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The comparison between deuterium and hydrogen plasmas at high current in the RFX-mod experiment proves that the reversed field pinch configuration experiences the isotope effect in a way analogous to tokamak experiments. Both energy and particle confinement exhibit a favourable scaling with the isotope mass Mi, respectively, as M0.3i and as M0.45i. This effect is mainly due to the mitigation of transport at the edge, which is driven by electrostatic fluctuations, although a mitigation of the stochastic transport in the plasma core is also observed. As in tokamaks, the MHD properties are modified when the gas mass is changed. The most evident modification regards the spectrum of tearing modes that are more stable in deuterium, so that the duration and the purity of quasi single helicity (QSH) phases are enhanced. The thermal structures that develop during the QSH phases enclose a plasma volume that is wider in deuterium discharges than in hydrogen ones.

In this paper we present a method to compute spatial and time evolution of electromagnetic forces in magnetic confinement fusion devices based on a combination of signal analysis of magnetic measurements with a simple electromagnetic modelling. The method allows analyzing the whole plasma discharge including fast transient phenomena such as fast terminations or disruptions. It has been tested and verified on RFX-mod, an experiment equipped with a non-continuous toroidal passive stabilizing shell, but it can be applied to cases with continuous wall such as tokamak devices, as well. An experimental plasma discharge, with a fast termination phenomenon at the end of the flat-top phase, has been analyzed and the related forces have been computed by using two different sets of data: synthetic magnetic field measurements provided by ANSYS simulation and real experimental ones. The results are in good agreement in all the phases of the plasma discharge. Moreover, because of the very low-computational requirements, it is shown that the presented method can be used as a tool for real-time monitoring of the electromagnetic forces on the shell to be integrated in the protection system of the future RFX-mod2 experiment.

In magnetic confinement fusion devices, close-fitting structures surrounding the plasma are needed to slow down the growth rate of MHD unstable modes to time scales accessible to real time feedback control systems. However, error fields are generated as the response of the passive structures to the dynamic equilibrium field configuration, due to the presence of the cuts needed to allow the penetration of electric and magnetic fields. Considerable improvements have been achieved in RFX-mod after starting operation of the active MHD control system, allowing the successful simultaneous feedback control of a wide spectrum of MHD instabilities. In this paper, a feasibility study of a new local active correction system of magnetic field errors is presented, together with a comparison of three different configurations of the passive structure cuts.

A major refurbishment of the toroidal load assembly is under study to extend the operational space of RFX-mod in both RFP and Tokamak configurations. It includes the removal of the vacuum vessel to increase the plasma-shell proximity and modifications of the support structure to obtain a new vacuum-tight chamber. This entails the design of a new electromagnetic measurement system, taking into account the requirements of both the equilibrium and MHD control system and physics analyses requirements in both RFP and shaped Tokamak configurations. The spatial resolution is constrained by the number of graphite tiles, 28 (poloidal) x 72 (toroidal), which cover the inner surface of the toroidal vacuum chamber. Alternative layouts of 4 x 72 and 7 x 72 are being considered to assure the calculation of the MHD mode spectrum up to (m = 0,1,2 or 3; n = 0,…,±35). A substantial advantage in terms of harmonic spectrum reconstruction is expected also in case of sensor faults with respect to the present 4x48 arrangement. Moreover, 12 poloidal arrays will include 14 sensors to compute the harmonic content needed by the plasma boundary reconstruction algorithm (m = 0,…,6). Due to the reduced room between the copper shell and the graphite tiles, the design of triaxial, vacuum fit pickup probes have started also for their convenience in compensating alignment errors.

A recent study [R. Paccagnella, Phys. Plasmas 23, 092512 (2016)] about the scaling with the aspect ratio (i.e., the ratio between the major and minor radius of the torus) of the dominant mode in single helical reverse field pinch plasmas has shown, at intermediate aspect ratio, that the dominant toroidal mode number in the helical states can be interpreted as the result of a relaxation process. In this work, the same theoretical model is compared and validated with the experimental data obtained in the low aspect ratio RELAX device [S. Masamune et al., J. Phys. Soc. Jpn. 76, 123501 (2007).]. Some difficulties have emerged in this comparison that may be interpreted either as related to a residual level of magnetic chaos in the RELAX plasmas or possibly to genuine toroidal effects not analyzed in this paper, where a cylindrical approximation is considered.

