Parametric Instabilities of Parallel Propagating Circularly Polarized Alfvén Waves: One-Dimensional Hybrid Simulations

By performing one-dimensional (1-D) hybrid simulations, we analyze in detail the parametric instabilities of the Alfvén waves with a spectrum in a low beta plasma. The parametric instabilities experience two stages. In the first stage, the density modes are excited and immediately couple with the pump Alfvén waves. In the second stage, each pump Alfvén wave decays into a density mode and a daughter Alfvén mode similar to the monochromatic cases. Furthermore, the proton velocity beam will also be formed after the saturation of the parametric instabilities. When the plasma beta is high, the parametric decay in the second stage will be strongly suppressed.