2D Galerkin Finite Element Method For Periodic Permanent Magnetic Focusing System

Microwave tubes have great significance in military equipments. The focusingsystem is an important component of the microwave tubes. The periodic permanentmagnetic (PPM) focusing system has been proven to be an useful method of focusingsystem in microwave tubes. It is very important to research the PPM techniques in thedevelopment of microwave tubes. As being a interdisciplinary issue, to design anadvanced focusing system in microwave tubes is a complicated task. Therefore, themethod of using the CAD software to model and simulate the focusing system inmicrowave tubes has been improved. In this paper, the PPM theories have beendiscussed and the corresponding simulation software based on two dimensional (2D)Galerkin finite element method (FEM) has been developed. This simulation softwarehas been well applied in modeling the axial-symmetric PPM systems. The main issuesof this dissertation will be listed as follows.Firstly, the basic principle of the magnetic focusing system has been analyzed,including the pulsating of electron injection, the design of the transition region, theinfluence of the thermal velocity, the end portion effect and the influence oftemperature on the magnetic focusing system. Meanwhile, the basic steps of designinga PPM focusing system, as well as its parametric selection, has also been discussed.Secondly, based on the magnetic current element model,2D Galerkin linear andsecond-order FEM has been studied. This theory has been applied in axial-symmetricPPM systems. The consistency between this theory and the Ritz FEM is proven by thecomparisons.Thirdly, based on the PPM and the Galerkin FEM theories, the Galerkin FiniteMagnetic Simulator (GFMS) has been developed for the axial-symmetric PPM systems.Three models, the single magnet model, the single-periodic model and the three-periodic model, have been simulated by GFMS. The corresponding simulated resultshave been compared with the results from the Maxwell (i.e. a commercial magneticsimulator), a smaller error of two software simulation results prove the accuracy of theGFMS simulation results. Some drawbacks, such as more computing time consumption, have been found because of poor meshing, boundary conditions or errordefining conditions. To avoid these drawbacks, some techniques, such as adaptive gridand multi-grid meshing technology, the open domain boundary conditions, as well asappropriate convergence conditions of error, have been applied to improve thecomputing efficiency.