CASTOR Inria

Research

CASTOR stands for the "Control of PlAsma inSTability, Optimization and model Reduction". CASTOR focuses on the development of innovative numerical tools to improve the modeling and control of complex plasma flows, governed by the equations of magnetohydrodynamics (MHD). The two main applications addressed in CASTOR are magnetic fusion plasmas and astrophysical plasmas, where MHD models can be used to describe turbulent transport and instabilities yielding transitions between equilibrium states. The objectives are to develop methods enabling real-time control of MHD flows and optimization of plasma discharge scenarios in tokamaks. Castor is a common project between Inria, Université Côte d'Azur and CNRS through the Laboratoire Jean-Alexandre Dieudonné (LJAD). It gathers researchers from the PDE and Numerical Analysis group and the Numerical Modeling and Fluid Dynamics group of LJAD. The models we consider possess different levels of complexity, ranging from single-fluid, incompressible to multi-component, compressible models. The main applications addressed in CASTOR are magnetic fusion plasmas and astrophysical plasmas, where MHD models can be used to describe turbulent transport and instabilities yielding transitions between equilibrium states. In both cases, adjoint methods as a tool to optimize or control the model outputs will be developed together with reduced models for a faster response, enabling real-time control of these flows and optimization of plasma discharge scenarios in tokamaks." The modeling of nuclear fusion plasmas in tokamaks relies heavily on magnetohydrodynamics (MHD), which treats the plasma as a conductive fluid influenced by magnetic fields. This framework has been crucial in predicting plasma behavior, particularly for understanding macroscopic instabilities such as kink modes, tearing modes, and edge-localized modes (ELMs). Current challenges in controlling these instabilities include the difficulty in predicting their onset conditions in realistic operational scenarios, or limitations in real-time response systems for instability mitigation. These challenges are central to international fusion projects like ITER, where maintaining plasma stability remains a critical hurdle to achieving sustainable fusion energy.

Computational Fluid Dynamics

The modeling of nuclear fusion plasmas in tokamaks relies heavily on magnetohydrodynamics, which treats the plasma as an electrically conducting fluid responding to magnetic fields. This framework has been crucial in predicting plasma behavior in tokamaks, particularly for understanding macroscopic instabilities such as kink modes, tearing modes, and edge-localized modes (ELMs). Current challenges in controlling these instabilities include the difficulty in predicting their onset conditions in realistic operational scenarios, or limitations in real-time response systems for instability mitigation. These challenges are central to international fusion projects like ITER, where maintaining plasma stability remains a critical hurdle to achieving sustainable fusion energy.

Modeling of turbulent flows

The modeling of nuclear fusion plasmas in tokamaks relies heavily on magnetohydrodynamics (MHD), which treats the plasma as a conductive fluid influenced by magnetic fields. This framework has been crucial in predicting plasma behavior, particularly for understanding macroscopic instabilities such as kink modes, tearing modes, and edge-localized modes (ELMs). Current challenges in controlling these instabilities include the difficulty in predicting their onset conditions in realistic operational scenarios, or limitations in real-time response systems for instability mitigation. These challenges are central to international fusion projects like ITER, where maintaining plasma stability remains a critical hurdle to achieving sustainable fusion energy.

Magnetohydrodynamics

Magnetohydrodynamics (MHD) couples Maxwell’s equations of electromagnetism with hydrodynamics to describe the macroscopic behavior of conducting fluids such as plasmas. It plays a crucial role in astrophysics, planetary magnetism, engineering and controlled nuclear fusion. The study of fluid dynamics is of key relevance for the simulation of environmental systems, including atmospheric and oceanic flows.

Modeling, Numerical Analysis, Scientific Computing, Plasma Physics.

Email: afeintou.sangam [at] univ-cotedazur.fr

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External Group Collaborator

Didier Clamond

Full professor at UniCA

Gravity Waves and Nonlinear Waves, Fluid and Continuum Mechanics, Mathematical and Numerical Modelling

Email: didier.clamond [at] univ-cotedazur.fr

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Yannick Ponty

Research director at CNRS

Magnetohydrodynamics, Fluid and dynamo instabilities, High Performance Computing.

