Equilibrium and localized flute instability of a tokamak with non-circular cross-section

The equilibrium equations are solved for tokamaks with non-circular cross-sections, by the method of the expansion in powers of the inverse aspect ratio. The analysis is extended to a more general class of equilibria, especially to study the effect of non-uniformity of plasma current distribution. For tokamaks with non-circular cross-sections, a simplified condition of stability against localized flute disturbances is obtained, which is a direct extension of Shafranov and Yurchenko's result. The kinds of variation of the cross-sections of the magnetic surfaces which improve the stability criterion are considered.