Developement of real time diagnostics and feedback algorithms for JET in view of the next step

Real time control of many plasma parameters will be an essential aspect in the development of reliable high performance operation of Next Step Tokamaks. The main prerequisites for any feedback scheme are the precise real-time determination of the quantities to be controlled, requiring top quality and highly reliable diagnostics, and the availability of robust control algorithms. A new set of real time diagnostics was recently implemented on JET to prove the feasibility of determining, with high accuracy and time resolution, the most important plasma quantities. With regard to feedback algorithms, new model–based controllers were developed to allow a more robust control of several plasma parameters. Both diagnostics and algorithms were successfully used in several experiments, ranging from H-mode plasmas to configuration with ITBs. Since elaboration of computationally heavy measurements is often required, significant attention was devoted to non-algorithmic methods like Digital or Cellular Neural/Nonlinear Networks. The real time hardware and software adopted architectures are also described with particular attention to their relevance to ITER.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France

A control-oriented model of the current profile in Tokamak plasma

International audienceThis paper proposes a control-oriented approach to the tokamak plasma current profile dynamics. It is established based on a consistent set of simplified relationships, in particular for the microwave current drive sources, rather than exact physical modelling. Assuming that a proper model for advanced control schemes can be established using the socalled cylindrical approximation and neglecting the diamagnetic effects, we propose a model that focuses on the flux diffusion (from which the current profile is inferred). Its inputs are some real-time measurements available on modern tokamaks and the effects of some major actuators, such as the magnetic coils, Lower Hybrid (LHCD), Electron and Ion Cyclotron Frequency (ECCD and ICRH) systems, are particularly taken into account. More precisely, the non-inductive current profile sources are modelled as 3-parameters functions of the control inputs derived either from approximate theoretical formulae for the ECCD and bootstrap terms or from experimental scaling laws specifically developed from Hard X-ray Tore Supra data for the LHCD influence. The use of scaling laws in this model reflects the fact that the operation of future reactors will certainly depend upon a great number of scaling laws and specific engineering parameters. The discretisation issues are also specifically addressed, to ensure the robustness with respect to discretisation errors and the efficiency (in terms of computation time) of the associated algorithm. This model is compared with experimental results and the CRONOS solver for Tore Supra Tokamak

Development and Validation of a Tokamak Skin Effect Transformer model

A control oriented, lumped parameter model for the tokamak transformer including the slow flux penetration in the plasma (skin effect transformer model) is presented. The model does not require detailed or explicit information about plasma profiles or geometry. Instead, this information is lumped in system variables, parameters and inputs. The model has an exact mathematical structure built from energy and flux conservation theorems, predicting the evolution and non linear interaction of the plasma current and internal inductance as functions of the primary coil currents, plasma resistance, non-inductive current drive and the loop voltage at a specific location inside the plasma (equilibrium loop voltage). Loop voltage profile in the plasma is substituted by a three-point discretization, and ordinary differential equations are used to predict the equilibrium loop voltage as function of the boundary and resistive loop voltages. This provides a model for equilibrium loop voltage evolution, which is reminiscent of the skin effect. The order and parameters of this differential equation are determined empirically using system identification techniques. Fast plasma current modulation experiments with Random Binary Signals (RBS) have been conducted in the TCV tokamak to generate the required data for the analysis. Plasma current was modulated in Ohmic conditions between 200kA and 300kA with 30ms rise time, several times faster than its time constant L/R\approx200ms. The model explains the most salient features of the plasma current transients without requiring detailed or explicit information about resistivity profiles. This proves that lumped parameter modeling approach can be used to predict the time evolution of bulk plasma properties such as plasma inductance or current with reasonable accuracy; at least in Ohmic conditions without external heating and current drive sources

Reconstruction of the equilibrium of the plasma in a Tokamak and identification of the current density profile in real time

The reconstruction of the equilibrium of a plasma in a Tokamak is a free boundary problem described by the Grad-Shafranov equation in axisymmetric configuration. The right-hand side of this equation is a nonlinear source, which represents the toroidal component of the plasma current density. This paper deals with the identification of this nonlinearity source from experimental measurements in real time. The proposed method is based on a fixed point algorithm, a finite element resolution, a reduced basis method and a least-square optimization formulation. This is implemented in a software called Equinox with which several numerical experiments are conducted to explore the identification problem. It is shown that the identification of the profile of the averaged current density and of the safety factor as a function of the poloidal flux is very robust

