The properties of plasma turbulence in the outer region of the Reversed Field Pinch experiments RFX and EXTRAP-T2R are reviewed. The statistical properties of fluctuations in the range of scales relevant for transport are presented. The observation of coherent structures emerging from the background turbulence and their interpretation in terms of vortices is reported. The interplay between these structures and the mean ExB flow of the plasma is demonstrated with emphasis to the action on the preferential rotation direction. The effect on the particle transport induced by the background turbulence and by the structures is discussed. Finally the methods tested to control turbulence and to mitigate the related transport are illustrated and discussed.
The results leading to the identification of coherent structures emerging from the background turbulence in the edge region of the reversed field pinch experiments EXTRAP-T2R and RFX are reviewed. These structures have traits of vortices in velocity field and blobs in density, and the reconstruction of their spatial structure and of their time evolution is discussed focusing on the analysis tools applied. The role of these structures in the particle anomalous transport is addressed, showing that their collisions can contribute up to 50% the total particle losses. This process is shown to be responsible for bursts in particle flux and it is found to set a characteristic collision time, which is in agreement with the statistical properties of laminar times for particle flux bursts.
The EXTRAP T2R is a large aspect ratio Reversed Field Pinch device. The main focus of interest for the experiments is the active feedback control of resistive wall modes [1]. With feedback it has been possible to prolong plasma discharges in T2R from about 20 ms to nearly 100 ms. In a series of experiments in T2R, in H- and D- plasmas with and without feedback, quantitative spectroscopy and passive collector probes have been used to study the flux of metal impurities. Time resolved spectroscopic measurements of Cr and Mo lines showed large metal release towards discharge termination without feedback. Discharge integrated fluxes of Cr, Fe, Ni and Mo were also measured with collector probes at wall position. Reasonable quantitative agreement was found between the spectroscopic and collector probe measurements. The roles of sputtering, thermal evaporation and arcing in impurity production are evaluated based on the composition of the measured impurity flux.
The EXTRAP T2R thin shell reversed-field pinch (RFP) device has recently resumed operation after a major rebuild including the replacement of the graphite armour with molybdenum limiters, a fourfold increase of the shell time constant, and the replacement of the helical coil used for the toroidal field with a conventional solenoid-type coil. Wall-conditioning using hydrogen glow discharge cleaning was instrumental for successful RFP operation. Carbon was permanently removed from the walls during the first week of operation. The initial results from RFP operation with relatively low plasma currents in the range I-p = 70-100 kA are reported. RFP discharges are sustained for more than three shell times. Significant improvements in plasma parameters are observed, compared to operation before the rebuild. There is a substantial reduction in the carbon impurity level. The electron density behaviour is more shot-to-shot reproducible. The typical density is n(e) = 0.5-1 x 10(19) m(-3). Monitors of H-alpha line radiation indicate that the plasma wall interaction is more toroidally symmetric and that there is less transient gas release from the wall. The minimum loop voltage is in the range V-t = 28-35 V, corresponding to a reduction by a factor of two to three compared to the value before the rebuild.
Experiments in EXTRAP T2R on RWM stabilization using intelligent shell feedback with a P-controller showed that mode suppression improves with increasing gain up to the system stability limit. A PD-controller gives faster response and allows operation with higher gain. The PI-controller is useful for suppression of modes driven by external resonant field error. Best mode suppression was in the present study achieved with a PID-controller.
Discharges in the thin shell reversed field pinch (RFP) device EXTRAP T2R without active feedback control are characterized by growth of non-resonant m = 1 unstable resistive wall modes (RWMs) in agreement with linear MHD theory. Resonant m = 1 tearing modes (TMs) exhibit initially fast rotation and the associated perturbed radial fields at the shell are small, but eventually TMs wall-lock and give rise to a growing radial field. The increase in the radial field at the wall due to growing RWMs and wall-locked TMs is correlated with an increase in the toroidal loop voltage, which leads to discharge termination after 3-4 wall times. An active magnetic feedback control system has been installed in EXTRAP T2R. A two-dimensional array of 128 active saddle coils (pair-connected into 64 independent m = 1 coils) is used with intelligent shell feedback control to suppress the m = 1 radial field at the shell. With feedback control, active stabilization of the full toroidal spectrum of 16 unstable m = 1 non-resonant RWMs is achieved, and TM wall locking is avoided. A three-fold extension of the pulse length, up to the power supply limit, is observed. Intelligent shell feedback control is able to maintain the plasma equilibrium for 10 wall times, with plasma confinement parameters sustained at values comparable to those obtained in thick shell devices of similar size.
