Control of heat and mass transfer processes by plasma equilibrium reconstruction in toroidal magnetic confinement nuclear fusion devices

Heat and mass transfers can be controlled by plasma equilibrium reconstruction in toroidal confinement nuclear fusion systems such as tokamaks. The Magnetohydrodynamic equilibrium in axisymmetric plasma is described by the Grad-Shafranov equation in terms of the magnetic flux. In this paper, we have proposed a new numerical solution to the Grad-Shafranov equation of an axisymmetric, transformed in quasi-cylindrical coordinates solved with the Chebyshev collocation method, when the source term (current density function) on the right hand side is quadratics as it is described by Atanasiu et al. The Chebyshev collocation method is a method for computing highly accurate numerical solutions differential equations. We have described a circular cross section of tokamak and presented numerical result of magnetic surfaces on the IR-T1 tokamak and compared the results with an analytical solution and then calculated the Shafranov shift using a minimization procedure based on the Newton method.