Strategies for Optimal Control of the Current and Rotation Profiles in the DIII-D Tokamak

The tokamak is currently the most promising device for realizing commercially-viable fusion energy production. The device uses magnetic fields to confine a circulating ring of hydrogen in the plasma state, i.e. a cloud of hydrogen ions and electrons. When sufficiently heated the hydrogen ions can overcome the electrostatic forces and fuse together, providing an overwhelmingly abundant energy source. However, stable, high-performance operation of a tokamak requires several plasma control problems to be handled simultaneously. Moreover, the complex physics which governs the tokamak plasma evolution must be studied and understood to make correct choices in controller design. In this thesis, two key control issues are studied intensely, namely the optimization and control of the plasma current profile and control of the plasma rotation (or flow).In order to maximize performance, it is preferable that tokamaks achieve advanced scenarios (AT) characterized by good plasma confinement, improved magnetohydrodynamic stability, and a largely non-inductively driven plasma current. A key element to the development of AT scenarios is the optimization of the spatial distribution of the current profile. Also, research has shown that the plasma rotation can stabilize the tokamak plasma against degradations in the desired MHD equilibrium.In this thesis, new model-based control approaches for the current profile and rotation profile are developed to allow experimental exploration of advanced tokamak scenarios. Methods for separate control of both the current profile and rotation are developed. The advanced model-based control methods presented in this thesis have contributed to theory of tokamak profile control and in some cases they have been successfully validated experimentally in the DIII-D tokamak

Plasma Shape and Current Density Profile Control in Advanced Tokamak Operating Scenarios

The need for new sources of energy is expected to become a critical problem within the next few decades. Nuclear fusion has sufficient energy density to potentially supply the world population with its increasing energy demands. The tokamak is a magnetic confinement device used to achieve controlled fusion reactions. Experimental fusion technology has now reached a level where tokamaks are able to produce about as much energy as is expended in heating the fusion fuel. The next step towards the realization of a nuclear fusion tokamak power plant is ITER, which will be capable of exploring advanced tokamak (AT) modes, characterized by a high fusion gain and plasma stability. The extreme requirements of the advanced modes motivates researchers to improve the modeling of the plasma response as well as the design of feedback controllers. This dissertation focuses on several magnetic and kinetic control problems, including the plasma current, position and shape control, and data-driven and first-principles-driven modeling and control of plasma current density profile and the normalized plasma pressure ratio βN.The plasma is confined within the vacuum vessel by an external electromagnetic field, produced primarily by toroidal and poloidal field coils. The outermost closed plasma surface or plasma boundary is referred to as the shape of the plasma. A central characteristic of AT plasma regimes is an extreme elongated shape. The equilibrium among the electromagnetic forces acting on an elongated plasma is unstable. Moreover, the tokamak performance is improved if the plasma is located in close proximity to the torus wall, which guarantees an efficient use of available volume. As a consequence, feedback control of the plasma position and shape is necessary. In this dissertation, an H∞-based, multi-input-multi-output (MIMO) controller for the National Spherical Torus Experiment (NSTX) is developed, which is used to control the plasma position, shape, and X-point position.Setting up a suitable toroidal current profile is related to both the stability and performance of the plasma. The requirements of ITER motivate the research on plasma current profile control. Currently, physics-based control-oriented modeling techniques of the current profile evolution can be separated into two major classes: data-driven and first-principles-driven. In this dissertation, a two-timescale linear dynamic data-driven model of the rotational transform profile and βN is identified based on experimental data from the DIII-D tokamak. A mixed-sensitivity H∞ controller is developed and tested during DIII-D high-confinement (H-mode) experiments by using the heating and current drive (H&CD) systems to regulate the plasma rotational transform profile and βN around particular target values close to the reference state used for system identification. The preliminary experimental results show good progress towards routine current profile control in DIII-D. As an alternative, a nonlinear dynamic first-principles-driven model is obtained by converting the physics-based model that describes the current profile evolution in H-mode DIII-D discharges into a form suitable for control design. The obtained control-oriented model is validated by comparing the model prediction to experimental data. An H∞ control design problem is formulated to synthesize a stabilizing feedback controller, with the goal of developing a closed-loop controller to drive the current profile in DIII-D to a desirable target evolution. Simulations show that the controller is capable of regulating the system around the target rotational transform profile in the presence of disturbances. When compared to a previously designed data-driven model-based controller, the proposed first-principles-driven model-based controller shows potential for improving the control performance

