High frequency behavior of a space charge rotating in a magnetic field

A theoretical discussion is given of the propagation of electromagnetic waves in a space charge which is rotating under the influence of a uniform magnetic field. Equations are derived for the relations between the amplitudes of the electric and magnetic fields, charge density, electron velocities, the applied magnetic field, the frequency, the phase velocities, and the effective dielectric constant of the space charge region. In particular, the natural frequencies are computed for such a space charge rotating about an infinitesimal conductor and enclosed by a coaxial conducting cylinder. The predicted resonant frequencies agree well with experimentally observed values for magnetron oscillators. The theory here developed is also applicable to other devices in which a rotating space charge is utilized.