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The RFX-mod Reversed Field Pinch device passive boundary is being improved: - Drastic reduction of resistivity of first shell surrounding the plasma; - Reduction of plasma-stabilizing conductor distance from b/a=1.11 to b/a=1.04. The RFX-mod core upgrades consist of: - Removal of Inconel vacuum vessel; - Modification of the stainless steel Support Structure to ensure Vacuum Tightness (VTSS); - Modification of the copper Passive Stabilizing Shell (PSS); - Installation of upgraded sensors inside the vacuum vessel. Initial main points of investigation in the new device are discussed.

The understanding of transport phenomena is one of the most challenging tasks in fusion plasmas. Among transport mechanisms, chaotic transport of magnetic field lines acquires a crucial importance due to the strong anisotropy that governs the plasma transport. Despite their apparent "randomness", chaotic magnetic fields lines display a remarkable amount of structures. These structures have a fundamental impact on the plasma transport. For the study of magnetic field dynamics, we exploit the so-called Lagrangian Coherent Structures (LCSs)[1].

Recent progress about helical self-organization studies is reported. Extensive exploita5on of 3D nonlinear visco-resistive modeling, SpeCyl code, which describes current-driven dynamics typical of pinch configura5ons in cylindrical geometry. Magnetic topology studies are based on the Field Line Tracing code NEMATO and a new refined tool to detect Lagrangian Coherent Structures is compared with results from a temperature equa/on solver. The following Physics Issues in helical self-organization are addressed: o Boundary Conditions and dimensionless parameters impact, (RFP, and circular Tokamak) o Forma5on of internal transport barriers, (RFP) o Temporary loss of opera5onal point, reconnec5on events, (RFP and circular Tokamak), o Alfvén waves excitation (RFP and circular Tokamak), RESULTS show: o Reasonable comparison (validation) with RFP experimental observations, o Similarities between RFP and Tokamak-like configuration.

We will briefly recall the features of the basic reconnection process within viscoresistive 2D nonlinear numerical MHD approximation for both the Reversed Field Pinch (RFP) and Tokamak pinch configurations. After the current sheet formation, plasmoid formation is observed [Fig.1(a,b)], when proper numerical resolution is used, which speeds up the process. Then, the full three dimensional reconnection processes will be revisited for the experimental-like RFP quasi helical regimes [1, 2]. The 3D RFP simulations show much larger and abrupt magnetic energy conversion into kinetic one, with respect to the 2D reconnection processes, overriding the fine structures observed in 2D approximation. Relaxation-reconnection events cyclically interrupt the formation of quasi helical regime, featuring 3D current sheets formation (Fig.2), mode-mode- phase locking, excitation of Alfvèn waves (Fig.3) [3, 4]. The process reflects in several respects the features highlighted in the past, including typical scaling laws, within the fully developed 3D MHD turbulence obtained in low collisional ideal boundary conditions [5, 6]. Such reconnection processes have been envisaged to provide direct ion heating in the RFP [7]. We will describe how we manage to suitably pace the relaxation cycle in simulation and experiments [8].

We will review key results from the 3D nonlinear MHD numerical modeling of Reversed-Field Pinch helical self-organization processes. Magnetic transport-barrier formation and nearly periodic reconnection events are found to be at play [1-4], akin to the experimental observation of thermal transport barriers and residual "back-transition" cycles when approaching helical regimes in high current discharges [4-7]. Similarities with Tokamak visco-resistive MHD snake/sawtooth-like phenomena will be discussed, as well as aspects at odds with the original Taylor's relaxation theory for the Reversed Field Pinch [8]. We will describe the recent successful technique to "channel" the system towards chosen "stimulated" macroscopic helical shapes by applying suitable (either Resonant or Non-Resonant) Magnetic Perturbations at the edge of the plasma, as predicted by nonlinear MHD modeling and observed in recent RFX-mod experiments [2]. In so doing, we are able to modify the transport properties of the configuration, with the two-fold objective of developing "handles" for the understanding of transport barrier formation processes and exploring new routes for optimization of pinch configurations. We have found that the magnetic chaos healing effect by helical structure development [9] appears to be more robust in the case of Non-Resonant helical regimes [2]. This line of research will be further explored in the upgraded RFX-mod2-device in Padova-Italy, expected to start operation in 2021.

