Low-aspect-ratio reversed field pinch (RFP) plasmas are expected to produce equilibria in which the resonant surfaces for tearing modes are well separated compared with high-aspect-ratio RFP plasmas. The profile of the safety factor, q, determines the mode separation of the resonant surfaces. The q profiles, the ratio of plasma pressure to magnetic energy, β, and the parallel current density to the magnetic field lines, μ, are studied with the varying aspect ratio, A. A new Mercier stable RFP plasma is proposed by introducing a finite surface toroidal current density at the plasma edge. The aim of this study is to investigate the effect of a finite surface toroidal current with a low-aspect-ratio (low A) on the profiles of q, μ, β and the ratio of plasma pressure to poloidal magnetic energy, βp. The investigation is performed using an equilibrium model with a finite pressure, in which unknown functions in the Grad–Shafranov (GS) equation are specified. Specified functions are composed of some numerical parameters that allow systematic variation of equilibria. The GS equation is solved in the toroidal coordinate for various A values, where the β limit of Mercier stable equilibria is determined. First we confirmed that q at the centre, q0, increases as A decreases. The result shows that the profiles of q, β and βp, strongly depend on A. The β and βp obtained decrease with decreasing A. In particular, the decrease in β differs from the case of a tokamak. The decrease in β is recovered, in spite of a low A, by setting the toroidal current to be finite at the plasma edge as a boundary condition.
Equilibrium properties at very low aspect ratio in the Pegasus toroidal experiment