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

Abstract

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.

Authors:
 [1]
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  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1543082
Alternate Identifier(s):
OSTI ID: 1546262
Report Number(s):
LLNL-JRNL-768920
Journal ID: ISSN 2470-0045; PLEEE8; 959410
Grant/Contract Number:  
AC52-07NA27344; 19-ERD-038
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 99; Journal Issue: 6; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

Shi, Yuan. Three-wave interactions in magnetized warm-fluid plasmas: General theory with evaluable coupling coefficient. United States: N. p., 2019. Web. doi:10.1103/PhysRevE.99.063212.
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Shi, Yuan. Three-wave interactions in magnetized warm-fluid plasmas: General theory with evaluable coupling coefficient. United States. https://doi.org/10.1103/PhysRevE.99.063212
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Shi, Yuan. Fri . "Three-wave interactions in magnetized warm-fluid plasmas: General theory with evaluable coupling coefficient". United States. https://doi.org/10.1103/PhysRevE.99.063212. https://www.osti.gov/servlets/purl/1543082.
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@article{osti_1543082,
title = {Three-wave interactions in magnetized warm-fluid plasmas: General theory with evaluable coupling coefficient},
author = {Shi, Yuan},
abstractNote = {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.},
doi = {10.1103/PhysRevE.99.063212},
journal = {Physical Review E},
number = 6,
volume = 99,
place = {United States},
year = {Fri Jun 28 00:00:00 EDT 2019},
month = {Fri Jun 28 00:00:00 EDT 2019}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1103/PhysRevE.99.063212
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Cited by: 6 works
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Figures / Tables:

FIG. 1 FIG. 1: Wave dispersion relations (a) and polarization angles (b) in magnetized warm-fluid electron-ion plasma when 〈k,B0〉 = 30°. The two electromagnetic (EM) waves are elliptically polarized R wave (blue) and L wave (red), which become transverse and approach the light cone $ω = ck$ when $ck → ∞$. Themore » other four branches are plasma waves, which become longitudinal when ck → ∞. In this limit and when 〈k,B0〉 → 90°, the yellow branch (P) is the upper-hybrid (UH) wave and the purple branch is the lower-hybrid (LH) wave. In the opposite limit $ck → 0$, the purple branch is the fast (F) wave, the green branch is the Alfvén (A) wave, and the cyan branch is the slow (S) wave. For all dispersion branches to be visible on the same scale (1012 rad/s), the mass ratio $m_i$/$m_e$ = 5 is artificial. The plasma density is $n_e$ = $n_i$ = 10 18 cm−3; the plasma temperature is $T_e$ = $T_i$ = 3.2 keV; the polytropic index is adiabatic $ξ_e = ξ_i = 3$; the magnetic field is $B_0$ = 2.5 MG such that |$Ω_e$|/$ω_{pe}$ ≈ 0.8 and $v_A$/$c_s$ ≈ 4, where $v_A$ is the Alfvén speed and $c_s$ is the sound speed.« less
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    Amplification of mid-infrared lasers via backscattering in magnetized plasmas
    journal, July 2019

    • Shi, Yuan; Fisch, Nathaniel J.
    • Physics of Plasmas, Vol. 26, Issue 7
    • DOI: 10.1063/1.5099513
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