This paper presents a field line tracing code (FLiT) developed to study particle and energy transport as well as other phenomena related to magnetic topology in reversed-field pinch (RFP) and tokamak experiments. The code computes magnetic field lines in toroidal geometry using curvilinear coordinates (r,theta,f) and calculates the intersections of these field lines with specified planes. The code also computes the magnetic and thermal diffusivity due to stochastic magnetic field in the collisionless limit. Compared to Hamiltonian codes, there are no constraints on the magnetic field functional formulation, which allows the integration of whichever magnetic field is required. The code uses the magnetic field computed by solving the zeroth-order axisymmetric equilibrium and the Newcomb equation for the first-order helical perturbation matching the edge magnetic field measurements in toroidal geometry. Two algorithms are developed to integrate the field lines: one is a dedicated implementation of a first-order semi-implicit volume-preserving integration method, and the other is based on the Adams-Moulton predictor-corrector method. As expected, the volume-preserving algorithm is accurate in conserving divergence, but slow because the low integration order requires small amplitude steps. The second algorithm proves to be quite fast and it is able to integrate the field lines in many partially and fully stochastic configurations accurately. The code has already been used to study the core and edge magnetic topology of the RFX-mod device in both the reversed-field pinch and tokamak magnetic configurations.

The edge of the RFX-mod (R=2m, a=0.46m) Reversed Field Pinch device is characterized by weak magnetic chaos affecting ion and electron diffusion. Edge particle transport is strongly influenced by a toroidal asymmetry caused by magnetic islands and an ambipolar radial electric field ensures local neutrality, in a way similar to the stochastic edge of tokamaks when resonant magnetic perturbations (RMPs) are applied. The H? emission and floating potential Vf measured in different poloidal and toroidal positions shows a helical shape of the Plasma Wall Interaction, fitting the spatial periodicity of the innermost resonant tearing mode (m/n=1/7) [1]. However, detailed measurements, along the poloidal (parallel) direction, of the electron density and temperature with the Thermal Helium Beam, and of the floating potential Vf with electrostatic probes, show that the response of the edge plasma depends on the poloidal angle, in a more complicated way than a pure 1/7 harmonic. In particular, multiple poloidal harmonics can be recognized in the measurements. The results are robust, because data analysis has been performed with different techniques: in terms of correlations between Vf signals and the corresponding local flux-surface displacement, by the conditional average technique applied at Vf signals, and finally also in terms of a travelling helical angle frame as reference of the measurements. The interpretation of the results is not obvious, but it highlights the fact that the correlation between magnetic islands and kinetic properties of the edge plasma is not a simple one-to-one causal relationship, as it is often assumed in RMP studies in tokamaks.

In the quest for new energy sources, the research on controlled thermonuclear fusion has been boosted by the start of the construction phase of the International Thermonuclear Experimental Reactor (ITER). ITER is based on the tokamak magnetic configuration, which is the best performing one in terms of energy confinement. Alternative concepts are however actively researched, which in the long term could be considered for a second generation of reactors. Here, we show results concerning one of these configurations, the reversed-field pinch (RFP). By increasing the plasma current, a spontaneous transition to a helical equilibrium occurs, with a change of magnetic topology. Partially conserved magnetic flux surfaces emerge within residual magnetic chaos, resulting in the onset of a transport barrier. This is a structural change and sheds new light on the potential of the RFP as the basis for a low-magnetic-field ohmic fusion reactor. © 2009 Macmillan Publishers Limited.

