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 tokomakplasma have been already obtained. None of these equations contain explicitly the triangularity δ and theelongation 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 setto 0, which leads to a G-S equation for circular cross section. Also, the magnetic field and current density obtainedfrom this new G-S equation is reduced to the quantities already derived for circular cross section.

Keywords:

Elongation , Triangularity , G-S equation , Magnetic field , Current density