Threewave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian
Abstract
Large amplitude waves in magnetized plasmas, generated either by external pumps or internal instabilities, can scatter via threewave interactions. While threewave scattering is well known in collimated geometry, what happens when waves propagate at angles with one another in magnetized plasmas remains largely unknown, mainly due to the analytical difficulty of this problem. In this study, we overcome this analytical difficulty and find a convenient formula for threewave coupling coefficient in cold, uniform, magnetized, and collisionless plasmas in the most general geometry. This is achieved by systematically solving the fluidMaxwell model to second order using a multiscale perturbative expansion. The general formula for the coupling coefficient becomes transparent when we reformulate it as the scattering matrix element of a quantized Lagrangian. Using the quantized Lagrangian, it is possible to bypass the perturbative solution and directly obtain the nonlinear coupling coefficient from the linear response of the plasma. To illustrate how to evaluate the cold coupling coefficient, we give a set of examples where the participating waves are either quasitransverse or quasilongitudinal. In these examples, we determine the angular dependence of threewave scattering, and demonstrate that backscattering is not necessarily the strongest scattering channel in magnetized plasmas, in contrast to whatmore »
 Authors:
 Princeton Univ., NJ (United States); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Princeton Univ., NJ (United States); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Univ. of Science and Technology of China, Hefei (China)
 Publication Date:
 Research Org.:
 Princeton Univ., NJ (United States); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1378090
 Alternate Identifier(s):
 OSTI ID: 1374944
 Grant/Contract Number:
 NA0002948; AC0209CH11466
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physical Review E
 Additional Journal Information:
 Journal Volume: 96; Journal Issue: 2; Journal ID: ISSN 24700045
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; effective field theory; highenergydensity plasmas; laserplasma interactions; nonlinear phenomena in plasmas; plasma waves; wavewave, waveparticle interactions; magnetized plasma; nonlinear waves; firstprinciples calculations in plasma physics; nonlinear dynamics
Citation Formats
Shi, Yuan, Qin, Hong, and Fisch, Nathaniel J. Threewave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian. United States: N. p., 2017.
Web. doi:10.1103/PhysRevE.96.023204.
Shi, Yuan, Qin, Hong, & Fisch, Nathaniel J. Threewave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian. United States. doi:10.1103/PhysRevE.96.023204.
Shi, Yuan, Qin, Hong, and Fisch, Nathaniel J. 2017.
"Threewave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian". United States.
doi:10.1103/PhysRevE.96.023204.
@article{osti_1378090,
title = {Threewave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian},
author = {Shi, Yuan and Qin, Hong and Fisch, Nathaniel J.},
abstractNote = {Large amplitude waves in magnetized plasmas, generated either by external pumps or internal instabilities, can scatter via threewave interactions. While threewave scattering is well known in collimated geometry, what happens when waves propagate at angles with one another in magnetized plasmas remains largely unknown, mainly due to the analytical difficulty of this problem. In this study, we overcome this analytical difficulty and find a convenient formula for threewave coupling coefficient in cold, uniform, magnetized, and collisionless plasmas in the most general geometry. This is achieved by systematically solving the fluidMaxwell model to second order using a multiscale perturbative expansion. The general formula for the coupling coefficient becomes transparent when we reformulate it as the scattering matrix element of a quantized Lagrangian. Using the quantized Lagrangian, it is possible to bypass the perturbative solution and directly obtain the nonlinear coupling coefficient from the linear response of the plasma. To illustrate how to evaluate the cold coupling coefficient, we give a set of examples where the participating waves are either quasitransverse or quasilongitudinal. In these examples, we determine the angular dependence of threewave scattering, and demonstrate that backscattering is not necessarily the strongest scattering channel in magnetized plasmas, in contrast to what happens in unmagnetized plasmas. Finally, our approach gives a more complete picture, beyond the simple collimated geometry, of how injected waves can decay in magnetic confinement devices, as well as how lasers can be scattered in magnetized plasma targets.},
doi = {10.1103/PhysRevE.96.023204},
journal = {Physical Review E},
number = 2,
volume = 96,
place = {United States},
year = 2017,
month = 8
}

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