MOTION OF AN ELECTRON IN THE FIELD OF A STANDING ELECTROMAGNETIC WAVE.

The classical equations of motion are analyzed for a relativistic electron in the superposition of a standing wave and a steady magnetic field, which gives an integral of motion relating the energy to the radius of the cyclotron orbit. The cases of finite and infinite motion are examined. The quantum approach is based on solving the Klein-Gordon equation and is supplemented by analysis of the energy spectrum as affected by the type of boundary conditions. One of the characteristic field configurations for devices of cyclotron-resonance maser type is the superposition of a standing wave and a steady magnetic field. It is therefore of interest to examine the interactions of an electron with such a field localized between two reflecttors (simple resonator).