On the resonant interaction of relativistic electrons with oblique whistler-mode waves

In the present study, we consider the problem of resonant interaction of the relativistic electrons with oblique monochromatic whistler-mode waves in the Earth's magnetosphere. The Hamiltonian theory of such an interaction has been developed, taking into account the peculiarities of relativistic case, e.g., the possibility for a resonance momentum to become zero on the particle trajectory. Using the approach of geometric optics we have calculated the field distribution of whistler-mode waves generated in the ionosphere by VLF transmitter or a lightning discharge. The motion of trapped electron in such a field have been investigated.