Triple point, defined as the junction of metal, dielectric, and vacuum, is the location where electron emission is favored in the presence of a sufficiently strong electric field. In addition to being an electron source, the triple point is generally regarded as the location where flashover is initiated in high voltage insulation, and as the vulnerable spot from which rf breakdown is triggered. In this paper, we focus on the electric field distribution at a triple point of a general geometry, as well as the electron orbits in its immediate vicinity. We calculate the orbit of the first generation electrons, the seed electrons. It is found that, despite the mathematically divergent electric field at the triple point, significant electron yield most likely results from secondary electron emission when the seed electrons strike the dielectric. The analysis gives the voltage scale in which this electron multiplication may occur. It also provides an explanation on why certain dielectric angles are more favorable to electron generation over others, as observed in previous experiments.

A phase-locking model has been developed from circuit theory to qualitatively explain the various regimes observed in magnetron injection-locking experiments. The experiments utilize two continuous-wave oven magnetrons: one functions as an oscillator and the other as a driver. The model includes both magnetron-specific electronic conductance and frequency-pulling parameter. Both time and frequency domain solutions are developed from the model, allowing investigations into the growth and saturation as well as the frequency response of the output signal. This simplified model recovers qualitatively many of the phase-locking frequency characteristics observed in the experiments.

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The condition for mutual, or peer-to-peer, locking of two magnetrons is derived. This condition reduces to Adler’s classical phase-locking condition in the limit where one magnetron becomes the “master” and the other becomes the “slave.” The formulation is extended to the peer-to-peer locking of N magnetrons, under the assumption that the electromagnetic coupling among the N magnetrons is modeled by an N-port network.