Generation of Intermittent Ion Acoustic Waves in Whistler Turbulence: Particle-In-Cell Simulation

Quasi-perpendicular collisionless shocks can be a cause of several microinstabilities which enhance ion acoustic waves, whistler waves, ripple structures, and etc. Cross-field currents associated with the steep gradient of magnetic field, nonlinear behaviors of shock front, and reflected ions are considered as energy source of electrostatic and electromagnetic fluctuations in the collisionless shocks. These fluctuations have important roles to scatter upstream plasma particles by wave-particle interactions. Observations of a quasi-perpendicular collisionless shocks showed that correlation of the electrostatic turbulence with gradient of the magnetic field strength [1]. They suggested that the fluctuations are ion acoustic waves driven by the crossfield currents. The most plausible instability for ion acoustic waves in the steep magnetic gradient is the ion acoustic instability [2]. The linear theory shows that the instability drives the ion acoustic waves more effectively at larger temperature ration between electron and ion Te/Ti [3, 4]. Observations seem to support the linear theory, showing higher powers of ion acoustic waves at higher temperature ratio [5]. However, they raised a problem that the ion acoustic waves observed at plasma environment with not only large Te/Ti but also Te~Ti. Further Thomsen et al. [6] noted that thicknesses of quasiperpendicular bow shocks were generally not thin enough to trigger the cross field ion acoustic instability, whose thickness is about ion inertial length [7]. The observations suggest that there are additional sources of ion acoustic waves that can be driven at Te~Ti. Recent full particle-in-cell simulations demonstrated that nonlinear whistler waves can be driven at the shock front [8]. The nonlinear whistlers in the foot region have been observed in quasi-perpendicular collisionless shocks [e.g. 9]. Balikhin et al. [10] also observed the whistler waves and they identified quasi-parallel propagating whistlers with respect to upstream magnetic field, whose propagation angle is estimated as about 24 degree. On the other hand, recent observations found finite amplitude whistler waves propagating in directions highly oblique to the background magnetic field [11]. They argued that these whistlers are not phase-standing mode at the ramp region, and propagating upstream as precursors. By their propagation to upstream, it is expected that nonlinear interactions of finite amplitude whistler waves develop into whistler turbulence and are dissipated through kinetic processes. Here we demonstrated by using a fully kinetic particle-in-cell simulation that nonlinear development of whistler turbulence generates intermittent ion acoustic waves through ion/ion streaming instability. The instability is driven by interaction between two ion components in ion phase space. Wavenumber of the enhanced ion acoustic waves is quasi-parallel to the background magnetic field. The simulation results suggest that finite amplitude whistler turbulence in the foot region of quasi-perpendicular collisionless shocks can be an additional source of ion acoustic waves observed in interplanetary shocks and Earth’s bow shock.