Theory of weakly nonlinear VLF interactions

Abstract

A mathematical description of the weakly nonlinear regime of the coherent cyclotron resonance instability in the magnetosphere which has hitherto been neglected in the literature has been developed. Using the concept that the fundamental role played by the inhomogeneity of the Earth's magnetic field is to limit the interaction time between the resonance electrons and whistler mode wave, perturbation expansions of the current equations to third order have been obtained. It is then found that the real component of resonance current can qualitatively account for excess growth found in some magnetospheric transmissions while the imaginary component gives a good quantitative estimate of frequency shifts observed in transmissions of the mains harmonics.