Phase locking of relativistic magnetrons has been achieved at power levels of ~3 GW at 2.8 GHz, exceeding previous phase-locking power levels by 3 orders of magnitude. Two relativistic magnetrons interact directly through a short waveguide of length l~~nX/2 to allow locking. Power-density enhancement due to source coherence is directly measured in the radiation field. Phase locking occurs in ~5 ns and is reproducible. Extension to 10-100 GW appears feasible with arrays of oscillators.
A new method is demonstrated for extracting radiation from a virtual cathode oscillator in transverse electric (TE) waveguide modes. The dominant radiation mechanism occurs in the region of the virtual cathode, and is not due to reflexing of electrons. Microwave radiation occurs simultaneously or just after beam pinching in the diode. Electrostatic signals show simultaneous occurrence of the virtual cathode and microwave radiation. At the same time, the electron population divides into a beam population and a reflexing electron population. Inhibition of pinching by an axial guide field suppresses microwave radiation.
Phase locking is considered both for a case in which an oscillator is driven by an external signal without feedback, and for a case in which two coupled oscillators drive each other. A comprehensive sustained oscillator model is used for the driven microwave cavity. The new locking conditions for two coupled oscillators show that phase locking can occur only when the connector contributes the zero or π phase delay. Temporal behavior is solved numerically. Calculations with large priming power agree with the experiments on a high-power magnetron driven vircator in which there is no feedback to the magnetron. The mutual drive calculations also agree with the experiments on high-power coupled magnetrons.
A two-dimensional model for the electron flow in the presence of a virtual cathode is presented. The model allows for electron reflexing and velocity distribution spread. Solutions with substantial radial flow agree closely with high-power microwave emission observed in experiments. The radial motion is the result of the self-magnetic field of the beam, which bends some of the electrons from propagating to side walls to reflex between real and virtual cathodes. The resulting plasma frequency solution agrees with the measured microwave frequency, which scales linearly with the diode current instead of the square-root scaling for a one-dimensional flow. Scaling laws are derived and agree with experimental measurements.
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