Cascading parametric decay coupling between whistler and ion acoustic waves: Darwin particle-in-cell simulations - Karbashewski, Scott; Sydora, Richard D.; Agapitov, Oleksiy V. (Frontiers in Astronomy and Space Sciences, 2022)
We present Darwin particle-in-cell (PIC) simulation studies of the parametric decay instability of whistler waves in the presence of an undamped ion acoustic wave (IAW). A monochromatic whistler wave is launched along a one-dimensional periodic grid and couples to a counter-propagating whistler mode and co-propagating ion acoustic mode. The coupling of the electromagnetic fields to the electrostatic field is modeled using a ponderomotive force that forms spatio-temporal beat patterns in the longitudinal electric field generated by the counter-propagating whistlers and pumps whistler wave. The threshold value for the instability is determined and agrees with a prediction using the ion decay instability. As the amplitude of the pump whistler wave is increased, secondary and tertiary decay thresholds are reached and are observed to cascade from the daughter whistler modes. At the largest amplitude ($δ B_w/B_0\sim 0.1$) the primary IAW evolves into a short-lived and highly nonlinear structure. The growth rates of the primary decay channel compare favorably with analytical expressions. We discuss the relevant space regimes where the instability could be observed and extensions to the parametric coupling of whistler waves with the electron acoustic wave (EAW)