Research On Numerical Calculation Of The Potential Distribution Of Vacuum Tank

The finite difference method is one of the first method to be applied in the numerical calculation of electromagnetic fields, it is simple, intuitive and widely used in the field of engineering problems. In this paper, electrostatic potential distribution produced by annular electrode in a vacuum tank to simulate the ionosphere for practical engineering problems, which based on the finite difference method is used to discrete Laplace equation under cylindrical coordinate system, and the three-dimensional symmetrical electrostatic field problem is transformed into a two-dimensional electrostatic field problem. At the same time, the potential value of the discrete points in all space are calculated by using MATLAB software, and the potential distribution map of three dimensional symmetric electrostatic field is plotted by using MATLAB software, which provide a theoretical basis and technical support for the analysis and design of the actual engineering problems.In this paper, electrostatic potential distribution in a two-dimensional vacuum tank is calculated by the MATLAB program which based on the finite difference method is used to discrete Laplace equation under rectangular coordinate system. And confirm the validity of equivalent rectangle method which to calculate the optimal convergence factor of over relaxation iteration method. At the same time, electrostatic potential distribution in the two-dimensional vacuum tank is calculated by PDE Toolbox which based on finite element and triangle mesh generation, and confirm the result of electrostatic potential distribution which calculated by MATLAB program.Electrostatic potential distribution in a three-dimensional vacuum tank is calculated by the MATLAB program which based on the finite difference method is used to discrete Laplace equation under cylindrical coordinate system, and the calculation results is validated by the EXCEL numerical method. The EXCEL numerical method which based on finite difference method to gain numerical solution by using the cell which in EXCEL to represent the discrete point, and using the function of formula replication and recalculate. The different potential gradient influence the performance of electronic device. At last, in order to achieve engineering requirement, the electrostatic potential distribution and the electric potential gradient in the three-dimensional vacuum tank with different distribution of annular electrode is calculated under expanding the function of MATLAB program, then we can determine the position for putting electronic device into vacuum tank.