ABSTRACT
This chapter considers a parabolic radial distribution of the plasma pressure and a weakly parabolic distribution of the longitudinal-current density. It explores the Mercier stability criterion for various concrete cases of tokamaks, including the tubular and disc-shaped tokamaks. The self-stabilization in the central region can be explained as a result of the appearance of ellipticity and triangularity of the magnetic surfaces induced by plasma pressure. Analysis of perturbations with an arbitrary ratio of radial to poloidal wavenumber in non-circular tokamak shows that, as in the case of the circular tokamak, such perturbations are stable if the Mercier stability criterion is satisfied. The ballooning-mode stability boundary in tokamaks has been studied in a great number of following numerical papers. The chapter analyzes the terms with magnetic well and ballooning effects contained in this criterion and find that it reduces to inequality.
