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Reconnection is a basic phenomenon in magnetized plasmas by which the plasma relaxes to a state oflower magnetic energy. It plays a fundamental role in a variety of instabilities common to most fusiondevices, as sawtooth or tearing modes. Often it occurs in impulsive events (crash phase), following alonger period in which the magnetic fields evolve slowly. Energy conversion and topological change are two highly linked aspects of reconnection.Hot fusion plasmas may contain multiple reconnection sites and this is particularly true for the Reversed Field Pinch (RFP), due to the peculiar current density distribution, associated to a variety ofresonant tearing modes. In addition, large RFPs involve large plasma currents and therefore a largeamount of available magnetic energy. This makes the RFP a good device to observe and analyze reconnection events.In this contribution the phenomenology of the impulsive and periodic reconnections in the RFX-mod device is analyzed in detail, through an ensemble average of the data from many reconnection eventsin high plasma current discharges (1.5 MA). Spatial and temporal scales are invoked as fundamental observables. Roughly speaking, an almost stationary helical state is considered typical of phases before the crash. The crash destroys this symmetry, and the plasma topology undergoes a transition to a more chaotic state with broad MHD spectra. The crash evolution is described as a sequence of events. A trigger of the crash has been associated for the first time to a slight change in the helical equilibrium, which pushes closer the inner most important resonant flux surfaces in the core. Reconnection starts when the resonant surfaces - and therefore the intense related current sheets- are close enough and a precursor of the crash is found in the locking in phase of these resonant modes. After these slowly evolving phases, fast reconnection takes place, which lasts about 1 ms.Plasma parameters and magnetic measurements suggest that crashes are related with the interaction between tearing modes at different radii, and the reconnection process evolves according to the safety factor profile.

The onset of Internal Transport Barriers (ITBs) is routinely observed during Quasi Single Helicity States in the Reversed Field Pinch experiment RFX-mod. ITBs appear as steep electron temperature gradients that enclose thermal structures. The characteristics of such thermal structures vary considerably, so that there are both narrow thermal structures enclosed by steep gradients and large thermal structures enclosed by milder gradients. The complexity increases considering that, while large thermal structures develop on helical states with a single helical axis (SHAx), narrow thermal structures can have both a single or double magnetic axis (DAx). In this paper we characterize the behavior of thermal structure width Wth and of ITB gradients, estimated from 84-point Thomson Scattering profiles, and of their helical equilibrium. Furthermore we present data analyses that show as Wth and the ITB gradients have a strong relationship with the magnetic turbulence of secondary modes [1,2]. In particular, as long as the secondary modes decrease, the DAx and SHAx narrow thermal structures widens (Wth increases) and their gradients become increasingly steeper. However, despite the very low value of secondary modes, the SHAx wide thermal structures exhibit gradients clearly milder than the gradients of DAx and SHAx narrow cases. The Wth behavior is quantitatively analyzed introducing the Quasi Separatrix Layer concept, used in astrophysics to explain the occurrence of solar flares in the absence of separatrix. This model provides also a qualitative explanation for the peculiar behavior of gradients.

In magnetically confined experiments the presence of rational surfaces allows perturbations (either self generated by the plasma or externally induced) to grow and break the magnetic topology of flux surfaces nested around a single axis. The bifurcated magnetic configuration takes the form of one or more islands embedded in the main plasma, each with their own magnetic axis. Stochastic layers develop around the flux surface containing the island X-point (the separatrix) and divide the nested flux surfaces of the islands from the nested flux surfaces of the bulk plasma. The presence of islands strongly modifies particle and heat fluxes. Transport studies in fusion community benefit of the availability of several well developed 1.5D transport codes (ASTRA, CRONOS, JETTO, RITM ...) that solve the flux surface averaged transport equations across shaped flux surfaces, on the grounds that the variation of physical quantities along the flux surfaces is small. They constitute a powerful and relatively user-friendly tool since they are able to capture the main features of transport phenomena without the complexity of 2D transport codes. However 1.5D codes are applicable nowadays only for flux surfaces nested around a single axis. Our goal is to develop a user friendly modelling tool applicable to 1.5D transport codes to be exploited in plasmas in the presence of single harmonic magnetic islands. To this aim a multiple domains scheme is adopted and three regions inside the plasma are identified: the first around the main magnetic axis (core), the second around the island axis (island) and the third that includes the separatrix stochastic area and the outer plasma (edge). In each domain the magnetic flux can be chosen as an effective radial coordinate. This scheme is independent from the equilibrium magnetic configuration hence it can be applied to tokamak, stellarator and Reversed Field Pinch. In this work we present the first study in this direction. We mimic the ASTRA transport module solving, in each domain, the 1.5D equation for the heat diffusion by means of a dedicated numerical code. A predictive simulation is performed providing the code with the diffusivity profile for the core, island and edge region, studying the mathematical issues arising in the context of the equation solution, in particular the matching at the common boundaries, in steady-state as well as time-dependent cases. Our study is carried out in synthetic but realistic scenarios from the RFX-mod Experiment. We show that qualitative agreement with experiments is quite easily recovered.

