Nasser, Ali S. Al; Khateeb, Ahmed M. Physica Scripta, Vol. 57, Issue 2 https://doi.org/10.1088/0031-8949/57/2/018	journal	February 1998
Stimulated scattering of a whistler off an ion Bernstein wave Kumar, Asheel; Tripathi, V. K. Physica Scripta, Vol. 84, Issue 6 https://doi.org/10.1088/0031-8949/84/06/065505	journal	November 2011
Nonlinear interaction of kinetic Alfvén wave with fast magnetosonic wave and turbulent spectrum Modi, K. V.; Sharma, R. P. Physics of Plasmas, Vol. 20, Issue 3 https://doi.org/10.1063/1.4794834	journal	March 2013
Parametric Decay of "Kinetic Alfvén Wave" and Its Application to Plasma Heating Hasegawa, Akira; Chen, Liu Physical Review Letters, Vol. 36, Issue 23 https://doi.org/10.1103/PhysRevLett.36.1362	journal	June 1976
Kinetic processes in plasma heating by resonant mode conversion of Alfvén wave Hasegawa, Akira; Chen, Liu Physics of Fluids, Vol. 19, Issue 12 https://doi.org/10.1063/1.861427	journal	January 1976
Modulational instability of finite-amplitude, circularly polarized Alfven waves Derby, N. F. , Jr. The Astrophysical Journal, Vol. 224 https://doi.org/10.1086/156451	journal	September 1978
An instability of finite amplitude circularly polarized Alfven waves Goldstein, M. L. The Astrophysical Journal, Vol. 219 https://doi.org/10.1086/155829	journal	January 1978
Parametric instabilities of circularly polarized Alfvén waves including dispersion Wong, H. K.; Goldstein, M. L. Journal of Geophysical Research, Vol. 91, Issue A5 https://doi.org/10.1029/JA091iA05p05617	journal	January 1986
Parametric instabilities of parallel-propagating Alfvén waves: Some analytical results Jayanti, V.; Hollweg, Joseph V. Journal of Geophysical Research: Space Physics, Vol. 98, Issue A11 https://doi.org/10.1029/93JA02208	journal	November 1993
Parametric instabilities of circularly polarized Alfvén waves in a relativistic electron-positron plasma Matsukiyo, S.; Hada, T. Physical Review E, Vol. 67, Issue 4 https://doi.org/10.1103/PhysRevE.67.046406	journal	April 2003
Parametric instabilities of finite amplitude Alfvén waves Brodin, G.; Stenflo, L. Physica Scripta, Vol. 37, Issue 1 https://doi.org/10.1088/0031-8949/37/1/013	journal	January 1988
Coupling Coefficients for Ion-Cyclotron Alfvén Waves Brodin, G.; Stenflo, L. Contributions to Plasma Physics, Vol. 30, Issue 3 https://doi.org/10.1002/ctpp.2150300308	journal	January 1990
Parametric instabilities of circularly polarized large-amplitude dispersive Alfvén waves: excitation of parallel-propagating electromagnetic daughter waves Viñas, Adolfo F.; Goldstein, Melvyn L. Journal of Plasma Physics, Vol. 46, Issue 1 https://doi.org/10.1017/S0022377800015981	journal	August 1991
On the dispersion relations for parametric instabilities of parallel-propagating Alfvén waves Jayanti, Venku; Hollweg, Joseph V. Journal of Geophysical Research: Space Physics, Vol. 98, Issue A8 https://doi.org/10.1029/93JA00920	journal	August 1993
Beat, modulational, and decay instabilities of a circularly polarized Alfvén wave Hollweg, Joseph V. Journal of Geophysical Research, Vol. 99, Issue A12 https://doi.org/10.1029/94JA02185	journal	January 1994
Three-wave coupling and parametric decay of kinetic Alfvén waves Voitenko, Yu. M. Journal of Plasma Physics, Vol. 60, Issue 3 https://doi.org/10.1017/S0022377898007090	journal	October 1998
Nonlinear effects associated with dispersive Alfvén waves in plasmas Shukla, P. K.; Stenflo, L.; Bingham, R. Plasma Physics and Controlled Fusion, Vol. 46, Issue 12B https://doi.org/10.1088/0741-3335/46/12B/030	journal	November 2004
The stability of parallel-propagating circularly polarized Alfvn waves revisited Ruderman, Michael S.; Simpson, David Journal of Plasma Physics, Vol. 70, Issue 2 https://doi.org/10.1017/S0022377803002599	journal	January 1999
Nonlinear Interactions Between Kinetic Alfvén and Ion-Sound Waves Brodin, G.; Stenflo, L.; Shukla, P. K. Solar Physics, Vol. 236, Issue 2 https://doi.org/10.1007/s11207-006-0125-2	journal	July 2006
