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This paper concerns the kinematic viscosity in reversed-field pinch fusion plasmas, including both the study of numerical magneto-hydrodynamics (MHD) simulations and the analysis of RFX-mod experimental data. In the first part, we study the role of non-uniform time-constant radial viscosity profiles in 3D non-linear visco-resistive MHD simulations. The new profiles induce a moderate damp (for the velocity field) and a correspondent enhancement (for the magnetic field) of the spectral components resonating in the regions where the viscosity is higher. In the second part, we evaluate the kinematic viscosity coefficient on a wide database of RFX-mod shots according to the transport theories of Braginskii (considering parallel, perpendicular and gyro viscosity coefficients), considering the action on viscosity of ITG modes (ion temperature gradient) and according to the transport theory of Finn. We then exploit the comparison with the visco-resistive MHD simulations (where the visco-resistive dissipation rules the MHD activity) to show that the classical Braginskii perpendicular viscosity produces the best agreement between simulations and data, followed by the Braginskii gyro-viscosity.

The properties and possible triggering mechanisms of Alfvén waves in the reversed-field pinch (RFP) and circular tokamak configurations are discussed in the framework of nonlinear 3D magnetohydrodynamics (MHD) modeling. Numerical simulations are performed with the SpeCyl code (Cappello and Biskamp 1996 Nucl. Fusion) that solves the equations of the viscoresistive MHD model in cylindrical geometry. Configurations with increasing levels of complexity are analyzed. First, single-wave numerical solutions are compared with analytical ones in the simplest case of a uniform axial magnetic field: an excellent agreement is obtained for both the shear Alfvén wave (SAW) and the compressional Alfvén eigenmodes (CAEs). Then, tokamak and RFP configurations are studied. Phenomena such as phase mixing of SAW, resonant absorption of CAEs and the appearance of the global Alfvén eigenmode are described. Finally, the fully 3D RFP case with typical sawtoothing activity is investigated, showing for the first time in nonlinear RFP simulations the excitation of Alfvén waves by magnetic reconnection events. The modeling results appear to be consistent with the experimental characterization of Alfvénic activity observed in RFX-mod.

The reversed-field pinch (RFP) is a configuration for the magnetic confinement of fusion plasmas, in which most of the toroidal field is generated by the plasma itself through a self-organized dynamo process, instead of being produced by external coils as in the tokamak. In the RFP, the nonlinear saturation of resistive-kink/tearing modes brings to the spontaneous emergence of helical states with improved confinement. This is observed both in nonlinear magnetohydrodynamics (MHD) modelling [1] and in RFP devices, especially at high current [2,3]. A major advance in the predictive capability of nonlinear MHD modelling for RFP plasmas was made possible by allowing helical perturbations of the radial magnetic field at the plasma boundary, which was suggested by analytical study of helical equilibrium equations [4]. A proper use of helical magnetic perturbations (MPs) in MHD modelling allowed to obtain experimental-like helical states [5] and to predict new helical states with chosen helical twist, successfully produced in RFX-mod [6]. The amplitude of the helical component and sawtooth frequency can be "tuned" as well, thus opening new routes to configuration optimization in several respects (ion heating, thermal and fast particle transport processes). Here, we discuss the effect of a more realistic magnetic boundary recently included in the modelling: a thin resistive shell and a vacuum layer between the plasma and the ideal shell are considered, similarly as in [7,8]. We present two main results: 1) The decrease of secondary modes by increased shell-plasma proximity (see Figure 1). This is of interest in view of the upgraded RFX-mod2 device (starting operation in 2021), in which the shell-plasma proximity will change from b/a=1.11 to b/a=1.04 [9]. 2) With a proper choice for the resistivity of the thin shell at the plasma boundary, helical states do emerge in a self-consistent way, as in the experiment, without the need to impose a fixed helical MP (see Figure 2). Finally, further extensions of the realistic boundary implementation, in order to take into account a double resistive shell and an active feedback control system, will be discussed.

The reversed-field pinch (RFP) is a configuration for the magnetic confinement of fusion plasmas, in which most of the toroidal field is generated by the plasma itself through a self-organized dynamo process, instead of being produced by external coils as in the tokamak. In the RFP, the nonlinear saturation of resistive-kink/tearing modes brings to the spontaneous emergence of helical states with improved confinement. This is observed both in nonlinear magnetohydrodynamics (MHD) modelling [1] and in RFP devices, especially at high current [2]. A major advance in the predictive capability of nonlinear MHD modelling for RFP plasmas was made possible by allowing helical perturbations of the radial magnetic field at the plasma boundary [3]. A proper use of helical magnetic perturbations (MPs) in MHD modelling allowed to obtain experimental-like helical states [4] and to predict new helical states with chosen helical twist, successfully produced in RFX-mod [5].Here, we describe a further refinement of the magnetic boundary modelling. Instead of applying fixed helical MPs, we study the helical self-organization in the presence of a thin resistive shell and a vacuum layer between the plasma and the ideal shell. Two main results are discussed. On the one hand, by varying the distance between the plasma and the ideal wall it is possible to provide a nonlinear estimate for the decrease of secondary modes by increased shell-plasma proximity. This is of interest in view of the upgraded RFX-mod2 device (starting operation in 2020), in which the shell-plasma proximity will change from b/a=1.11 to b/a=1.04 [6]. On the other hand, it is observed that with a proper choice for the resistivity of the conducting shell at the plasma boundary, experimental-like helical states do emerge in a self-consistent way, as in the experiment, without the need to impose a fixed helical MP. Finally, further extensions of the realistic boundary implementation, in order to take into account a double resistive shell and a feedback control system, will be discussed.

