Nonlinear dynamics of foreshock structures: Application of nonlinear autoregressive moving average with exogenous inputs model to Cluster data

Nonlinear processes identification techniques based on multi-input nonlinear autoregressive moving average with exogenous inputs model has been applied to four-point Cluster measurements in order to study nonlinear processes that take place in the terrestrial foreshock. It is shown that both quadratic and cubic processes are involved in the evolution of shocklets in particular in the steepening of their leading edge and generation of whistler precursor. Nonlinear processes do not play an essential role in the dynamics and propagation of small-amplitude whistler packets. However, for large-amplitude wave packets, cubic processes lead to the considerable modification of apparent propagation velocity.