Laser Amplification in $e^{-}$-$\mu^{-}$-ion Plasmas

We investigate laser amplification in $e^{-}$-$\mu^{-}$-ion plasmas, where negative muons partially replace electrons. Theoretical results reveal a hybrid plasma wave, called $\mu$-wave that exhibits ion-acoustic behavior in long-wavelength regime and Langmuir-like behavior in short-wavelength regime. Besides, the Landau damping of $\mu$-wave is smaller than that of Langmuir wave. Particle-in-cell (PIC) simulations confirm the theoretical results of instabilities in$e^{-}$-$\mu^{-}$-ion plasmas. The $\mu$-wave enables efficient laser amplification by suppressing pump-driven spontaneous instabilities through enhanced Landau damping of Langmuir waves. Compared to Raman amplification, $\mu$-wave amplification can maintain the Gaussian waveform of the seed laser, avoiding pulse splitting. Compared to strongcoupling Brillouin amplification, $\mu$-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 $e^{-}$-$\mu^{-}$-ion plasma as a promising medium for advanced laser amplification schemes.