The low-aspect-ratio (A) reversed field pinch (RFP) offers attractive properties such as enhanced bootstrap current and simpler MHD mode dynamics. The RELAX (REversed field pinch of Low-Aspect ratio eXperiment) machine with the world's lowest A of 2 (R/a = 0.5 m/0.25 m) has been constructed to explore the RFP properties in low-A regime. In flat-topped low-A RFP discharges in RELAX, plasma current of ~50 kA has been attained with discharge duration of ~2 ms. In round-topped discharges with plasma current of ~70 kA, quasi-periodic growth of a single helical mode has been observed. When the dominant m = 1/n = 4 mode grows, the toroidal mode spectrum looks like that of the quasi-single helicity (QSH) RFP state with higher amplitude. MHD equilibrium analyses using a reconstruction code have shown that the bootstrap current fraction is lower than ~5% in the present RELAX plasmas, and it will be ~25% if we could achieve the plasma density of 4 × 10 19 m -3 and electron temperature of 300 eV at plasma current of ~100 kA.

Aiming at predictive simulation of the plasma magnetic parameters during the RFX-mod discharges, a model was designed to simulate the poloidal field power supply system, detailing each individual switching unit and the single ac-dc converter with its local control circuit, together with the magnet system and the complete multi-variable feedback system devoted to the plasma shape and position control. The model was realized by coupling a linear model of the axi-symmetric evolution of the plasma with a detailed implementation of the RFX-mod circuit developed by means of the SimPowerSystem Toolbox in the framework of the Matlab-Simulink(TM) package. In order to evolve the plasma current, a Bessel Function Model (BFM) is adopted to implement the energy transfer from the toroidal to the poloidal field. The axi-symmetric controller is implemented to close the loop and is the same running on the VME nodes of the real control system. The model was successfully tested against experimental data, showing good agreement between measured and calculated waveforms. (C) 2007 Elsevier B.V. All rights reserved

The modified RFX is a very flexible device used for a variety of control schemes for MHD instabilities and for advanced reverse field pinch scenarios. Relative to the previous machine, RFX-mod has a thin Cu shell with vertical field penetration time τS, lowered from 450 to 50 ms and shell/plasma proximity from b/a ≤ 1.24-1.1. Toroidal equilibrium is feedback-controlled and new power supplies provide better Bφ control. Newly designed graphite tiles protect the vessel from localized power deposition. A mesh of 192 external saddle coils, supervised by a digital feedback system, controls radial fields due to field errors and MHD modes. The paper presents an overview of the very encouraging results obtained using both new and 'standard' advanced operational modes in the current range 0.3-1 MA. A dramatic improvement of plasma performance was obtained by using the saddle coils to cancel all the radial field components, an operation mode dubbed virtual shell (VS). The toroidal voltage was lowered by more than 25% and the pulse length was tripled, up to 7 times the τS. Steady-state RFP pulses are now limited only by the applied volt-seconds. The improved magnetic boundary also has an effect on the tearing modes underlying the sustainment of the RFP, whose core amplitude is more than halved. The VS combined with new schemes for the active rotation of the MHD dynamo modes has allowed us to obtain reliable and well-controlled long RFP pulses in the MA current range. This results in a 100% increase in the particle and energy confinement time relative to the previous experiment and opens the possibility of exploring the machine performance in the 2 MA design range. © 2007 IAEA.

The results leading to the identification of coherent structures emerging from the background turbulence in the edge region of the reversed field pinch experiments EXTRAP-T2R and RFX are reviewed. These structures have traits of vortices in velocity field and blobs in density, and the reconstruction of their spatial structure and of their time evolution is discussed focusing on the analysis tools applied. The role of these structures in the particle anomalous transport is addressed, showing that their collisions can contribute up to 50% the total particle losses.This process is shown to be responsible for bursts in particle flux and it is found to set a characteristic collision time, which is in agreement with the statistical properties of laminar times for particle flux bursts. © 2006 The Royal Swedish Academy of Sciences.

The results of an edge biasing experiment in RFX are reported. The particle balance has been interpreted by a zero-dimensional model which allows the particle confinement time to be adjusted in order to reproduce the experimental behaviour of the plasma density. It is found that, despite the substantial reduction of the electrostatic transport by a factor of three, the particle confinement time does not increase by more than 35%. This behaviour has been interpreted as an indication that another loss channel must be considered which is responsible for a particle flux twice as large as that carried by electrostatic fluctuations and it has been identified in the perturbation due to the locked mode.

