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The Greenwald density limit is a phenomenological limit that restricts the achievable density in a thermonuclear fusion device. This is a longstanding issue for research in this field, since density appears in the figure of merit defining the efficiency of the future fusion reactor, namely the triple product nrT . Despite this importance, the density limit defies a unified, convincing theoretical explanation. Recently a series of papers [1,2,3] point out the role of a combination of radiative collapse and magnetohydrodynamic (MHD) instabilities resonating in the edge plasma, in determining the limit.

Self-organized helical states are a ubiquitous feature in astrophysical and in current carrying hot magnetic-fusion plasmas. In the latter, self-organized helical states are observed locally in the core of the tokamak - associated with strong 3D magnetohydrodynamics activity - and globally in reversed-field pinch (RFP) plasmas. In RFP helical states spontaneously develop from a dominant resistive-kink/tearing mode, creating a hot central region bounded by transport barriers. In this contribution, we first report a milestone in magnetohydrodynamics modeling of hot RFP plasmas [1, 2] and experimental observation of helical states, namely, we show that experiments in RFX-mod confirm the nonlinear fluid modelling prediction of previously unobserved self-organized helical states. The key element is the use of a small edge magnetic perturbation [3, 4], with a helical periodicity different than the spontaneous dominant one observed in standard discharges, which can convey its helical pitch to the whole plasma column. As a second result, we find a higher magnetic order in numerical simulations where magnetic perturbations are applied with a non-resonant helical twist. In such new states we observe a broader zone where magnetic field lines lie on conserved magnetic surfaces and a reduction of magnetic field-lines transport with respect to standard regimes. Interestingly and counterintuitively, such new global helical regimes are obtained when exploiting non-resonant Resistive Wall Modes, usually deemed dangerous for plasma discharges. First examples of experimental confirmation of such dynamical and topological results are described. As a third result, we introduce a novel technique which reveals confining structures, Cantori sets, in the shadow of the KAM tori [5]. We will also introduce preliminary results from the numerical solution of the time-dependent, anisotropic temperature transport equation [6] applied to such new helical regimes coming from the MHD simulation codes. The novel possibility of changing the global helical twist of the plasma column, and therefore its safety factor, open new opportunities to deepen the theoretical interpretation of transport barrier formation and sustainment in hot-magnetic fusion plasma devices, including tokamaks and stellarators.

Self-organized helical states are an ubiquitous feature in astrophysical and magnetic fusion plasmas. In the reversed-field pinch plasmas quasi-helical states are observed both in high current experiments and in nonlinear magnetofluid numerical simulations. We show the 3D nonlinear MHD prediction that small edge helical magnetic perturbations can shape the whole plasma column with their helical twist, a result confirmed by dedicated experiments in RFX-mod. When a non-resonant twist is imposed chaos healing results in a higher area of conserved magnetic surfaces and in reduced diffusion of magnetic field lines. Barriers to the transport of magnetic field lines are detected: they can be identified as cantori of the magnetic field, and can explain the observation of electron temperature transport barriers in experiments.