A 3-D frequency-domain nonlinear theory of the backward wave oscillator (BWO) with an inclined rectangular electron beam (IRB) is presented in this article. The ohmic losses, space-charge effects, and full 3-D motion of electrons are considered in the nonlinear theory. A set of self-consistent differential equations that describe the nonlinear beam–wave interaction in the BWO with an IRB (IRB BWO) is given, and a calculation code called IRB BWO-3-D is written. Particle-in-cell (PIC) simulations verify the nonlinear theory of the IRB BWO. The effects of the width of the electron beam, the thickness of the electron beam, and the inclination angle on the output power and efficiency of the IRB BWO are also discussed.

中文翻译：

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具有倾斜矩形电子束的 BWO 的 3-D 频域非线性理论

本文介绍了具有倾斜矩形电子束 (IRB) 的后向波振荡器 (BWO) 的 3-D 频域非线性理论。非线性理论考虑了欧姆损耗、空间电荷效应和电子的全 3-D 运动。给出了一组自洽微分方程，描述了 BWO 与 IRB (IRB BWO) 的非线性波束相互作用，并编写了称为 IRB BWO-3​​-D 的计算代码。细胞内粒子 (PIC) 模拟验证了 IRB BWO 的非线性理论。还讨论了电子束宽度、电子束厚度和倾角对 IRB BWO 输出功率和效率的影响。