Analysis of Relaxed States in Coaxial Helicity Injection Tokamaks on the Basis of Analytical Solutions

The principle of the minimum energy dissipation rate is applied to toroidal plasmas with a coaxial direct current helicity injection. The relaxed states are analysed based on the analytical solutions of the resulting Euler-Lagrangian equations. Three typical states are found. The relaxed states are close to the Taylor state if the ratio of current density to magnetic field on the boundary is small enough. The states will deviate from the Taylor state when the ratio increases, but when it approaches a critical value the central part of relaxed plasmas may approach a force free state and above the critical value both current and magnetic field may reverse in the central part.