We report the first nonlinear three-dimensional magnetohydrodynamic (MHD) numerical simulations of the reversed-field pinch (RFP) that exhibit a systematic repetition of quasisingle helicity states with the same dominant mode in between reconnection events. This distinctive feature of experimental self-organized helical RFP plasmas is reproduced in MHD simulations at low dissipation by allowing a helical modulation of the plasma magnetic boundary similar to the experimental one. Realistic mode amplitudes and magnetic topology are also found.

In the reversed field pinch RFX-mod strong electron temperature gradients develop when the Single-Helical-Axis regime is achieved. Gyrokinetic calculations show that in the region of the strong temperature gradients microtearing instabilities are the dominant turbulent mechanism acting on the ion Larmor radius scale. The quasi-linear evaluation of the electron thermal conductivity is in good agreement with the experimental estimates.

We provide a survey of the recent progresses in theoretical/numerical studies on the physics of the quasi helical RFP regime. Such regime systematically characterizes RFX-mod experiments at high currents (Ip>1.2 MA), producing clear electron transport barriers about mid-radius. Several approaches, ranging from macroscopic to microscopic description, have been used to tackle the related complex physics. MHD analytical calculation of ohmic helical states by perturbation theory has been developed. A necessary criterion for field reversal at the edge is derived, proved to be satisfied in a large database of RFX-mod pulses. Numerical simulations show that the criterion works for large perturbations of the pinch configuration too, in particular those leading to states with a single helical axis. The addition of heat transport dynamics is expected to improve the 3D nonlinear MHD modelling of RFP self-organization. To this end the PIXIE3D initial value code has been implemented for RFP dynamics. Recently, for the first time in MHD simulation, the mandatory step of numerical verification has been completed by careful benchmarking PXIE3D and SpeCyl codes. The effect of chaos healing by separatrix expulsion, believed to favor the formation of transport barriers, has been reviewed using a volume preserving field line tracing code (NEMATO). The nature of additional physical mechanisms responsible for the actual transport in such regimes is matter of study. ITG microturbulence has been considered first. In 2008 Guo showed analytically that ITG modes are more stable in RFPs than in tokamaks because of a stronger Landau damping. In the last two years different numerical tools have been adapted to the RFP: the nonlinear gyrokinetic GS2 code and the fluid TRB code. An integral eigenvalue approach, retaining finite Larmor radius effects has also been used. All approaches agree that ITG modes can hardly become linearly unstable but could be envisaged in future higher-current experiments. Impurities and trapped electrons effect on ITGs are under consideration, first results show a destabilizing effect by impurities, while a negligible one by trapped electrons. Trapped Electron Modes may appear across high density gradient regions. Microtearing turbulence is expected to play an important role at the transport barriers.

Nonlinear fluid modelling predictions of qualitatively new self-organized helical states in the reversed-field pinch configuration are confirmed by experiments in the RFX-mod device. The new states are realized by using a seed edge magnetic field, which can impose its helical pitch to the whole plasma. In simulations, we show increased magnetic order and reduced transport of magnetic field lines in regimes with the twist of a non-resonant mode. We reveal the existence of Cantori, encompassing the region characterized by conserved magnetic surfaces, which act as barriers to transport of magnetic field lines. This opens a new research line for transport studies in hot magnetized plasmas and highlights a path towards reversed-field pinches with high confinement at high current.

An interesting result of magnetic chaos reduction in RFX-mod high current discharges is the development of strong electron transport barriers. An internal heat and particle transport barrier is formed when a bifurcation process changes the magnetic configuration into a helical equilibrium and chaos reduction follows, together with the formation of a null in the q shear. Strong temperature gradients develop, corresponding to a decreased thermal and particle transport. Turbulence analysis shows that the large electron temperature gradients are limited by the onset of micro-tearing modes, in addition to residual magnetic chaos. A new type of electron transport barrier with strong temperature gradients develops more externally (r/a = 0.8) accompanied by a 30% improvement of the global confinement time. The mechanism responsible for the formation of such a barrier is still unknown but it is likely associated with a local reduction of magnetic chaos. These external barriers develop primarily in situations of well-conditioned walls so that they might be regarded as attempts towards an L–H transition. Both types of barriers occur in high-current low-collisionality regimes. Analogies with tokamak and stellarators are discussed.