Single and multiple helicity Ohmic states in reversed-field pinches

Abstract

The properties of single helicity and multiple helicity Ohmic states in reversed-field pinches (RFP’s) are investigated by a combination of analytic and numerical methods. The single helicity results show that toroidal field reversal can be provided in a helical Ohmic equilibrium driven by a toroidal loop voltage, and that reversal in helical symmetry is related to stellarator transform. Nevertheless, a constant λ≡j∥/B state cannot be sustained because λ must reverse at the toroidal field reversal surface. This helical equilibrium can be thought of as the saturated state of an unstable tearing mode. For a force-free plasma, helical reversal can be maintained by a relatively small value of δB/B because it is accompanied by an inward paramagnetic pinch velocity. Conversely, in models with △⋅v=0, a large outward diffusive velocity must build up to balance the inward paramagnetic pinch velocity, requiring poloidal beta to be of order unity. It is shown that in three dimensions no multihelical Ohmic equilibrium can exist if there is an area of destroyed flux surfaces. Numerical simulations in three dimensions (3D) indeed show that Ohmic states exist, but with fields varying on a resistive time scale. Also, a bifurcation is found between two distinct classes of solutions in 3D. The first is a broad spectrum multihelical state with almost no flux surfaces. The other class consists of narrow spectrum nearly single helicity states with a large fraction of the plasma volume occupied by good flux surfaces. The existence of this second class of states indicates the possibility of operating RFP’s in a single helicity mode with good flux surfaces.