Cyclotron Wave-Particle Interactions in the Whistler-Mode Waveguide

We study the cyclotron interaction of energetic electrons and whistler waves in plasma waveguides formed by inhomogeneous distribution of cold plasma. Such waveguides can be formed in the Earth's magnetosphere, e.g., by the plasmapause or by ducts with enhanced background-plasma density. In this paper, we consider a cylindrically symmetric model of a magnetospheric duct with enhanced cold-plasma density in a homogeneous magnetic field. The spatial structure of the eigenmodes of such a waveguide is found. We obtain a set of self-consistent quasilinear equations for cyclotron instability with eigenmode structure taken into account, thus generalizing the quasilinear theory of a magnetospheric cyclotron maser.