# Three-wave 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 three-wave interactions. While three-wave 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 three-wave coupling coefficient in cold, uniform, magnetized, and collisionless plasmas in the most general geometry. This is achieved by systematically solving the fluid-Maxwell 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 three-wave 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; AC02-09CH11466

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review E

- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 2; Journal ID: ISSN 2470-0045

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; effective field theory; high-energy-density plasmas; laser-plasma interactions; nonlinear phenomena in plasmas; plasma waves; wave-wave, wave-particle interactions; magnetized plasma; nonlinear waves; first-principles calculations in plasma physics; nonlinear dynamics

### Citation Formats

```
Shi, Yuan, Qin, Hong, and Fisch, Nathaniel J.
```*Three-wave 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.
```*Three-wave 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. Mon .
"Three-wave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian". United States.
doi:10.1103/PhysRevE.96.023204. https://www.osti.gov/servlets/purl/1378090.
```

```
@article{osti_1378090,
```

title = {Three-wave 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 three-wave interactions. While three-wave 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 three-wave coupling coefficient in cold, uniform, magnetized, and collisionless plasmas in the most general geometry. This is achieved by systematically solving the fluid-Maxwell 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 three-wave 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 = {Mon Aug 14 00:00:00 EDT 2017},

month = {Mon Aug 14 00:00:00 EDT 2017}

}

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