In order to test the self-organized criticality (SOC) paradigm in transport processes, a novel technique has been applied for the first time to plasmas confined in reversed field pinch configuration. This technique consists of an analysis of the probability distribution function of the times between bursts in density fluctuations measured by microwave reflectometry and electrostatic probes. The same analysis has also been applied to intermittent events sorted out from the Gaussian background. In both cases, the experimental results disagree with the predictions for a SOC system.

The reversed field pinch (RFP) is a configuration for plasma magnetic confinement. It has been traditionally viewed as dominated by a bath of MHD instabilities producing magnetic chaos and high energy transport. We report experimental results which go beyond this view. They show a decrease of magnetic chaos and the formation of a coherent helical structure in the plasma, whose imaging and temperature profile are provided for the first time. These quasi-single-helicity states are observed both transiently and in stationary conditions. The last case is consistent with a theoretically predicted bifurcation. Our results set a new frame for improving confinement in high current nonchaotic RFP's.

An array of single Langmuir probes is routinely used in the RFX reversed field pinch for time-resolved measurements of edge electron density and temperature. In order to allow an automatic analysis of the large number of current - voltage characteristics, three different methods have been developed, which consider restricted subsets of data with voltage lower than an upper cutoff value. The first one determines this limiting voltage by a neural network based technique, combined with criteria for the rejection of too noisy characteristics. In the second one a standard fitting routine is applied repeatedly to the data while varying the upper cutoff voltage. The third one consists of a numerical technique, where the best fit is obtained by minimizing a properly defined cost function. An error index is also calculated, which allows the reliability of the results to be easily estimated. The best results have been achieved using the last two methods.

The study of electron temperature profiles of quasi-single helical states (QSH) in RFX-Mod (and, in general, in other RFP machines) was carried out in the past mainly using Thomson scattering, thus being limited to a time resolution of the order of some milliseconds and to the collection of single, isolated cases, which displayed clear transport barriers. A new multichord double filter SXR spectrometer was developed and installed. Temperature profiles are now measured up to a frequency of some kHz, allowing one to determine the entire time evolution of electron temperature during a QSH cycle. A mapping technique, originally developed for Thomson temperature profiles, is adapted to deal with the line-integrated nature of the SXR diagnostic. In particular, temperature gradients related to the presence of transport barriers are reconstructed and analysed in a helical reference system, coherently with the underlying plasma equilibrium. The method is discussed in its capabilities and limits and then applied to a wide QSH database. As a result, a clear difference in temperature gradient behaviour between the rising phase of QSH and the saturated (or flattop) phase is observed. In the rising phase the expected correlation of temperature gradient with magnetic spectrum is confirmed, showing a positive trend between dominant mode amplitude and thermal structure dimension, as well as a negative correlation of secondary mode amplitudes and temperature gradient. On the other hand, in the flattop phase the presence of a thermal structure is intermittent, and much less influenced by the magnetic dynamics. This suggests the simultaneous presence of different mechanisms that enhance energy transport.

Experimental evidences of short wavelength electromagnetic modes are found in the reversed-field-pinch configuration device RFX-mod by means of in-vessel magnetic probes. The modes are revealed during the helical states of the plasma. Their amplitude is well correlated to the electron temperature gradient strength in the core. On the basis of linear gyrokinetic calculations we interpret these instabilities as microtearing modes.

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.

The edge region of the reversed field pinch experiment RFX has been investigated with Langmuir and calorimetric probes. The energy flux measurements reveal a spatial structure that is consistent with the presence of a superthermal tail in the energy distribution function of the electrons, as expected according to the kinetic dynamo theory (KDT). In the framework of this model, the value of the magnetic field line diffusion coefficient in the edge region has been derived. The radial electric field obtained from the plasma potential gradient is opposite in sign to the ambipolar electric field expected in a stochastic magnetic field. The discrepancy is discussed in terms of particle recycling at the wall.

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

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.

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.

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.

