An investigation into the nonlinear frequency shift in magnetospherically propagated VLF pulses

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Abstract
When ducted narrow‐band VLF pulses pass through the Earth's magnetosphere, small frequency shifts of ∼1 Hz may be observed at the receiving site on the ground. Such shifts may be due to Doppler effects, but nonlinear electron cyclotron resonance near the magnetospheric equator may also play a part. This paper is a study of nonlinear frequency shifts induced by wave‐particle interaction effects. The development assumes strong nonlinearity and the dominance of particle trapping. The VLF pulses are considered to be much shorter than the scale length of the interaction region; however, for long pulses the results remain valid for the front part of the pulse as seen at the receiving site. Numerical simulations for the NAA and Siple transmitters are performed using a Vlasov code. The results are in general agreement with the theoretical analysis. Experimental observations are reviewed, and future active experiments are suggested.