Stable High-β equilibria for cylindrical symmetry

A certain class of MHD equilibria (the current density profile being the result of a variational principle) is investigated. The corresponding Grad-Shafranov equilibrium equation is solved for the straight circular cylinder in the plasma-on-the-wall case. The solution is appropriate for the description of tokamaks as well as high-β pinches. The maximum achievable stable β-values are limited to 50% and proportional to the percentage of the longitudinal current density at the plasma surface. These large β values can only be achieved in the case of diamagnetic confinement systems and high-β pinches. The highest stable β-values for the conventional paramagnetic tokamaks are found to be less than 1%. A remarkable agreement with the experimental data is found for the reversing of the Reversed Field pinches. 6 references, 2 figures