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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.

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.

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.

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 toroidal plasma containment device. Magnetohydrodynamic equilibrium bifurcation occurs in a reversed-field pinch when the innermost resonant magnetic perturbation grows to a large amplitude, reaching up to 8% of the mean field strength. Magnetic topology evolution is determined by measuring the Faraday effect, revealing that, as the perturbation grows, toroidal symmetry is broken and a helical equilibrium is established. © 2011 American Physical Society.

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 reversed field pinch (RFP) is a magnetic configuration alternative to the tokamak that can be considered for a second generation of reactors. In this paper new remarkable results obtained in the RFP experiment RFX-mod are presented, showing that an internal transport barrier delimitates a large fraction of the plasma volume in a RFP when the current is raised to ∼1.5 MA. The formation of this transport barrier is related to a profound, spontaneous modification of the magnetic topology. Due to the occurrence of a saddle node bifurcation the plasma enters in the single helical axis state, which is theoretically known to be more resilient to chaos. This bifurcation is driven by the amplitude of the helical perturbation which dominates the mode spectrum. © 2009 American Institute of Physics.

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.

The transition to a new magnetic topology, characterized by a quasi-single-helicity state with a single helical magnetic axis has been experimentally observed for the first time in a reversed-field-pinch plasma. The occurrence of the new state, which has been dubbed a single-helical-axis state, was found to provide magnetic chaos healing and enhanced thermal content of the plasma. The helical structure extends on both sides of the vessel geometric axis, and is related to exceeding a threshold in the ratio between the amplitude of the dominant MHD mode and the amplitude of the secondary ones. © 2008 The American Physical Society.

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.

Electrostatic turbulence in the edge region of the RFX device has been shown to be intermittent, i.e. not self-similar. In fact the probability distribution function of fluctuations at large scales is Gaussian in shape, whereas it displays strong tails for small scale fluctuations. The events responsible for these heavy tails are associated with turbulent structures with well defined density and floating potential spatial profiles, which have been characterised using arrays of probes. These structures tend to occur preferentially in correspondence to large scale magnetic relaxation events driven by core-resonant tearing modes. They also display an inclination related to the average velocity shear.

The reversed field pinch magnetohydrodynamics (MHD) is characterized by a broad spectrum of interacting resistive tearing modes with poloidal mode number mainly m = 0,1. According to the nonlinear coupling theory, the modes phase lock together if their amplitudes exceed a critical value. In the Reversed Field Pinch Experiment (RFX) [L. Fellin et al., Fusion Eng. Des. 25, 315 (1995)] they are always locked in phase, determining a global nonaxisymmetric magnetic perturbation. In this work a detailed experimental characterization of the magnetic perturbation is presented. The typical toroidal profiles and spectra, for both the m = 0 and the m = 1 components, are shown. In particular the phase relationship under locking conditions between the interacting m = 0,1 modes is investigated and compared with the theoretical predictions. The results of three-dimensional (3D) MHD numerical simulations are also discussed. © 2001 American Institute of Physics.

Plasmas confined in reversed field pinch configuration are investigated. The self-organized criticality (SOC) paradigm in tranport process in the plasmas is analyzed a technique consists of an analysis of the probability density function of the times between bursts in density fluctuations. These bursts are measured using microwave reflectometry and electrostic probes.

A study of transport processes in reversed-field-pinch plasmas was performed. Statistical properties of particle fluxes driven by electrostatic turbulence were also compared with those predicted by the self-organized-criticality (SOC) model. The statistical analysis revealed that laminar times between bursts carrying more than 50% of the particle transport at the edge exhibited a power law decay. The decomposition of particle flux fluctuations in the edge region of RFX showed that fluctuations were not self-similar in character.

The reversed field pinch (RFP), a configuration for plasma magnetic confinement was initially viewed as dominated by magnetohydrodynamic (MHD) instabilities producing magnetic chaos and high energy transport. Experiments showed that in case of plasmas where imaging and temperature profile were provided for the first time, there was a decrease of magnetic chaos and the formation of coherent helical structure.

The experimental determination of the radial electric field Er and the associated E × B drift velocity at the edge of RFX is presented and possible mechanisms responsible for its generation are discussed. Er measurements by means of an array of Langmuir probes and those deduced from Doppler spectroscopy of impurity lines agree fairly well. In particular the rotation velocity of the plasma edge has been determined from the Doppler shift of a C III emission line. The observation of other ions characterised by different radial positions, such as B IV and C V, has allowed an estimate of the velocity shear. Typical values of plasma rotation at the edge are around 10 km/s while the velocity shear is of the order of (105-106)s-1 in the spontaneous layer, a few cm thick, usually observed in standard discharges. Plasma rotation has been artificially modified by both positive and negative edge biasing and the associated increase or decrease of the fluid velocity is well in agreement with the radial electric field change. The modification of Er during edge biasing and Pulsed Poloidal Current Drive (PPCD) are also reported and interpreted within a momentum balance model. Analytical and self-consistent Monte Carlo models at the plasma edge suggest that impurities have a relevant role in the generation of the radial electric field, due to their relatively large Larmor radius.