Consequences of finite ion temperature effects on parametric instabilities of circularly polarized Alfvén waves: ION TEMPERATURE EFFECTS ON ALFVÉN WAVES Nariyuki, Y.; Hada, T. Journal of Geophysical Research: Space Physics, Vol. 112, Issue A10 https://doi.org/10.1029/2007JA012373	journal	October 2007
Three‐ and four‐wave interactions in plasmas Boyd, T. J. M.; Turner, J. G. Journal of Mathematical Physics, Vol. 19, Issue 6 https://doi.org/10.1063/1.523842	journal	June 1978
Parametric instabilities in a magnetized plasma Liu, C. S.; Tripathi, V. K. Physics Reports, Vol. 130, Issue 3 https://doi.org/10.1016/0370-1573(86)90108-0	journal	January 1986
Resonant three-wave interactions in plasmas Stenflo, L. Physica Scripta, Vol. T50 https://doi.org/10.1088/0031-8949/1994/T50/002	journal	January 1994
Three-wave coupling coefficients for a magnetized plasma Brodin, G.; Stenflo, L. Physica Scripta, Vol. 85, Issue 3 https://doi.org/10.1088/0031-8949/85/03/035504	journal	February 2012
Parametric instabilities of circularly polarized large-amplitude dispersive Alfvén waves: excitation of obliquely-propagating daughter and side-band waves Viñas, Adolfo F.; Goldstein, Melvyn L. Journal of Plasma Physics, Vol. 46, Issue 1 https://doi.org/10.1017/S0022377800015993	journal	August 1991
Three-wave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian Shi, Yuan; Qin, Hong; Fisch, Nathaniel J. Physical Review E, Vol. 96, Issue 2 https://doi.org/10.1103/PhysRevE.96.023204	journal	August 2017
Effective-action approach to wave propagation in scalar QED plasmas Shi, Yuan; Fisch, Nathaniel J.; Qin, Hong Physical Review A, Vol. 94, Issue 1 https://doi.org/10.1103/PhysRevA.94.012124	journal	July 2016
Laser-plasma interactions in magnetized environment Shi, Yuan; Qin, Hong; Fisch, Nathaniel J. Physics of Plasmas, Vol. 25, Issue 5 https://doi.org/10.1063/1.5017980	journal	May 2018
Development of the indirect‐drive approach to inertial confinement fusion and the target physics basis for ignition and gain Lindl, John Physics of Plasmas, Vol. 2, Issue 11 https://doi.org/10.1063/1.871025	journal	November 1995
Direct-drive inertial confinement fusion: A review Craxton, R. S.; Anderson, K. S.; Boehly, T. R. Physics of Plasmas, Vol. 22, Issue 11 https://doi.org/10.1063/1.4934714	journal	November 2015
Fast Compression of Laser Beams to Highly Overcritical Powers Malkin, V. M.; Shvets, G.; Fisch, N. J. Physical Review Letters, Vol. 82, Issue 22 https://doi.org/10.1103/PhysRevLett.82.4448	journal	May 1999
Amplification of Ultrashort Laser Pulses by Brillouin Backscattering in Plasmas Weber, S.; Riconda, C.; Lancia, L. Physical Review Letters, Vol. 111, Issue 5 https://doi.org/10.1103/PhysRevLett.111.055004	journal	July 2013
Dynamic Control of the Polarization of Intense Laser Beams via Optical Wave Mixing in Plasmas Michel, P.; Divol, L.; Turnbull, D. Physical Review Letters, Vol. 113, Issue 20 https://doi.org/10.1103/PhysRevLett.113.205001	journal	November 2014
Two decades of progress in understanding and control of laser plasma instabilities in indirect drive inertial fusion Montgomery, David S. Physics of Plasmas, Vol. 23, Issue 5 https://doi.org/10.1063/1.4946016	journal	April 2016
Megagauss Magnetic Field Generation and Plasma Jet Formation on Solid Targets Irradiated by an Ultraintense Picosecond Laser Pulse Borghesi, M.; MacKinnon, A. J.; Bell, A. R. Physical Review Letters, Vol. 81, Issue 1 https://doi.org/10.1103/PhysRevLett.81.112	journal	July 1998
Self-generated magnetic fields in direct-drive implosion experiments Igumenshchev, I. V.; Zylstra, A. B.; Li, C. K. Physics of Plasmas, Vol. 21, Issue 6 https://doi.org/10.1063/1.4883226	journal	June 2014
Kinetic simulations of laser parametric amplification in magnetized plasmas Jia, Qing; Shi, Yuan; Qin, Hong Physics of Plasmas, Vol. 24, Issue 9 https://doi.org/10.1063/1.4998168	journal	September 2017
