Theoretical Analysis of Sheet Beam Electron Gun for Terahertz Vacuum Electron Devices

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
$\times0.14$
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.