On the interaction of a gyrating electron beam with a cold plasma

A study is made of a gyrating electron beam interaction with a cold plasma in the presence of an external magnetic field. Relativistic effects are shown to be essential even for non-relativistic beam velocities. A special emphasis is placed on the cyclotron excitation of fast waves whose phase velocities are of the order of the velocity of light or higher. Waves propagating both across the external magnetic field and at an arbitrary angle to it are investigated. The excitation of whistler mode and slow waves corresponding to the quasi-static approximation is considered.