A complete description of the effects of magnetic perturbation on the edge region of RFX-mod is here reported. The flexibility of the RFX-mod device [1] allows for the operation of the machine both as a reversed field pinch (RFP, with maximum current 2 MA) and as a low-current, circular ohmic tokamak (I-p,I-max = 0.15 MA). The present paper summarizes the most recent results obtained in both configurations with either spontaneous or induced edge radial magnetic perturbation. Emphasis will be devoted to the experimental characterization of the edge flow, focusing on the phase relation between flow and perturbed magnetic field. These informations are provided for natural and stimulated helical discharges in RFPs, and for tokamak safely operated, thanks to the unique RFX-mod MHD control system, in a wide range of edge safety factor 1.9 less than or similar to q(a)

An experimental analysis of particle dynamics is presented in both tokamak and reversed-field pinch (RFP) Deuterium plasmas produced in the RFX-mod device. Particular attention is dedicated to effect of magnetic reconnection processes occurring spontaneously in the plasma. The diagnostics is made of a Neutral Particle Analyzer (NPA) and of a couple of neutron and gamma-ray detectors. The NPA can resolve the energy distribution of the neutral atoms produced by charge-exchange processes and exiting the plasma on the low field side on equatorial plane of the machine on 11 energy channels, being the energy and mass dispersion produced by a E//B combination. Neutron and gamma-ray fluxes are measured by means of 2 scintillators (EJ-301 liquid and NaI(Tl)) coupled to flat-panel photomultipliers, suitable for operation under magnetic fields. The production of neutrons and gamma rays in RFP plasmas is found to be strongly influenced by the Ohmic input power, with a threshold value of about 1.2MA in terms of plasma current level. Below such current value a low rate of gamma rays and almost no neutrons are detected. Neutral Deuterium atoms fluxes, neutron and gamma productions are strongly determined by the MHD activity measured in the plasma. In particular, a bursty behavior of neutron yields, correlated to the spontaneous magnetic reconnection events, occurring almost cyclically in the RFP plasmas are observed. Magnetic reconnection also modifies the energy distribution of neutral atoms having impact on both the Maxwellian component and on the observed higher energy tail. This is true also in tokamak plasmas during the sawtoothing activity mostly seen in low q(a) condition. The role of particle acceleration and ion heating during such events is discussed.

A fully geometric approach is used to study the mutual spectral properties of different classes of MHD equilibria with symmetries defined by action-angle coordinates. We refer mostly to the helical equilibria of tokamak and reversed field pinch plasmas compared to the axisymmetric counterpart. Based on the existence of different coordinate systems, we show how the magnetic field and the vector potential are correspondingly evaluated, and how their spectral decompositions may largely vary. Most notably, a monochromatic perturbation in a reference frame can appear with a rich spectrum in another frame. The consequences on the interpretation of the measurements and the implications on the effectiveness of the externally applied magnetic fields on the plasma are discussed with practical examples.

In a Reversed Field Pinch discharge (RFP), magnetic reconnection events are related to selforganized processes[1]. Along with the action of the continuous dynamo process, discrete quasicyclic relaxation events, leading to rearrangement of magnetic field topology through magnetic reconnection phenomena, have been seen in RFP plasmas, with a dynamics resembling that of sawtooth in tokamak plasmas. In RFX-mod (R = 2m,a = 0.459m), it was shown that a relaxation event is associated with the rapid formation of a localized magnetic perturbation characterized by a main m=0 periodicity [2], resonant on the reversal surface where q = 0. This perturbation corresponds to the formation of a poloidal current sheet. The m=0 activity starts in a localized region around a given toroidal position and then moves with the plasma in a direction opposite to the toroidal current. In this contribution, a characterization of the m=0 perturbations, through the use of a statistical method for the detection of intermittent structures, is presented. Data analysis here reported refers to the toroidal magnetic field perturbations collected by ISIS (Integrated System of Internal Sensors [3]), whose magnetic sensors are placed just below the graphite first-wall (r = 1.03a). A statistical analysis on the magnetic field intermittent structures suggests that current sheets, associated with magnetic reconnection phenomena, are subject to a fragmentation process. This result is in agreement with what predicted by simulations presented in the literature [4], which highlight two important aspects: a current sheet could be naturally subject to fragmentation and a fragmented current sheet represents a more efficient particle accelerator with respect to a monolithic one, because it offers multiple particle acceleration sites [5]. Indeed, we found a relationship between relaxation events in RFP discharges and the neutron fluxes due to DD fusion reactions, suggesting the coupling among relaxation events, particle acceleration and magnetic reconnection phenomena.