The reversed-field pinch (RFP) is a configuration for the magnetic confinement of fusion plasmas, in which most of the toroidal field is generated by the plasma itself through a self-organized dynamo process, instead of being produced by external coils as in the tokamak. In the RFP, the nonlinear saturation of resistive-kink/tearing modes brings to the spontaneous emergence of helical states with improved confinement. This is observed both in nonlinear magnetohydrodynamics (MHD) modelling [1] and in RFP devices, especially at high current [2,3]. A major advance in the predictive capability of nonlinear MHD modelling for RFP plasmas was made possible by allowing helical perturbations of the radial magnetic field at the plasma boundary, which was suggested by analytical study of helical equilibrium equations [4]. A proper use of helical magnetic perturbations (MPs) in MHD modelling allowed to obtain experimental-like helical states [5] and to predict new helical states with chosen helical twist, successfully produced in RFX-mod [6]. The amplitude of the helical component and sawtooth frequency can be "tuned" as well, thus opening new routes to configuration optimization in several respects (ion heating, thermal and fast particle transport processes). Here, we discuss the effect of a more realistic magnetic boundary recently included in the modelling: a thin resistive shell and a vacuum layer between the plasma and the ideal shell are considered, similarly as in [7,8]. We present two main results: 1) The decrease of secondary modes by increased shell-plasma proximity (see Figure 1). This is of interest in view of the upgraded RFX-mod2 device (starting operation in 2021), in which the shell-plasma proximity will change from b/a=1.11 to b/a=1.04 [9]. 2) With a proper choice for the resistivity of the thin shell at the plasma boundary, helical states do emerge in a self-consistent way, as in the experiment, without the need to impose a fixed helical MP (see Figure 2). Finally, further extensions of the realistic boundary implementation, in order to take into account a double resistive shell and an active feedback control system, will be discussed.

The reversed-field pinch (RFP) is a configuration for the magnetic confinement of fusion plasmas, in which most of the toroidal field is generated by the plasma itself through a self-organized dynamo process, instead of being produced by external coils as in the tokamak. In the RFP, the nonlinear saturation of resistive-kink/tearing modes brings to the spontaneous emergence of helical states with improved confinement. This is observed both in nonlinear magnetohydrodynamics (MHD) modelling [1] and in RFP devices, especially at high current [2]. A major advance in the predictive capability of nonlinear MHD modelling for RFP plasmas was made possible by allowing helical perturbations of the radial magnetic field at the plasma boundary [3]. A proper use of helical magnetic perturbations (MPs) in MHD modelling allowed to obtain experimental-like helical states [4] and to predict new helical states with chosen helical twist, successfully produced in RFX-mod [5].Here, we describe a further refinement of the magnetic boundary modelling. Instead of applying fixed helical MPs, we study the helical self-organization in the presence of a thin resistive shell and a vacuum layer between the plasma and the ideal shell. Two main results are discussed. On the one hand, by varying the distance between the plasma and the ideal wall it is possible to provide a nonlinear estimate for the decrease of secondary modes by increased shell-plasma proximity. This is of interest in view of the upgraded RFX-mod2 device (starting operation in 2020), in which the shell-plasma proximity will change from b/a=1.11 to b/a=1.04 [6]. On the other hand, it is observed that with a proper choice for the resistivity of the conducting shell at the plasma boundary, experimental-like helical states do emerge in a self-consistent way, as in the experiment, without the need to impose a fixed helical MP. Finally, further extensions of the realistic boundary implementation, in order to take into account a double resistive shell and a feedback control system, will be discussed.

In recent years the use of dynamical techniques to investigate the transport features in magnetized plasmas assumed an important role, especially in plasmas with low collisionality. In this regime transport is highly anisotropic, collisions are no longer the main actors and, as it has been shown, e.g. in Reversed Field Pinch (RFP) and Stellarator studies1,2, the magnetic topology plays a very important role: neglecting the finite Larmor radius and drifts, in this regime thermal particles move essentially along magnetic field lines. The transport properties in such systems are usually analyzed drawing the Poincaré map of the magnetic field. Unfortunately, especially when strong chaos affects the system, the Poincaré map gives only a general picture of the transport neglecting that there exist coherent patterns governing the transport process. Moreover, the Poincaré map can be applied only under some circumstances: the system has to be periodic and thus, for an evolving 3D magnetic configuration, this means to study the confinement properties at fixed time instant. The goal of the present work is to go beyond these limits applying Lagrangian Coherent Structures (LCS) technique3, borrowed from the study of Dynamical Systems, to magnetic field configurations in order to underline coherent patterns and thus regions of the system having different transport characteristics. In our work the LCS technique has been applied to carry on three studies. The first study focuses on a simplified model that allows us to consider explicitly the case where the magnetic field evolves in time on timescales comparable to the particles transit time through the configuration4,5. In contrast with previous works on this topic6, this analysis requires that a system that is aperiodic in time be investigated. The second study, expanding previous works7, extends our analysis to realistic numerical reproduction of a RFP configuration. In particular we focus in two different situations with resonant and non resonant dominant mode. In this two frame, a further distinction regards the amplitude of the dominant mode respect to the others: two time instants, with different level of field line chaos, are analyzed. Finally in the third part, starting from the cases of previous study, an effective magnetic field8,9 for non-thermal particles is constructed and analyzed. This allows us to show the different coherent patterns that determinates the transport of thermal and non-thermal particles and thus how different energy particles obey to different transport.

