Plasma equilibrium reconstruction for the nuclear fusion of magnetically confined hydrogen isotopes

• An extended analytic solution to the Grad-Shafranov equation was presented.
• The equilibrium magnetic surfaces for IR-T1 tokamak were determined.
• These analytical solutions can be used as an input of feedback control system.

Analytical solutions of electromagnetism driven Grad-Shafranov equation (GSE) can be used for theoretical studies of plasma equilibrium, transport and Magnetohydrodynamic stability of tokamaks. In this research, an extended analytic solution to the Grad-Shafranov equation was presented. The solution describes standard tokamaks configurations. It allows the simulation magnetic surfaces of plasmas with elongation and triangularity, with an independent choice of pressure and plasma current. We have determined equilibrium magnetic surfaces in IR-T1 tokamak. With applying these solutions to IR-T1 tokamak, a small, air core, low beta and large aspect ratio tokamak with a circular cross section, we have calculated poloidal magnetic flux. Due to the generality and high accuracy of the first exact solution for all of the magnetic configurations of interest, the result of this solution for IR-T1 tokamak is acceptable equilibrium compare to the second one for this tokamak. These analytical solutions can be used as an input of feedback control system.