Parametric Coupling Between ion Waves and Electromagnetic Waves Sjölund, A.; Stenflo, L. Applied Physics Letters, Vol. 10, Issue 7 https://doi.org/10.1063/1.1754910	journal	April 1967
Parametric instabilities of electromagnetic waves in plasmas Drake, J. F. Physics of Fluids, Vol. 17, Issue 4 https://doi.org/10.1063/1.1694789	journal	January 1974
Theory of stimulated scattering processes in laser-irradiated plasmas Forslund, D. W.; Kindel, J. M.; Lindman, E. L. Physics of Fluids, Vol. 18, Issue 8 https://doi.org/10.1063/1.861248	journal	January 1975
Strongly Enhanced Stimulated Brillouin Backscattering in an Electron-Positron Plasma Edwards, Matthew R.; Fisch, Nathaniel J.; Mikhailova, Julia M. Physical Review Letters, Vol. 116, Issue 1 https://doi.org/10.1103/PhysRevLett.116.015004	journal	January 2016
Laser-driven magnetized liner inertial fusion Davies, J. R.; Barnak, D. H.; Betti, R. Physics of Plasmas, Vol. 24, Issue 6 https://doi.org/10.1063/1.4984779	journal	June 2017
Laser-driven magnetized liner inertial fusion on OMEGA Barnak, D. H.; Davies, J. R.; Betti, R. Physics of Plasmas, Vol. 24, Issue 5 https://doi.org/10.1063/1.4982692	journal	May 2017
Ulysses solar wind plasma observations from pole to pole Phillips, J. L.; Bame, S. J.; Barnes, A. Geophysical Research Letters, Vol. 22, Issue 23 https://doi.org/10.1029/95GL03094	journal	December 1995
The Large-Scale Density Structure of the Solar Corona and the Heliospheric Current Sheet Guhathakurta, Madhulika; Holzer, Thomas E.; MacQueen, R. M. The Astrophysical Journal, Vol. 458 https://doi.org/10.1086/176860	journal	February 1996
Alfven Waves in the Solar Corona Tomczyk, S.; McIntosh, S. W.; Keil, S. L. Science, Vol. 317, Issue 5842 https://doi.org/10.1126/science.1143304	journal	August 2007
Nonlinear optics Amar, Henri Journal of the Franklin Institute, Vol. 280, Issue 4 https://doi.org/10.1016/0016-0032(65)90326-1	journal	October 1965
Nonlinear Optics Firth, W. J. Journal of Modern Optics, Vol. 40, Issue 5 https://doi.org/10.1080/09500349314551011	journal	May 1993
Weak Alfven-Wave Turbulence Revisited Schekochihin, A. A.; Nazarenko, S. V.; Yousef, T. A. arXiv https://doi.org/10.48550/arxiv.1110.6682	text	January 2011
Strongly Enhanced Stimulated Brillouin Backscattering in an Electron-Positron Plasma Edwards, Matthew R.; Fisch, Nathaniel J.; Mikhailova, Julia M. arXiv https://doi.org/10.48550/arxiv.1512.00744	text	January 2015
Effective action approach to wave propagation in scalar QED plasmas Shi, Yuan; Fisch, Nathaniel J.; Qin, Hong arXiv https://doi.org/10.48550/arxiv.1603.03967	text	January 2016
Laser Pulse Compression Using Magnetized Plasmas Shi, Yuan; Qin, Hong; Fisch, Nathaniel J. arXiv https://doi.org/10.48550/arxiv.1612.09214	text	January 2016
On the Nature of Incompressible Magnetohydrodynamic Turbulence Gogoberidze, G. arXiv https://doi.org/10.48550/arxiv.astro-ph/0611894	text	January 2006

Cited By (1)

Amplification of mid-infrared lasers via backscattering in magnetized plasmas Shi, Yuan; Fisch, Nathaniel J. Physics of Plasmas, Vol. 26, Issue 7 https://doi.org/10.1063/1.5099513	journal	July 2019

Figures / Tables (4)

Similar Records

Amplification of mid-infrared lasers via backscattering in magnetized plasmas

Journal Article · Wed Jul 24 00:00:00 EDT 2019 · Physics of Plasmas · OSTI ID:1543082

Shi, Yuan; Fisch, Nathaniel J.

Enhanced collisionless laser absorption in strongly magnetized plasmas

Journal Article · Fri Nov 04 00:00:00 EDT 2022 · Physics of Plasmas · OSTI ID:1543082

Manzo, Lili; Edwards, Matthew R.; Shi, Yuan

Three-wave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian

Journal Article · Mon Aug 14 00:00:00 EDT 2017 · Physical Review E · OSTI ID:1543082

Shi, Yuan; Qin, Hong; Fisch, Nathaniel J.

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY