Abstract:The theory of periodic permanent magnetic focusing system is studied. 2D second-order finite element method is used to simulate magnetic displacement of axisymmetric permanent magnetic models in cylindrical coordinates. First the convergence is compared between linear finite element method and second-order finite element method. Second-order finite element method has better convergence and faster convergence rate. Then the single magnetic ring model and the single period model are simulated. These results are compared with the results of Ansoft Maxwell 2D and UESTC-PPM. 2D second-order finite element method is more accurate.