F. Sattin

Consorzio RFX

We present a quasi-linear treatment of the drift-kinetic equation in the presence of a stochastic magnetic field, which provides a self-contained description of particle, parallel momentum and heat transport. Explicit analytical expressions, which satisfy the Onsager reciprocal relations, are obtained by approximating the distribution function by a...

Time series of observables measured from complex systems do often exhibit non-normal statistics, their statistical distributions (PDF's) are not gaussian and often skewed, with roughly exponential tails. Departure from gaussianity is related to the intermittent development of large-scale coherent structures. The existence of these structures is roo...

In magnetically confined experiments the presence of rational surfaces modifies the magnetic configuration with one or more islands embedded in the main plasma. The islands strongly modify particle and heat fluxes, hence their role must be included in the study of the transport properties. Two examples of this phenomenology are here presented: a co...

Superstatistics [C. Beck and E.G.D. Cohen, Physica A 322, 267 (2003)] is a formalism aimed at describing statistical properties of a generic extensive quantity E in complex out-of-equilibrium systems in terms of a superposition of equilibrium canonical distributions weighted by a function P(beta) of the intensive thermodynamic quantity beta conjuga...

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...

The commonly adopted scaling for the maximum achievable plasma density in tokamak fusion devices, the so-called 'Greenwald limit', refers to the line-averaged density along a central chord and depends only on the average plasma current density. However, the Greenwald limit has been exceeded in tokamak experiments in the case of peaked density profi...

Recent theoretical studies of the reversed-field pinch (RFP) have demonstrated the possibility of stimulating new quasi-single helicity (QSH) regimes by allowing a small helical deformation of the magnetic boundary. In particular, QSH states based on non-resonant helicities are predicted to be more resilient to magnetic stochasticity induced by sec...

A limit for the edge density, ruled by radiation losses from light impurities, is established by a minimal cylindrical magneto-thermal equilibrium model. For ohmic tokamak and reversed field pinch the limit scales linearly with the plasma current, as the empirical Greenwald limit. The auxiliary heating adds a further dependence, scaling with the 0....

The reversed field pinch (RFP) device RFX-mod features strong internal transport barriers when the plasma accesses states with a single dominant helicity. Such transport barriers enclose a hot helical region with high confinement whose amplitude may vary from a tiny one to an amplitude encompassing an appreciable fraction of the available volume. T...

In inhomogeneous environments several expressions for the flux of a diffusing quantity may apply--from Fick-Fourier's to Fokker-Planck's--depending upon the system studied. The integro-differential Master Equation (ME) provides a fairly generic framework for describing the dynamics of arbitrary systems driven by stochastic rules. Diffusive dynamics...

The RFX-mod device is operated both as a reversed field pinch (RFP), where advanced regimes featuring helical shape develop, and as a tokamak. Due to its flexibility, RFX-mod is contributing to the solution of key issues in the roadmap to ITER and DEMO, including MHD instability control, internal transport barriers, edge transport and turbulence, i...

The first part of this work reviews the algebraic matricial approach to transport data inversion. It works for the convection–diffusion transport equation used for periodic signals and provides a formally exact solution, as well as a quantitative assessment of error bars. The standard methods of reconstruction infer the diffusivity D and pinch V by...

DOI:https://doi.org/10.1103/PhysRevLett.112.159901

A long-standing puzzle in fusion research comes from experiments where a sudden peripheral electron temperature perturbation is accompanied by an almost simultaneous opposite change in central temperature, in a way incompatible with local transport models. This Letter shows that these experiments and similar ones are fairly well quantitatively repr...

Experiments featuring fast heat propagation, or so called "non-local" transport, were a puzzle for almost two decades. However recently it was shown, and it is recalled here, that a collective ideal MHD response of the plasma provides a quantitative agreement with these experiments, whereas transport plays just a secondary role. Then this work revi...

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 linea...

Microtearing modes are an important drive of turbulent heat transport in present-day fusion plasmas. We investigate their linear stability under very-low collisionality regimes, expected for the next generations of devices, using gyrokinetic and drift-kinetic approaches. At odds with current opinion, we show that collisionless microtearing instabil...

