Critical beta in flux conserving Tokamak equilibrium theory

Two ways of computing flux conserving families of tokamak equilibria have been used by previous authors. Either the normalized pressure profile was kept fixed while beta was increased, or the variation of this profile due to plasma heating was taken into account. It is shown here that with the former naive constraint the equilibrium ceases to exist as beta exceeds a critical value, while in the latter more realistic approach no such limitation occurs.