A cyclotron resonance mechanism for very-low-frequency whistler-mode sideband wave radiation. I. Introduction and description of external resonances

Abstract

The first part of the paper introduces the reader to the physical and mathematical aspects of the problem of sideband formation associated with very-low-frequency whistler-mode waves propagating in ducts in the magnetosphere. It starts with an introduction to the general problem of charge distribution in the duct and looks at the effect of monochromatic electromagnetic waves acting on such distributions. It describes sidebands as due to wave-wave interactions occurring in the magnetosphere through electron cyclotron resonances, and concentrates on sideband radiation coming from resonances located outside the wave potential wells (external resonances). It also presents a general solution to the electron equation of motion, based on the Kolmogorov–Arnold–Moser theorem, that lists the possible sideband radiation frequencies. Both an analytical treatment, based on Lie transform perturbation theory, and a numerical treatment, based on phase plots, are used in the detailed part of the analysis. Effects of the inhomogeneity of the magnetic field of the Earth are mainly neglected in the first part of the paper.