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

A role of the second-order cyclotron resonance effect in the self-consistent approach to the problem of triggered ELF/VLF emissions is estimated. The self-consistency includes the calculation of energetic electron beams produced by a quasimonochromatic whistler wave packet and the analysis of secondary whistler wave generation by this beam with the magnetic field inhomogeneity taken into account. The theory allows one to estimate the maximum amplification of the secondary waves, as well as the dynamic frequency spectrum of a triggered emission. A simple computer program has been realized to find dynamic spectrograms of triggered VLF signals in particular cases with realistic dependences of electron beam velocity and geomagnetic field on the spatial coordinate and time. The main and general conclusions are summarized as follows: (1) The second-order cyclotron resonance effects give an important contribution to the formation of the dynamic frequency spectrum of triggered 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 packets (pulse durations 0.9-1.3 s) generate predominantly rising tones. (3) There are critical maximal and minimal values for the pump wave pulse duration, when triggered emissions are not generated in the absence of an external electron beam.