We introduced a phase-locking mechanism of millimeter-wave magnetrons coupled through a carefully designed coupling bridge. For such a structure, two Ka-band 22-vane rising-sun magnetron circuits operated in the $\pi $ -mode were phase-locked tightly as a whole through a double-ridged coupler. Moreover, the double-ridged coupler was optimized to suppress mode competition between zero-phase and $\pi $ -phase difference mode, which achieved high-efficiency phase-locking. Total output power of the two identical magnetrons nearly doubled the output power of a free-running magnetron and efficiencies of them were nearly the same. Extension of this phase-locking mechanism to high-power applications appears feasible with more elements in an array of the millimeter-wave magnetrons.

In vacuum electronics, the influence of the uniformity of electron beams on the performance of two- or multi-beam devices is a key scientific problem in the development of compact, high power millimeter-wave and terahertz (THz) sources. In this letter, we focus on this problem in extended interaction oscillators (EIOs) and propose a tractable extended resonant circuit that has no requirement for the uniformity of beams. The circuit design builds up a TM ₁₃ mode mechanism to support two nonuniform beams, based on maintaining the same electromagnetic characteristics of conventional resonant circuits used in single-beam EIOs. To verify this idea, we designed and simulated a 0.22-THz EIO with the proposed circuit. As the current of one beam is I ₁ and that of another beam is increased from 0 to 4I ₁ , the EIO has shown the behavior of linearly increasing the output power and then becoming saturated through particle-in-cell (PIC) simulations. The ideal case is the currents of the two beams are the same at the same voltage to drive the EIO. This case can reduce the high current density required for start oscillation in single-beam EIOs and obtain high power. Simulation results show that the power of 0.22-THz wave over 1.32 kW is obtained using double beams at 22.2 kV and each current of 0.25 A.

The conventional mutual coupling phase-locking technique uses waveguides to directly connect magnetrons to operate as a whole device. However, this method is not suitable for large-scale phase-locked array applications due to the considerable challenges in achieving the required vacuum level. Thus, the modular magnetron applied to the mutual coupling phase-locking technique was proposed. First, the coupling structure was designed to combine a double-ridged waveguide and a rectangular waveguide for incorporating an RF window. Therefore, a single magnetron could be vacuumed as a modular unit. Subsequently, in simulation, two modular X -band magnetrons connected by a coupling bridge were verified to operate in a phase-locked state with a 0 $^{\circ}$ phase difference, with a phase-locking efficiency of 97.2%. Second, an experimental scheme capable of characterizing directly the phase difference between magnetrons was proposed. In the experiment, multiple sets of time-domain signal data were randomly sampled when the magnetrons were in a stable operating state. The experimental results were essentially consistent with the expected design phase difference of 0 $^{\circ}$ , as the phase difference between the two magnetrons remained consistently between 3 $^{\circ}$ and 5 $^{\circ}$ , with the phase-locking efficiency measured at 91.9%.

An improved topology of Extended interaction oscillators (EIO) is presented with enhanced efficiency at 0.35 THz. A bi-periodic ladder-type structure is used for optimizing the performance of the TM $_{{31}}- 2\pi $ mode operation, based on bi-periodic interaction gaps composed of staggered short and long slots. The bi-periodic interaction mechanism permits to operate the circuit with a standing-wave field between the $\pi $ and $2\pi $ modes, thus providing the potential to combine the advantages of both $\pi $ and $2\pi $ modes in terms of both coupling and output performance. The resulting transverse TM ₃₁ operating mechanism exhibits a good agreement with the bi-periodic structure in terms of coupling performance, with the short slot length positively correlated with the value of effective characteristic impedance ${M}^{\,{2}}{R}/{Q}$ . The circuit demonstrates attractive coupling and output characteristics by optimization of ${M}^{\,{2}}{R}/{Q}$ and ${Q}_{e}$ . A state-of-the-art value ${M}^{\,{2}}{R}/{Q}$ of 59.69 $\Omega $ and a moderate ${Q}_{e}$ of 2523.52 are achieved for a proposed eight-period ladder-type EIO. An RF power of 540 W is obtained with a 42.5 kV, 0.6 A sheet beam, with 2.1% electronic efficiency at 0.35 THz.

To meet the phase control requirements of magnetrons in large-scale array applications, the advantages of injection locking and cascaded mutual coupling phase locking are fully integrated. A hybrid phase-locking system for magnetrons is proposed. By performing external injection on just one magnetron within the cascaded mutual coupling structure, simultaneous frequency locking of both magnetrons can be achieved. Simulation and experimental results indicate that two phase-locking regions emerge during one period of phase variation. By quantifying the power flow across the four ports of the phase locker, it is determined that the power necessary for phase locking is less than 1% of the total output power. External frequency tuning enables the stabilization of the frequencies of both magnetrons, resulting in a purer spectrum. With an injection ratio of -18.97 dB, the mutual coupling phase locker can be adjusted to vary the phase difference between the output signals of the two magnetrons within the range from -126^∘ to 171^∘. This facilitates phase control of the output signals from the two magnetrons. The phase-locking efficiency of this system is 88.2%. The hybrid phase-locking approach achieves high-efficiency phase locking and power output. This approach is particularly suited for coherent power synthesis and phase scanning in large-scale array applications.

The scheme of a high-efficiency phase locking based on a novel multiorder cascaded coupling structure is proposed to establish a high-power $2\times 2$ array consisting of four megawatt-level, S-band magnetrons. Every magnetron is designed with only one coupling port to match the cascaded coupling structure, in which a matched, cascaded, standing-wave field is built up to support the phase-locked mode with 0 phase difference between them. To obtain high-efficiency phase locking, the two-order, cascaded, standing-wave field is produced with a small portion of stored energy, which matches with four $\pi $ modes in four magnetrons. Particle-in-cell (PIC) simulation results show that a 0-phase difference between four magnetrons is obtained with every magnetron delivering a peak power of 2.4 MW, which is almost the same as the power of a free-running magnetron. The array can deliver a total power of up to 9.6 MW. The power conversion efficiency of the array is 65.2%, which is almost the same as that of the free-running magnetron. This demonstrates the high-efficiency phase locking. The scheme is promising in developing a large-scale array for higher-power microwave generation.