Abstract :
Satisfactory theories are available for oscillations in linear magnetrons with thin sheet beams of electrons, but when high currents are considered it is difficult to find a suitable steady-state beam configuration on which to base an analysis. For circular magnetrons even the thin rotating sheet beam is unsuitable, because the anode voltage for radial equilibrium of the electrons does not satisfy the Hartree threshold-voltage criterion. In a thick linear beam the electron velocity varies across the width, and coupling to a circuit wave is inefficient. The same objection arises for thick circular beams emitted from conventional cathode arrangements. However, if cathode restrictions are set aside, a high-current circular steady-state may be considered with an electron cloud of uniform space-charge density, extending to the anode and rotating uniformly with angular velocity synchronous with the circuit wave. The density is chosen so that the electrons are everywhere in radial equilibrium and the voltage is equal to the threshold voltage. The high-frequency convection currents, induced in the cloud by a wave on the slow-wave circuit, are free from divergence, so that the space-charge density remains constant and ripples form on the surfaces. The small-amplitude theory of interaction between the ripples on the electron cloud and the waves on the circuit leads to a linear differential equation. The solutions, for various sets of boundary conditions, represent the high-frequency field configurations in steady-state operation of magnetron amplifiers and attenuators and transient build-up in magnetron oscillators.
