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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.

Fusion-Fission Hybrid Reactor (FFHR), neutron-producing fusion core surrounded by a fission blanket, benefits from a renovated interest because of (i) its potentiality to address energy production before the availability of pure fusion reactors, (ii) its capability of fission fuel fertilization and (iii) waste management. The core fusion reactor of a FFHR requires less stringent performances respect to DEMO or the fusion power plants: it has to produce less than a hundred of MW of fusion power with Q = 1-5 and comes with a reduced fast neutron wall load, sustainable by the available nuclear material. While the Reversed Field Pinch (RFP) has yet an energy confinement too low for a high Q reactor, it is an alternative configuration to tokamak and stellarator for this application. Its disruption-free configuration, the need of a much weaker toroidal magnetic field coils and the capability of reaching thermonuclear temperatures without additional heating, but only by ohmic heating (due to no intrinsic plasma current limit and the strong winding of current lines due to the low q values), are significant advantages. New studies are in progress in order to revisit the status and the potentiality of the RFP as a fusion core in FFHR, taking into account the recent progress and expected improvement in RFP physics brought by the results of the RFX-mod experiment (R=2, a=0.46, Ip=2MA) and its underway upgrade. Scaling from the obtained experimental results opens the possibility, with increased machine size and plasma current, to realize a more robust and simple fusion neutron source respect to the other considered solutions; starting from these result, the possibility to realize a preliminary pilot experiment with a RFP (R=4m, a=0.8m, Ip=12-14MA) as a simplified neutron fusion source is in progress.

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.

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.

Self-organized helical states are a ubiquitous feat ure in astrophysical and magnetic confinement curre nt carrying plasmas. In the reversed-field pinch toroi dal plasmas quasi-helical states are observed both in high current experiments [1] and in nonlinear magne tofluid numerical simulations [2]. In the tokamak helical self-organization is an essential part of t he dynamics in advanced regimes [3]. In this work w e show two main advancements in our 3D nonlinear visc o-resistive magnetohydrodynamic (MHD) studies. First, we study the effect of a macroscopi c plasma rotation on helical states, to model both reversed-field pinches and tokamaks: in particular, we analyze the interaction between an external momentum source and/or seed magnetic perturbations (MPs), both static and rotating. We find the expected interplay between plasma rotation and appl ied MPs in tokamaks [4] confirming MPs screening over a threshold in normalized plasma rot ation. We then focus on the reversed-field pinch case: starting from previous works [5,6,7], where i t is shown that a mean flow arises from and interac ts with nonlinearly coupled kink/tearing modes, and th en introducing a momentum source, we analyse the impact of mean plasma flow on self-organized helica l regimes. Our modelling indicates that an external momentum source of sufficiently high intensity can prevent the formation of a helical state, while a moderate one is compatible with a slight enhancemen t of the intensity of the helical state. We present a novel study in the realistic cases [2] of experimen tal-like helical states stimulated by MPs: the pres ence of a plasma flow, previously not considered, introd uces quantitative changes to their properties. As a final novelty, we here also show (for the first tim e) that the typical intermittency with reconnection events displayed in the RFP helical self-organizati on process is accompanied by the excitation of both compressional and shear Alfvén waves, in reasonable agreement with experimental measurement [8].

The Reversed Field Pinch (RFP) is recognized as an attractive fast neutron source from D-T fusion in hybrid reactors due to the possibility to reach fusion condition with ohmic heating only and to the intrinsic simplicity of the machine (no large toroidal field coils, no additional heating systems, no divertor). In previous studies, a continuous pulsed operation, able to guarantee a quasicontinuous 14.1 MeV neutron production, has been identified, utilizing a purely inductive plasma rise and sustainment. Scaling laws, derived from the experimental results obtained in RFX-mod, allow predicting the plasma temperature and the loop voltage vs. the machine sizes and plasma current level. Considering these laws and on the basis of a preliminary poloidal coil design, it was investigated the relationship between the machine size and the attainable stored volt-second. The obtainable plasma parameters (current, loop voltage, pulse duration and temperature) with reasonable machine sizes, R=6 and a=1 for examples, match very well the performances required for an hybrid reactor in terms of neutron flux and machine stresses. Based on this configuration a blanket, surrounding the torus, composed by a lithium-lead eutectic mixture for tritium production and a three fission sectors fuelled by steel rods containing Pu+MA (60%)-Zr (40%) embedded in liquid lead was studied and designed. The nuclear analysis of this simple configuration shows the possibility to operate at keff ~ 0.97 corresponding to a total fission power of about 1.2 GW. Improvements of the RFX-mod machine are underway, introducing a new load assembly with reduced distance between plasma and conducting shell which will provide a smoother magnetic boundary. On the basis of present experimental data and model simulations, this is expected to produce an enhancement of the plasma confinement properties, confirming or even improving the present scaling laws towards higher currents and increasing the attractiveness of this fusion-fission reactor solution. This contribution, which will present in detail the above summarized aspects, is aimed at proposing on this basis a robust, innovative, highly reliable FFHR.