This paper deals with helical self-organization in current-carrying toroidal pinches for the magnetic confinement of fusion plasmas. We perform our study in the framework of 3D nonlinear visco-resistive magnetofluid modelling, where a large set of simulations is now available. A global picture is derived about how visco-resistive transport coefficients and magnetic boundary conditions rule the self-organized helical states for the reversed-field pinch configuration. Decreasing visco-resistive dissipation causes a transition from steady ohmic helical equilibria to intermittent states (sawtoothing activity), while selected helical magnetic perturbations applied at the boundary favor steady global quasi-helical solutions. The sawtoothing frequency decreases together with visco-resistive dissipation, while sawtoothing amplitude decreases when applying non-resonant magnetic perturbations. Simulations of the tokamak configuration allow us to draw a tight parallelism with reversed-field pinches: a similar role of dissipation and magnetic boundary conditions on the dynamics of the internal kink mode is found, with decreasing sawtoothing frequency and amplitude by decreasing dissipation and by applying suitable helical boundary conditions. Magnetic chaos healing is the topological feature of the transition from intermittent to quasi-quiescent helical states in reversed-field pinches. Bundles of Lagrangian coherent structures (LCS) in the weakly stochastic region surrounding the helical core constitute the skeleton of chaos healing, and behave as barriers to the transport of magnetic field lines. In this work, they are detected during the whole temporal evolution and it is proved that they can withstand the nonlinear dynamics even during sawtoothing activity. Furthermore, we show that LCS are connected to regions with strong gradients of the connection length of magnetic field lines to the edge. This provides a further indication of their possible role in the formation of electron temperature barriers. As a final result it is shown that a reasonable value of plasma rotation can further enhance the intensity of the dominant helical mode.

Nonlinear MHD modeling of toroidal pinch configurations (reversed-field pinch and tokamak) for hot plasma confinement describes several features of the helical self-organization, observed in both reversed-field pinches and tokamaks. It can also give a hint on why transport barriers are formed, by far one of the more interesting observations in experiments. The research work will be summarized in two points. The first one regards the recent successful technique to "channel" reversed-field pinches into a chosen macroscopic helical shape through the use of small edge magnetic perturbations. Helical self-organization is predicted in nonlinear MHD modeling, successfully tested in RFX-mod experiment in Padova and awaits further exploration in the updated device RFX-mod2. The upgraded machine, soon starting operation, is characterized by a shell-plasma proximity reduction, likely improving feedback coils action, thus favoring the study of the beneficial properties of helical states built upon helixes not resonating with the safety factor profile. The second point regards the MHD description of the process of formation of transport barriers by macroscopic magnetic chaos healing, which allows the emergence of hidden Lagrangian structures acting as barriers to the transport. The radial position of such structures is observed to correspond to higher gradients of magnetic field lines connection length to the edge and to higher temperature gradients, computed by numerically solving the anisotropic heat flow equation. Comparison with thermal measurements in RFX-mod will also be offered.

The reversed-field pinch (RFP) is a configuration for the magnetic confinement of fusion plasmas, in which most of the toroidal field is generated by the plasma itself through a self-organized dynamo process, instead of being produced by external coils as in the tokamak. In the RFP, the nonlinear saturation of resistive-kink/tearing modes brings to the spontaneous emergence of helical states with improved confinement. This is observed both in nonlinear magnetohydrodynamics (MHD) modelling [1] and in RFP experiments, especially at high current [2,3]. A major advance in the predictive capability of nonlinear MHD modelling for RFP plasmas was made possible by allowing helical perturbations of the radial magnetic field at the plasma boundary, assuggested by analytical calculations based on helical equilibrium equations[4]. A proper use of helical magnetic perturbations (MPs) in MHD modelling allowed to obtain experimental-like helical states [5] and to predict new helical states with chosen helical twist, successfully produced in RFX-mod [6]. Here, we describe a further refinement of the magnetic boundary modelling. We study the helical self-organization in the presence of a thin resistive shell at the plasma boundary r=a, surrounded by a vacuum layer and an ideal shell at r=b. The new magnetic boundary is implemented in the SpeCyl code [7] in a similar way as in Refs. [8,9]. Two main results are discussed. On the one hand, by varying the distance between the plasma and the ideal shell it is possible to provide a nonlinear estimate for the decrease of secondary modes by increased shell proximity to the plasma. This is of interest in view of the upgraded RFX-mod2 device (starting operation in 2021), in which the shell proximity will change from b/a=1.11 to b/a=1.04 [10]. Based on nonlinear MHD modelling,a factor of 2 reduction of the edge radial magnetic field is expected going from RFX-mod to RFX-mod2, with the beneficial consequence of a milder plasma-wall interaction. On the other hand, it is observed that with a proper choice for the resistive diffusion time of the thin shell at r=a, helical states do emerge in a spontaneous and systematic way, as in the experiment, without the need to impose a fixed helical MP. Finally, further extensions of the realistic boundary implementation, in order to take into account a double resistive shell and a feedback control system, will be discussed.

