The XMGUN Particle Path FEM Code

Abstract

This work reports some initial results of a 2-D electron gun design code (XMGUN) based on the finite-element method (FEM). Using the Galerkin weak formulation, the nodal analysis, and the first-order elements, the Poisson equation was solved for the electron gun electrostatic potential. The nonrelativistic particle paths were numerically calculated by a fourth-order Runge-Kutta method. An iterative scheme was repeated until the electron paths convergence was achieved under full space-charge limited condition. In order to validate the algorithm, the focusing properties of a 2-D Pierce electron gun with planar symmetry were studied. The quality of the beam was evaluated based on the particle's final position, the transit time, and the particle energy evaluations. Using these three parameters, a good agreement was found between the theoretical and calculated results. Absolute current density errors of less than 1% were found, even with a coarse discretization of the domain. The XMGUN tool was used to design a 30-kV, 7.1-A, and 1.37-μPerv axis-symmetric high-power electron gun for use in vacuum microwave devices. The figure of merit used as reference to measure the quality of the electron beam was the normalized transverse velocity.