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.