Active feedback stabilization of multiple independent resistive wall modes is experimentally demonstrated in a reversed-field pinch plasma. A reproducible simultaneous suppression of several nonresonant resistive wall modes is achieved. Coupling of different modes due to the limited number of the feedback coils is observed in agreement with theory. The feedback stabilization of nonresonant RWMs also has an effect on tearing modes that are resonant in the central plasma, leading to a significant prolongation of the discharge pulse.
An array of saddle coils having Nc =16 equally spaced positions along the toroidal direction has been installed for feedback control of resistive wall modes (RWMs) on the EXTRAP T2R reversed-field pinch [P. R. Brunsell, H. Bergsaker, M. Cecconello, Plasma Phys. Controlled Fusion 43, 1457 (2001)]. Using feedback, multiple nonresonant RWMs are simultaneously suppressed for three to four wall times. Feedback stabilization of RWMs results in a significant prolongation of the discharge duration. This is linked to a better sustainment of the plasma and tearing mode toroidal rotation with feedback. Due to the limited number of coils in the toroidal direction, pairs of modes with toroidal mode numbers n, n′ that fulfill the condition ∫n- n′ ∫ = Nc are coupled by the feedback action from the discrete coil array. With only one unstable mode in a pair of coupled modes, the suppression of the unstable mode is successful. If two modes are unstable in a coupled pair, two possibilities exist: partial suppression of both modes or, alternatively, complete stabilization of one target mode while the other is left unstable.
A two-dimensional array of saddle coils at M-c poloidal and N-c toroidal positions is used on the EXTRAP T2R reversed-field pinch (Brunsell P R et al 2001 Plasma Phys. Control. Fusion 43 1457) to study active control of resistive wall modes (RWMs). Spontaneous growth of several RWMs with poloidal mode number m = 1 and different toroidal mode number n is observed experimentally, in agreement with linear MHD modelling. The measured plasma response to a controlled coil field and the plasma response computed using the linear circular cylinder MHD model are in quantitive agreement. Feedback control introduces a linear coupling of modes with toroidal mode numbers n, n' that fulfil the condition vertical bar n - n'vertical bar = N-c. Pairs of coupled unstable RWMs are present in feedback experiments with an array of Mc x Nc = 4 x 16 coils. Using intelligent shell feedback, the coupled modes are generally not controlled even though the field is suppressed at the active coils. A better suppression of coupled modes may be achieved in the case of rotating modes by using the mode control feedback scheme with individually set complex gains. In feedback with a larger array of Mc x Nc = 4 x 32 coils, the coupling effect largely disappears, and with this array, the main internal RWMs n = -11, -10, +5, +6 are all simultaneously suppressed throughout the discharge (7-8 wall times). With feedback there is a two-fold extension of the pulse length, compared to discharges without feedback.
Pulsed poloidal current drive (PPCD) experiments have been conducted in the resistive shell EXTRAP T2R reversed-field pinch experiment. During the current profile modification phase, the fluctuation level of the m = 1 internally resonant tearing modes decreases, and the velocity of these modes increases. The m = 0 modes are not affected during PPCD, although termination occurs with a burst in the m = 0 amplitude. The PPCD phase is characterized by an increase in the central electron temperature (up to 380 eV) and in the soft x-ray signal. Spectroscopic observations confirm an increase in the central electron temperature. During PPCD, the plasma poloidal beta increases to 14%, and the estimated energy confinement time doubles, reaching 380 mus. The reduction in the fluctuation level and the corresponding increase in the energy confinement time are qualitatively consistent with a reduction in parallel transport along stochastic magnetic field lines.
An extensive investigation of the global confinement properties in different operating scenarios in the rebuilt EXTRAP T2R reversed-field pinch (RFP) experiment is reported here. In particular, the role of a fast gas puff valve system, used to control plasma density, on confinement is studied. Without gas puffing, the electron density decays below 0.5 x 10(19) M-3. The poloidal beta varies between 5% and 15%, decreasing at large I/N. The energy confinement time ranges from 70 to 225 mus. With gas puffing, the density is sustained at n(e) approximate to 1.5 x 10(19) m(-3). However, a general slight deterioration of the plasma performances is observed for the same values of I/N: the plasma becomes cooler and more radiative. The poloidal beta is comparable to that in the scenarios without puff but the energy confinement time drops ranging from 60 to 130 mus. The fluctuation level and the energy confinement time have been found to scale with the Lundquist number as S-0.05+/-0.07 and S0.5+/-0.1, respectively. Mode rotation is typical for all the discharges and rotation velocity is observed to increase with increasing electron diamagnetic velocity.
