# Suppression of parametric instabilities in inhomogeneous plasma with multi-frequency light

## TL;DR

This paper investigates how using multi-frequency laser beams in inhomogeneous plasma can suppress parametric instabilities, with theoretical analysis and numerical simulations showing effective control even at high intensities.

## Contribution

It introduces a theoretical model and numerical validation demonstrating that multi-frequency laser beams can decouple and suppress parametric instabilities in plasma.

## Key findings

- Parametric instabilities can be decoupled when frequency difference exceeds certain thresholds.
- Numerical simulations confirm low-level instability development with multiple beamlets.
- Control of instabilities is effective even at high laser intensities (~10^15 W/cm^2).

## Abstract

The development of parametric instabilities in a large scale inhomogeneous plasma with an incident laser beam composed of multiple-frequency components is studied theoretically and numerically. Firstly, theoretical analyses of the coupling between two laser beamlets with certain frequency difference $\delta\omega_0$ for parametric instabilities is presented. It suggests that the two beamlets will be decoupled when $\delta\omega_0$ is larger than certain thresholds, which are derived for stimulated Raman scattering (SRS), stimulated Brillouin scattering (SBS), and two plasmon decay (TPD), respectively. In this case, the parametric instabilities for the two beamlets develop independently and can be controlled at a low level provided the laser intensity for individual beamlet is low enough. Secondly, numerical simulations of parametric instabilities with two or more beamlets ($N\sim20$) have been carried out and the above theory model is validated. Simulations confirm that the development of parametric instabilities with multiple beamlets can be controlled at a low level, provided the threshold conditions for $\delta\omega_0$ is satisfied, even though the total laser intensity is as high as $\sim10^{15}$W/cm$^2$. With such a laser beam structure of multiple frequency components ($N\gtrsim20$) and total bandwidth of a few percentages ($\gtrsim4\%$), the parametric instabilities can be well-controlled.