Collisional particle transport is examined in several toroidal plasma devices in the presence of perturbations typical of modes leading up to a disruption, of saturated tearing modes, or of unstable Alfven modes. The existence of subdiffusive transport for electrons is found to occur in some cases at very low mode amplitudes and to also exist even for ions of high energy. Orbit resonances can produce long time correlations and traps for particle trajectories at perturbation amplitudes much too small for the orbits to be represented as uniformly chaotic. The existence and nature of subdiffusive transport is found to depend on the nature of the mode spectrum and frequency as well as the mode amplitudes.

The tearing mode (TM) is a resistive instability that can arise in magnetically confined plasmas. The TM can be driven unstable by the gradient of the plasma current. When the mode grows it destroys the magnetic field symmetry and reconnects the magnetic field in the form of a so-called magnetic island. The TMs are inherent to a type of device called the reversed-field pinch (RFP), which is a device for toroidal magnetic confinement of fusion plasmas. In the RFP, TMs arise at several resonant surfaces, i.e. where the field lines and the perturbation have the same pitch angle. These surfaces are closely spaced in the RFP and the neighboring TM islands can overlap. Due to the island overlap, the magnetic field lines become tangled resulting in a stochastic magnetic field, i.e. the field lines fill a volume instead of lying on toroidal surfaces. Consequently, a stochastic field results in an anomalously fast transport in the radial direction. Stochastic fields can also arise in other plasmas, for example, the tokamak edge when a resonant magnetic perturbation (RMP) is applied by external coils. This stochastization is intentional to mitigate the edge-localized modes. The RMPs are also used for control of other instabilities. Due to the finite number of RMP coils, however, the RMP fields can contain sidebands that decelerate and lock the TMs via electromagnetic torques. The locking causes an increased plasma-wall interaction. And in the tokamak, the TM locking can cause a plasma disruption which is disastrous for future high-energy devices like the ITER. In this thesis, the TM locking was studied in two RFPs (EXTRAP T2R and Madison Symmetric Torus) by applying RMPs. The experiments were compared with modern mode-locking theory. To determine the viscosity in different magnetic configurations where the field is stochastic, we perturbed the momentum via an RMP and an insertable biased electrode. In the TM locking experiments, we found qualitative agreement with the mode-locking theory. In the model, the kinematic viscosity was chosen to match the experimental locking instant. The model then predicts the braking curve, the short timescale dynamics, and the mode unlocking. To unlock a mode, the RMP amplitude had to decrease by a factor ten from the locking amplitude. These results show that mode-locking theory, including the relevant electromagnetic torques and the viscous plasma response, can explain the experimental features. The model required viscosity agreed with another independent estimation of the viscosity. This showed that the RMP technique can be utilized for estimations of the viscosity. In the momentum perturbation experiments, it was found that the viscosity increased 100-fold when the magnetic fluctuation amplitude increased 10-fold. Thus, the experimental viscosity exhibits the same scaling as predicted by transport in a stochastic magnetic field. The magnitude of the viscosity agreed with a model that assumes that transport occurs at the sound speed -- the first detailed test of this model. The result can, for example, lead to a clearer comparison between experiment and visco-resistive magnetohydrodynamics (MHD) modeling of plasmas with a stochastic magnetic field. These comparisons had been complicated due to the large uncertainty in the experimental viscosity. Now, the viscosity can be better constrained, improving the predictive capability of fusion science. QC 20171122