Many reversed-field pinch (RFP) experiments exhibit a coherent oscillatory behaviour that is characteristic of discrete dynamo events and is associated with intermittent current profile self-organisation phenomena. However, in the vast majority of the discharges in the resistive shell RFP experiment EXTRAP T2, the dynamo activity does not show global, coherent oscillatory behaviour, The internally resonant tearing modes are phase-aligned and wall-locked resulting in a large localised magnetic perturbation. Equilibrium and plasma parameters have a level of high frequency fluctuations but the average values are quasi-steady. For some discharges, however, the equilibrium parameters exhibit the oscillatory behaviour characteristic of the discrete dynamo events. For these discharges, the trend observed in the tearing mode spectra, associated with the onset of the discrete relaxation event behaviour, is a relative higher amplitude of m = 0 mode activity and relative lower amplitude of the m = 1 mode activity compared with their average values. Global plasma parameters and model profile calculations for sample discharges representing the two types of relaxation dynamics are presented.
Studies of non-linear dynamics of MHD tearing modes in the EXTRAP reversed-field pinch experiments [1] have demonstrated such phenomena as mode rotation, phase-locking and wall locking.
Optimal feedback control of resistive-wall modes (RWM) is of common interest for toroidal fusionconcepts that use conducting walls for stabilization of ideal MHD modes. From the RWM control point of view,the RFP situation is in many respects similar to the advanced tokamak situation in the presence of very lowplasma rotation, where the most effective stabilizing mechanism is the feedback action of a set of active coils.Results from EXTRAP T2R (Sweden) and RFX-mod (Italy) RFP experiments have shown that full feedbackcontrol of multiple RWMs is possible and their deleterious effects can be completely suppressed. However it isnow important to optimize the RWM control systems both for the RFP and tokamak configuration for futureimplementation. Important aspects of optimization are effective mode identification and tracking capability,avoidance of the harmful effects of sideband modes (aliasing) in the control spectrum, minimized powerrequirements and robust controller stability. The paper describes collaborative work carried out on the two RFPexperiments. Controller models based on the mode harmonic control concept and on a state-space multipleinputmultiple-output intelligent shell concept are studied. Progress in development of optimal control schemesare presented both through experimental studies and simulations.
Active feedback control of resistive wall modes (RWMs) has been demonstrated in the EXTRAP T2R reversed-field pinch experiment. The control system includes a sensor consisting of an array of magnetic coils (measuring mode harmonics) and an actuator consisting of a saddle coil array (producing control harmonics). Closed-loop (feedback) experiments using a digital controller based on a real time Fourier transform of sensor data have been studied for cases where the feedback gain was constant and real for all harmonics (corresponding to an intelligent-shell) and cases where the feedback gain could be set for selected harmonics, with both real and complex values (targeted harmonics). The growth of the dominant RWMs can be reduced by feedback for both the intelligent-shell and targeted-harmonic control systems. Because the number of toroidal positions of the saddle coils in the array is half the number of the sensors, it is predicted and observed experimentally that the control harmonic spectrum has sidebands. Individual unstable harmonics can be controlled with real gains. However if there are two unstable mode harmonics coupled by the sideband effect, control is much less effective with real gains. According to the theory, complex gains give better results for (slowly) rotating RWMs, and experiments support this prediction. In addition, open loop experiments have been used to observe the effects of resonant field errors applied to unstable, marginally stable and robustly stable modes. The observed effects of field errors are consistent with the thin-wall model, where mode growth is proportional to the resonant field error amplitude and the wall penetration time for that mode harmonic.
A model to estimate the heat transport in the EXTRAP T2R reversed field pinch (RFP) is described. The model, based on experimental and theoretical results, divides the RFP electron heat diffusivity chi(e) into three regions, one in the plasma core, where chi(e) is assumed to be determined by the tearing modes, one located around the reversal radius, where chi(e) is assumed not dependent on the magnetic fluctuations and one in the extreme edge, where high chi(e) is assumed. The absolute values of the core and of the reversal chi(e) are determined by simulating the electron temperature and the soft x-ray and by comparing the simulated signals with the experimental ones. The model is used to estimate the heat diffusivity and the energy confinement time during the flat top of standard plasmas, of deep F plasmas and of plasmas obtained with the intelligent shell.