This contribution focuses on 3D nonlinear MHD modeling and nonlinear gyrokinetic tools for studies of helical configurations in the Reversed Field Pinch regime. We present first 3D nonlinear visco-resistive MHD toroidal simulations with the PIXIE3D code. Stationary helical RFP regimes are found to spontaneously develop in toroidal geometry, similar...

The results of the experimental analysis of quasi-coherent magnetic activity during quasi single helicity (QSH) states of a reversed field pinch plasma are presented. A system of in vessel coils, measuring the fluctuations of the three components of the magnetic field at the edge of the RFX-mod plasma column, allows to determine the spectral proper...

DOI:https://doi.org/10.1103/PhysRevLett.109.129901

The estimate of coefficients of the Convection-Diffusion Equation (CDE) from experimental measurements belongs in the category of inverse problems, which are known to come with issues of ill-conditioning or singularity. Here we concentrate on a particular class that can be reduced to a linear algebraic problem, with explicit solution. Ill-condition...

The calculation of transport profiles from experimental measurements belongs in the category of inverse problems which are known to come with issues of ill-conditioning or singularity. A reformulation of the calculation, the matricial approach, is proposed for periodically modulated experiments, within the context of the standard advection-diffusio...

ITG modes have been found to be rarely unstable in reversed-field pinch pure-hydrogen plasmas, close to marginality only in correspondence to the transport barriers arising during single helicity states. We revisit this topic considering more realistic multi-species plasmas, to understand the possible excitement of ITG or impurity-drift instabiliti...

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 inter...

This paper presents the most recent results in theoretical/numerical studies on the physics of the quasi-helical regime in reversed field pinch (RFP) configurations. Such regime systematically characterizes RFX-mod experiments at high currents (Ip > 1.2 MA), producing clear internal electron transport barriers. Several approaches, ranging from a ma...

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...

The core region of high-current RFX-mod reversed field pinch plasmas spontaneously organizes into high-temperature helical flux tubes with almost intact magnetic surfaces. Accordingly, radial diffusion due to magnetic chaos is expected to be vanishingly small. Notwithstanding this, the temperature profile within these structures is flat, suggesting...

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 config...

We study the role of trapped electrons in the anomalous transport induced by microinstabilities in the Reversed Field Pinch. This investigation is justified by the fraction of trapped particles present in the core, which is almost the same as in the tokamak. ootnotetextM. Gobbin et al., J. Plasma Fusion Res. Series 8, 1147 (2009) This fraction turn...

In the reversed field pinch RFX-mod strong electron temperature gradients develop when the single-helical-axis regime is achieved. Gyrokinetic calculations show that in the region of the strong temperature gradients microtearing instabilities are the dominant turbulent mechanism acting on the ion Larmor radius scale. The quasilinear evaluation of t...

Present-days Reversed Field Pinches (RFPs) are characterized by quasi-laminar magnetic configurations in their core, whose boundaries feature sharp internal transport barriers, in analogy with tokamaks and stellarators. The abatement of magnetic chaos leads to the reduction of associated particle and heat transport along wandering field lines. At t...

We present here a study about the stability of ion-temperature-gradient drift turbulence in the quasi-single-helicity regime of RFX-mod reversed field pinch (RFP) using the TRB fluid electrostatic turbulence code. Our results suggest that present-day RFP plasmas are marginally stable against this kind of turbulence. The onset of the instability may...

We present here a study about the stability of Ion-Temperature-Gradient drift turbulence in the Quasi-Single-Helicity regime of RFX-mod Reversed Field Pinch (RFP) using the TRB fluid electrostatic turbulence code. Our results suggest that present-days RFP plasmas are marginally stable against this kind of turbulence. The onset of the instability ma...

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 t...

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 t...

The Reversed Field Pinch Experiment RFX-mod is characterized by a complex edge magnetic topology which is correlated with strong pressure gradients. It features also the presence of coherent electron pressure structures, resulting from nonlinear couplings between electron density, temperature and magnetic field. In this work we present measurements...

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 k...

In the edge region of fusion devices coherent structures (blobs) are commonly observed. In order to investigate their evolution and the possible driving mechanisms, we studied the relationship between the size of the coherent structures and the local characteristic length Lp of the edge electron pressure profile Pe(r), together with the effect of m...