Self-organized helical states are a ubiquitous feature in astrophysical and in current carrying hot magnetic-fusion plasmas. In the latter, self-organized helical states are observed locally in the core of the tokamak - associated with strong 3D magnetohydrodynamics activity - and globally in reversed-field pinch (RFP) plasmas. In RFP helical states spontaneously develop from a dominant resistive-kink/tearing mode, creating a hot central region bounded by transport barriers. In this contribution, we first report a milestone in magnetohydrodynamics modeling of hot RFP plasmas [1, 2] and experimental observation of helical states, namely, we show that experiments in RFX-mod confirm the nonlinear fluid modelling prediction of previously unobserved self-organized helical states. The key element is the use of a small edge magnetic perturbation [3, 4], with a helical periodicity different than the spontaneous dominant one observed in standard discharges, which can convey its helical pitch to the whole plasma column. As a second result, we find a higher magnetic order in numerical simulations where magnetic perturbations are applied with a non-resonant helical twist. In such new states we observe a broader zone where magnetic field lines lie on conserved magnetic surfaces and a reduction of magnetic field-lines transport with respect to standard regimes. Interestingly and counterintuitively, such new global helical regimes are obtained when exploiting non-resonant Resistive Wall Modes, usually deemed dangerous for plasma discharges. First examples of experimental confirmation of such dynamical and topological results are described. As a third result, we introduce a novel technique which reveals confining structures, Cantori sets, in the shadow of the KAM tori [5]. We will also introduce preliminary results from the numerical solution of the time-dependent, anisotropic temperature transport equation [6] applied to such new helical regimes coming from the MHD simulation codes. The novel possibility of changing the global helical twist of the plasma column, and therefore its safety factor, open new opportunities to deepen the theoretical interpretation of transport barrier formation and sustainment in hot-magnetic fusion plasma devices, including tokamaks and stellarators.

Magnetic islands are spontaneously present in the reversed-field pinch (RFP) and the stellarator edge, and they are produced via magnetic perturbations (MP) in the tokamak edge for various purposes (ideal mode stabilization, ELM suppression, etc.). In a chaotic edge, the ion and electron drifts yield a predominantly electron driven radial diffusion when approaching the island X-point, while ion diffusivities are generally an order of magnitude smaller. This results in a strong, positive radial electric field Er > 0 pointing outward the island O-point. This mechanism has been often neglected on the grounds that electron drifts are small [1], but this is not the case in a chaotic environment. The electric field is associated with a convective cell, which can dominate transport within the island with respect to the ordinary chaotic radial diffusion. The convective cell has, at a first approximation, the same symmetry m/n as the parent island. An analytical model for the plasma potential is implemented in the Hamiltonian, guiding-centre code ORBIT [2], and analyses of the ambipolar flow/radial electric field (in RFX-mod [3] and TEXTOR devices [4]) show that both ion- and electron-dominated transport regimes can exist, known as ion and electron roots in stellarators. This gives the hint that localized ECRH/ICRH heating can modify the ambipolar solution and therefore greatly influence transport near the island. In addition to this, recent results [5] show that the electrostatic response to the island has symmetry m/n only at a first approximation: higher harmonics (m?k)/n, k=1,2..., with the same n, toroidally couple to the base mode, influencing the electrostatic and kinetic response to the MP. We will show that this phenomenon is deeply rooted in the magnetic topology itself, by using the standard analysis of connection lengths, plus a more sophisticated metric, such as the Poincaré recurrence time analysis.

Magnetically confined fusion (MCF) plasmas are typically subject to several unstable modes. The growth of one mode can limit the plasma energy confinement and might cause a termination of the plasma. Externally applied resonant magnetic perturbations (RMPs) are used to control and to mitigate some of the unstable modes. Examples are, mitigation of edge localized modes and steering of neoclassical tearing mode position for stabilization by electron cyclotron current drive. Consequently, use of RMPs are considered necessary in planned future fusion machines. There are however negative consequences, the RMP interaction with a tearing mode (TM) of the same resonance can cause deceleration of the TM and possibly wall-locking. If a TM is non-rotating relative the machine-wall, it can grow and degrade fusion plasma performance and lead to a plasma disruption. Thus, all fusion confinement machines want to avoid wall-locked modes. Resonant magnetic fields can also be present in the form of machine-error-fields, which can produce the same effects. Clearly, it is of importance to understand the TM-RMP interaction. Typically, the modes with long wavelength are described by magnetohydrodynamic (MHD) theory. Considering the finite plasma resistivity, MHD predicts a mode that tears and reconnects magnetic field lines, called a tearing mode (TM). TMs occur at surfaces where the magnetic field lines close on themselves after a number of (m) toroidal and (n)poloidal turns. These surfaces are resonant in the sense that magnetic field and helical current perturbation has the same helicity, which minimize stabilizing effect of magnetic field line bending. In this thesis, the mechanisms of TM locking and unlocking due to external resonant magnetic perturbations (RMPs) are experimentally studied. The studies are conducted in two MCF machines of the type reversed-field pinch (RFP): EXTRAP T2R and Madison Symmetric Torus (MST). The studied machines exhibit multiple rotating TMs under normal operation. In EXTRAP T2R TM locking and unlocking are studied by application of a single harmonic RMP. Observations show that after the TM is locked, RMP amplitude has to be reduced significantly in order to unlock the TM. In similar studies in MST unlocking is not observed at all after turn-off of the RMP. Hence, in both machines, there is hysteresis in the locking and subsequent unlocking of a tearing mode. Results show qualitative agreement with a theoretical model of the TM evolution when subjected to an RMP. It is shown that the RMP cause a reduction of TM and plasma rotation at the resonant surface. The velocity reduction is opposed by a viscous torque from surrounding plasma. After TM locking, relaxation of the whole plasma rotation is observed, due to the transfer of velocity reduction via viscosity. This results in a reduced viscous resorting torque, which explains the observed hysteresis. The hysteresis is further deepened by the increase in amplitude of a locked mode. QC 20160111

