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 dual-frequency radiation scheme of a G-band extended interaction oscillator (EIO) has been proposed. The analytic estimates of structure, mode characteristics, and oscillation-starting condition of the overmoded double-sheet-beam oscillator have been presented. The counterstreaming beams and optimized parameters were employed to reduce the fundamental mode competition in a TM₂₁ mode EIO, allowing the high-order transverse mode (TM₂₁⁺⁻) and the fundamental mode (TM₂₁⁺⁺) to operate simultaneously. The analyses are verified by simulations using 3-D particle-in-cell codes. The newly designed EIO was simulated with copper as a background material, and the dual-frequency radiation power of ~517 W is achieved when a double electron beam with 0.4 A and 21.5 kV is injected.

This paper presents a theoretical study on a start current of a 0.378 THz sheet beam extended interaction oscillator (SB-EIO), and the design of this device driven by thermionic cathode stands a chance to realize a compact and powerful THz coherent continuous radiation sources. After theoretical study, the SB-EIO with eleven gaps is designed to operate at 2π mode. The coupling and interaction abilities are optimized to meet the synchronization conditions and thus improve the output power and efficiency. The start current analysis is preliminarily accomplished, and the advantages are: (1) At the operation frequency of 0.378 THz, the start current and current density of the device are optimized to 20 A/cm² and 8.4 mA, and the output power is 14 W. (2) It works in the condition of smooth copper plane in simulation, and the output power is still about 20 W when an electron beam with 252 mA and 41 kV is injected. The research gives an estimation of up to 3.5 times decline in output power when the surface roughness emerges. (3) The results of the simulation show that a relatively high efficiency of ∼13% in particle-in-cell (PIC) was observed, and a stable output power range from 98 W to 234 W is found when the injected electron beam (0.35 mm × 0.12 mm) is 16.8–42 mA and 42 kV. Moreover, the reliability of PIC results is verified in this paper.

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.

The applications of multiple beams in the extended-interaction oscillator (EIO) with coaxial structure permit a significant increase in the average output power at millimeter wavelength. The study of the TM mode in the coaxial structure shows it can operate in the base mode with a large diameter (relative to the operating wavelength). Through periodically connect the coaxial structure along the axis, the newly developed circuit is formed. The analysis of these circuits shows that the TM₀₁₀ mode of the circuits with a large volume can interact with the multiple beams efficiently. To demonstrate this capability, a Ka-band EIO with coaxial structure has been designed. A five-beam with a total current of 6 A (evenly divided among five beams) at a voltage of 19 kV was used in this device. Simulations with a 3-D Particle-in-Cell-code computer simulation technology predict an output power up to 25 kW at 35.5 GHz; the efficiency is about 21.9%.