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An international experiment, ITER is proposed as the next essential and critical step on the path to demonstrating the scientific and technological feasibility of fusion energy. ITER would give unique opportunities to explore, in reactor…

Plasma Physics · Physics 2009-11-10 Adrianus C. C. Sips

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

Inaccurate description of the equilibrium can yield to spurious effects in gyrokinetic turbulence simulations. Also, the Vlasov solver and time integration schemes impact the conservation of physical quantities, especially in long-term…

An efficient numerical scheme for solving transport equations for tokamak plasmas within an integrated modelling framework is presented. The plasma transport equations are formulated as diffusion-advection equations in two coordinates (a…

Computational Physics · Physics 2024-06-17 Andrei Ludvig-Osipov , Dmytro Yadykin , Pär Strand

Designing superconducting coils for a tokamak fusion device is a highly coupled, non-linear design problem. The coils have many disparate engineering requirements from structural to power electronics, as well strict limits placed on the…

Plasma Physics · Physics 2025-12-19 Nathan Welch , Chris Marsden

Global gyrokinetic simulations are performed for the first time to investigate cross-scale interactions between electromagnetic ion temperature gradient (ITG) turbulence and fishbone instability in tokamak plasmas. The investigation of…

Plasma Physics · Physics 2025-11-07 Yuehao Ma , Bin Zhang , Pengfei Liu , Jian Bao , Zhihong Lin , Huishan Cai , Liutian Gao , AhDi Liu , Hailin Zhao , Tao Zhang

In this work, we focus on the development of the particle-in-cell scheme and the application to the studies of Alfv\'en waves and energetic particle physics in tokamak plasmas. The $\delta f$ and full $f$ schemes are formulated on the same…

Plasma Physics · Physics 2022-10-11 Zhixin Lu , Guo Meng , Roman Hatzky , Matthias Hoelzl , Philipp Lauber

Simulating gas flow within the divertor, which is a crucial component in nuclear fusion reactors, is essential for assessing and enhancing its design and performance. Traditional methods, such as the direct simulation Monte Carlo and the…

Plasma Physics · Physics 2024-09-11 Wei Li , Yanbing Zhang , Jianan Zeng , Lei Wu

This paper combines results from a local gyrokinetic code with analytical theory to reconstruct the global eigenmode structure of the linearly unstable ion-temperature-gradient (ITG) mode with adiabatic electrons. The simulations presented…

Plasma Physics · Physics 2014-08-05 P. A. Abdoul , D. Dickinson , C. M. Roach , H. R. Wilson

Microinstabilities drive turbulent fluctuations in inhomogeneous, magnetized plasmas. In the context of magnetic confinement fusion devices, this leads to an enhanced transport of particles, momentum, and energy, thereby degrading…

Plasma Physics · Physics 2024-03-20 Georgia Acton , Michael Barnes , Sarah Newton , Hanne Thienpondt

This paper is devoted to the numerical approximation of a nonlinear temperature balance equation, which describes the heat evolution of a magnetically confined plasma in the edge region of a tokamak. The nonlinearity implies some numerical…

Numerical Analysis · Mathematics 2011-05-31 Francis Filbet , Claudia Negulescu , Chang Yang

In the presented field line map approach the simulation domain of a tokamak is covered with a cylindrical grid, which is Cartesian within poloidal planes. Standard finite-difference methods can be used for the discretisation of…

Plasma Physics · Physics 2015-05-11 Andreas Stegmeir , David Coster , Omar Maj , Klaus Hallatschek , Karl Lackner

We have developed a hybrid code GMEC: Gyro-kinetic Magnetohydrodynamics (MHD) Energetic-particle Code that can numerically simulate energetic particle-driven Alfv\'en eigenmodes and energetic particle transport in tokamak plasmas. In order…

Plasma Physics · Physics 2024-02-23 Z. Y. Liu , P. Y. Jiang , S. Y. Liu , L. L. Zhang , G. Y. Fu

Gyrokinetic simulations are essential for understanding and controlling turbulence in fusion plasmas, yet they are oftentimes implemented in legacy codebases, in many cases CPU-bound. These are both hard to maintain and especially…

Plasma Physics · Physics 2026-04-08 Gianluca Galletti , Eric Volkmann , Johannes Brandstetter

In this work, an implicit scheme for particle-in-cell/Fourier electromagnetic simulations is developed and applied to studies of Alfv\'en waves in one dimension and three-dimensional tokamak plasmas. An analytical treatment is introduced to…

Plasma Physics · Physics 2021-02-03 Z. X. Lu , G. Meng , M. Hoelzl , Ph. Lauber

One of the most well-established codes for modeling non-linear Magnetohydrodynamics (MHD) for tokamak reactors is JOREK, which solves these equations with a B\'ezier surface based finite element method. This code produces a highly sparse…

Plasma Physics · Physics 2023-08-31 Alex Quinlan , Vandana Dwarka , Ihor Holod , Matthias Hoelzl

The key basis for tokamak plasma disruption modeling is to understand how currents flow to the plasma facing surfaces during plasma disruption events. In ITER tokamak, the occurrence of a limited number of major disruptions will…

Plasma Physics · Physics 2022-01-26 Cǎlin V. Atanasiu , Leonid E. Zakharov , Karl Lackner , Matthias Hoelzl

Geodesic acoustic modes (GAMs) are studied by means of the gyrokinetic global particle-in-cell code ORB5. Linear electromagnetic simulations in the low electron beta limit have been performed, in order to separate acoustic and Alfv\'enic…

Impacts of isotope ion mass on trapped electron mode (TEM) driven turbulence and zonal flows in magnetically confined fusion plasmas are investigated. Gyrokinetic simulations of TEM-driven turbulence in three-dimensional magnetic…

Plasma Physics · Physics 2026-02-27 Motoki Nakata , Masanori Nunami , Hideo Sugama , Tomo-Hiko Watanabe

Modern Tokamaks have evolved from the initial axisymmetric circular plasma shape to an elongated axisymmetric plasma shape that improves the energy confinement time and the triple product, which is a generally used figure of merit for the…

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