The interaction of a static resonant magnetic perturbation (RMP) with a tearing mode (TM) is becoming a relevant topic in fusion plasma physics. RMPs can be generated by active coils and then used to affect the properties of TMs and of the corresponding magnetic islands. This paper shows how the feedback system of the EXTRAP T2R reversed field pinch (RFP) can produce a RMP that affects a rotating TM and stimulate the transition to the so-called quasi-single helicity (QSH) regime, a RFP plasma state characterized by a magnetic island surrounded by low magnetic chaos. The application of the RMP can increase the QSH probability up to 10% and enlarge the size of the corresponding island. Part of the experimental results are supported by a theoretical study that models the effect of the active coils on the magnetic island.
The heat transport inside the magnetic island generated in a quasi-single-helicity regime of a reversed-field pinch device is studied by using a numerical code that simulates the electron temperature and the soft x-ray emissivity. The heat diffusivity chi(e) inside the island is determined by matching the simulated signals with the experimental ones. Inside the island, chi(e) turns out to be from one to two orders of magnitude lower than the diffusivity in the surrounding plasma, where the magnetic field is stochastic. Furthermore, the heat transport properties inside the island are studied in correlation with the plasma current and with the amplitude of the magnetic fluctuations.
Feedback systems are important tools for an advanced control of the MHD instabilities in fusion plasmas, both for the suppression of undesired modes, such as RWMs, and for the generation of external perturbations for ELM suppression. A good knowledge of the diffusion time through the machine wall of each external harmonics is necessary for reaching optimal performances of the feedback algorithms.A correct theoretical estimation is not easy due the presence of three-dimensional mechanical structures in the devices, such as shell cuts and external conductive structures that need to be considered. Identification of differences in the vertical and horizontal diffusion time are not simple from a theoretical point of view.This work will present a relatively simple technique to experimentally estimate the diffusion time for each harmonic. The technique is based on the generation of rotating external magnetic perturbations in vacuum and on the quantification of the wall screening from the measured field inside the wall. The technique will be able to quantify possible differences among the horizontal and vertical diffusion time. In the final part of the work, the comparison with the results obtained with a closed-loop identification algorithm of the machine plant will be discussed.
The effect of resonant magnetic perturbations (RMPs) on the tearing mode (TM) velocity is studied in EXTRAP T2R. Experimental results show that the RMP produces TM braking until a new steady velocity or wall locking is reached. The braking is initially localized at the TM resonance and then spreads to the other TMs and to the rest of the plasma producing a global velocity reduction via the viscous torque. The process has been used to experimentally estimate the kinematic viscosity profile, in the range 2-40 m 2 s -1, and the electromagnetic torque produced by the RMP, which is strongly localized at the TM resonance. Experimental results are then compared with a theoretical model which gives a reasonable qualitative explanation of the entire process.
The EXTRAP T2R feedback system (active coils, sensor coils and controller) is used to study and develop new tools for advanced control of the MHD instabilities in fusion plasmas. New feedback algorithms developed in EXTRAP T2R reversed-field pinch allow flexible and independent control of each magnetic harmonic. Methods developed in control theory and applied to EXTRAP T2R allow a closed-loop identification of the machine plant and of the resistive wall modes growth rates. The plant identification is the starting point for the development of output-tracking algorithms which enable the generation of external magnetic perturbations. These algorithms will then be used to study the effect of a resonant magnetic perturbation (RMP) on the tearing mode (TM) dynamics. It will be shown that the stationary RMP can induce oscillations in the amplitude and jumps in the phase of the rotating TM. It will be shown that the RMP strongly affects the magnetic island position.
The effect of a resonant magnetic perturbation (RMP) on the tearing mode (TM) dynamics is experimentally studied in the EXTRAP T2R device. EXTRAP T2R is equipped with a set of sensor coils and active coils connected by a digital controller allowing a feedback control of the magnetic instabilities. The recently upgraded feedback algorithm allows the suppression of all the error field harmonics but keeping a selected harmonic to the desired amplitude, therefore opening the possibility of a clear study of the RMP effect on the corresponding TM. The paper shows that the RMP produces two typical effects: (1) a weak oscillation in the TM amplitude and a modulation in the TM velocity or (2) a strong modulation in the TM amplitude and phase jumps. Moreover, the locking mechanism of a TM to a RMP is studied in detail. It is shown that before the locking, the TM dynamics is characterized by velocity modulation followed by phase jumps. Experimental results are reasonably explained by simulations obtained with a model.
