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

International audienceThe 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

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

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

International audienceThe 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

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

New applications of Equinox code for real-time plasma equilibrium and profile reconstruction for tokamaks

Recent development of real-time equilibrium code Equinox [1] using a fixed-point algorithm [2] allow major plasma magnetic parameters to be identified in real-time, using rigorous analytical method. The code relies on the boundary flux code providing flux values on the first wall of vacuum vessel. By means of least-square minimization of differences between magnetic field obtained from previous solution and the next measurements the code identifies the source term of the non-linear Grad-Shafranov equation [3]. The strict use of analytical equations together with a flexible algorithm offers an opportunity to include new measurements into stable magnetic equilibrium code and compare the results directly between several tokamaks while maintaining the same physical model (i.e. no iron model is necessary inside the equilibrium code). The successful implementation of this equilibrium code for JET and Tore Supra have been already published [1], in this paper, we show the preliminary results of predictive runs of the Equinox code using the ITER geometry.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France

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 machine-learning-based tool for last closed magnetic flux surface reconstruction on tokamak

Nuclear fusion power created by tokamak devices holds one of the most promising ways as a sustainable source of clean energy. One main challenge research field of tokamak is to predict the last closed magnetic flux surface (LCFS) determined by the interaction of the actuator coils and the internal tokamak plasma. This work requires high-dimensional, high-frequency, high-fidelity, real-time tools, further complicated by the wide range of actuator coils input interact with internal tokamak plasma states. In this work, we present a new machine learning model for reconstructing the LCFS from the Experimental Advanced Superconducting Tokamak (EAST) that learns automatically from the experimental data of EAST. This architecture can check the control strategy design and integrate it with the tokamak control system for real-time magnetic prediction. In the real-time modeling test, our approach achieves over 99% average similarity in LCFS reconstruction of the entire discharge process. In the offline magnetic reconstruction, our approach reaches over 93% average similarity

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