The high-frequency range of power spectra of turbulent fluctuating quantities measured at the edge of magnetized plasmas displays a variety of trends: from power laws with different spectral indices to exponential. We propose a model able to account for the whole phenomenology simply by tuning the distribution in the duration of the signal spikes....

In the quest for new energy sources, the research on controlled thermonuclear fusion1 has been boosted by the start of the construction phase of the International Thermonuclear Experimental Reactor2 (ITER). ITER is based on the tokamak magnetic configuration3, which is the best performing one in terms of energy confinement. Alternative concepts are...

The nature of plasma edge turbulence has been studied in the Reversed Field Pinch (RFP) RFX-mod, making use of a Gas Puffing Imaging (GPI) diagnostic, with high time (2MHz) and space (5mm) resolution. The edge turbulence has been characterized in terms of toroidal phase velocity of fluctuations, vϕ, of the width of emission structures, 2σ, and of t...

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 cu...

Probability Distributions Functions (PDFs) of fluctuations of plasma edge parameters are skewed curves fairly different from normal distributions, whose shape appears almost independent of the plasma conditions and devices. We start from a minimal fluid model of edge turbulence and reformulate it in terms of uncoupled Langevin equations, admiting a...

Reversed field pinches (RFPs) share with tokamaks and stellarators the experimental evidence of an upper limit for the maximum value of the electron density at which they can operate. Above a certain density level, well described by the Greenwald law for tokamaks and RFPs, a radiative collapse with strong plasma cooling is observed, predominantly d...

In this paper we present a statistical study of edge fluctuations taken with the Gas Puffing Imaging (GPI) diagnostics. We carry out a comparison of GPI signal from an extensive database including four devices (two Tokamaks and two Reversed Field Pinches). The data are analyzed in terms of their statistical moments Skewness and Kurtosis, as done in...

In this work we investigate the origin of the parabolic relation between skewness and kurtosis often encountered in the analysis of experimental time-series. We argue that the numerical values of the coefficients of the curve may provide informations about the specific physics of the system studied, whereas the analytical curve per se is a fairly g...

The Fokker-Planck equation (FPE) is a quite flexible tool for experimental and numerical data analysis. However, advective-diffusive effects may compete with a curvature pinch or the impact of a localized source to determine profiles of transported quantities. Depending on the statistics of interest and/or on the radial extension of the transport p...

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-organi...

The negative ion production and extraction are critical aspects of the neutral beam injector for ITER, so that improvements in their physical understanding are expected to contribute to the optimization of the injector design. A self-consistent 2-D model of the formation and acceleration of a beam of negative ions (including the sheath) is presente...

The presence and role of trapped particles in the Reversed Field Pinch (RFP) configuration is considered, with an estimate of their relative population and a description of the characteristic trajectories, in particular for the RFX-mod [1] geometry. The particle's orbit scale lengths (e.g. banana width, mean free path) are classified both for ions...

The edge turbulence of different plasma fusion devices (Tokamaks and Reversed Field Pinches) is studied by means of the Gas Puff Imaging (GPI) diagnostic and Langmuir probes. It is shown that the Probability Density Functions (PDF) of edge fluctuations depend on the time scales of the fluctuations themselves: they are clearly non-Gaussian for small...

The spatial scales of edge turbulence structures and the corresponding toroidal phase velocity vphi are routinely measured in RFX-mod with a Gas Puffing Imaging (GPI) diagnostic for the whole plasma pulse duration and in all plasma conditions without the frozen turbulence hypothesis. A new Thermal Helium Beam (THB) diagnostic has been coupled to th...

Quasi Single Helicity in RFX-mod. In the Reversed Field Pinch (RFP) configuration the plasma can access regimes in which a single tearing mode dominates the magnetic perturbations spectrum (Quasi Single Helicity state, QSH) [1]. Thermal measurements performed in the RFX-mod experiment [2] (Padua, Italy) during QSH states have shown clear helical st...

In inhomogeneous environments, the correct expression of the diffusive flux is often not given by the Fick's law $\Gamma = - D \nabla n $. The most general hydrodynamic equation modelling diffusion is indeed the Fokker-Planck Equation (FPE). The microscopic dynamics of each specific system may affect the form of the FPE, either establishing connect...

