Cédric Boulbe

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.

Quasi-static free-boundary equilibrium of toroidal plasma with CEDRES++: Computational methods and applications

We present a comprehensive survey of the various computational methods in CEDRES++ for finding equilibria of toroidal plasma. Our focus is on free-boundary plasma equilib-ria, where either poloidal field coil currents or the temporal evolution of voltages in poloidal field circuit systems are given data. Centered around a piecewise linear finite element representation of the poloidal flux map, our approach allows in large parts the use of established numerical schemes. The coupling of a finite element method and a boundary element method gives consistent numerical solutions for equilibrium problems in unbounded domains. We formulate a new Newton method for the discretized non-linear problem to tackle the various non-linearities, including the free plasma boundary. The Newton method guarantees fast convergence and is the main building block for the inverse equilibrium problems that we can handle in CEDRES++ as well. The inverse problems aim at finding either poloidal field coil currents that ensure a desired shape and position of the plasma or at finding the evolution of the voltages in the poloidal field circuit systems that ensure a prescribed evolution of the plasma shape and position. We provide equilibrium simulations for the tokamaks ITER and WEST to illustrate the performance of CEDRES++ and its application areas.

Real-time plasma equilibrium reconstruction in a Tokamak

The problem of equilibrium of a plasma in a Tokamak is a free boundary problemdescribed by the Grad-Shafranov equation in axisymmetric configurations. The right hand side of this equation is a non linear source, which represents the toroidal component of the plasma current density. This paper deals with the real time identification of this non linear source from experimental measurements. The proposed method is based on a fixed point algorithm, a finite element resolution, a reduced basis method and a least-square optimization formulation.

Computing Beltrami Fields

For solving the nonlinear equations governing force-free fields, an iterative methodology based on the splitting of the problem is described. On the basis of this splitting, three families of subproblems have to be solved numerically. The first problem consists to find a potential field. A mixed hybrid method is used to solve it. The second problem, which is a curl-div system, is solved by means of a mixed method. The last problem is a transport equation which is approximated using a streamline diffusion technique. Numerical three-dimensional experiments and results are given to illustrate the efficiency of the method.

Innovative signal processing and data analysis methods on JET for control in the perspective of next-step devices

In the last few years, it has been realized that more sophisticated control schemes are necessary to push the boundaries of tokamak operation and the performance of reactor-like machines. In addition, JET needs to operate safely with the new metallic wall and such protection will be needed for ITER. These objectives have motivated the development, benchmark and validation of new signal processing and data analysis methods. Two new approaches for the determination of the magnetic topology in real time have been validated on an extensive database of JET discharges, including advanced tokamak scenarios. Robust methods of confinement regime identification and disruption prediction are a prerequisite for safe, general control schemes. New identifiers have been developed and their success rates exceed 99% in determining whether plasmas are in the L or H mode. A new disruption predictor is being developed and has already provided success rates higher than 90% in realistic real-time conditions. Moreover, the generalization capability of this new predictor has been confirmed by applying it to new experimental campaigns not used for the training. The success rate remains high even more than ten campaigns, or about four years, after the last one used for the training. The deployment of video cameras in real time requires the development of new image processing algorithms, which have already been implemented and validated successfully on JET for the real-time identification of hot spots with a time resolution of tens of milliseconds. A series of new feedback schemes has also been explicitly developed not much to control the plasma but to really improve the physics understanding of some phenomena. Particularly interesting are the simultaneous control of the safety factor and pressure profiles and the real-time tracking of toroidal Alfven eigenmode instabilities. These advanced feedback schemes for physics understanding often require more advanced signal processing techniques like adaptive filtering, which have already been implemented. The paper concludes by discussing the use of these real-time analysis and control developments in next-step machines such as ITER.

2D interpolation and extrapolation of discrete magnetic measurements with toroidal harmonics for equilibrium reconstruction in a tokamak

We present a method based on the use of toroidal harmonics and on a modelization of the poloidal field coils and divertor coils for the 2D interpolation and extrapolation of discrete magnetic measurements in a tokamak. The method is generic and can be used to provide the Cauchy boundary conditions needed as input by a fixed domain equilibrium reconstruction code like Equinox (Blum et al 2012 J. Comput. Phys. 231 960–80). It can also be used to extrapolate the magnetic measurements in order to compute the plasma boundary itself. The proposed method and algorithm are detailed in this paper and results from numerous numerical experiments are presented. The method is foreseen to be used in the real-time plasma control loop on the WEST tokamak (Bucalossi et al 2011 Fusion Eng. Des. 86 684–8).