A new method for the estimate of the wall diffusion time of non-axisymmetric fields is developed. The method based on rotating external fields and on the measurement of the wall frequency response is developed and tested in EXTRAP T2R. The method allows the experimental estimate of the wall diffusion time for each Fourier harmonic and the estimate of the wall diffusion toroidal asymmetries. The method intrinsically considers the effects of three-dimensional structures and of the shell gaps. Far from the gaps, experimental results are in good agreement with the diffusion time estimated with a simple cylindrical model that assumes a homogeneous wall. The method is also applied with non-standard configurations of the coil array, in order to mimic tokamak-relevant settings with a partial wall coverage and active coils of large toroidal extent. The comparison with the full coverage results shows good agreement if the effects of the relevant sidebands are considered.
The non-resonant magnetic perturbation (MP) braking is studied in the EXTRAP T2R reversed-field pinch (RFP) and the experimental braking torque is compared with the torque expected by the neoclassical toroidal viscosity (NTV) theory. The EXTRAP T2R active coils can apply magnetic perturbations with a single harmonic, either resonant or non-resonant. The non-resonant MP produces velocity braking with an experimental torque that affects a large part of the core region. The experimental torque is clearly related to the plasma displacement, consistent with a quadratic dependence as expected by the NTV theory. The work show a good qualitative agreement between the experimental torque in a RFP machine and NTV torque concerning both the torque density radial profile and the dependence on the non-resonant MP harmonic.
A loop voltage is required to sustain the reversed-field pinch (RFP) equilibrium. The configuration is characterized by redistribution of magnetic helicity but with the condition that the total helicity is maintained constant. The magnetic field shell penetration time, tau(s), has a critical role in the stability and performance of the RFP Confinement in the EXTRAP device has been studied with two values of tau(s), first (EXTRAP-T2) with tau(s), of the order of the typical relaxation cycle timescale and then (EXTRAP-T2R) with tau(s), much longer than the relaxation cycle timescale, but still much shorter than the pulse length. Plasma parameters show significant improvements in confinement in EXTRAP-T2R. The typical loop voltage required to sustain comparable electron poloidal beta values is a factor of 3 lower in the EXTRAP-T2R device. The improvement is attributed to reduced magnetic turbulence.
A method of determining radial impurity emission profiles is outlined. The method uses correlations between line integrated signals and is based on the assumption of cylindrically symmetric fluctuations. Measurements at the reversed field pinch EXTRAP T2R show that emission from impurities expected to be close to the edge is clearly different in raw as well as analyzed data to impurities expected to be more central. Best fitting of experimental data to simulated correlation coefficients yields emission profiles that are remarkably close to emission profiles determined using more conventional techniques. The radial extension of the fluctuations is small enough for the method to be used and bandpass filtered signals indicate that fluctuations below 10 kHz are cylindrically symmetric. The novel method is not sensitive to vessel window attenuation or wall reflections and can therefore complement the standard methods in the impurity emission reconstruction procedure.
Mode rotation studies in a resistive shell reversed-field pinch, EXTRAP T2R [P. R. Brunsell , Plasma Phys. Control. Fusion 43, 1 (2001)] are presented. The phase relations and nonlinear coupling of the resonant modes are characterized and compared with that expected from modeling based on the hypothesis that mode dynamics can be described by a quasi stationary force balance including electromagnetic and viscous forces. Both m=0 and m=1 resonant modes are studied. The m=1 modes have rotation velocities corresponding to the plasma flow velocity (20-60 km/s) in the core region. The rotation velocity decreases towards the end of the discharge, although the plasma flow velocity does not decrease. A rotating phase locked m=1 structure is observed with a velocity of about 60 km/s. The m=0 modes accelerate throughout the discharges and reach velocities as high as 150-250 km/s. The observed m=0 phase locking is consistent with theory for certain conditions, but there are several conditions when the dynamics are not described. This is not unexpected because the assumption of quasi stationarity for the mode spectra is not fulfilled for many conditions. Localized m=0 perturbations are formed in correlation with highly transient discrete dynamo events. These perturbations form at the location of the m=1 phase locked structure, but rotate with a different velocity as they spread out in the toroidal direction. (C) 2004 American Institute of Physics.