New edge diagnostics and detailed analysis of magnetic topology have significantly improved the comprehension of the processes developing at the boundary of a reversed-field pinch (RFP) plasma in RFX-mod (a = 0.46 m, R = 2 m). An upper critical density n C ≈ 0.4 n G (n G Greenwald density) is found to limit the operational space for the improved quasi-single helical (QSH) regime: magnetic topology reconstructions and diagnostic observations suggest that this limit is due to a helical plasma–wall interaction which determines toroidally and poloidally localized edge density accumulation and cooling. The experimental evidence is provided by a variety of diagnostics: the magnetic boundary as reconstructed from equilibrium codes reveals a helical deformation, which is well correlated with the modulation of edge pressure profile as reconstructed from the thermal helium beam diagnostic. Correlations with the helical deformation are also observed on the space- and time-resolved patterns of the floating potential measured at the wall, and with the edge plasma flow, obtained from different diagnostics. The relevance of these findings is that understanding the mechanisms that limit the operational space of QSH is decisive in achieving the goal of high-density stationary helical RFP equilibrium.

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.

Edge turbulent structures are commonly observed in fusion devices and are generally believed to be responsible for confinement degradation. Among their origin Drift-Alfven turbulence is one of the most commonly suggested. Drift-Alfven paradigm allows the existence of localized vortex-like structures observed also in various systems. Here we present the evidence of the presence of drift-Alfv\'en vortices in the edge region of RFX-Mod RFP device, showing how these structures are responsible for electromagnetic turbulence at the edge and its intermittent nature., Comment: 4 pages, 5 figures, Revised version submitted for publication to Physical Review Letters

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

With the exploration of the MA plasma current regime in up to 0.5 s long discharges, RFX-mod has opened new and very promising perspectives for the reversed field pinch (RFP) magnetic configuration, and has made significant progress in understanding and improving confinement and in controlling plasma stability. A big leap with respect to previous knowledge and expectations on RFP physics and performance has been made by RFX-mod since the last 2006 IAEA Fusion Energy Conference. A new self-organized helical equilibrium has been experimentally achieved (the Single Helical Axis - SHAx - state), which is the preferred state at high current. Strong core electron transport barriers characterize this regime, with electron temperature gradients comparable to those achieved in tokamaks, and by a factor of 4 improvement in confinement time with respect to the standard RFP. RFX-mod is also providing leading edge results on real-time feedback control of MHD instabilities, of general interest for the fusion community. © 2009 IAEA, Vienna.

The RFX-mod machine (Sonato et al 2003 Fusion Eng. Des. 66 161) recently achieved, for the first time in a reversed-field pinch, high plasma current up to 1.6 MA with good confinement. Magnetic feedback control of magnetohydrodynamic instabilities was essential to reach the goal. As the current is raised, the plasma spontaneously accesses a new helical state, starting from turbulent multi-helical conditions. Together with this raise, the ratio between the dominant and the secondary mode amplitudes increases in a continuous way. This brings a significant improvement in the magnetic field topology, with the formation of helical flux surfaces in the core. As a consequence, strong helical transport barriers with maximum electron temperature around 1 keV develop in this region. The energy confinement time increases by a factor of 4 with respect to the lower-current, multi-helical conditions. The properties of the new helical state scale favourably with the current, thus opening promising perspectives for the higher current experiments planned for the near future.

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 analysis of plasma dynamics during impulsive magnetic reconnection events in the RFX-mod reversed field pinch (RFP) is performed by means of a large set of magnetic in-vessel coils and of an insertable edge probe, equipped with a matrix of electrostatic (Langmuir) and magnetic probes. It is observed that reconnection of field lines, which leads to a global reconfiguration of the magnetic topology (relaxation), is associated with the rapid formation of a strongly localized magnetic perturbation characterized by a main m = 0 periodicity, due to enhanced dynamo modes activity. Soon after its formation, the m = 0 perturbation is observed to move in the toroidal direction and is shown to correspond to a poloidal current sheet, whose existence was predicted by three-dimensional MHD numerical simulations on RFP sustainment through magnetic reconnection processes. A reconstruction of the current density structure associated with the rotating magnetic perturbation is performed by means of the insertable probe, along with an investigation of the large induced modification of electron temperature, density and plasma velocity shear at the edge.

