Parametric decay of oblique whistler waves in the Earth's magnetosphere: 2-D PIC simulations

Whistler mode waves in the Earth's magnetosphere have already been widely investigated in the linear or quasi-linear regime, but there is still lack of research on nonlinear physical processes. In this paper, with a 2-D PIC simulation model, we have studied the parametric decay of oblique whistler waves for the first time. The parametric decay of an oblique whistler wave first occurs along its propagating direction, which involves a backward daughter whistler wave and a forward ion acoustic mode. This is quite similar to the parametric decay of parallel whistler waves in 1-D simulations. Interestingly, the parametric decay will then take place along the perpendicular direction, which can generate a family of daughter whistler waves along the perpendicular direction with the nearly same parallel wave number. Meanwhile, the highly oblique whistler waves will also be excited during this perpendicular decay, whose wave normal angle can even reach up to the resonant cone angle. Moreover, the parametric decay tends to be stronger for the pump whistler wave with a larger frequency or larger amplitude. But the growth rate of the parametric decay has little change when the wave normal angle of the pump whistler wave varies within a limited range. Interestingly, parallel whistler waves can also experience the similar decay process, which may suggest that the parametric decay of whistler waves should be a multi-dimensional process in nature. During the decay process, the generated ion acoustic waves can accelerate a part of protons through the Landau resonance. Our simulation results not only uncover the evolution pattern of whistler waves during the parametric decay in a two-dimensional regime but also propose a potential nonlinear physical process related to whistler waves in the Earth's magnetosphere.