The Fokker-Planck equation, applied to transport processes in fusion plasmas, can model several anomalous features, including uphill transport, scaling of confinement time with system size, and convective propagation of externally induced perturbations. It can be justified for generic particle transport provided that there is enough randomness in t...

A common feature of magnetized plasmas is the presence of fluctuations, which can lead to fully developed turbulence. Often large events—called bursts—emerge from the remaining low-level turbulence, giving an intermittent character to fluctuations; namely the statistical properties of fluctuations are found to depend on the temporal scale over whic...

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...

Particle transport in toroidal confinement devices is often described in terms of a diffusion constant and an inward pinch velocity [1]: this phenomenological description can be justified by a probabilistic approach (random walk) that simplifies the particle dynamics when the orbits are small enough compared to the system size. This results in a di...

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 i...

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...

Transport in toroidal devices is usually described as the sum of diffusion and convection, gamma= - D ∇n + v .n, and v is interpreted as the spatial variation D/r of D. When the magnetic field is chaotic and it is near the stochastic threshold (as it is the case for the reversed-field pinch, RFP), the assumption that particles moving along chaotic...

Plasma density fluctuations in the edge plasma of the RFX-mod device are measured through the Gas Puffing Imaging Diagnostics. Statistical features of the signal are quantified in terms of the Probability Distribution Function (PDF), and computed for several kinds of discharges. The PDFs from discharges without particular control methods are found...

Collisional radiative models (CRM) are needed to simulate experimental line brightnesses and emissivities from fusion devices. CRM are built for H-like and He-like carbon and oxygen ions, following a detailed review of the published literature on the required atomic data (including both collision rate coefficients and atomic transition probabilitie...

The statistical properties of the intermittent signal generated by a recent model for self-organized criticality are examined. A successful comparison is made with previously published results of the equivalent quantities measured in the electrostatic turbulence at the edge of a fusion plasma. This result reestablishes self-organized criticality as...

The superstatistics approach recently introduced by Beck [C. Beck and E.G.D. Cohen, Physica A 322, 267 (2003)] is a formalism that aims to deal in a unifying way with a large variety of complex nonequilibrium systems, for which spatio-temporal fluctuations of one intensive variable (“the temperature” 1/β) are supposed to exist. The intuitive ex...

The turbulent fluctuations of the edge plasma in fusion experiments are characterised by large-amplitude events in the plasma potential and pressure. These electrostatic events are considered the main cause of anomalous particle transport both in RFP (1) and tokamak (2) experiments and so a great effort is concentrated on their investigation. To th...

In the reversed Field Pinch Experiment RFX-mod a Gas Puffing Imaging Diagnostic (GPID) is used to investigate the turbulence of the edge plasma. The system consists of a gas puffing nozzle and 32 optical channels to measure the HeI (668 nm) line emission from an area normal to the main magnetic field. A method based on Fourier expansion is develope...

The classical Tonks-Langmuir one dimensional (1D) free fall ion model of sheath is adapted and generalized to two dimensional (2D) geometries, giving a rigorous base to ion tracing codes. The reduction of integro-differential equations to a coupled system of partial differential equation (PDE), suitable for 2D applications, is performed. The distin...

The probability distribution function of plasma density fluctuations at the edge of fusion devices is known to be skewed and strongly non-Gaussian. The causes of this peculiar behavior are, up to now, largely unexplored. On the other hand, understanding the origin and the properties of edge turbulence is a key issue in magnetic fusion research. In...

Transport of field lines is studied for a realistic model of magnetic field configuration in a Reversed Field Pinch. It is shown that transport is anomalous, i.e., it cannot be described within the standard diffusive paradigm. To fit numerical results we present a transport model based upon the Continuous Time Random Walk formalism. Fairly good qua...

In the Reversed Field Pinch RFX the upper boundary of the density operating space matches fairly well the Greenwald limit. Typically reaching the ceiling procures a soft termination; hard terminations may however occur at high currents (>0.9 MA) in presence of particularly large error fields. Radiation losses are always a relatively small fracti on...

RFX has been recently modified to improve its capability of controlling different MHD phenomena by means of fast, feedback controlled amplifiers and distributed radial field inductors. The paper, after summarizing the principal results obtained in the past by means of active control of magnetic fields in RFX, describes the recent modifications to t...

