Laser Amplification in $e^{-}$-$μ^{-}$-ion Plasmas

TL;DR

This work investigates laser amplification in plasmas containing two negatively charged species, electrons and muons, forming $e^{-}$-$μ^{-}$-ion plasmas. It introduces the $μ$-wave, a hybrid electrostatic mode that behaves like an ion-acoustic wave at long wavelengths and a Langmuir wave at short wavelengths, with reduced Landau damping relative to Langmuir waves. Using a 1D two-fluid model and fully kinetic PIC simulations, the authors derive and verify growth rates for $μ$-wave and Raman instabilities, showing that $μ$-wave amplification can suppress pump-driven spontaneous instabilities and preserve seed Gaussian profiles, outperforming conventional Raman and SC-SBS schemes under many conditions. The results suggest that $μ$-wave amplification offers a robust, high-fidelity route for advanced laser amplification in exotic plasmas and may generalize to other double-negative-species systems, though practical realization hinges on muon source development.

Abstract

We investigate laser amplification in $e^{-}$-$μ^{-}$-ion plasmas, where negative muons partially replace electrons. Theoretical results reveal a hybrid plasma wave, called $μ$-wave that exhibits ion-acoustic behavior in long-wavelength regime and Langmuir-like behavior in short-wavelength regime. Besides, the Landau damping of $μ$-wave is smaller than that of Langmuir wave. Particle-in-cell (PIC) simulations confirm the theoretical results of instabilities in$e^{-}$-$μ^{-}$-ion plasmas. The $μ$-wave enables efficient laser amplification by suppressing pump-driven spontaneous instabilities through enhanced Landau damping of Langmuir waves. Compared to Raman amplification, $μ$-wave amplification can maintain the Gaussian waveform of the seed laser, avoiding pulse splitting. Compared to strongcoupling Brillouin amplification, $μ$-wave amplification exhibits weaker filamentation instability. Our theoretical model can be generalized to other plasma systems containing two species of negatively charged particles, such as two-temperature electron plasmas and negative-ion plasma. These findings establish $e^{-}$-$μ^{-}$-ion plasma as a promising medium for advanced laser amplification schemes.

Figures (6)

• Figure 1: (a) The frequency of electron plasma waves by two-fluid model Eq. (\ref{['eq:4a']})(black straight line) and the Langmuir waves approximation solutions by Eq. (\ref{['wlw']}) (red dashed line) with $\eta =0.5$. (b) The frequency of electron plasma waves by two-fluid model Eq. (\ref{['eq:4b']}) (black straight line), the approximation solutions of $\mu$-wave by Eq. (\ref{['mulw']}) (red dashed line) at short-wavelength regime and the approximation solutions of $\mu$-wave by Eq. (\ref{['mulw2']}) (blue dotted line) at long-wavelength regime.
• Figure 2: (a)The dispersion relations of three branches of wave modes when $\eta = 0.5$, (b)The dispersion relations of three branches of wave modes when $\eta = 0.2$. Langmuir wave (blue straight lines), $\mu$-wave (black straight lines) and ion acoustic wave(green straight lines ), they are obtained by numerically solving Eq. (\ref{['Bfluid_eq15']}). The purple dashed lines are the approximate solution of $\mu$-wave by Eq. (\ref{['mulw2']}), red dashed lines are the approximate solution of ion acoustic wave by Eq. (\ref{['threecom2']}).
• Figure 3: One dimensional PIC results, the seed lasers after amplifications with electron fraction $\eta = 0.2$. Cases where the seed laser wavelength is approximately $804$$\rm{nm}$ belong to $\mu$-wave amplification, while cases with a seed laser wavelength around $880$$\rm{nm}$ belong to Raman amplification.
• Figure 4: (a) The growth rate of laser plasma instabilities in electron-muon plasmas by Eq. (\ref{['fA19']}), the black line is the growth rate of Raman scattering with different $\eta$, the red dashed line is the growth rate of $\mu$-wave scattering with different $\eta$ (b) PIC simulation results, the seed laser intensities for Raman amplifications (black squares) and $\mu$-wave amplifications (red circles) with different $\eta$. Both simulation and theoretical results demonstrate consistent trends. (c) The Landau damping of Langmuir waves for different $\eta$. (d) The Landau damping of $\mu$-waves for different $\eta$.
• Figure 5: (a) The SC-SBS amplification in electron-ion plasma by PIC simulation.(b)The Raman amplification in electron-ion plasma by PIC simulation. (c)The $\mu$-wave amplification in muon-containing plasma with $\eta = 0.2$. The inset diagram displays the wavevector spectrum corresponding to the seed laser. (d) The density of muons in $\mu$-wave amplification with $\eta = 0.2$. (d) The density of protons in $\mu$-wave amplification with $\eta = 0.2$.