Laser amplification in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:mtext>−</mml:mtext> <mml:msup> <mml:mi>μ</mml:mi> <mml:mo>−</mml:mo> </mml:msup> </mml:mrow>

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 strong-coupling 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.