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.

Magnetic self-organization in toroidal pinches takes a peculiar helical shape when the ratio between toroidal current and toroidal magnetic flux (Pinch Parameter) is pushed above a characteristic threshold. This is clearly seen in the form of core kink instability in Tokamaks (so called Kruskal-Shafranov instability) and as a global helical shape in Reversed Field Pinch experiments (RFP). In this last case the nonlinear saturation approaching an ohmic helical equilibrium can be recognized. In fact, MHD modeling has been largely used to successfully capture such a basic phenomenon, quite evading the famous Taylor's theory for RFP relaxation. The globally helical RFP has been shown to bring interesting confinement properties, featuring internal transport barriers, which might be understood as a result of magnetic topological structures like Cantori sets or Lagrangian Coherent Structures, and magnetic chaos healing. Together with summarizing these general features, we here discuss the recent successful MHD prediction of alternative helical regimes, achievable by using edge magnetic perturbations with suitable choice of amplitude and helical pitch. In this way, typical features like helical amplitude and dithering frequency can be tuned almost at will, with impact on transport properties. A first set of RFX-mod experiments substantially confirms modeling predictions.

Magnetic chaos healing in 3DMHD modeling of helical regimes, achievements and open issues

The reversed-field pinch configuration for the magnetic confinement of fusion plasmas is characterized by the emergence of self-organized quasi-helical states found both in magnetohydrodynamic (MHD) simulations and in high current experiments 1, 2, 3. Numerical modeling can reproduce with high fidelity the MHD dynamics of high current RFP experiments, which are characterized by the formation of helical states 4 . Such helical states are quasi-periodically interrupted by transient relaxation to 3D states associated with strong reconnection events. Seed helical perturbations at the magnetic boundary are predicted to affect the helicity and the intermittency of the emergent helical states and first experimental tests have indeed confirmed this capability. Of particular interest is the possibility to stimulate non-resonant helical states, which feature better topological properties with respect to magnetic chaos healing 5,6 . This opens a new path to configuration optimization. Simulation results and first experimental evidence of alternative helical states formation in RFX-mod will be presented, together with a discussion of the different magnetic topology properties and their impact on transport barrier formation.

This work investigates the formation of helical core equilibria in toroidal fusion plasmas, focussing on the role of dynamo, or magnetic flux pumping mechanisms in determining the equilibrium current profile. Dynamo effects determine the safety factor profile of the final 3D equilibrium, with important consequences on MHD stability and transport. We compare experimental results from multiple machines (RFX-Mod, MST, AUG, DIII-D) and nonlinear MHD modeling. Two paradigmatic cases of helical state formation are considered and common physics is identified, by direct measurements of dynamo effects and MHD simulations: spontaneous formation in high-current reversed-field pinch (RFP) plasmas r1s and the hybrid scenario in high- tokamak plasmas r2s. Helical cores form in both cases, either spontaneously via saturation of MHD modes, or due to the marginally-stable ideal MHD response to external 3D fields. Direct measurements of the dynamo emf associated to 3D plasma distortions will be presented for a database of helical RFP plasmas from RFX-Mod and MST, covering a wide range of plasma parameters. Similar measurements were also done in helical states forming in response to external 3D fields in Ohmic RFX-Mod tokamak plasmas and in DIII-D high- hybrid plasmas. Experimental results qualitatively agree with nonlinear MHD modeling performed with the codes SpeCyl r3s, PIXIE3D r4s, and NIMROD r5s. They indicate that central current is redistributed by a dominantly electrostatic MHD dynamo. The underlying physics common to RFP and tokamak is thus revealed: a helical core displacement modulates parallel current density along flux tubes, which requires a helical electrostatic potential to build up, giving rise to a helical dynamo flow. Similar results were also recently obtained with the M3D-C1 code r6s.