The primary objective of fusion research is to realize a thermonuclear fusion power plant. The main method to confine the hot plasma is by using a magnetic field. The reversed-field pinch is a type of magnetic confinement device which suffers from variety of magnetohy- drodynamic (MHD) instabilities. A particular unstable mode that is treated in this work is the resistive wall mode (RWM), which occurs due to the current gradient in the RFP and has growth rates of the order of the magnetic diffusion time of the wall. Application of control engineering tools appears to allow a robust and stable RFP operation.A model-based approach to stabilize the RWMs is pursued in this thesis. The approach consists of empirical modeling of RWMs using a class of subspace identification methodology. The obtained model is then used as a basis for a model based controller. In particular the first experimental results of using a predictive control for RWM stabilization are obtained. It is shown that the formulation of the model based controller allows the user to incorporate several physics relevant phenomena along with the stabilization of RWM. Another use of the model is shown to estimate and compensate the inherent error field. The results are encouraging, and the methods appear to be generically useful as research tools in controlled magnetic confinement fusion. Fusionsforskningens primära mål är att förverkliga en ny typ av kraftverk baserade på termonukleär fusion. Den viktigaste metoden för att innesluta det heta plasmat är användandet av magnetfält. ”Reverserat-fält pinch” (RFP) är en typ av anläggning för magnetisk inneslutning av fusionsplasma som uppvisar ett flertal magneto-hydrodynamiska instabiliteter. En specifik instabil mod som behandlas i detta arbete är”resistiv-vägg” moden (RWM). Den orsakas av strömgradienten i RFPn och tillväxer med en tidskonstant som är av samma storleksordning som magnetfältets diffusionstid i det omgivande metallskalet. Tillämpning av verktyg från reglerteknikområdet förefaller tillåta en robust och stabil RFP drift. I detta arbete används ett modell-baserat tillvägagångssätt för kompensering av RWM. Det innefattar empirisk modellering av RWM med användning av ”subspace” system-identifieringsmetoder. Den erhållna modellen används sedan som grund för en modell-baserad regulator. De första experimentella resultaten från modell-prediktiv kompensering av RWM har erhållits. I detta arbete har också visats att formuleringen av den modellbaserade regulatorn tillåter användaren att integrera flera relevanta fysikaliska aspekter förutom RWM. Ytterligare en användning av modellen är för att göra uppskattning och kompensering av avvikelser i anläggningens magnetfält, så kallade fält-fel. Resultaten är uppmuntrande, och det förefaller som om de undersökta metoderna är allmänt användbara som verktyg för forskning om magnetisk inneslutning av fusionsplasma. QC 20170202

This paper reviews measurements of edge plasma turbulence in toroidal magnetic fusion devices with an emphasis on recent results in tokamaks. The dominant feature of edge turbulence is a high level of broadband density fluctuations with a relative amplitude delta n/n - 5-100%, accompanied by large potential and electron temperature. fluctuations. The frequency range of this turbulence is -10 kHz-1 MHz, and the size scale is typically -0.1-10 cm perpendicular to the magnetic field but many metres along the magnetic field, i.e. the structure is nearly that of 2D 'filaments'. Large intermittent bursts or 'blobs' are usually observed in the scrape-off layer. Diagnostic and data analysis techniques are reviewed and the main experimental results are summarized. Recent comparisons of experimental results with edge turbulence theory are discussed, and some directions for future experiments are suggested.

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 to be adequately described by a Gamma function, consistently with the recent results by Graves et al [J.P. Graves, et al, Plasma Phys. Control. Fusion 47, L1 (2005)]. On the other hand, pulses with external methods for plasma control feature modified PDFs. A first empirical analysis suggests that they may be interpolated through a linear combination of simple functions. An inspection of the literature shows that this kind of PDFs is common to other devices as well, and has been suggested to be due to the simultaneous presence of different mechanisms driving respectively coherent bursts and gaussian background turbulence. An attempt is made to relate differences in the PDFs to plasma conditions such as the local shift of the plasma column. A simple phenomenological model to interpret the nature of the PDF and assign a meaning to its parameters is also developed., Comment: 27 pages. Published in PPCF

