Application of a Grad Shafranov solver in SINP tokamak experiments

Several important equilibrium parameters of SINP tokamak experiments have been estimated using a Grad-Shafranov (GS) solver. The software has been developed to solve the problem of axi-symmetric magnetostatic equilibria using standard explicit finite-difference techniques. The GS equation posed as an Eigen value problem can be written as ∇2 Ψ=-λ μO Rjφ where the terms have their usual meanings. From the solution of Ψ, we can estimate equilibrium, parameters like the total plasma current, position of the magnetic axis, the magnetic field distribution internal and external to the plasma along with various other parameters. These parameters can also be measured during an experiment using Rogowski coil, sin θ and cosθ coils, internal magnetic probe and magnetic pickup coils. Attempts have been made to fit the GS solution to the experimental measurements by proper choice of jφ which in turn depends upon the pressure profile and terms representing the poloidal current. From the best fitted solution of Ψ, we have made estimates of important efficiency parameters such as β, βp, βt, stability parameters like safety factor profile, shear and other parameters like the internal inductance of the plasma. The results obtained using the combined constraints of external and internal magnetic probe data seem to be more accurate than those obtained using only the external magnetic probe data. The results seem to be very useful and encouraging, especially, in relation to the experiments being carried out in the SINP tokamak. (author)