Spiky parallel electrostatic ion cyclotron and ion acoustic waves

One of the interesting observations from the FAST satellite is the detection of strong spiky waveforms in the parallel electric field in association with ion cyclotron oscillations in the perpendicular electric fields. We report here an analytical model of the coupled nonlinear ion cyclotron and ion-acoustic waves, which could explain the observations. Using the fluid equations for the plasma consisting of warm electrons and cold ions, a nonlinear wave equation is derived in the rest frame of the propagating wave for any direction of propagation oblique to the ambient magnetic field. The equilibrium bulk flow of ions is also included in the model to mimic the field-aligned current. Depending on the wave Mach number M defined by M = V/Cs with V and Cs being the wave phase velocity and ion-acoustic speed, respectively, we find a range of solutions varying from a sinusoidal wave form for small amplitudes and low M to sawtooth and highly spiky waveforms for nearly parallel propagation. The results from the model are compared with the satellite observations.