A Thomson scattering diagnostic is used in the RFX reversed field pinch experiment to measure single pulse, multipoint electron temperature (T-e) profiles. Recent significant improvements have provided reliable and routine operation of the diagnostic. Custom developed CAMAC charge analog-to-digital converters have been introduced, which sample the plasma light 170 ns after the laser light and have greater sensitivity. The spectrometer configuration and the calibration procedure have been optimized. These upgrades have finally led to better fitted scattering spectra and more regular estimates of T-e profiles, allowing the measurement of temperatures as low as 20 eV. The introduction of a second spectrometer has recently added a further ten positions to the original ten point profile, resolving the often steep T-e edge gradient. On axis values are in good agreement with other T-e measurements from SXR diagnostics (either SiLi and double filter method). T-e profiles are typically rather flat, but some dependence on the plasma parameters, like density and pinch parameter, has been drawn. Significant T-e profile modifications have been observed during transient events like pulsed poloidal current drive and pellet injection. The diagnostic will be completed soon, allowing production of 27 point profiles, with the introduction of the third spectrometer. Double pulse operation of the laser is in progress. (C) 1999 American Institute of Physics. [S0034-6748(99)69401-1].

In the framework of adding new information to the reversed field pinch (RFP) confinement database, the radiation emitted by RFX plasmas has been investigated using an eight chord bolometric camera, whose detectors have been calibrated absolutely. From the experimental data the emissivity profiles have been reconstructed by means of a generalized tomography reconstruction algorithm. This analysis confirms that the radiation emitted in RFX is systematically concentrated at the edge. The dependence of the emitted power on the plasma density shows that the radiation increases approaching the high density regime, but it rarely goes beyond 30% of the input power for stationary discharges. This behaviour is strongly dependent on the concentration of impurities but, in any case, in RFX there is no evidence of disruptions. A simple local energy balance allows a preliminary evaluation of the radial heat flux profile to be obtained. These measurements indicate that an active impurity screening mechanism is acting in the edge and that transport is the major energy loss mechanism in RFX.

The work presented in this thesis is inserted in the field of the research on plasma physics conducted with magnetically confined devices, whose ultimate goal is the demonstration of the feasibility of the energy production through fusion reactions between nuclei of hydrogen isotopes. One of the major issues in the operation of a magnetically confined plasma, both in a present device and in a future reactor, is the presence in the plasma of other elements besides the main gas: the so called impurities. These originate mainly by the interaction of the hot plasma with the plasma facing materials, which can both be eroded and release atmospheric gases previously adsorbed. Once these impurities enters the plasma they get ionised and start emitting radiation through bremsstrahlung and atomic processes (line and recombination radiation). If impurities accumulate in the core plasma, where the temperature is highest, this can lead to a dramatic increase in radiation losses, drive radiative instabilities and dilute the plasma with negative consequences on plasma reactivity. In this regard it is extremely important to keep as low as possible the total impurity content and to control the impurity peaking, i.e. where impurities accumulate. The first point can be addressed by a correct choice of the plasma facing components and by conditioning the first wall. The second point needs a study of the impurity transport in different scenarios, understanding what prevents the accumulation of ions in the core. The radial impurity flux is usually expressed by means of two transport coefficients: the diffusion coefficient and the convective velocity. The determination of these coefficients in different scenarios allows to understand and control the impurity peaking. The Ph.D. activity developed during these three years is focused on this topic: the understanding of the impurity transport behaviour in different scenarios by means of the determination of the transport coefficients. This analysis has been conducted on a particular magnetic configuration: the reversed-field pinch. It has been carried out on the two main devices operating in this configuration: RFX-mod located in Padua (Italy) and MST located in Madison (WI, USA). The analysis method consists in the reproduction by means of a 1D impurity transport code of the plasma signals which are mainly affected by the presence of impurities. In order to discriminate the two coefficients, transients in the plasma signals are needed, which are then reproduced by the code. These transients are usually induced by means of artificially introduced impurities; the code reproduces the variations in the emission patterns or in the impurity density (depending on the available measurements) which are caused by the introduced atoms. By matching the simulation with the measurements an estimation of the transport coefficients is obtained. Once the coefficients have been estimated, they are compared with theoretical models in order to understand the nature of the transport in a particular plasma scenario. For both machines, through the application of this method, the transport of different species of impurities (intrinsic and not) in different magnetic regimes has been studied. In RFX-mod, experiments with injected pellets of carbon and lithium have been carried out and subsequently reproduced with the code, allowing to determine the transport coefficients for the two elements. Moreover, first experiments with introduced tungsten have been conducted; its emission spectrum has been acquired and its penetrating capability investigated. In MST time-dependent impurity density measurements were available for different intrinsic species in two magnetic regimes; their reproduction with the transport code allowed to estimate the transport coefficients. This manuscript is organised in two main parts: first three chapters form the introductory part, chapters four and five form the original work of this thesis. Chapter 1 introduces the role of impurities in fusion plasmas. The production processes are described as well as the impurity effects on the plasma properties. Emitted radiation from impurities is divided into its components (continuum and produced by atomic processes) and briefly characterised. Then the different models used to describe the ion populations are presented: coronal, local thermodynamic and collisional-radiative. Finally the impurity radial transport is depicted in its analytical form, according to the classical and neo-classical formulation. Chapter 2 describes the reversed-field pinch magnetic configuration. Particle transport in this configuration is analytically presented. Chapter 3 gives the details of the simulation tool used in this thesis for reproducing experimental measurements. The code consists of a transport model coupled to a collisional-radiative model for various species. Both models are detailed as well as the inputs and outputs to the code. Chapter 4 reports the analysis performed at RFX-mod on impurity transport. The transient experiments conducted through pellets injection of carbon and lithium are described and the results presented. Transport coefficients are estimated for the different species in different magnetic scenarios. Then experiments with tungsten injection through the laser-blow off technique are presented and the results discussed and compared with reports from other devices. Chapter 5 deals with the analysis realised at MST on impurity transport. Impurity density measurements carried out for different intrinsic species in different plasma regimes are reproduced with the code. The estimated transport coefficients are presented and compared with theoretical models. Chapter 6 concludes the thesis with a discussion of the most important results achieved and an overview of possible future developments.