This paper summarizes the main achievements of the RFX fusion science program in the period between the 2008 and 2010 IAEA Fusion Energy Conferences. RFX-mod is the largest reversed field pinch in the world, equipped with a system of 192 coils for active control of MHD stability. The discovery and understanding of helical states with electron internal transport barriers and core electron temperature >1.5 keV significantly advances the perspectives of the configuration. Optimized experiments with plasma current up to 1.8 MA have been realized, confirming positive scaling. The first evidence of edge transport barriers is presented. Progress has been made also in the control of first-wall properties and of density profiles, with initial first-wall lithization experiments. Micro-turbulence mechanisms such as ion temperature gradient and micro-tearing are discussed in the framework of understanding gradient-driven transport in low magnetic chaos helical regimes. Both tearing mode and resistive wall mode active control have been optimized and experimental data have been used to benchmark numerical codes. The RFX programme also provides important results for the fusion community and in particular for tokamaks and stellarators on feedback control of MHD stability and on three-dimensional physics. On the latter topic, the result of the application of stellarator codes to describe three-dimensional reversed field pinch physics will be presented. © 2011 IAEA, Vienna.

The phenomenology of reconnection events, associated to relaxations in high-current (similar to 1.5 MA) plasmas of the reversed-field pinch device RFX-mod, is shown. Each relaxation event can be described as a series of stages starting in the core and propagating towards the plasma edge. In an initial stage (trigger), the evolution of the q profile brings resonant layers closer together, allowing for an interaction of the current sheets associated to tearing modes at the respective rational values of q. The phase locking of the resonant modes then initiates the reconnection process that, once started, changes the magnetic topology bringing the initially helical state to a more chaotic configuration.

The RFX-mod experiment is a fusion device designed to operate as a reversed field pinch (RFP), with a major radius R = 2 m and a minor radius a = 0.459 m. Its high versatility recently allowed operating it also as an ohmic tokamak, allowing comparative studies between the two configurations in the same device. The device is equipped with a state of the art MHD mode feedback control system providing a magnetic boundary effective control, by applying resonant or non-resonant magnetic perturbations (MP), both in RFP and in tokamak configurations. In the fusion community the application of MPs is widely studied as a promising tool to limit the impact of plasma filaments and ELMs (edge localized modes) on plasma facing components. An important new research line is the exploitation of the RFX-mod active control system for ELM mitigation studies. As a first step in this direction, this paper presents the most recent achievements in term of RFX-mod tokamak explored scenarios, which allowed the first investigation of the ohmic and edge biasing induced H-mode. The production of D-shaped tokamak discharges and the design and deployment of an insertable polarized electrode were accomplished. Reproducible H-mode phases were obtained with insertable electrode negative biasing in single null discharges, representing an unexplored scenario with this technique. Important modifications of the edge plasma density and flow properties are observed. During the achieved H-mode ELM-like electromagnetic composite filamentary structures are observed. They are characterized by clear vorticity and parallel current density patterns.

Quasi-single helicity (QSH) state has been widely observed in reversed field pinch devices to sustain thermal structures, enclosed by steep temperature gradients interpreted as electron internal transport barriers (eITB). Within the evolution of a QSH cycle, three sub-states can be identified in the RFX-mod experiment, named DAx, SHAx(n) and SHAx(w), where the subscript n and w indicate narrow and wide thermal structures, respectively. Such sub-states feature different magnetic topologies as well as different width of the thermal structures. This paper presents a characterization of the three QSH sub-states mainly devoted to describe the properties of the eITB temperature gradients. The analyses show a decreasing trend of the absolute value of the thermal gradient as the dominant mode increases. Further study on the thermal diffusivity confirms that these behaviors are essentially due to the local change of the heat transport. Besides, the thermal gradient in DAx and SHAxn groups shows an increasing trend with the decrease of secondary modes. Such behavior has been studied and it can be explained by stochastic transport in agreement with what found for SHAX(w) (Lorenzini et al 2012 Nucl. Fusion 52 062004). As for SHAxw group, the thermal gradient suddenly decreases with respect to DAx and SHAxn values. This behavior can still be explained in the framework of stochastic transport considering the structure of magnetic perturbations at the location of thermal gradients (Lorenzini et al 2016 Phys. Rev. Lett. 116 185002). The total energy confinement time T-E has also been evaluated, adopting a more appropriate method. The result shows that the energy confinement time increases up to 40% from DAx to SHAx(w).