The results of an extensive investigation of electrostatic and magnetic turbulence in the edge region of two European Reversed Field Pinch (RFP) experiments EXTRAP-T2R and RFX are reported. In both experiments particle transport is driven by turbulence and almost 50% of the particle losses is due to coherent structures emerging from the fluctuation...

Negative ion source for spallation sources or neutral beam injectors (NBI) for tokamaks requires carefully matched electric and magnetic fields in the beam formation area due to the presence of three species of particles: the collisional and fully magnetized electrons; the slightly magnetized positive ions; the negative ions, formed within few cm f...

Confinement in the Reversed Field Pinch (RFP) configuration is la rgely determined, at least in the inner plasma region, by magnetic perturbations w hose origin is well described by visco-resistive MHD (1). These fluctuations are rec ognized to be responsible for the RFP sustainment through dynamo action but, at the sa me time, they lead to stochas...

The Probability Distribution Function (PDF) Pn(n) of the particle density at the edge of several magnetic fusion devices, including tokamaks, stellarators, and linear devices, is known to be strongly non-gaussian. In this paper we present experimental results from RFX Reversed Field Pinch (RFP) [Rostagni G 1995 Fusion Eng. Design 25 301], confirmin...

The Probability Distribution Function (PDF) Pn(n) of the particle density at the edge of several magnetic fusion devices, including tokamaks, stellarators, and linear devices, is known to be strongly non-gaussian. In this paper we present experimental results from RFX Reversed Field Pinch [G. Rostagni, Fus. Eng. Design 25, 301 (1995)], confirming t...

In this paper we elaborate on the recently proposed superstatistics formalism [C. Beck, E.G.D. Cohen, Physica A 322 (2003) 267], used to interpret unconventional statistics. Their interpretation is that unconventional statistics in dynamical systems arise as weighted averages of the ordinary statistics obeyed by these systems over a statistical dis...

The equilibrium of a finite-beta cylindrical RFP plasma in the presence of saturated-amplitude tearing modes is investigated. The singularities arising from the perturbative analysis of the MHD force balance equation JxB=grad(p) are resolved through a proper regularization of the cylindrical symmetric component of the pressure and parallel current...

In this work we develop the recently suggested concept of superstatistics [C. Beck and E.G.D. Cohen, Physica A 322, 267 (2003)], face the problem of devising a viable way for estimating the correct statistics for a system in the absence of sufficient knowledge of its microscopical dynamics, and suggest to solve it through the maximum-entropy princi...

The results of an extensive study on transport mechanisms and on improved confinement scenarios in RFX are reported. The scaling of the thermal conductivity in the core with the Lundquist number indicates that the magnetic field in this region is not fully stochastic, as proved by the existence of thermal barriers observed in single helicity config...

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 plas...

In this work we review the classical recipe for estimating partial cross sections for electron capture into selected energy levels within the Classical Trajectory Monte Carlo (CTMC) method [R.L. Becker and A.D. MacKellar, J. Phys. B: At. Mol. Phys. 17 (1984) 3923], and point to a deficiency of the method when applied to the CTMC in its r-version, a...

The radial electric field Er at the edge of the RFX plasma changes sign, from negative (inward) to positive, when an m=0 perturbation is externally applied. Similar behaviour had been previously observed in presence of wall locked (m=1) modes, whereby the much stronger plasma–wall interaction made data interpretation more complex. The findings are...

A coherence-based, or interferometric approach to spectral analysis of charge-exchange recombination (CXR) emission radiation from high-temperature plasma probed or heated using energetic neutral beams, offers a number of advantages over wavelength-domain instruments. The spectral-line shift and broadening are obtained from measurements of the spec...

In this letter, we present classical trajectory Monte Carlo calculations for single- and multiple-electron ionization of argon atoms and ions in the threshold region. We are able to recover the Wannier exponents, alpha, for the power-law behaviour of the cross section, sigma, versus excess energy: the exact value of the exponent, as well as the exi...

Tsallis' non-extensive statistical mechanics is claimed to be the correct tool to describe the behaviour of low-dimensional dissipative maps at the edge of chaos. Indeed, many different approaches confirm that, for those systems, the evolution is governed by power-laws, not exponential, trends; this coincides with predictions from generalized therm...