Study Of Three Dimensional Finite Element Theory And CAD Technique For Permanent Magnet Focusing System Of Microwave Tubes

Microwave tube is an important microwave/millimeter wave electric vacuum device.Moreover,it is widely used in communication systems,radar,electronic warfare,etc.The permanent magnet focusing system has been proved to be the useful method of magnetic focusing system in microwave tube,and is one of the most important component of electron optic of the microwave tube.Permanent magnet focusing system is used to retain and focus the electron beam in the microwave tubes especially in traveling tubes.It influences power,efficiency and stability of the microwave tube directly.However,previous design formulation of magnetic focusing system for microwave tube is built with several assumptions.Moreover,it can only give a simple estimate method for the structures of magnetic focusing system.In order to improve design accuracy,modeling and simulation techniques have been applied to design permanent magnet focusing system.Meanwhile,some new-type permanent magnet focusing structures also required to carry out the three dimensional magnetic field simulation.So the permanent magnet system CAD technology for microwave tube has been an important tool in production microwave tubes.In this background,this paper has deeply researched the finite element theory of permanent magnet focusing system and a CAD software simulating magnetic field have been developed.The main work and innovations of this dissertation are listed as below.First,the finite element methods of magnetic vector potential and magnetic scalar potential are discussed for permanent magnet focusing system of microwave tube respectively.Firstly,the equations of magnetic vector potential and magnetic scalar potential are built by the Maxwell's equation.Second,the finite element theories of magnetic vector potential and magnetic scalar potential are built for permanent magnet focusing system.Third,a permanent ring is computed by the finite element method of magnetic vector potential and magnetic scalar potential.As a result,the finite element method of magnetic vector potential needs more computer resources and much more computational time than finite element method of magnetic scalar potential.Second,the computational method of nonlinear material magnetic field is studied.For nonlinear pole material,some nonlinear iteration methods are described.Meanwhile,Newton-Raphson with parabola method is proposed.And the convergence and computational performance of the iteration methods are discussed by the simulations of period permanent magnet.As a result,Newton-Raphson with parabola method is better than other methods.For nonlinear permanent magnet material,an iteration method is proposed.In addition,the convergence of iteration method is discussed by the simulations of the permanent magnet ring.Third,the open-boundary magnetic field problem is studied.For axial symmetric permanent magnet structures,the asymptotic boundary condition of magnetic vector potential is built.Taking the permanent magnet ring and three period permanent magnet as the examples,the convergence of truncation boundary and asymptotic boundary is discussed with the size of vacuum region.The results show that the convergence of the asymptotic boundary condition with the size of vacuum region is faster than truncation boundary in the 2D finite element method of magnetic vector potential.For non-axial symmetric permanent magnet structures,the asymptotic boundary condition of magnetic scalar potential is built.Taking three period permanent magnet,three period permanent magnet with open permanent magnet ring and wiggler as the examples,the convergence of truncation boundary,Neumann boundary and asymptotic boundary with the size of vacuum region is discussed.The results show that the convergence rate of asymptotic boundary with the size of vacuum region is slightly better than that of truncation boundary and Neumann boundary in the 3D finite element method of magnetic scalar potential.Fourth,based on the symmetry of some structure in permanent magnet focusing system,a 1/N symmetric algorithm is applied in the three-dimensional simulation.The symmetric algorithm can reduce the computational time and the computer memory effectively without decreasing the computational accuracy.Fifth,the adaptive mesh refinement technique is studied.The adaptive mesh method includes a posteriori error estimation method which to choose one parameter to decide if the mesh need to be refined and an element refinement controlling method to determine how to refine the mesh.The adaptive mesh refinement method has been applied to the magnetic field simulator,electron optic simulator and high frequency circuit simulator.In addition,a mesh refinement algorithm for the electron gun is proposed.Sixth,based on the above-mentioned numerical simulation technique,a three dimensional finite element design tool for the design of permanent magnet focusing system called magnetic field simulator is developed.The magnetic field simulator(MFS)consists of the following three main parts: preprocessing,which includes a solid modeling tool and calculation parameters setting,solver of magneto-static field and post-processing for analysis and display of results.Besides,all parameters include structure and material parameters can be replaced by variables in MFS,so we can scan the variables to analyze the sensitivity of permanent magnet structures in the microwave tubes.Meanwhile,the results of MFS can be used in the external magnetic field for EOS and BWIS.