Minimally Constrained Model of Self-Organized Helical States in Reversed-Field Pinches

We show that the self-organized single-helical-axis (SHAx) and double-axis (DAx) states in reversed field pinches can be reproduced in a minimally constrained equilibrium model using only five parameters. This is a significant reduction on previous representations of the SHAx which have required an infinite number of constraints. The DAx state, which has a nontrivial topology, has not previously been reproduced using an equilibrium model that preserves this topological structure. We show that both states are a consequence of transport barrier formation in the plasma core, in agreement with experimental results. We take the limit of zero pressure in this work, although the model is also valid for finite pressure.

Figure 1

Comparison of the ideal MHD representation of the SHAx state in RFX-mod and the minimal model (MRXMHD) of this state presented in this work. Figures (a–b) show the (poloidal) magnetic flux contours of the ideal MHD plasma equilibrium at toroidal angles covering one quarter of the period of the helical solution. Figures (c)–(d) show Poincaré plots of the minimal model at the same toroidal locations as (a)–(b). The thick black lines mark the location of the transport barrier separating the two plasma volumes. The minimal model corresponds to the $\lambda =0.3$ configuration of Fig. 3.

Figure 2

Five constraints are needed to specify the two-volume MRXMHD plasma equilibrium: the toroidal flux in each volume, ${\psi }_{t,i}$; the poloidal flux in the outer volume, ${\psi }_{p,i}$; and the magnetic helicities in each volume, $K_i$.

Figure 3

Plot of the plasma energy for different plasma equilibria as a function of the magnetic flux surface $\lambda$ chosen as the transport barrier in the MRXMHD model. The ideal MHD flux surfaces are labeled by the normalized enclosed poloidal flux ($0\le \lambda \le 1$).

Figure 4

A comparison between the magnetic structure computed from the model presented in this Letter and soft x-ray measurements from RFX-mod. Figures (a)–(e): Poincaré plots for single-barrier MRXMHD equilibria for different values of $\lambda$, the ideal MHD flux surface chosen to act as the transport barrier. Figures (f)–(h): Tomographic inversions of soft x-ray emissivity for plasmas in the (f) double-axis state, (g) the single helical-axis state and (h) the axisymmetric multiple-helicity state. Note that the structures in Figs. (f) and (g) are helical in nature.