Frequency-time structure of vlf emissions

Non-linear wave-particle interaction in the whistler mode in a non-uniform magnetic field is considered. The effect of the second order resonant particles arising due to nonuniformity of the ambient magnetic field is found to be dominant near the equatorial plane of the Earth. The equations describing the time development of the amplitude and phase of the wave packet have been solved numerically by computing the resonant particle current in a self-consistent manner. The growth of the waves because of trapped particles is found to be substantial for triggering an emission and the changes in phase lead to the frequency-time structure. It is capable of reproducing all kinds of frequency time structure as observed in the case of a morse pulse.