Nonlinear MHD modeling of toroidal pinch configurations (reversed-field pinch and tokamak) for hot plasma confinement describes several features of the helical self-organization, observed in both reversed-field pinches and tokamaks. It can also give a hint on why transport barriers are formed, by far one of the more interesting observations in experiments. The research work will be summarized in two points. The first one regards the recent successful technique to "channel" reversed-field pinches into a chosen macroscopic helical shape through the use of small edge magnetic perturbations. Helical self-organization is predicted in nonlinear MHD modeling, successfully tested in RFX-mod experiment in Padova and awaits further exploration in the updated device RFX-mod2. The upgraded machine, soon starting operation, is characterized by a shell-plasma proximity reduction, likely improving feedback coils action, thus favoring the study of the beneficial properties of helical states built upon helixes not resonating with the safety factor profile. The second point regards the MHD description of the process of formation of transport barriers by macroscopic magnetic chaos healing, which allows the emergence of hidden Lagrangian structures acting as barriers to the transport. The radial position of such structures is observed to correspond to higher gradients of magnetic field lines connection length to the edge and to higher temperature gradients, computed by numerically solving the anisotropic heat flow equation. Comparison with thermal measurements in RFX-mod will also be offered.

The reversed-field pinch (RFP) is a configuration for the magnetic confinement of fusion plasmas, in which most of the toroidal field is generated by the plasma itself through a self-organized dynamo process, instead of being produced by external coils as in the tokamak. In the RFP, the nonlinear saturation of resistive-kink/tearing modes brings to the spontaneous emergence of helical states with improved confinement. This is observed both in nonlinear magnetohydrodynamics (MHD) modelling [1] and in RFP experiments, especially at high current [2,3]. A major advance in the predictive capability of nonlinear MHD modelling for RFP plasmas was made possible by allowing helical perturbations of the radial magnetic field at the plasma boundary, assuggested by analytical calculations based on helical equilibrium equations[4]. A proper use of helical magnetic perturbations (MPs) in MHD modelling allowed to obtain experimental-like helical states [5] and to predict new helical states with chosen helical twist, successfully produced in RFX-mod [6]. Here, we describe a further refinement of the magnetic boundary modelling. We study the helical self-organization in the presence of a thin resistive shell at the plasma boundary r=a, surrounded by a vacuum layer and an ideal shell at r=b. The new magnetic boundary is implemented in the SpeCyl code [7] in a similar way as in Refs. [8,9]. Two main results are discussed. On the one hand, by varying the distance between the plasma and the ideal shell it is possible to provide a nonlinear estimate for the decrease of secondary modes by increased shell proximity to the plasma. This is of interest in view of the upgraded RFX-mod2 device (starting operation in 2021), in which the shell proximity will change from b/a=1.11 to b/a=1.04 [10]. Based on nonlinear MHD modelling,a factor of 2 reduction of the edge radial magnetic field is expected going from RFX-mod to RFX-mod2, with the beneficial consequence of a milder plasma-wall interaction. On the other hand, it is observed that with a proper choice for the resistive diffusion time of the thin shell at r=a, helical states do emerge in a spontaneous and systematic way, as in the experiment, without the need to impose a fixed helical MP. Finally, further extensions of the realistic boundary implementation, in order to take into account a double resistive shell and a feedback control system, will be discussed.

Magnetically confined plasmas of fusion interest display phenomena that find several analogies in astrophysics and other complex systems. This is the case of toroidal pinches where magnetic self-organization molds the plasma into a peculiar helical shape when the ratio of plasma current to toroidal magnetic flux exceeds the socalled Kruskal-Shafranov limit. In this case, a core kink instability ("sawtoothing" and/or "snake") tends to develop in Tokamaks 1 . Similarly, a global helical shape (so-called Quasi Single Helical, QSH, regimes) forms in Reversed Field Pinch experiments (RFP)2,3 , helically modulating the plasma up to the edge 4,5 . MHD modeling has been largely successful in capturing the basic features of such a phenomenon 6,7,8 , quite evading the famous Taylor's relaxation theory for RFP 9,10 . Nearly periodic relaxation events involving current sheet reconnection can be observed 6,9 , together with a magnetic chaos healing effect when the helical states are robustly achieved11,8 . The latter effect is presently the best candidate to explain the formation of internal electron transport barriers2 observed in RFP helical regimes. In particular, "hidden" magnetic field lines transport barriers have been recently detected in experimental-like numerical simulations, which are associated with "fine" topological structures like Cantori sets or Lagrangian Coherent Structures 12 . After summarizing these general features, we here discuss the recent successful MHD prediction of alternative helical regimes, obtained by seed edge magnetic perturbations with suitable choice of helical pitch. A first set of RFXmod experiments substantially confirms modeling predictions 13 . The new helical regimes obtained as plasma response to edge Magnetic Perturbations are predicted to favor magnetic chaos healing in the case of non-resonant seeds. After first indications obtained in RFX-mod experiment 13 , we expect to validate modeling predictions concerning transport properties in the modified device RFX-mod2 starting operation in 2020. The device, characterized by reduced plasma-wall/feedback coils distance, will provide efficient control action in order to negotiate at best with RFP helical magnetic self- organization.