In the reversed-field pinch (RFP) edge, measured transport and flows are strongly influenced by magnetic islands (Vianello 2013 Nucl. Fusion 53 073025). In fact, these islands determine a differential radial diffusion of electrons and ions which, interacting with the wall, give rise to a characteristic edge ambipolar potential. Such island structures also arise in tokamak plasmas, when resonant magnetic perturbations (RMPs) are applied for control of edge-localized modes. They impose a characteristic modulation to edge electron density and temperature fields, in close correlation with the local magnetic vacuum topology (Schmitz 2012 Nucl. Fusion 52 054001). In order to develop a generic picture of particle transport with magnetic islands located in the plasma edge between RFPs and tokamaks with RMP, test-particle transport simulations are done on TEXTOR with the same tool used in RFX-mod, namely, the guiding-centre code ORBIT (White and Chance 1984 Phys. Fluids 27 2455-67). A typical TEXTOR discharge in the (m, n) = (12, 4) configuration is reconstructed and analysed with ORBIT. We use Poincare and connection length analysis of electrons and ion orbits to analyse the magnetic structure taking into account the different gyro-orbits of both constituents. Density distributions of test ions and electrons are calculated and used to obtain an initial estimate of the plasma potential and radial electric field around the island.

According to classical linearized resistive magnetohydrodynamics theory, pressuredriven modes are unstable in the reversed-field pinch (RFP) due to unfavorable magnetic field line curvature. The result is based on the assumption of an adiabatic energy equation where anisotropic thermal conduction effects are ignored as compared to convection and compression. In this thesis the effects of heat conduction in the energy equation have been studied. We have examined these effects on the linear stability of pressure-driven resistive modes using boundary value theory (Δ´ ) and a novel initial-value full resistive MHD code employing the Generalized Weighted Residual Method (GWRM). In the Δ´ method, a shooting technique is employed by integrating from the resistive layer to boundaries. The GWRM method, on the other hand, is a time-spectral Galerkin method in which the fully linearized MHD equations are solved. For detailed computations, efficiency requires the temporal and spatial domains to be divided into subdomains. For this purpose, a number of challenging test cases including linearized ideal MHD equations are treated. Numerical and analytical investigations of equilibria reveal that thermal conduction effects are not stabilizing for reactor relevant values of Lundquist number, S0, and normalized pressure, βθ, for tearing-stable plasmas. These studies show that growth rate scales as γ~_ S0−1/5 , which is weaker than for the adiabatic case, γ~_ S0−1/3. A numerical study of optimized confinement for an advanced RFP scenario including ohmic heating and heat conduction, is also part of this thesis. The fully nonlinear resistive MHD code DEBSP has been employed. We have identified, using both Δ´ and GWRM methods, that the observed crash of the high confinement is caused by resistive, pressure-driven modes. QC 20130503

Modified Reversed-Field eXperiment is an experiment of magnetic confinement of thermonuclear plasma in the Reversed- Field Pinch configuration. The toroidal device is designed to operate with hydrogen plasmas, and the most internal wall is entirely covered with polycrystalline graphite tiles. The disadvantage of graphite walls is the progressive hydrogen accumulation in graphite during operation. To overcome this problem, some graphite conditioning procedures are necessary (e.g. boronization, lithization and glow discharge). The critical role of graphite walls on plasma control suggested the use of secondary ion mass spectrometry (SIMS) technique for the evaluation of conditioning procedures efficacy. SIMS analyses of graphite samples after their exposure to plasmas or wall conditioning treatments are presented in this work. The SIMS technique resulted fundamental on the investigation of the boron distribution in the graphite tiles, and sample comparisons indicated the need for glow discharge cleaning system upgrading to improve the conditioning process and boronization uniformity

