Single-helicity states in compressible magnetohydrodynamics simulations of the reversed-field pinch with nonuniform resistivity

Using a magnetohydrodynamics numerical code that includes the description of density and pressure evolution and anisotropic thermal conductivity, it is shown that single-helicity states in the reversed-field pinch (RFP) configuration are obtained when the resistivity has a radial profile sharply increasing close to the wall. In contrast, a uniform resistivity produces multiple-helicity states. A radially increasing resistivity profile is determined in RFP experiments by the temperature difference between the plasma core and the wall. The results of the simulations presented in this letter are an indication that quasi-single-helicity states observed in experiments with high toroidal currents may be a consequence of the resistivity profile determined by the high temperatures reached in the plasma core in high-current discharges. The reversed-field pinch (RFP) is a toroidal configuration used for magnetic confinement of plasmas in fusion machines [1, 2]. In the RFP most of the toroidal and poloidal magnetic fields are generated by currents flowing in the plasma and the configuration is sustained against resistive diffusion by a dynamo effect produced by magnetic field and velocity fluctuations due to the growth of magnetohydrodynamic (MHD) instabilities. The RFP configuration is characterized by a toroidal magnetic field at the wall that is reversed with respect to its direction in the core. The theoretical possibility of realizing the RFP configuration in the singlehelicity (SH) state [3, 4], where the dynamo effect is provided by the growth and saturation of a single MHD mode, is important for plasma confinement because it results in well conserved magnetic surfaces, which ensure better confinement properties with respect to multiple-helicity (MH) states. In MH states, many MHD instabilities with different mode numbers are simultaneously present with comparable amplitudes and the superposition of different magnetic islands at different radial locations gives rise to a chaotic magnetic field, with poor confinement properties. Different experiments showed the existence of quasi-single-helicity (QSH) states, where a dominant mode is present together with small amplitude secondary modes [5–10]. A reduction of energy and particle transport has been observed in QSH states with respect to MH states [11–13]. Recently, RFP experiments have shown, for increasing toroidal currents, a clear tendency of the plasma towards a SH state [14, 15]. The possibility of obtaining SH states is of considerable importance in order to achieve better confinement performances. Higher toroidal currents produce hotter plasmas, which correspond to a higher Lundquist number (the ratio of the resistive diffusion time to the Alfvén time). The persistence of the QSH states increases with the