Filament or blob structures have been observed in all magnetic configurations with very similar features despite the difference in the magnetic geometry, and are believed to play an important role in convecting particles and energy towards the wall. Despite their different generation mechanism, turbulent structures and edge-localized mode (ELM) filaments share some common physical features. The electromagnetic effects on filament structures deserve particular interest, among others reasons for the implication they could have for ELM, related for instance to their dynamics in the transition region between closed and open field lines or to the possibility, at high beta regimes, of causing line bending which could enhance the interaction of blobs with the first wall. A direct characterization of the effects of active modification of the edge topology on EM turbulent filament structures is presented, comparing reversed field pinch and tokamak configurations. Measurements are obtained in the RFX-mod device, which allows operation in both configurations and with different equilibria. The RFX-mod experiment versatility is exploited also from the point of view of the active control of the edge magnetic topology, equipped with an advanced system for edge boundary feedback control. Three different case studies of actively controlled magnetic perturbations are shown, focusing on the filament interaction with local magnetic islands. High-frequency fluctuations, characterizing electrostatic and magnetic filament features, and the associated transport coefficients have been observed to be strongly affected by the island proximity and topology.

Electromagnetic features of turbulent filaments, emerging from a turbulent plasma background, have been studied in four different magnetic configurations: the stellarator TJ-II, the Reversed Field Pinch RFX-mod, a device that can be operated also as a ohmic tokamak, and the Simple Magnetized Torus, TORPEX. By applying an analogous diagnostic concept in all cases, direct measurements of both field-aligned current density and vorticity were performed inside the filament. The inter-machine comparison reveals a clear dependence of the filament vorticity upon the local time-averaged E × B flow shear. Furthermore, a wide range of local beta was explored allowing concluding that this parameter plays a fundamental role in the appearance of filament electromagnetic features.

This paper reports the main recent results of the RFX-mod fusion science activity. The RFX-mod device is characterized by a unique flexibility in terms of accessible magnetic configurations. Axisymmetric and helically shaped reversed-field pinch equilibria have been studied, along with tokamak plasmas in a wide range of q(a) regimes (spanning from 4 down to 1.2 values). The full range of magnetic configurations in between the two, the so-called ultra-low q ones, has been explored, with the aim of studying specific physical issues common to all equilibria, such as, for example, the density limit phenomenon. The powerful RFX-mod feedback control system has been exploited for MHD control, which allowed us to extend the range of experimental parameters, as well as to induce specific magnetic perturbations for the study of 3D effects. In particular, transport, edge and isotope effects in 3D equilibria have been investigated, along with runaway mitigations through induced magnetic perturbations. The first transitions to an improved confinement scenario in circular and D-shaped tokamak plasmas have been obtained thanks to an active modification of the edge electric field through a polarized electrode. The experiments are supported by intense modeling with 3D MHD, gyrokinetic, guiding center and transport codes. Proposed modifications to the RFX-mod device, which will enable further contributions to the solution of key issues in the roadmap to ITER and DEMO, are also briefly presented. © 2017 IAEA, Vienna.

An overview of recent results from the MST programme on physics important for the advancement of the reversed field pinch (RFP) as well as for improved understanding of toroidal magnetic confinement more generally is reported. Evidence for the classical confinement of ions in the RFP is provided by analysis of impurity ions and energetic ions created by 1 MW neutral beam injection (NBI). The first appearance of energetic-particle-driven modes by NBI in a RFP plasma is described. MST plasmas robustly access the quasi-single-helicity state that has commonalities to the stellarator and 'snake' formation in tokamaks. In MST the dominant mode grows to 8% of the axisymmetric field strength, while the remaining modes are reduced. Predictive capability for tearing mode behaviour has been improved through nonlinear, 3D, resistive magnetohydrodynamic computation using the measured resistivity profile and Lundquist number, which reproduces the sawtooth cycle dynamics. Experimental evidence and computational analysis indicates two-fluid effects, e.g., Hall physics and gyro-viscosity, are needed to understand the coupling of parallel momentum transport and current profile relaxation. Large Reynolds and Maxwell stresses, plus separately measured kinetic stress, indicate an intricate momentum balance and a possible origin for MST's intrinsic plasma rotation. Gyrokinetic analysis indicates that micro-tearing modes can be unstable at high beta, with a critical gradient for the electron temperature that is larger than for tokamak plasmas by roughly the aspect ratio.