The reversed-field pinch (RFP) is a device for magnetic confinement of fusion plasmas. The main objective of fusion plasma research is to realise cost-effective thermonuclear fusion power plants. The RFP is highly unstable as can be explained by the theory of magnetohydrodynamics (MHD). Feed-back control technology appears to enable a robustly stable RFP operation. Experimental control and identification of nonaxisymmetric multimode MHD is pursued in this thesis. It is shown that nonparametric multivariate identification methods can be utilised to estimate MHD spectral characteristics from plant-friendly closed-loop operational input-output data. It is also shown that accurate tracking of the radial magnetic field boundary condition is experimentally possible in the RFP. These results appear generically useful as tools in both control and physics research in magnetic confinement fusion. QC 20120508

In this work starting from a set of magnetohydrodynamic (MHD) equations that describe the dynamical evolution for the pressure driven resistive/interchange modes in a magnetic confinement system, global solutions for the plasma flow relevant for toroidal pinches like tokamaks and reversed field pinches (RFPs) are derived. Analytical solutions for the flow stream function associated with the dominant modes are presented.

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.

In this paper insights into the behaviour of resistive wall modes (RWMs) in the RFX-mod reversed field pinch device are given, with a focus on 3D issues in the characterization of the m spectrum of the mode and on the study of multi-harmonic coupling. In the first part of the paper the interaction between multiple unstable RWMs is studied and the presence of a coupling between different poloidal components of the most unstable RWM is demonstrated, taking advantage of the flexibility of the RFX-mod control system. In the second part of the work, the dependence of the growth rates of RWMs on a complete set of plasma parameters is studied in order to create a complete and homogeneous database, which permits a careful validation of stability codes. Finally, the experimental data are compared with the code predictions which take into account the 3D structure of conductors around the plasma. The different effects that modify the simple description, where unstable modes can be identified with single Fourier harmonics, appear to be explained by a mixture of toroidicity-induced and 3D eddy current effects.

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.

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.

The edge Thomson scattering (edge TS) diagnostic has been used during the last experimental campaign on the modified reversed field experiment (RFX-mod) under various plasma conditions. The optical system for spectral analysis has been modified with respect to the initial design to improve sensitivity: now it resembles the scheme of the main Thomson scattering (main TS) which includes optical delay lines, filter polychromators with APDs and waveform digitizers. The system so configured has proved to be reliable and to fulfil the experimental requirements. The spatial resolution is now 2 cm, with six measuring points in the outer plasma region at 0.7 < r/a < 1, which is only partially covered by the main TS, up to r/a < 0.8. The time synchronization of main and edge TS systems provides a full coverage of the plasma diameter and a complete pressure profile. Alternatively, the operation of the two systems with a controlled time delay allows two-time measurements of the evolution of edge T(e), n(e) and p(e) profiles in transient events such as pellet injection or dynamo relaxations.

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.

The magnetic topology of quasi-single helicity (QSH) regimes, in the reversed field pinch experiment RFX-mod, is characterized by a helical magnetic structure surrounded by partially chaotic field lines. In this paper we investigate the transport mechanisms within these helical structures, in particular, the particle diffusion due to the residual magnetic chaos. The diffusion coefficients have been estimated for different plasma temperatures, collisionality and magnetic perturbation amplitudes. In the typical high temperature QSH regimes of RFX-mod, ambipolar transport between ions and electrons is found to be ensured by the non-zero but very low level of secondary modes and by the reduced collisionality. Trapped ions give the largest contribution to particles diffusion, while those passing are almost well confined within the helical structure. In the best QSH experimental performances, ion diffusion coefficients computed by numerical simulations are not affected significantly by the residual magnetic chaos and are very close to those expected in a regime with only helical conserved surfaces.

RFX-mod reliably operates at 1.5 MA, the highest current ever achieved on a reversed field pinch device thanks to the the feedback control on multiple magnetohydrodynamic modes. In these high current discharges magnetic topology spontaneously self-organizes in an Ohmic helical symmetry, the quasi single helicity (QSH) state, in which the magnetic dynamics is dominated by the innermost resonant mode, with the new magnetic axis helically twisting around the geometrical axis of the torus. Inside the helical structure energy confinement is enhanced and electron temperatures exceeding 1 keV are measured, with steep gradients, which identify an internal transport barrier. Separatrix expulsion and symmetric electron temperature profiles with high gradients are obtained for ratios between the dominant mode and total B above about 4%. The measured electron temperature peak involves a large fraction of the plasma cross section, corresponding to an improvement in the global electron energy confinement up to a factor 2. The steep temperature profiles obtained in QSH conditions correspond to an electron thermal diffusivity reduced by more than one order of magnitude. Perturbative experiments (pellets and impurity laser blow off injections) have been performed to study particle confinement inside and outside the thermal island. Inside the helical structure experimental evidence of main gas confinement increase has been obtained, while for impurities there is no evidence of confinement increase.