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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…

Numerical Analysis · Mathematics 2011-03-18 Jacques Blum , Cedric Boulbe , Blaise Faugeras

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…

Numerical Analysis · Mathematics 2009-11-26 Jacques Blum , Cédric Boulbe , Blaise Faugeras

In this paper, we present a new static and time-dependent MagnetoHydroDynamic (MHD) equilibrium code, TokaMaker, for axisymmetric configurations of magnetized plasmas, based on the well-known Grad-Shafranov equation. This code utilizes…

Plasma Physics · Physics 2024-02-28 C. Hansen , I. G. Stewart , D. Burgess , M. Pharr , S. Guizzo , F. Logak , A. O. Nelson , C. Paz-Soldan

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…

Numerical Analysis · Mathematics 2009-09-10 Jacques Blum , Cédric Boulbe , Blaise Faugeras

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…

Numerical Analysis · Mathematics 2016-11-27 Didier Mazon , Jacques Blum , Cédric Boulbe , Blaise Faugeras , A. Boboc , M. Brix , P. De Vries , S. Sharapov , L. Zabeo

Equilibrium reconstruction, which infers internal magnetic fields, plasmas current, and pressure distributions in tokamaks using diagnostic and coil current data, is crucial for controlled magnetic confinement nuclear fusion research.…

A new axisymmetric equilibrium solver has been written, called FEQIS (Flexible EQuIlibrium Solver), which purpose is to be used inside integrated modeling of tokamak plasmas. The FEQIS code solves the Grad-Shafranov equation and the…

Plasma Physics · Physics 2025-05-07 E. Fable , G. Tardini , L. Giannone , the ASDEX Upgrade Team

A new global two-fluid electromagnetic turbulence code, CENTORI, has been developed for the purpose of studying magnetically-confined fusion plasmas on energy confinement timescales. This code is used to evolve the combined system of…

Computational Physics · Physics 2015-05-30 P. J. Knight , A. Thyagaraja , T. D. Edwards , J. Hein , M. Romanelli , K. G. McClements

High-temperature superconducting (HTS) magnets and other advances have led to renewed interest in magnetic mirrors for fusion energy. The non-Maxwellian nature of mirror plasmas necessitates kinetic modeling to predict, optimize and design…

Plasma Physics · Physics 2026-05-29 Maxwell H. Rosen , Manaure Francisquez , Ammar Hakim , Gregory W. Hammett

JOREK is a massively parallel fully implicit non-linear extended MHD code for realistic tokamak X-point plasmas. It has become a widely used versatile code for studying large-scale plasma instabilities and their control developed in an…

In this work, we propose a novel physics informed neural network based algorithm for real time plasma boundary reconstruction in tokamak devices. The approach is based on a single Extreme Learning Machine network used to solve the…

Plasma Physics · Physics 2025-12-19 Federico Fiorenza , Sara Dubbioso , Gianmaria De Tommasi , Alfredo Pironti

A free-boundary, axisymmetric magnetohydrodynamic (MHD) equilibrium code, pyIPREQ, has been developed for Tokamak plasmas using finite difference and Green's function approach. The code builds upon the foundational frameworks of the PEST…

Plasma Physics · Physics 2025-10-06 Udaya Maurya , Amit K. Singh , Suman Aich , Jagabandhu Kumar , Rohit Kumar , Daniel Raju

A neural network model, EFITNN, has been developed capable of real-time magnetic equilibrium reconstruction based on HL-3 tokamak magnetic measurement signals. The model processes inputs from 68 channels of magnetic measurement data…

Plasma Physics · Physics 2024-05-21 Guohui Zheng , Songfen Liu , Zongyu Yang , Rui Ma , Xinwen Gong , Ao Wang , Shuo Wang , Wulyu Zhong

Equilibria in magnetic confinement devices result from force balancing between the Lorentz force and the plasma pressure gradient. In an axisymmetric configuration like a tokamak, such an equilibrium is described by an elliptic equation for…

Numerical Analysis · Mathematics 2025-06-13 Daniel A. Serino , Qi Tang , Xian-Zhu Tang , Tzanio V. Kolev , Konstantin Lipnikov

The accurate construction of tokamak equilibria, which is critical for the effective control and optimization of plasma configurations, depends on the precise distribution of magnetic fields and magnetic fluxes. Equilibrium fitting codes,…

The Grad-Shafranov (GS) equation is a nonlinear elliptic partial differential equation that governs the ideal magnetohydrodynamic equilibrium of a tokamak plasma. Previous studies have demonstrated the existence of multiple solutions to the…

Plasma Physics · Physics 2025-07-29 K. Pentland , N. C. Amorisco , P. E. Farrell , C. J. Ham

A hybrid spectral/finite-element code is developed to numerically solve the resistive finite-pressure magnetohydrodynamic equilibria without the necessity of postulating nested magnetic flux surfaces in the non-axisymmetric toroidal…

Plasma Physics · Physics 2024-12-30 Jian Zhang , Ping Zhu , Chris C. Hegna

The optimisation of scenarios and design of real-time-control in tokamaks, especially for machines still in design phase, requires a comprehensive exploration of solutions to the Grad-Shafranov (GS) equation over a high-dimensional space of…

Plasma Physics · Physics 2024-04-03 A. Agnello , N. C. Amorisco , A. Keats , G. K. Holt , J. Buchanan , S. Pamela , C. Vincent , G. McArdle

Various MHD (magnetohydrodynamic) equilibrium tools, some of which being recently developed or considerably updated, are used on the COMPASS tokamak at IPP Prague. MHD equilibrium is a fundamental property of the tokamak plasma, whose…

Plasma Physics · Physics 2014-12-08 J. Urban , L. C. Appel , J. F. Artaud , B. Faugeras , J. Havlicek , M. Komm , I. Lupelli , M. Peterka

A new force balance model for the EFIT magnetohydrodynamic equilibrium technique for tokamaks is presented which includes the full toroidal flow and anisotropy changes to the Grad-Shafranov equation. The free functions are poloidal flux…

Plasma Physics · Physics 2015-06-12 Michael Fitzgerald , Lynton C. Appel , Matthew J. Hole
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