Model-based estimation of tokamak plasma profiles and physics parameters: algorithm overview and application to ITER

Abstract Combining dynamic models and measurements into a consistent plasma state estimate is an important challenge for ITER and DEMO, due to the inherent limitations regarding diagnostic coverage in a nuclear fusion reactor environment. In this work, a model-based estimation algorithm is proposed to improve real-time and post-shot estimation of tokamak plasma profiles. The RAPTOR rapid transport solver is employed as a dynamic state observer for the parallel current density <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>j</mml:mi> <mml:mrow> <mml:mi>par</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , the electron temperature <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> and the electron density <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>n</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , applying an Extended Kalman Filter (EKF). The implementation of an EKF which, in addition to the plasma profiles, estimates model disturbances and model parameters has enabled us to account for systematic model-reality mismatches and provides an avenue to automatically validate simple transport models that are easily interpretable and machine-independent, based on raw experimental data. Estimates of transport model coefficients can be directly used to find adequate settings for launching a predictive simulation, accelerating inter-discharge scenario design. Furthermore, a method for maximum likelihood identification of model uncertainty statistics from a database of recorded measurement data is proposed. The RAPTOR EKF is tested for reconstruction of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>j</mml:mi> <mml:mrow> <mml:mi>par</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>n</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> profile evolution for an ITER Q = 10 plasma discharge, from ramp-up to ramp-down, based on synthetic Thomson scattering and boundary poloidal flux measurements, generated by adding realistic measurement noise to a DINA-JINTRAC simulation. This approach enables improved safety factor profile estimation in the absence of direct internal current density measurements.