The article discusses the results of the development of a one-dimensional disk mathematical model of the electrodynamic system of a multi-beam klystron, taking into account the non-identical conditions for the interaction of electron beams with the fields of ring resonators. An equivalent circuit of a ring resonator operating on the highest form of oscillations is presented, based on the equations of electromagnetic wave propagation in a waveguide with losses and adequately tracking the amplitude and phase unevenness of the microwave field in the ring gaps of the resonator interaction. The unevenness of the field in the interaction gap can be caused by the influence of communication elements with the load, unequally grouped electron beams and other factors.
$^1$AO "Pluton"
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