Email: yannick.ponty [at] oca.eu

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Team Assistant at Inria

Nathalie Nordmann

Email: nathalie.nordmann [at] inria.fr

Doc. students

Raphaël Granger

PhD student

Email: raphael.granger [at] inria.fr

Clément Mariot

PhD student

Email: clement.mariot [at] inria.fr

Aleksandar Stojcheski

PhD student

Email: aleksandar.stojcheski [at] inria.fr

Predocs

Sarah Ali

Email: sarah.ali [at] inria.fr

Lucas Bongiorno

Email: lucas.bongiorno [at] inria.fr

Postdocs

Mustapha Bahari

Email: mustapha.bahari [at] inria.fr

Software

NICE (Newton direct and Inverse Computation for Equilibrium)

The NICE code computes tokamak plasma equilibria. Its equilibrium reconstruction functionalities are routinely used at CEA on the WEST tokamak, and at UKAEA by the STEP team since 2023. NICE is a code that fits with the required standards of the IMAS platform. This code allows for industrial applications. IMAS is a platform adopted from the fusion community in order to collect and operate different codes (plasma equilibrium, transport, and many others) together and which is/will be used for all physics modeling and analysis in tokamaks, particularly ITER. It uses a modular approach that builds around a standardized data representation that can describe both experimental and simulation data for any tokamak.

NICE contains dedicated solvers for several problems of free-boundary plasma equilibrium:

Real-time plasma free-boundary only reconstruction and magnetic measurements interpolation.

The method used for this computation mode is based on the use of toroidal harmonics and on a modeling of the poloidal field coils and divertor coils to perform the 2D interpolation and extrapolation of discrete magnetic measurements in a tokamak and the identification of the plasma boundary. The method is generic and can be used to provide the Cauchy boundary conditions needed as input by a fixed domain equilibrium reconstruction computation. It can also be used to extrapolate the magnetic measurements to compute the plasma boundary itself.

Feature point two

Full free-boundary equilibrium reconstruction from magnetic measurements and possibly internal measurements (interferometry, classical linear approximation polarimetry or Stokes model polarimetry, Motional Stark Effect, and pressure). In this mode, the problem solved consists of the identification of the plasma current density, a non-linear source in the 2D Grad-Shafranov equation, which governs the axisymmetric equilibrium of plasma in a Tokamak.

Feature point three

Direct and inverse, static and quasi-static evolution free-boundary equilibrium computations. In a Tokamak, at the slow resistive diffusion time scale, the magnetic configuration in the plasma can be described by the MHD equilibrium equations are inside the plasma, and Maxwell equations are outside. Moreover, the magnetic field is often supposed not to depend on the azimuthal angle. Under this assumption of axisymmetric configuration, the equilibrium in the whole space reduces to solving a 2D problem in which the magnetic field in the plasma is described by the well-known Grad Shafranov equation. The unknown of this problem is the poloïdal magnetic flux. In this computation mode, the direct problem consists of computing the magnetic configuration and the plasma boundary, given a plasma current density profile and the total current in each poloïdal field coil. The aim of the inverse problem is to find currents in the PF coils that best fit a given plasma shape. NICE gathers in a single finite-element framework different equilibrium computation modes and numerical methods from the former VACTH, EQUINOX and CEDRES++ codes developed within Castor project.

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NICE project leaders: B.Faugeras, C. Boulbe.

The JOREK non-linear MHD Code

Part of the Castor team participates actively to the non-linear extended MHD code JOREK resolves realistic toroidal tokamak X-point geometries with a G1 continuous flux-surface aligned grid including main plasma, scrape-off layer and divertor region.

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Contact: H. Guillard, B. N'Konga.

Open positions

PhD Position in Turbulent Flows

We are seeking a highly motivated PhD candidate to join our research group. The project focuses on experimental investigation of turbulent flows using advanced measurement techniques.

Requirements:

- Master's degree in Mechanical Engineering, Physics, or related field

- Strong background in fluid mechanics

- Experience with experimental techniques

Contact: castor.permanents [at] inria.fr

Postdoctoral Position in CFD

A postdoctoral position is available in the area of computational fluid dynamics, focusing on developing new numerical methods for complex flow simulations.

Requirements:

- PhD in Mechanical Engineering, Applied Mathematics, or related field

- Strong programming skills

- Experience with CFD software

Contact: castor.permanents [at] inria.fr