The Solution Of Equilibrium Equation In Tokamak With Fixed Boundary

In present controlled fusion research, It is necessary to obtain the internal magnetic surface,poloidal magnetic field,toroidal magnetic field and the safety factor for high-temperature plasma with D-type configuration. Therefore, in this article at first starting from the MHD equilibrium equations derived of the expression of Grad-Shafranov equation in theory which describe the plasma equilibrium problems, and analysis many methods to solve the Grad-Shafranov equation with fixed boundary, and then the pressure distribution in a given situation, a variational method based on an energy principle is applied to convert the second order partial differential equations of elliptic boundary value problem into a first-order ordinary differential equations of the initial value problem, and this first-order ordinary differential equations for the numerical solution, and obtained the poloidal flux with D-type configuration, and magnetic surface contour lines,poloidal magnetic field and the toroidal magnetic field are obtained, the distribution of safety factor is also obtained, Finally the program for solving the relevant physical quantities for magnetic surface average is obtained.The results are compared with foreign results in a good consistency. so the method and programming we adopted, as well as the results obtained using the calculation program are credible. the results in this paper have important reference value to the further study in the questions of plasma equilibrium in tokamak .