The understanding of fusion plasmas benefits from investigating the same phenomena in different magnetic configurations such as the tokamak, the stellarator, and the reversed - field pinch (RFP) [1 - 4] . Here, the same approach is applied i n the framework of nonlinear 3D MHD modelling . We first focus on sawtoothing, i.e. , the quasiperiodic magnetic relaxation of RFP and tokamak plasma s . Sawtooth ing manifests itself together with magnetic reconnection events , and with the formation of current sheets and of dynamo electric fields . Such processes are relevant to laboratory and astrophysical plasmas as well. In both tokamak and RFP configurations , sawtoothing is quenched leading to long - l a sting helical states whenever visco - resistive dissipation is increased [ 5 ,6 ] or small helical mag netic perturbations (MPs) are applied [ 7 ,8 ]. A similar effect of MPs has been observed in the RFX - mod device [ 9 ]. We secondly consider the topological properties of partially ergodic magnetic field s , which characterize helical states in the RFP [7] . Barriers to the stochastic diffusion of field lines (the so - called cantori also studied in the tokamak configuration [10] ) are diagnosed in the weakly stochastic core of the helical RFP [ 1 1 ] , which could explain experimentally observed internal transport barriers. C hains of magnetic island s naturally occur at the RFP edge [1 2 ] . Such chains may be exploited to realize a so - called island divertor, which may alleviate plasma - wall interaction s like in the stellarator [3]. Numerical results are provided by two MHD codes , successfully benc hmarked against one another [ 6 ].

With this internal note we want to make available to the RFX colleagues the study performed for the invited talk "Effect of helical magnetic perturbations on the 3D MHD self-organization of fusion plasmas" given by D. Bonfiglio at the 7th IAEA Technical Meeting on "Theory of Plasmas Instabilities" held in Frascati, Italy on 4-6 March 2015. The proceeding papers of invited and contributed talks, including a version of this internal note, will be published on the conference website http://www.iaeatm-inst2015.enea.it/

Preliminary simulations of stellarator-like configurations with the nonlinear 3D MHD codes SPECYL and PIXIE3D are reported in this work. SPECYL [1] solves the zero-b visco-resistive MHD equations in cylindrical geometry, whereas PIXIE3D [2] can run in toroidal geometry as well and with finite plasma pressure. The mathematical correctness of the two codes was proven by a nonlinear crossbenchmark study [3]. Both codes have been used to study the nonlinear MHD dynamics of reversed-field pinch (RFP) and tokamak plasmas. Qualitative agreement with respect to experimental observations in the RFX-mod device, operated both in RFP and tokamak modes, has been demonstrated, in particular with the application of external magnetic perturbations [4,5,6]. More recently, helical perturbations of the magnetic boundary have been used in both codes to produce stellarator fields within an axisymmetric computational domain [6]. Here, we first focus on zero-b stellarator configurations in both cylindrical and toroidal geometry. The equilibrium properties such as the i profile and the magnetic field topology are discussed. Magnetic islands and stochastic regions appear when the helical symmetry provided by the dominant helical perturbation is violated. As expected, this occurs in the cylindrical case when secondary magnetic perturbations are applied, and in the toroidal case due to geometric effects, even without secondary perturbations. The connection length of field lines to the wall provides a measure of edge stochasticity. Finite-b stellarator simulations are then considered with the PIXIE3D code in cylindrical geometry. The finite-b helical equilibria obtained with increasing heating sources are described and compared with the zero-b solution.

