The magnetosphere of the Earth presents a large scale plasma physics laboratory in which the complex interacting plasma phenomena are involved: global convecting plasma dynamics, wave–particle interactions in the bow shock and transmitted shock waves/impulses and magnetic field reconnection in the plasma current sheets. The NASA magnetospheric multiscale mission (MMS) provides unique observations of the thin structures and wave–particles interactions at the shock-like impulses while the spacecrafts were located at the dawn terminator (the time is 2016-03-07 20:00:00 UTC). It was assumed that these impulses may be created by the interaction between the background flow and plasma clouds. It was also assumed that those clouds were produced by either flux-transfer events or by coalescence/reconnection processes at the magnetopause current layer or by the mirror instabilities inside the low latitude boundary layer. 3-D hybrid kinetic code with separate description of the background and cloud ions was used for interpretation of the observed impulse structures. In this report we will discuss the effects of particle heating and acceleration inside the foreshock of the shock-like impulses, effects of the ion and electron non-Maxwellian velocity distributions, and particle finite gyroradius, and triggering the electromagnetic instability.