Robust stabilization of the current profile in tokamak plasmas using sliding mode approach in infinite dimension

International audienceThis paper deals with the robust stabilization of the spatial distribution of tokamak plasmas current profile using a sliding mode feedback control approach. The control design is based on the 1D resistive diffusion equation of the magnetic flux that governs the plasma current profile evolution. The feedback control law is derived in the infinite dimensional setting without spatial discretization. Numerical simulations are provided and the tuning of the controller parameters that would reject uncertain perturbations is discussed. Closed loop simulations performed on realistic test cases using aphysics based tokamak integrated simulator confirm the relevance of the proposed control algorithm in view of practical implementation

Modelling and validation of neutral particle flow by means of stochastic algorithms using the example of a fusion divertor

Die Partikelabfuhr ist ein Schlüsselprozess, der die Plasmakerndichte und das Abpumpen der Heliumasche, die aus den Kernreaktionen resultiert, steuert. In Fusionsanlagen wie dem Tokamak in seiner Divertorkonfiguration, steht die Partikelströmung im Divertor und in der Subdivertor-Region in Zusammenhang mit dem Druck und dem Gas, welches durch das Toruspumpensystem abgepumpt wird. Deshalb ist die vorausschauende Modellierung der Neutralpartikel-Abfuhr von entscheidender Bedeutung für das Verständnis sowie für die Optimierung des Betriebs von Vakuumsystemen in Fusionsanlagen. Das Hauptziel der hier vorliegenden Dissertation ist die Entwicklung eines numerischen Tools, das auf der Direct Simulation Monte Carlo Methode basiert ist. Dieses soll die Neutralgasströmung in Fusionsanwendungen beschreiben. Der im Funktionsumfang der Open-Source C++ Toolbox für Computational Fluid Dynamik, OpenFOAM, enthaltene DSMC Solver dsmcFoam wird erstmals im Rahmen der Kernfusion zur Modellierung, Simulation und Validierung von Neutralgas-Strömungen im Divertorbereich angewendet. Ein erforderlicher erster Schritt für die Anwendung des dsmcFoam in der Divertorregion ist es, sicherzustellen, dass der Solver die Gasströmungen in einer einfachen Geometrie vorhersagen kann. Hierzu wird dsmcFoam mit theoretischen Vorhersagen verifiziert und mit unabhängigen numerischen Berechnungen abgeglichen. Die Sensitivi-tätsanalyse der Modellierungsparameter zeigt die Auswirkungen auf das Strömungsfeld in Abhängigkeit von Zeitschritt, Zellgrößenabhängigkeit und Anzahl der modellierten Partikel. Im zweiten Schritt werden die Solver-Funktionalitäten weiterentwickelt, um die Gasabsorption an Oberflächen über die Stickingkoeffizient (Haftwahrscheinlichkeit) zu modellieren. Mit dieser neuen Funktionalität des dsmcFoam-Solvers wird die Analyse der Partikelabfuhr im Subdivertor des Tokamaks JT-60SA durchgeführt. Die Analyse umfasst die Studie der Gasströmung mit und ohne Wechselwirkungen von Neutralteilchen. Die Studie bestätigt, dass die Berücksichtigung von Kollisionen zwischen Teilchen eine wesentliche Rolle in der Beschreibung des Neutralgastransports und der Gasströmungsentwicklung in Tokamak-Subdivertoren spielt. Dies zeigt sich in den Druckwerten des DSMC-Kollisionsmodells, welche im Vergleich zu den Druckwerten vom kollisionslosen DSMC-Modell um etwa 25% bzw. 40% ansteigen. Dieser Vergleich ist der erste seiner Art im Anwendungskontext der Kernfusion. Die zweite Anwendung des dsmcFoam besteht in der Analyse der Gasströmung in einem Divertor-Hochdruckszenario im Tokamak ITER. Die Neutralgasströmung wird für einen 10 Pa Divertordruck in der ITER-2009-Designgeometrie untersucht. Dabei wird gezeigt, dass die Gaszirkulations-Effekte durch den Divertor in direkter Abhängigkeit zum Druck am Pumpenauslass stehen. Der Zusammenhang zwischen dem Gas, das zur Plasmahauptkammer strömt und dem Druck am Pumpenauslass, wird festgestellt. Die Simulationen haben ergeben, dass der Druckanstieg am Pumpenauslass die Gasströmung auf der Niederfeldseite (LFS) verstärkt, während auf der Hochfeldseite (HFS) kein Effekt zu beobachten ist. Die Studie zeigt, dass sich die Erhöhung der Gasströmung auf der Niederfeldseite durch eine Rückströmung am Pumpenausfluss ergibt. Durch die Kombination von Experimentaldaten mit DSMC-Modellierung wird die Berechnung der Gasströmung im gesamten Subdivertor des Tokamaks ASDEX Upgrade (AUG) ermöglicht. Mit dem installierten Divertor III in AUG wurden Experimente, die mit Fokus auf die Partikelabfuhr im Betrieb des Tokamaks bei voller Leistung der kryogenen Pumpen durchgeführt wurden, mit DSMC modelliert. Die Modellierung zeigt, dass die Partikelflüsse unterhalb der Divertordome-Region und am LFS mit den experimentellen Messungen vergleichbar sind. Zwischen den kalkulierten Gasströmungen in der Modellierung und den Messungen an den HFS-Manometern wurde hinter den Divertortarget eine Diskrepanz festgestellt. Die Sensitivitäten zur AUG-Modellierung haben die Abhängigkeiten zwischen den Subdivertor-Parametern aufgezeigt, die für den Divertorbetrieb von Bedeutung sind