The magnetic configuration reversed field pinch is sustained by the MHD dynamo process that provides the poloidal plasma current needed for the field reversal. In the virtual shell discharges of the RFX-mod experiment the dynamo process occurs in a discrete way, during the so-called dynamo relaxation events (DREs). In this paper the dynamo effect on the confinement is studied through the electron density behaviour during the DRE. The analyses show that the occurrence of a DRE is accompanied by a local, non-axisymmetric loss of particle confinement. Such local loss occurs at the toroidal angle lock where the MHD tearing modes lock in phase between themselves and at the wall. The analyses performed with a field line tracing code show that nearby lock several magnetic lines lying in the plasma core punch through the confinement barrier located in the proximity of the field reversal and directly connect the plasma core to the wall. The formation of this path towards the wall agrees with the local particle loss observed experimentally. © 2008 IOP Publishing Ltd.

Optimization of machine operation, including plasma position control, density control and especially feedback control on multiple magnetohydrodynamic modes, has led RFX-mod to operate reliably at 1.5 MA, the highest current ever achieved on a reversed field pinch (RFP). At high current and low density the magnetic topology spontaneously self-organizes in an Ohmical helical symmetry, with the new magnetic axis helically twisting around the geometrical axis of the torus. The separatrix of the island disappears leaving a wide and symmetric thermal structure with large gradients in the electron temperature profile. The new topology still displays an intermittent nature but its overall presence has reached 85% of the current flat-top period. The large gradients in the electron temperature profile appear to be marginal for the destabilization of ion temperature gradient modes on the assumption that ions and electrons have the same gradients. There are indications that higher currents could provide the conditions under which to prove the existence of a true helical equilibrium as the standard RFP configuration. © 2008 IOP Publishing Ltd.

A simple one-dimensional time-dependent model for simulating the magnetic field profiles in a reversed field pinch (RFP) plasma is presented. The model, which is derived from basic MHD equations with the addition of a phenomenological dynamo electric field, is able, through the tuning of a few free parameters, to simulate the time evolution of RFP discharges in a large range of operating conditions, successfully reproducing quantities such as the average toroidal field, the loop voltage and the on-axis safety factor. The application to several experimental conditions obtained on the RFX-mod machine [P. Sonato, Fusion Eng. Des. 66, 161 (2003)], including oscillating poloidal current drive (OPCD) is shown and the simulation outcome is discussed. © 2008 American Institute of Physics.

In the Reversed Field Pinch eXperiment RFX-mod a Gas Puffing Imaging Diagnostic (GPID) is used to investigate the dynamical structure of plasma edge turbulence. The GPID measures the radiation emitted from He gas puffed in H discharges and allows the investigation of edge plasma properties with high time and space resolution at high plasma current during the entire discharge. The characterization of edge turbulence has been carried out in terms of power spectrum, cross-correlation and toroidal velocity of structures. The scaling of such velocity with the density corresponds to different values of the dimensionless ratio nu(ci)/nu(ei) (ion cyclotron frequency/electron-ion collision frequency) ranging from below to above unity. The toroidal characteristic length of intermittent structures at different time scales has been determined by applying the conditional average technique on the structures identified by the continuous wavelet transform. These lengths are in the range 15-45 mm, while the number of structures increases with the electron density, the propagation velocity, opposite to the plasma current, decreases with the density and saturates at -20 km/s. (c) 2007 Elsevier B.V. All rights reserved.

RFX-mod is a reversed field pinch (RFP) experiment equipped with a system that actively controls the magnetic boundary. In this paper we describe the results of a new control algorithm, the clean mode control (CMC), in which the aliasing of the sideband harmonics generated by the discrete saddle coils is corrected in real time. CMC operation leads to a smoother (i.e. more axisymmetric) boundary. Tearing modes rotate (up to 100 Hz) and partially unlock. Plasma-wall interaction diminishes due to a decrease of the non-axisymmetric shift of the plasma column. With the ameliorated boundary control, plasma current has been successfully increased to 1.5 MA, the highest for an RFP. In such regimes, the magnetic dynamics is dominated by the innermost resonant mode, the internal magnetic field gets close to a pure helix and confinement improves. © 2007 IOP Publishing Ltd.

