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

## TL;DR

This paper derives a general, evaluable formula for three-wave coupling coefficients in magnetized warm-fluid plasmas, enabling precise analysis of wave interactions in contexts like fusion and solar physics.

## Contribution

It introduces a novel, general formula for coupling coefficients in magnetized warm-fluid plasmas, applicable to arbitrary wave angles and interactions.

## Key findings

- Coupling coefficients for laser scattering in magnetized plasmas are calculated.
- Growth rates of laser scattering are affected by magnetic fields and oblique angles.
- Decay of Alfvén waves shows slight preference for backward geometry in solar conditions.

## Abstract

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. As one example, coupling coefficient governing laser scattering is evaluated. In conditions relevant to magnetized inertial confinement fusion experiments, lasers scatter from magnetized plasma waves and the growth rates are modified at oblique angles. As another example, coupling coefficient between two Alfv\'en waves via a sound wave is evaluated. In conditions relevant to solar corona, the decay of a parallel Alfv\'en wave only slightly prefers exact backward geometry.