Sparse Representation of Signals: from astrophysics to real-time data analysis for fusion plasmas and system optimization analysis for ITER and TCV

Efficient, real-time and automated data analysis is one of the key elements for achieving scientific success in complex engineering and physical systems, of which two examples are the JET and ITER tokamaks. One problem which is common to these fields is the determination of pulsation modes from irregularly sampled time-series. To this end, there is a wealth of signal processing techniques that are being applied to post-pulse and real-time data analysis in such complex systems. Here we wish to present a review of the applications of a method based on the Sparse Representation of Signals, using examples of the synergies that can be exploited when combining ideas and methods from very different fields, such as astronomy and astrophysics and thermonuclear fusion plasmas. Examples of this work in astronomy and astrophysics are the analysis of pulsation modes in various classes of stars and the orbit determination software of the Pioneer spacecrafts. Two examples of this work in thermonuclear fusion plasmas are the detection of magneto-hydrodynamic instabilities, which is now performed routinely in JET in real-time on a sub-millisecond time-scale, and the studies leading to the optimization of the magnetic diagnostic system in ITER and TCV. These questions have been solved formulating them as inverse problems, despite the fact that these applicative frameworks are extremely different from the classical use of Sparse Representations, on both the theoretical and computational points of view. Requirements, prospects and ideas for the signal processing and real-time data analysis applications of this method to routine operation of ITER will also be discussed. Finally, a very recent development has been an attempt at the application of this method to the deconvolution of the measurement of electric potential performed during a ground-based survey of a proto-Villanovian necropolis in central Italy.

Sparse representation of signals: from astrophysics to real-time data analysis for fusion plasmas and system optimization analysis for ITER and TCV

Mattia Albergante, Patrick Blanchard, Ambrogio Fasoli, Jonathan Bryan Lister, Theodoros Panis, Duccio Testa

2016

Analysis of plasma dynamic response to modulated electron cyclotron heating in TCV tokamak

Ilya Pavlov

The need of durable, economically acceptable and safe energy sources continues to stimulate studies in a field of thermonuclear fusion. The most successful solution for controlled magnetic fusion is the tokamak. The improvement of tokamak performance depends on the optimization of pressure and current density spatial distributions which can be modified by means of an auxiliary heating and a current drive. Electron cyclotron heating, in particular is a very important tool for the study and control of basic physical processes governing plasma confinement and stability, particularly because it allows the injection of highly localized intense power. ECH power deposition location plays a crucial role in sawtooth control and suppression, it is also important for tearing mode stabilization, and for implementation of closed loop systems for automatic control/suppression of magnetohydrodynamic activity. A part of the ECH power can be modulated (MECH), and used to identify where the ECH power has been deposited, and can also be useful in the experimental analysis of the electron transport in general. Nevertheless, despite the goal of MECH being a diagnostic and analysis tool, MECH can couple to plasma oscillations, such as sawteeth. MECH-sawtooth phase coupling adds significant complications in ECH deposition location and transport analysis, in some cases making the interpretations of results misleading. This is why it is important to get an insight into the phenomenon of MECH-sawtooth interaction, and to establish the boundaries where conventional types of modulation analysis can be successfully implemented. This thesis presents the analysis and interpretation of perturbative MECH experiments performed in the TCV tokamak with particular attention paid to the non-linear phase coupling of heat waves. TCV is equipped with a very flexible and high power ECH system. Two independent ECH systems permit MECH to be deposited at two different spatial locations, with two different types of modulating signals. This set-up was used to study simultaneous propagation of heat waves induced by MECH in non-sawtoothing plasmas, and in discharges with sawtooth activity. A new analysis method for the characterization of the plasma non-linear dynamic response to modulated heating was developed on the basis of Higher Order Spectral Analysis (HOSA) technique. This method applied to signals from different diagnostics, such as electron cyclotron emission and soft X-ray measurements, was extensively used to quantitatively characterize the effect of nonlinear phase coupling. In sawtooth free discharges a detailed analysis of the propagation of heat waves demonstrated that their phase coupling is solely related to properties of heat sources. It was demonstrated that if two heat waves are induced by non-coupled power sources (multi-beam MECH) then no phase coupling occurs. In the opposite case, when a source of perturbation (MECH) contains coupled harmonics, the corresponding heat waves demonstrate phase coupling. It was shown that these coupled heat waves loose their phase coherence while propagating in plasma. The dissipation of phase coupling is due to different phase velocities of heat waves and their diffusive damping. The new type of ECH power modulation accompanied with bicoherence analysis was proposed as a candidate for a reliable identification of EC power deposition location in a case of high frequency and low modulation depth MECH, including multi-beam heating. This type of MECH can be particularly important for real time control applications. In cases when MECH is applied to sawtoothing plasmas a direct experimental evidence of MECH-sawtooth non-linear phase coupling has been demonstrated using HOSA techniques, in particular bispectrum and bicoherence profiles. The detailed analysis presented here demonstrates a direct proof of periodic modification of sawtooth behavior by modulated ECH. It was shown that a simple diffusive model for the perturbed electron temperature with MECH source term can not be used for transport analysis in the presence of MECH-sawtooth coupling. Self-consistent time dependant transport simulations including a sawtooth relaxation model is capable of properly reproducing the effect of MECH-sawtooth phase coupling and can be used for transport analysis. On the basis of these simulations, an hypothesis for MECH-sawtooth coupling based on periodic modifications of magnetic shear was proposed. Additional information provided by HOS analysis enabled a correct interpretation of the plasma dynamic response to modulated heating in the presence of MECH-sawtooth coupling.