The reversed-field pinch configuration for the magnetic confinement of fusion plasmas is characterized by the emergence of self-organized quasi-helical states found both in magnetohydrodynamics (MHD) simulations and in high current RFP experiments. Numerical modeling can reproduce with high fidelity the MHD dynamics of high current RFP experiments, which are characterized by the formation of helical states, quasi-periodically relaxed to 3D states by strong reconnection events [1]. Seed helical perturbations at the magnetic boundary are expected to direct the plasma towards alternative helical states and first experimental tests have indeed confirmed this capability. Of particular interest is the possibility to stimulate non-resonant helical states, which feature better topological properties [2, 3]. Simulation results and first experimental evidence of alternative helical states formation in RFX-mod will be presented, together with a discussion of the different magnetic topology properties and their impact on transport barrier formation [4]. [1] Bonfiglio et. al. "Experimental-like Helical Self-Organization in Reversed-Field Pinch Modeling", PRL 111, 085002 (2013) [2] Veranda et. al. "Impact of helical boundary conditions on nonlinear 3D magnetohydrodynamic simulations of reversed-field pinch", PPCF 55 074015 (2013) [3] Veranda et. al. in preparation [4] Rubino et. al. "Detection of magnetic barriers in a chaotic domain: first application of Finite Time Lyapunov Exponent method to a magnetic confinement configuration", PPCF 57 085004 (2015)

The magnetic confinement of fusion plasmas is sought in various configurations. One of them is the reversed-field pinch which is characterized by the emergence of self-organized quasi-helical states both in high current experiments and in magnetohydrodynamic (MHD) simulations. These simulations reproduce such states very well together with their quasi-periodic relaxation to 3D states involving a domain of chaotic magnetic field lines. This work presents the characterization of the transport-related properties of these 3D states. Lagrangian Coherent Structures in the chaotic domain are revealed by the Finite Time Lyapunov Exponent (FTLE) method as ridges of the FTLE field: ridges are defined as special lines whose points are locally at the highest point in the FTLE field transverse to the ridge. They are diagnosed to represent strong barriers for the magnetic field lines, which are effectively limited in their motion inside the chaotic sea. Quantitative information can be obtained by the analysis of the magnetic field line diffusion coefficient in a stochastic field using the NEMATO code for magnetic field lines tracing. This allows the optimization of low-transport helical states in the reversed-field pinch.

Externally applied magnetic perturbations (MPs) provide an effective handle to control the internal dynamics of fusion plasmas. In magnetic configurations such as the tokamak and the reversed-field pinch (RFP), external coil systems are traditionally used for error field correction and feedback control of MHD instabilities like the resistive wall mode [1] and the tearing mode [2]. In the tokamak, MPs are also used for edge-localized modes (ELMs) suppression [3] and drive of neoclassical toroidal rotation [4]. More recently, MPs have been shown to govern the MHD dynamics in the RFX-mod device operated in both Ohmic tokamak and RFP configurations. In this talk, the effect of helical magnetic perturbations on the nonlinear 3D MHD modelling of fusion plasmas is discussed, with particular attention to the RFP and tokamak magnetic configurations. MHD simulation studies show that a key ingredient to capture the physics of helical self-organization observed in RFP experiments is the application of MPs consistent with the experimental helical deformation of the plasma magnetic boundary [5]. In addition, with the application of helical MPs it is possible to select the dominant helicity of helical RFP states [6], as confirmed in RFX-mod [7]. Also consistently with experimental observations, in both tokamak and RFP configurations helical MPs provide a way to mitigate the spontaneously occurring quasi periodic sawtooth oscillations. In the tokamak case, the toroidal mode coupling is shown to play an important role for the mitigation of sawteeth [8]. Finally, the use of MPs to approach realistic geometries within a circular computational domain is discussed. MHD simulations are provided by the SPECYL and PIXIE3D codes, whose nonlinear verification study is reported in Ref. [9]. [1] M. S. Chu and M. Okabayashi, Plasma Phys. Control. Fusion 52, 123001 (2010) [2] P. Zanca et al., Nucl. Fusion 47, 1425 (2007) [3] T. E. Evans et al., Phys. Rev. Lett 92, 235003 (2004) [4] A. M. Garofalo et al., Phys. Rev. Lett. 101, 195005 (2008) [5] D. Bonfiglio et al., Phys. Rev. Lett. 111, 085002 (2013) [6] M. Veranda et al., Plasma Phys. Control. Fusion 55, 074015 (2013) [7] S. Cappello et al., 24th IAEA Fusion Energy Conference, San Diego (2012) http://www-naweb.iaea.org/napc/physics/FEC/FEC2012/papers/199_THP216.pdf [8] D. Bonfiglio, P. Martin and P. Piovesan, 40th EPS Conference on Controlled Fusion and Plasma Physics, Espoo (2013) http://ocs.ciemat.es/EPS2013PAP/pdf/P2.145.pdf [9] D. Bonfiglio et al., Phys. Plasmas 17, 082501 (2010)