BOUNDARY-ONLY INTEGRAL EQUATION APPROACH BASED ON POLYNOMIAL EXPANSION OF PLASMA CURRENT PROFILE TO SOLVE THE GRAD-SHAFRANOV EQUATION

This paper contains 27 pages of text, 1 table and 9 figures. 1 A new type of boundary element method has been applied to solve the Grad-Shafranov equation and to give a distribution of magnetic flux function in a Tokamak nuclear fusion device. The quantity ϕµ jr0 related to the plasma current profile is expanded into two-dimensional polynomial. Using the particular solution of the Grad-Shafranov equation with this inhomogeneous polynomial source and applying Green’s second identity, the domain integral related to the plasma current is transformed into an equivalent boundary integral. Domain discretization is not required in this formulation, thus preserving all the advantages of the boundary element method. Numerical computations of all boundary integrals are only required in the initial stage of the eigenvalue iteration, so that the number of eigenvalue iterations does not hamper the total computing time. Test calculations demonstrated that the present method provides stable and accurate solutions