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Evolution of the parametric decay instability (PDI) of a circularly polarizedAflv\'en wave in a turbulent low-beta plasma background is investigated using3D hybrid simulations. It is shown that the turbulence reduces the growth rateof PDI as compared to the linear theory predictions, but PDI can still exist.Interestingly, the damping rate of ion acoustic mode (as the product of PDI) isalso reduced as compared to the linear Vlasov predictions. Nonetheless,significant heating of ions in the direction parallel to the backgroundmagnetic field is observed due to resonant Landau damping of the ion acousticwaves. In low-beta turbulent plasmas, PDI can provide an important channel forenergy dissipation of low-frequency Alfv\'en waves at a scale much larger thanthe ion kinetic scales, different from the traditional turbulence dissipationmodels.

Parametric Decay Instability and Dissipation of Low-frequency Alfv\'en Waves in Low-beta Turbulent Plasmas