Equilibrium and Transport for Quasi Helical Reversed Field Pinches

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.