REAL-TIME EQUILIBRIUM RECONSTRUCTION IN A TOKAMAK

This paper deals with the numerical reconstruction of the plasma current density in a Tokamak and of its equilibrium. The problem consists in the identification of a non‐linear source in the 2D Grad‐Shafranov equation, which governs the axisymmetric equilibrium of a plasma in a Tokamak. The experimental measurements that enable this identification are the magnetics on the vacuum vessel, but also polarimetric and interferometric measures on several chords, as well as motional Stark effect or pressure measurements. The reconstruction can be obtained in real‐time using a finite element method, a non‐linear fixed‐point algorithm and a least‐square optimization procedure.

Validation of Magnetic Reconstruction Codes for Real-Time Applications

Abstract The real-time reconstruction of the plasma magnetic equilibrium in a tokamak is a key point to access high-performance regimes. Indeed, the shape of the plasma current density profile is a direct output of the reconstruction and has a leading effect for reaching a steady-state high-performance regime of operation. The challenge is thus to develop real-time methods and algorithms that reconstruct the magnetic equilibrium from the perspective of using these outputs for feedback control purposes. In this paper the validation of the JET real-time equilibrium reconstruction codes using both a Bayesian approach and a full equilibrium solver named Equinox will be detailed, the comparison being performed with the off-line equilibrium code EFIT (equilibrium fitting) or the real-time boundary reconstruction code XLOC (X-point local expansion). In this way a significant database, a methodology, and a strategy for the validation are presented. The validation of the results has been performed using a validated database of 130 JET discharges with a large variety of magnetic configurations. Internal measurements like polarimetry and motional Stark effect have been also used for the Equinox validation including some magnetohydrodynamic signatures for the assessment of the reconstructed safety profile and current density.

A New Simulation Framework Based on the Kepler and Scicos Open-Source Software for the Design and Qualification of Tokamak Control Algorithms: First Test Case Results

Abstract Plasma control is recognized to be a crucial issue for the achievement of ITER objectives. One of the most challenging tasks for the preparation of the ITER operation will therefore be the design and qualification of a variety of control algorithms. This highlights the need for a simulation platform capable of supporting the design, integration and test of advanced control algorithms on complex physics models. With this aim, a generic multi-purpose “flight” simulator (GMFS) is being developed at IRFM (Institut de Recherche sur la Fusion par confinement Magnétique), CEA Cadarache, France. The GMFS is based on Kepler, a free interdisciplinary open-source Java software. Kepler will be used as a simulation platform to test and improve control algorithms before their actual use in the real control system. The physics and engineering codes complementary to the control algorithms will be supplied by the EFDA Integrated Tokamak Modelling Task Force (ITM-TF). The GMFS will be benchmarked, at the beginning, on the Tore Supra Tokamak. In this paper we will report on a test case suitable to demonstrate the feasibility of a part of GMFS, namely the development of workflows where to create and verify ITER plasma boundary feedback control algorithms. It consists of: a) derivation of a linear plasma response model; b) design of a control diagram under the ScicosLab/Scicos open-source software; c) porting of the diagram under Kepler; d) substitution of the Kepler controller with a controller generated by a special Scicos extension; e) substitution of the simplified static linear model with the free-boundary equilibrium code CEDRES++. The test case demonstrated the feasibility of employing Kepler, ScicosLab/Scicos and other expressly-made codes in view of the conception of valuable instruments for the active control of ITER and it can be considered as a first step in this direction.

Real-time identification of the current density profile in the JET tokamak: method and validation

The real-time reconstruction of the plasma magnetic equilibrium in a Tokamak is a key point to access high performance regimes. Indeed, the shape of the plasma current density profile is a direct output of the reconstruction and has a leading effect for reaching a steady-state high performance regime of operation. In this paper we present the methodology followed to identify numerically the plasma current density in a Tokamak and its equilibrium. In order to meet the real-time requirements a C++ software has been developed using the combination of a finite element method, a nonlinear fixed point algorithm associated to a least square optimization procedure. The experimental measurements that enable the identification are the magnetics on the vacuum vessel, the interferometric and polarimetric measurements on several chords and the motional Stark effect. Details are given about the validation of the reconstruction on the JET tokamak, either by comparison with ‘off-line’ equilibrium codes or real time software computing global quantities.