  A simplified analytical model of the resonant interaction of the beam of
Larmor electrons drifting in the crossed constant fields of a magnetron with a
synchronous wave providing a phase grouping of the drifting charge was
developed to optimize the parameters of an rf resonant injected signal driving
the magnetrons for management of phase and power of rf sources with a rate
required for superconducting high-current accelerators. The model, which
considers the impact of the rf resonant signal injected into the magnetron on
the operation of the injection-locked tube, substantiates the recently
developed method of fast power control of magnetrons in the range up to 10 dB
at the highest generation efficiency, with low noise, precise stability of the
carrier frequency, and the possibility of wideband phase control. Experiments
with continuous wave 2.45 GHz, 1 kW microwave oven magnetrons have verified the
correspondence of the behavior of these tubes to the analytical model. A proof
of the principle of the novel method of power control in magnetrons, based on
the developed model, was demonstrated in the experiments. The method is
attractive for high-current superconducting rf accelerators. This paper also
discusses vector methods of power control with the rates required for
superconducting accelerators, the impact of the rf resonant signal injected
into the magnetron on the rate of phase control of the injection-locked tubes,
and a conceptual scheme of the magnetron transmitter with highest efficiency
for high-current accelerators.
