A role of the second-order cyclotron resonance effect in a self-consistentapproach to triggered VLF emissions

A role of the second-order cyclotron resonance effect in the self-consisten t approach to the problem of triggered ELF/VLF emissions is estimated. The self-consistency includes the calculation of energetic electron beams produ ced by a quasimonochromatic whistler wave packet and the analysis of second ary whistler wave generation by this beam with the magnetic field inhomogen eity taken into account. The theory allows one to estimate the maximum ampl ification of the secondary waves, as well as the dynamic frequency spectrum of a triggered emission. A simple computer program has been realized to fi nd dynamic spectrograms of triggered VLF signals in particular cases with r ealistic dependences of electron beam velocity and geomagnetic field on the spatial coordinate and time. The main and general conclusions are summariz ed as follows: (1) The second-order cyclotron resonance effects give an imp ortant contribution to the formation of the dynamic frequency spectrum of t riggered ELF/VLF emissions. (2) The short pump whistler wave packets (with pulse durations 0.5-0.7 s in our case) generate fallers, while the long pac kets (pulse durations 0.9-1.3 s) generate predominantly rising tones. (3) T here are critical maximal and minimal values for the pump wave pulse durati on, when triggered emissions are not generated in the absence of an externa l electron beam.