A better understanding of the edge phenomena regulating plasma transport and turbulence is of primary importance for the whole fusion community. In particular, in reversed field pinches (RFPs) the edge properties are found to have a strong relation with the magnetic topology. The flexibility of the RFX-mod RFP experiment (Sonato et al 2003 Fusion Eng. Des. 66-68 161-8) enables exploring different topological regimes, and the insertion of a probe equipped with a two-dimensional array of electrostatic sensors allows the characterization of the outermost plasma regions (up to 10% of the minor radius). The electric field radial profiles and its dynamics are found to be highly influenced by the presence of edge magnetic islands modelled with a Field Line Tracing code (FLiT). When a helical perturbation is applied through the saddle coil feedback system a strong modification of the edge electrostatic properties is observed. The E × B velocity field results in a convective cell-like structure according to the externally imposed toroidal periodicity. Finally, an analysis of the long-range correlations in the floating potential fluctuations (measured by two toroidally separated probes) is presented and discussed along with the electric field measurements and the edge topology.

RFX-mod [Sonato et al., Fusion Eng. Des. 66, 161 (2003)] exploits its 192 active coils in both reversed-field pinch (RFP) and tokamak configurations with varying degrees of 3D shaping, providing also a test bed for validating stellarator codes and 3D nonlinear magnetohydrodynamic codes. This makes RFX-mod a unique and flexible facility for comparative studies on 3D shaping and control. The paper discusses how 3D fields allow access to RFP and tokamak advanced regimes. 3D fields are used to feedback control Single Helicity (SH) RFP equilibria with 1/7 helicity up to similar to 2 MA. They also allow accessing SH regimes with higher density (Greenwald fraction up to 0.5), presently inaccessible in spontaneous SH regimes. Feedback on the 2/1 resistive-wall mode in RFX-mod tokamak plasmas allows for safe operation at q(a) < 2, an almost unexplored promising regime. Forcing the 2/1 mode to saturate at finite but small level, a helical tokamak equilibrium with significant n=1 modulation is produced and a new way to tailor sawteeth is found. The effects of different levels of 3D shaping on momentum transport in both RFP and tokamak helical states are discussed.

An extensive statistical characterization of the electromagnetic turbulence in the edge region of RFX-mod, operated as a tokamak and as a Reversed Field Pinch, is presented. Striking similarity are observed on the intermittent character of the electrostatic turbulence between the two configurations whereas the difference between magnetic turbulence is likely to be imputed to the different beta value of the two configurations. Blobs are characterized in terms of their spatial structure, the associated enstrophy and energy and the mechanism of energy and enstrophy transfer between intermittent fluctuation at different scales is addressed.

Single helical axis (SHAx) states obtained in high current reversed field pinch (RFP) plasmas feature an internal transport barrier delimiting the hot helical core region. The electron temperature jump across this region, and the related temperature gradient, display a clear relationship with the normalized amplitude of the secondary MHD modes. A transport analysis performed with the ASTRA code, taking into account the helical geometry, yields values of the thermal conductivity in the barrier region as low as 5 m2 s−1. The thermal conductivity is also related to the secondary mode amplitude. Since such amplitude is reduced when plasma current is increased, it is expected that higher current plasmas will display even steeper thermal gradients and hotter helical cores.

Single Helical Axis (SHAx) configurations are emerging as the natural state for high current reversed field pinch (RFP) plasmas. These states feature the presence of transport barriers in the core plasma. Here we present a method for computing the equilibrium magnetic surfaces for these states in the force-free approximation, which has been implemented in the SHEq code. The method is based on the superposition of a zeroth order axisymmetric equilibrium and of a first order helical perturbation computed according to Newcomb's equation supplemented with edge magnetic field measurements. The mapping of the measured electron temperature profiles, soft X-ray emission and interferometric density measurements on the computed magnetic surfaces demonstrates the quality of the equilibrium reconstruction. The procedure for computing flux surface averages is illustrated, and applied to the evaluation of the thermal conductivity profile. The consistency of the evaluated equilibria with Ohm's law is also discussed., Submitted to Plasma Physics and Controlled Fusion

