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Various methods of phase and power control in magnetron RF sources of superconducting accelerators intended for ADS-class projects were recently developed and studied with conventional 2.45 GHz, 1 kW, CW magnetrons operating in pulsed and CW regimes. Magnetron transmitters excited by a resonant (injection-locking) phasemodulated signal can provide phase and power control with the rates required for precise stabilization of phase and amplitude of the accelerating field in Superconducting RF (SRF) cavities of the intensity-frontier accelerators. An innovative technique that can significantly increase the magnetron transmitter efficiency at the widerange power control required for superconducting accelerators was developed and verified with the 2.45 GHz magnetrons operating in CW and pulsed regimes. High efficiency magnetron transmitters of this type can significantly reduce the capital and operation costs of the ADSclass accelerator projects.

A concept of a high-power magnetron transmitter utilizing the vector addition of signals of Continuous Wave (CW) magnetrons, injection-locked by phase-modulated signals, and intended to operate within a wideband control feedback loop in phase and amplitude, is presented. This transmitter is proposed to drive Superconducting RF (SRF) cavities for intensity-frontier GeV-scale proton/ion linacs, including linacs for Accelerator Driven System (ADS). The transmitter performance was verified in experiments with CW, S-Band, 1 kW magnetrons. A wideband dynamic control of magnetrons, required for the superconducting linacs, was realized using the magnetrons, injectionlocked by the phase-modulated signals. The capabilities of the magnetrons injection-locked by the phase-modulated signals and adequateness for feeding of SRF cavities have been verified by measurements of the transfer function magnitude characteristics of single and 2-cascade magnetrons in the phase modulation domain, by measurements of the magnetrons phase performance and by measurements of spectra of the carrier frequency of the magnetrons. At the ratio of power of locking signal to output power of ≥ -13 dB (in 2-cascade scheme per magnetron, respectively) we demonstrated a phase modulation bandwidth of over 1.0 MHz for injection-locked CW single magnetrons and a 2-cascade setup, respectively. The carrier frequency spectrum (width of ~ 1 Hz at the level of <-60 dBc) of the magnetron, injection-locked by a phase-modulated signal, did not demonstrate broadening at wide range of magnitude and frequency of the phase modulation. The wideband dynamic control of output power of the transmitter model has been first experimentally demonstrated using two CW magnetrons, combined in power and injection-locked by the phasemodulated signals. The experiments with the injection-locked magnetrons adequately emulated the wideband dynamic control with a feedback control system, which will allow to suppress parasitic modulation of the accelerating field in the SRF cavities, resulted from mechanical noises, phase perturbations, caused by cavity beam loading and cavity dynamic tuning errors, low-frequency ripples of the magnetron power supplies, etc. The magnetron transmitter concept, tests of the transmitter models and injection-locking of magnetrons by phase-modulated signals are discussed in this work.

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.

Reciprocity is a fundamental physical principle that roots in the time‐reversal symmetry of physical laws. It allows making predictions on any arbitrary complex system's response and operation and hence simplifies the analysis. However, there are many practical situations in which it is advantageous to break reciprocity, e.g., isolators preventing wave scattering back to lasers and generators, full‐duplex systems for multiplexing transmission and receiving in the same channel, nonreciprocal cavity excitation, and protection of fragile states of superconductor quantum computers from thermal noise. The most widespread approach to time‐reversal symmetry breaking and nonreciprocity based on magnetic field biasing suffers from bulkiness, cost ineffectiveness, and loss, motivating researchers and engineers to search for more practical approaches. Herein, the up‐and‐coming advances in optical nonreciprocity, including new materials (Weyl semimetals, topological insulators, metasurfaces), active structures, time‐modulation, parity‐time (PT)‐symmetry breaking, nonlinearity combined with a structural asymmetry, quantum nonlinearity, unidirectional gain and loss, chiral quantum states and valley polarization are overviewed. A general description of nonreciprocal systems is provided and the pros and cons of the mentioned approaches to nonreciprocity are discussed.