In the terahertz band, the vacuum electron devices with planar and miniaturized structures require the ultrahigh-precision description of high-density electron beams for formation and transportation with the theoretical analysis and simulation. Thus, the absence of the available theory for the sheet beam electron is put forward to investigate the 3-D spatial potential using a differential geometry and tensor analysis. The equation of electron beam potential can be derived by establishing a moving coordinate frame, carrying out the numerical calculations, and doing series expansion. To solve the complex sheet beam description of the existence of four corner singularities, the Riemann method and conformal mapping are adopted to overcome this difficulty. Then, a 0.22-THz vacuum electron tube using a sheet beam electron gun and corresponding optical system are designed. The beam voltage and current are 16.5 kV and 0.5 A, respectively, with a beam channel size of 1.4 mm ×0.14\times0.14 mm and a uniform magnetic field of 5980G. With the 3-D simulation, the high-density sheet electron beam can transport 18 mm successfully. The spatial potential of numerical calculation with the obtained sheet beam theoretical function and the simulation model are compared to verify the theoretical description. Both the results are with good consistency, which preliminarily proves the effectiveness of the theoretical function. This work will give the deep physical mechanics vision for the development of high-power and high-efficiency sheet beam terahertz tube in the future.

中文翻译：

---

太赫兹真空电子器件片束电子枪的理论分析


在太赫兹波段，平面化、小型化结构的真空电子器件需要对高密度电子束的形成和传输进行超高精度的描述和理论分析与模拟。因此，由于缺乏可用的片束电子理论，因此提出使用微分几何和张量分析来研究 3-D 空间势。通过建立移动坐标系，进行数值计算，进行级数展开，可以推导出电子束势方程。为了解决存在四个角奇点的复杂板梁描述，采用黎曼方法和共形映射来克服这一困难。然后，设计了使用片束电子枪的0.22-THz真空电子管和相应的光学系统。束流电压和电流分别为16.5 kV和0.5 A，束流通道尺寸为1.4 mm×0.14×0.14 mm，均匀磁场为5980G。通过3D模拟，高密度片状电子束可以成功传输18毫米。将数值计算的空间潜力与所获得的板梁理论函数和仿真模型进行比较，以验证理论描述。两者结果具有良好的一致性，初步证明了理论功能的有效性。这项工作将为未来高功率、高效片束太赫兹管的发展提供深层次的物理力学视野。