An interesting result of magnetic chaos reduction in RFX-mod high current discharges is the development of strong electron transport barriers. An internal heat and particle transport barrier is formed when a bifurcation process changes the magnetic configuration into a helical equilibrium and chaos reduction follows, together with the formation of a null in the q shear. Strong temperature gradients develop, corresponding to a decreased thermal and particle transport. Turbulence analysis shows that the large electron temperature gradients are limited by the onset of micro-tearing modes, in addition to residual magnetic chaos. A new type of electron transport barrier with strong temperature gradients develops more externally (r/a = 0.8) accompanied by a 30% improvement of the global confinement time. The mechanism responsible for the formation of such a barrier is still unknown but it is likely associated with a local reduction of magnetic chaos. These external barriers develop primarily in situations of well-conditioned walls so that they might be regarded as attempts towards an L–H transition. Both types of barriers occur in high-current low-collisionality regimes. Analogies with tokamak and stellarators are discussed.

RFX-mod self-organized single helical axis (SHAx) states provide a unique opportunity to advance 3D fusion physics and establish a common knowledge basis in a parameter region not covered by stellarators and tokamaks. The VMEC code has been adapted to the reversed-field pinch (RFP) to model SHAx equilibria in fixed boundary mode with experimental measurements as constraint. The averaged particle diffusivity over the helical volume, estimated with the Monte Carlo code ORBIT, has a neoclassical-like dependence on collisionality and does not show the 1/ trend of un-optimized stellarators. In particular, the helical region boundary, corresponding to an electron transport barrier with zero magnetic shear and improved confinement, has been investigated using numerical codes common to the stellarator community. In fact, the DKES/PENTA codes have been applied to RFP for local neoclassical transport computations, including radial electric field, to estimate thermal diffusion coefficients in the barrier region for typical RFX-mod temperature and density profiles. A comparison with power balance estimates shows that residual chaos due to secondary tearing modes and small-scale turbulence still contribute to drive anomalous transport in the barrier region. © 2011 American Institute of Physics.

The traditional and widely used reflectometric schemes are not able to probe the edge density layers of the reversed field pinches (RFPs) due to the presence of a high level of density fluctuations. In order to overcome this limitation, an ultrafast microwave reflectometer has been developed and the first Ka-band has been successfully operational on the RFX-mod experiment [1] since mid-2009. The actual diagnostics configuration (frequency sweep 26.5–30.5 GHz in 1 µs) allows us to evaluate the radial distance of the relative cut-off density layer with a high time resolution. The first results are presented and discussed in this paper. In particular, a relation between edge density and local magnetic topology is proposed as well as a systematic study of the average behaviour over several global operative conditions of the machine. An outlook on the future diagnostic developments is also given.

We report the first direct measurement of the internal magnetic field structure associated with a 3D helical equilibrium generated spontaneously in the core of an axisymmetric, magnetically-confined, toroidal plasma. Magnetohydrodynamic equilibrium bifurcation occurs in MST RFP plasmas when the innermost resonant magnetic perturbation grows to large amplitude, reaching up to 8{\%} of the mean field strength. Evolution of the magnetic topology is determined by measuring the Faraday effect, revealing that as the perturbation grows, toroidal symmetry is broken, and a helical equilibrium is established. Computational reconstruction of the magnetic field and electron density profiles based on a 3D topology agrees well with experimental data, providing a better fit than reconstructions based on a standard 2D cylindrical topology. These helical plasmas sometimes exhibit an improvement in electron particle confinement and increased temperature.

Single helical axis (SHAx) states are the improved confinement RFP helical states, which have been observed at high plasma currents (beyond 1 MA) in the RFX-mod device. A reconstruction of these equilibrium configurations has been implemented in a code named SHEq, where SHAx states are modelled as pure single helicity (SH) states. We consider the helical flux in this work, which happens to be a good flux function for SH equilibrium, and its contours give the shape of the flux surfaces in the helical equilibrium. New curvilinear and non-orthogonal 'helical' coordinate systems are defined in SHEq, with the fundamental request that angles are defined with respect to the helical axis. We look for helical coordinates beginning from the canonical form of the magnetic field B and the Hamiltonian mechanics theory enables us to obtain straight-field-line helical coordinates computing action-angle coordinates. These coordinate systems are used to determine the helical safety factor q, using the simple formula valid in action-angle coordinates. Very good agreement with the computation of the safety factor using the ORBIT code has been found. © 2011 IOP Publishing Ltd.