EPFL2008

Modeling and control of the current density profile in tokamaks and its relation to electron transport

Costanza Zucca

The current density in tokamak plasmas strongly affects transport phenomena, therefore its understanding and control represent a crucial challenge for controlled thermonuclear fusion. Within the vast framework of tokamak studies, three topics have been tackled in the course of the present thesis: first, the modelling of the current density evolution in electron Internal Transport Barrier (eITB) discharges in the Tokamak à Configuration Variable (TCV); second, the study of current diffusion and inversion of electron transport properties observed during Swing Electron Cyclotron Current Drive (Swing ECCD) discharges in TCV; third, the analysis of the current density tailoring obtained by local ECCD driven by the improved EC system for sawtooth control and reverse shear scenarios in the International Thermonuclear Experimental Reactor (ITER). The work dedicated to the study of eITBs in TCV has been undertaken to identify which of the main parameters, directly related to the current density, played a relevant role in the confinement improvement created during these advanced scenarios. In this context, the current density has to be modeled, there being no measurement currently available on TCV. Since the Rebut-Lallia-Watkins (RLW) model has been validated on TCV ohmic heated plasmas, the corresponding scaling factor has often been used as a measure of improved confinement on TCV. The many interpretative simulations carried on different TCV discharges have shown that the thermal confinement improvement factor, HRLW, linearly increases with the absolute value of the minimum shear outside ρ > 0.3, ρ indicating a normalized radial coordinate. These investigations, performed with the transport code ASTRA, therefore confirmed a general observation, formulated through previous studies, that the formation of the transport barrier is correlated with the magnetic shear reversal. This was, indeed, found to be true in all cases studied, regardless of the different heating and current drive schemes employed. The increase of confinement with the negative magnetic shear was observed to be gradual, but constant, and did not depend on specific values of the safety factor. Therefore, the transition from standard to improved confinement appeared to be smooth, although it can be very fast. The flexible EC system in TCV allowed us to attain strong global confinement improvement to produce eITB regimes. It also permitted us to perform transport studies on plasmas characterized by low confinement, in which we modified the magnetic shear profile, locally, around the deposition location. For instance, alternate and periodic injection of co- and counter-ECCD within the same plasma discharge has been realized on TCV, while maintaining the same amount of total input EC power. Such a heating scheme has been the basis of Swing ECCD experiments, which were initially carried out using nearly on-axis EC deposition locations in the plasma, in order to maximize the EC power absorption, and therefore the magnetic shear variation. ASTRA, interfaced with the experimental data and the CQL3D code for the computation of the EC heating and current drive sources, has again been used as a reliable tool for transport analysis and planning of new experiments. The simulations have pointed out the effects of Swing ECCD on the magnetic shear and on the electron temperature profile around the radius at which the EC waves are absorbed. Both profiles turned out to be modulated at the same frequency as the frequency of the Swing ECCD. Moreover, the maximum magnetic shear variation has been observed to be independent of the transport models used for the simulations, therefore underlying the robustness of the modeling. Additionally, the numerical results have motivated further experiments with more off-axis EC deposition, which were found roughly in agreement with recent gyrokinetic predictions, according to which, at higher positive values of the magnetic shear, an inversion of the transport properties should occur. The aim of the study regarding the ITER project has been to analyse the capabilities of a possible variant of the EC system, recently proposed with the intent to optimize the combined action of the Upper and Equatorial EC Launchers and, therefore, to allow a broader operational domain for ITER. This variant will maintain the main goals for which the ITER EC system has originally been designed, namely the stabilization of Neoclassical Tearing Modes (NTMs) and of the sawtooth instability. This is a necessary feature that has been carefully analyzed in the present study. Besides allowing excellent performance in controlling NTMs and the sawtooth period, the suggested variant paves a way for further exploitation of EC waves for ITER. The present ITER base-line design has all EC launchers providing only co-ECCD. The performed numerical modeling has shown that the possibility to drive counter-ECCD with one of the three rows of equatorial mirrors offers greater control of the plasma current density. The counter-ECCD may also be balanced with co-ECCD to provide pure EC heating, with no net driven current. This would be an additional asset if EC waves were found to be needed to assist the L-H transition during plasma ramp-up. The overall decrease in co-ECCD, by turning one row to counter-ECCD, is estimated to be negligible, because the difference between full off-axis co-ECCD using all 20 MW from the Equatorial Launcher or co-ECCD driven by 2/3 from the Equatorial Launcher and 1/3 from the Upper Launcher is small. Therefore the latter analysis provides, in our opinion, a strong evidence of the substantial gain in flexibility if the suggested variant of the ITER EC system were accepted as the base-line design.

EPFL2009