Statistical properties of intermittent fluctuations in the boundary of fusion plasmas

Paper I, II, III and V are not available in Munin. Paper I: Theodorsen, A., Garcia, O.E., Horacek, J, Kube, R & Pitts, R.A. (2016). Scrape-off layer turbulence in TCV: evidence in support of stochastic modelling. Available in Plasma Physics and Controlled Fusion, 58(4), 044006 (12pp). Paper II: Theodorsen, A., Garica, O.E. & Rypdal, M. (2017). Statistical properties of a filtered Poisson process with additive random noise: distributions, correlations and moment estimation. Available in Physica Scripta, 92(5), 054002. Paper III: Theodorsen, A., Garica, O.E., Kube, R., LaBombard, B & Terry, J.L. (2017). Relationship between frequency power spectra and intermittent, large-amplitude bursts in the Alcator C-Mod scrape-off Layer. Available in Nuclear Fusion, 57, 114004 (7pp). Paper V: Theodorsen, A. & Garcia, O.E. (2018). Probability distribution functions for intermittent scrape-off layer plasma fluctuations. Available in Plasma Physics and Controlled Fusion, 034006 (14pp).Fluctuation-induced plasma–wall interactions is a major concern for the next generation, high duty-cycle magnetic confinement fusion devices. The turbulence is generated in the outboard midplane transition region between the confined core plasma and the scrape-off layer where magnetic field lines intersect material walls. Here, filaments of hot and dense plasma, elongated in the field direction, detach from the main plasma and move radially outwards, driven by interchange motion. These filaments cause enhanced plasma–wall interactions compared to the level estimated by only considering time-averaged plasma parameters, reduce the efficiency of radio frequency wave heating and is likely related to the empirical discharge density limit. When measured as a time series from a stationary point (either as ion saturation current from electrical probes probes or as emitted light intensity from gas puff imaging), the statistical properties of the turbulent fluctuations in the scrape-off layer are robust across devices, confinement modes and plasma parameters. The highly intermittent fluctuations exhibit skewed and flattened probability density functions and power spectra that are flat for low frequencies and have a power-law tail for high frequencies. Conditional averaging reveals that large-amplitude structures have a sharp, exponential rise and a slower, exponential decay. Both the peak amplitudes of these structures and the waiting time between them are exponentially distributed. In this thesis, a stochastic model describing the time series as a superposition of uncorrelated, two-sided exponential pulses with exponentially distributed amplitudes arriving according to a Poisson process is analysed and its assumptions and predictions are compared with measurement data. This model is consistent with all the above statistical properties. The predictive capabilities of the model are improved by deriving expressions for the rate of threshold crossings and the time the signal spends above a given threshold level. The effects of additive noise and different amplitude distributions are also considered. Parameter estimation from moments, probability density functions and characteristic functions is examined using Monte-Carlo simulations. The model predictions are favorably compared to measurement data from experiments on the TCV and Alcator C-Mod devices