A spontaneous transition to a helical equilibrium with an electron internal transport barrier is observed in RFX-mod as the plasma current is raised above 1 MA (Lorenzini R et al 2009 Nature Phys. 5 570). The helical magnetic equilibrium can be controlled with external three-dimensional (3D) magnetic fields applied by 192 active coils, providing proper helical boundary conditions either rotating or static. The persistence of the helical equilibrium is strongly increased in this way. A slight reduction in the energy confinement time of about 15% is observed, likely due to the increased plasma-wall interaction associated with the finite radial magnetic field imposed at the edge. A global helical flow develops in these states and is expected to play a role in the helical self-organization. In particular, its shear may contribute to the ITB formation and is observed to increase with the externally applied radial field. The possible origins of this flow, from nonlinear visco-resistive magnetohydrodynamic (MHD) and/or ambipolar electric fields, will be discussed. © 2011 IOP Publishing Ltd.

The relationship between edge flow features and local magnetic topology has been studied by means of ad hoc transient experiments, so that different plasma equilibria are compared within the same discharge, and of the edge flow monitor of helical magnetic islands in the RFX-mod Reversed Field Pinch experiment. The different components of the plasma flow characterizing the edge region and their shear are obtained by combining and comparing information provided by a noticeable set of edge diagnostics including insertable probes, toroidally distributed arrays of sensors and optical diagnostics. In particular a Gundestrup probe head is applied which allows obtaining information on both parallel and perpendicular Mach number. This probe head has been used with all the pins collecting floating potential signals and a model has been developed in order to reconstruct the flow.

We define the safety factor q for the helical plasmas of the experiment RFX-mod by accounting for the actual three-dimensional nature of the magnetic flux surfaces. Such a profile is not monotonic but goes through a maximum located in the vicinity of the electron transport barriers measured by a high resolution Thomson scattering diagnostic. Helical states with a single axis obtained in viscoresistive magnetohydrodynamic numerical simulations exhibit similar nonmonotonic q profiles provided that the final states are preceded by a magnetic island phase, like in the experiment. © 2011 The American Physical Society.

The full three-dimensional (3D) approach is now becoming an important issue for all magnetic confinement configurations. It is a necessary condition for the stellarator but also the tokamak and the reversed field pinch (RFP) now cannot be completely described in an axisymmetric framework. For the RFP the observation of self-sustained helical configurations with improved plasma performances require a better description in order to assess a new view on this configuration. In this new framework plasma configuration studies for RFX-mod have been considered both with tools developed for the RFP as well as considering codes originally developed for the stellarator and adapted to the RFP. These helical states are reached through a transition to a very low/reversed shear configuration leading to internal electron transport barriers. These states are interrupted by MHD reconnection events and the large Te gradients at the barriers indicate that both current and pressure driven modes are to be considered. Furthermore the typically flat Te profiles in the helical core have raised the issue of the role of electrostatic and electromagnetic turbulence in these reduced chaos regions, so that a stability analysis in the correct 3D geometry is required to address an optimization of the plasma setup. In this viewtheVMECcode proved to be an effectiveway to obtain helical equilibria to be studied in terms of stability and transport with a suite of well tested codes. In this work, the equilibrium reconstruction technique as well as the experimental evidence of 3D effects and their first interpretation in terms of stability and transport are presented using both RFP and stellarator tools. © 2010 IOP Publishing Ltd.

Single Helical Axis (SHAx) states obtained in high current reversed field pinch (RFP) plasmas display, aside from a dominant mode in the m=1 spectrum, also a dominant m=0 mode, with the same toroidal mode number as the m=1 one. The two modes have a fixed phase relationship. The island chain created by the m=0 mode across the reversal surface gives rise, at shallow reversal of the toroidal field, to an X-point structure which separates the last closed flux surface from the first wall, creating a divertor-like configuration. The plasma-wall interaction is found to be related to the connection length of the field lines intercepting the wall, which displays a pattern modulated by the dominant mode toroidal periodicity. This configuration, which occurs only for shallow toroidal field reversal, could be exploited to realize an island divertor in analogy to stellarators., 12 pages, 9 figures Submitted to Nuclear Fusion

The reversed field pinch configuration is characterized by the presence of magnetic structures both in the core and at the edge: in the core, at high plasma current the spontaneous development of a helical structure is accompanied by the appearance of internal electron transport barriers; at the edge strong pressure gradients, identifying an edge transport barrier, are observed too, related to the position of the field reversal surface. The aim of this paper is the experimental characterization of both the internal and edge transport barriers in relation to the magnetic topology, discussing possible analogies and differences with other confinement schemes. © 2009 IOP Publishing Ltd.

