A new form of Grad-Shafranov equation for a tokomak with an elongated cross section

Different forms of the well-known Grad-Shafranov (G-S) equations that define the equilibrium behavior of tokomak plasma have been already obtained. None of these equations contain explicitly the triangularity δ and the elongation ratio ks. The aim of this work is to obtain a new form of G-S equation which includes both thetriangularity and the elongation ratio. For verifying the correctness of the obtained equation, the triangularity is set to 0, which leads to a G-S equation for circular cross section. Also, the magnetic field and current density obtained from this new G-S equation is reduced to the quantities already derived for circular cross section.