Parametric decay instability of circularly polarized Alfvén waves in magnetically dominated plasma

We investigate parametric decay instability (PDI) of circularly polarized Alfvén wave into daughter acoustic wave and backward Alfvén wave in magnetically dominated plasma, in which the magnetization parameter σ (energy density ratio of background magnetic field to matter) exceeds unity. We analyze relativistic magnetohydrodynamics (MHD), focusing on wave frequencies sufficiently lower than the plasma and cyclotron frequencies. We derive analytical formulas for the dispersion relation and growth rate of the instability as a function of the magnetization σ, wave amplitude η, and plasma temperature θ. We find that PDI persists even in high magnetization σ, albeit with a decreased growth rate up to σ→∞. Our formulas are useful for estimating the decay of Alfvén wave into acoustic wave and heat in high magnetization σ plasma, which is a ubiquitous phenomenon such as in pulsars, magnetars, and fast radio bursts.