An overview of recent results from the MST reversed field pinch programme is presented. With neutral beam injection, bursty energetic particle (EP) modes are observed. The profiles of the magnetic and density fluctuations associated with these EP modes are measured using a far infrared interferometer-polarimeter. Equilibrium reconstructions of the quasi-single-helicity 3D helical state are provided by the V3FIT code that now incorporates several of MST's advanced diagnostics. The orientation of the helical structure is controlled using a new resonant magnetic perturbation technique. Gyrokinetic simulations based on experimental equilibria predict unstable trapped-electron modes (TEMs), and small-scale density fluctuations are detected in improved-confinement plasmas with TEM-like features. Upgraded pellet injection permits study of density and beta limits over MST's full range of operation, and an MST-record line-average density of 0.9 ×1020 m3 (n/nG = 1.4) has been obtained. Impurity ion temperature measurements reveal a charge-to-mass-ratio dependence in the rapid heating that occurs during a sawtooth crash. Runaway of NBI-born fast ions during the impulsive sawtooth event agrees with test-particle theory. Magnetic self-organization studies include measurements of the dynamo emf with an applied ac inductive electric field using oscillating field current drive.

This paper reports the highlights of the RFX-mod fusion science programme since the last 2010 IAEA Fusion Energy Conference. The RFX-mod fusion science programme focused on two main goals: exploring the fusion potential of the reversed field pinch (RFP) magnetic configuration and contributing to the solution of key science and technology problems in the roadmap to ITER. Active control of several plasma parameters has been a key tool in this endeavour. New upgrades on the system for active control of magnetohydrodynamic (MHD) stability are underway and will be presented in this paper. Unique among the existing fusion devices, RFX-mod has been operated both as an RFP and as a tokamak. The latter operation has allowed the exploration of edge safety factor q edge < 2 with active control of MHD stability and studies concerning basic energy and flow transport mechanisms. Strong interaction has continued with the stellarator community in particular on the physics of helical states and on three-dimensional codes. © 2013 IAEA, Vienna.

In present fusion research a strong effort is devoted to the studies of non-axisymmetric magnetic perturbations and consequent field ergodization on the external region of the plasma. On this topic interesting results can be drawn from the helical configuration observed in high-current regimes in reversed field pinches (RFPs) where the small edge helical ripple is sufficient to modulate the plasma-wall interaction and the plasma kinetic properties. This paper presents the most recent experimental results and physical interpretation of the phenomena observed in the edge region of the RFX-mod RFP device. Experimental observations indicate that plasma pressure and floating potential are spatially modulated according to the helical deformation. Helical flow is observed at the edge as a consequence of an ambipolar electric field. Emphasis will be devoted to the determination of the actual phase relation between magnetic perturbation and velocity perturbation. Evidence of the influence of the helical ripple on turbulence properties at the edge is also reported.

In the reversed field pinch experiment RFX-mod, plasma currents larger than 1 MA show a spontaneous transition from an axisymmetric to a helical configuration, where electron internal transport barriers (eITB) are observed in the proximity of the maximum of the q safety factor. 3D MHD simulations predict a helical flow pattern associated with the helical deformation of the magnetic flux surfaces. This paper reports the recent experimental findings on plasma flow in these helical regimes. Passive spectroscopy measurements of carbon and boron line Doppler shift allow the reconstruction of the m = 1 component of the velocity pattern associated with the helical equilibrium in a poloidal cross-section. The helical plasma flow is observed to form a m = 1 convective cell creating a localized sheared flow outside the region of strong electron temperature gradients characterizing the eITB. The experimental pattern is compared with the results of 3D MHD simulations (by means of the SpeCyl code). While the code predicts a flow shear peaking in the proximity of the null of the magnetic shear, where the safety factor is maximum, experimentally the maximum flow shear is found to be more external, leaving as a still open question the role played by the flow shear for the thermal barrier formation in RFX-mod helical plasmas.

High-frequency magnetic activity has been detected at the edge region of the RFX-mod reversed-field pinch (RFP) device. The analysis, performed by means of an insertable probe measuring the magnetic field fluctuations, shows coherent modes clearly depending on the Alfvén velocity, at a frequency in the range 0.1–1.5 MHz. Two main distinct modes are observed, characterized by low (|n| ⩽ 1) toroidal periodicity, with the features of discrete Alfvén eigenmodes. A splitting of the mode frequency is detected, a sign of the relevance of non-linearity in the physical process under study. The experimental observations could suggest an interpretation of the modes in terms of global Alfvén eigenmodes. Some hints about the possible drive mechanisms are also given.