A computational and theoretical analysis of falling frequency VLF emissions

Recently much progress has been made in the simulation and theoretical understanding of rising frequency triggered emissions and rising chorus. Both PIC and Vlasov VHS codes produce risers in the region downstream from the equator toward which the VLF waves are traveling. The VHS code only produces fallers or downward hooks with difficulty due to the coherent nature of wave particle interaction across the equator. With the VHS code we now confine the interaction region to be the region upstream from the equator, where inhomogeneity factor S is positive. This suppresses correlated wave particle interaction effects across the equator and the tendency of the code to trigger risers, and permits the formation of a proper falling tone generation region. The VHS code now easily and reproducibly triggers falling tones. The evolution of resonant particle current J(E) in space and time shows a generation point at -5224 km and the wavefield undergoes amplification of some 25 dB in traversing the nonlinear generation region. The current component parallel to wave magnetic field (J(B)) is positive, whereas it is negative for risers. The resonant particle trap shows an enhanced distribution function or 'hill', whereas risers have a 'hole'. According to recent theory (Omura et al., 2008, 2009) sweeping frequency is due primarily to the advective term. The nonlinear frequency shift term is now negative (similar to-12 Hz) and the sweep rate of -800 Hz/s is approximately nonlinear frequency shift divided by T-N, the transition time, of the order of a trapping time.