A Finite Element Analysis for Vacuum Amplifier Electron Gun of Fine Pencil Beam

In the terahertz band, vacuum electronic devices (VEDs) encounter several challenges. One of the key issues is the formation and maintenance of fine pencil beam. This article proposes a numerical simulation code, called the 2-D finite element electron gun (2D_FE_EG), to simulate and analyze the fine pencil beam. The code utilizes the Galerkin method of finite element to solve the Poisson equation and generate an axisymmetric electrostatic field solver. To accurately track the trajectory of the fine pencil beam, the entire solution region is discretized using inhomogeneous triangular meshes, with locally refined meshes in specific areas, such as the emitting surface and electron beam tunnel. The beam trajectory is determined using the fourth-order Runge-Kutta method, and the space charge density of the mesh node is calculated by generating discretized flow tubes with a fraction of the beam current. Additionally, a self-consistent iterative process is implemented to account for the thermal initial velocity and the space-charge-limited emission. The electrostatic field and space charge density in the spherical diode region are iterated until the emission current is stabilized, followed by the convergence of the beam trajectory in the drift tube region. Experimental tests using the electron gun of a D-band traveling wave tube (TWT) are conducted to validate the simulation code.