High frequency peaks in the spectra of magnetic field signals have been detected at the edge of Extrap-T2R [P. R. Brunsell, H. Bergsåker, M. Cecconello, J. R. Drake, R. M. Gravestijn, A. Hedqvist, and J.-A. Malmberg, Plasma Phys. Controlled Fusion, 43, 1457 (2001)]. The measured fluctuation is found to be mainly polarized along the toroidal direction, with high toroidal periodicity n and Alfv́nic scaling (f∝B mi ni). Calculations for a reversed field pinch plasma predict the existence of an edge resonant, high frequency, high- n number toroidicity-induced Alfv́n eigenmode with the observed frequency scaling. In addition, gas puffing experiments show that edge density fluctuations are responsible for the rapid changes of mode frequency. Finally a coupling with the electron drift turbulence is proposed as drive mechanism for the eigenmode. © 2005 American Institute of Physics.

Coherent structures identified in two reversed field pinch experiments are interpreted as a dynamic balance of dipolar and monopolar vortices growing and evolving under the effect of the ExB flow shear. For the first time their contribution to the anomalous transport has been estimated in fusion related plasmas, showing that they can account for up to 50% of the total plasma diffusivity. The experimental findings indicate that the diffusion coefficient associated with the coherent structures depends on the relative population of the two types of vortices and is minimum when the two populations are equal. An interpretative model is proposed to explain this feature.

The effect of the E × B velocity shear on the particle flux carried by electrostatic fluctuations at the edge is discussed comparing the results of the experiments T2R (R = 1.2 m, a = 0.18 m) and RFX (R = 2 m, a = 0.5 m). In both experiments electrostatic turbulence accounts for most of the particle flux. The shear of the E × B velocity is close or larger than the value required for turbulence suppression or reduction. Particle fluxes exhibit bursts which carry a large fraction of the total particle flux, and which tend to cluster during magnetic relaxation phase. On the average a Bohm estimate of the experimental plasma diffusivity accounts for the experimental data. Finally a discussion on the methods for turbulence control is given. © 2003 Elsevier Science B.V. All rights reserved.

In this paper, we analyse the main features of the pulsed poloidal current drive (PPCD) technique, used in the reversed field pinch configuration to achieve improved confinement conditions. In the RFX experiment, PPCD corresponds to a decrease of the magnetic fluctuations, to a peaking of the temperature profile, and to a reduced transport and plasma-wall interaction. A three-dimensional MHD nonlinear code and one-dimensional time-dependent transport models have been applied to study the effect of PPCD on the magnetic and plasma profiles. The three-dimensional MHD simulations show that the external inductive drive pinches and peaks the current profile driving the configuration through a transient phase, where the spontaneous turbulent dynamo action is quenched. The one-dimensional transport codes indicate that the experimental profile modifications associated with PPCD are consistent with a reduction of the stochastic transport.

This paper shows that the superthermal electron tail observed at the edge of plasmas confined in reversed field pinch (RFP) configuration can be explained as the distortion of the distribution function due to the dynamo electric field. To support this view, the distribution function has been simulated with a 2D Fokker-Planck code. The results show that both the slope of the tail of the distribution function and the asymmetry of the energy fluxes with respect to the direction of the local magnetic field can be reproduced with reasonable values of the dynamo field. To support our view, we present a detailed comparison of code predictions with measurements made in the edge region of the RFX experiment.

Edge turbulence and blobs are studied in the three-dimensional magnetic topology of the RFX-mod reversed field pinch. The edge of the RFX-mod shows a three-dimensional structure dominated by a helical equilibrium with (1, -7) symmetry, which gives the same space-time modulation to all of the kinetic properties. The interaction between the edge turbulence and this magnetic topology is studied. It is shown that the edge blobs are current-carrying filaments aligned with the magnetic field, and in the perpendicular plane each blob is a positive peak of electron density and a valley of temperature. The inner nature of these blobs is not affected by the presence of the O and X points of the (1, -7) island; however, the statistical properties are sensitive to them, pointing to the influence of the magnetic topology on the edge fluctuations.