This paper reports experimental results showing that coherent helical structures are formed in the reversed field pinch (RFP) self-organizing plasma core as a result of transitions to states where the n-spectrum of the m=1 modes is dominated by a single (1,n(max)) geometrical helicity. These states are dubbed quasi-single helicity (QSH) states. Their magnetic and thermal properties measured in the reverse field experiment (RFX) [G. Rostagni, Fusion Eng. Des. 25, 301 (1995)] device are described. The present theoretical understanding of QSH states is discussed and some recent theoretical results are presented. The role of aspect ratio is discussed. These results represent a significant step to open a path beyond the standard paradigm that a bath of magnetohydrodynamic (MHD) modes is intrinsic to the RFP.

Positive and negative edge biasing experiments induced by electrodes have been performed in the reversed field pinch experiment RFX at 300-400 kA toroidal plasma current; in both conditions the edge radial electric field has been modified. A model, based on the Ohm's law and the momentum balance equation, has been developed in analogy to tokamaks to interpret the observed values of the toroidal flow velocity and its modification due to the electrode operation. Anomalous perpendicular viscosity due to anomalous particle diffusion has been assumed and the equations have been written in cylindrical co-ordinates. Preliminary results of a numerical code based on this model show a good agreement with the experimental data without biasing and justify the toroidal velocity variations induced by the electrode current.

This paper presents results obtained on the Reversed Field eXperiment, RFX [G. Rostagni, Fusion Engineering and Design 25, 301 (1995)], on the study of local transport properties of the RFP configuration both in the standard regime and during improved confinement phases obtained with poloidal current drive. The plasma core is dominated by magnetic turbulence, as indicated by both energy and particle transport analysis. Diffusivity decreases toward the edge and is reduced in the core at high Lundquist number. The edge region is apparently not affected by dynamo mode turbulence and determines global confinement in standard operation. Particle and heat diffusivity in this region show a favorable dependence with increasing density. The most interesting feature of the edge region of RFX consists of a sheared radial electric field with shearing rate comparable to that observed in tokamaks. Indications of turbulence reduction in the shear layer have been obtained. Enhanced energy confinement has been produced by pulsed poloidal current drive (PPCD). A clear reduction of the dynamo activity has been observed with a decrease of core thermal diffusivity to level comparable to the edge and global confinement improvement up to a factor of 3. © 1999 American Institute of Physics.

An analysis of experimental data from the reversed field experiment (RFX) reversed field pinch machine [L. Fellin, P. Kusstatscher, and G. Rostagni, Fusion Eng. Des. 25, 315 (1995)] is carried out to investigate the possible existence of deterministic chaos in the edge plasma region. The mathematical tools used include Lyapunov exponents, Kaplan-Yorke dimension, minimum embedding dimension estimates and nonlinear forecasting. The whole analysis agrees in ruling out the possibility of low-dimensional chaos: The dimension of the underlying dynamical system is estimated to be >10. From a critical rereading of the literature it emerges that the findings of this work are likely to be common to all reversed field pinches.

The electrostatic turbulence in the edge plasma of the RFX reversed field pinch experiment has been studied using Langmuir probes and a homodyne reflectometer.The radial particle flux driven by electrostatic fluctuations has been measured in the region where a double E×B velocity shear layer occurs.It is found that almost 100% of the particle flux at the edge is driven by electrostatic fluctuations.The naturally occurring E×B velocity shear has been shown to be close to that required by the Biglari-Diamond-Terry criterion for turbulence radial decorrelation.

In the RFX reversed field pinch experiment the radial electric field at the edge gives rise to a spontaneous double velocity shear layer. The velocity shear affects the properties of electrostatic turbulence and the related particle transport. Preliminary results of an experiment of edge biasing by electrodes are reported, showing that with electrode currents higher than 5 kA the radial electric field can be significantly modified.

The first evidence of an electrostatic potential well at the edge of plasmas confined in a reversed field pinch configuration is reported, based on measurements made on the RFX experiment. The radial width of the well decreases with plasma current, whereas the potential drop is a few times the electron temperature at the edge, almost independent of plasma current. The resulting radial electric field points inward at the edge and this behavior has been related to finite Larmor radius losses as in tokamaks. Because of the spatial structure of the plasma potential, a naturally occurring double velocity shear layer has been identified at the edge with a shear value comparable to that of tokamaks and stellarators.

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.