Study of Tokamak Equilibria using Variational Moment Method

Abstract

Grad Shafranov equation is equilibrium solution of ideal MHD. Several method is developed to compute it numerically [6], [7] but in this project a variational moment method is studied to estimate the solution to the Grad-shafranov equation which is generalized to nd approximate free boundary solutions to the grad-shafranov equation. Some ordinary di erential equation had to be solved to calculate the poloidal magnetic ux ψ(R, Z) those were nothing but Grad-Shafranov equation's moments. Grad-Shafranov equation's moment are fourier amplitudes of the inverse mapping of R(ψ, θ) and Z(ψ, θ). Numerical and Analytical solutions of moment equations are constructed whose results concur well with two dimensional equilibrium code . The main advantage of the variational moment method is that it signicantly reduces the computational time required to determine two-dimensional equilibria without sacrifi cing accuracy. In future the code will further be developed to calculate the fl ux surface at separatrix and location of strike points.