Equilibrium and transport for quasi-helical reversed field pinches

This paper presents the most recent results in theoretical/numerical studies on the physics of the quasi-helical regime in reversed field pinch (RFP) configurations. Such regime systematically characterizes RFX-mod experiments at high currents (I-p > 1.2 MA), producing clear internal electron transport barriers. Several approaches, ranging from a macroscopic (MHD) to a microscopic (transport) description, have been used to tackle the related complex physics. From the macroscopic point of view, we derive analytically the electrostatic velocity field consistent with a generic helical ohmic equilibrium. We also provide the first MHD initial-value simulation results in toroidal geometry obtained with the PIXIE3D code. Concerning transport, the effect of magnetic chaos healing by mode separatrix expulsion, believed to favour the formation of transport barriers, is discussed. Results indicate that helical equilibria originated by non-resonant modes are more resilient to chaos formation. Finally, gyrofluid and gyrokinetic tools have been used towards a first assessment of the role of microturbulence in the RFP. Concerning the electrostatic branches, ion temperature gradient mode stability is robustly improved in RFP with respect to tokamaks, due to stronger Landau damping effects, and the marginality condition is estimated to be only spottily reached in present experimental regimes, unless the effects of impurities are considered. Impurities, which in RFX-mod accumulate in the edge, may also significantly impact the stability of the impurity-driven modes. On the electromagnetic side, microtearing turbulence is found to probably play a role at the transport barriers.