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Title: Study of plasma equilibrium in toroidal fusion devices using mesh-free numerical calculation method

Abstract

Plasma confinement using external magnetic field is one of the successful ways leading to the controlled nuclear fusion. Development and validation of the solution process for plasma equilibrium in the experimental toroidal fusion devices is the main subject of this work. Solution of the nonlinear 2D stationary problem as posed by the Grad-Shafranov equation gives quantitative information about plasma equilibrium inside the vacuum chamber of hot fusion devices. This study suggests solving plasma equilibrium equation which is essential in toroidal nuclear fusion devices, using a mesh-free method in a condition that the plasma boundary is unknown. The Grad-Shafranov equation has been solved numerically by the point interpolation collocation mesh-free method. Important features of this approach include truly mesh free, simple mathematical relationships between points and acceptable precision in comparison with the parametric results. The calculation process has been done by using the regular and irregular nodal distribution and support domains with different points. The relative error between numerical and analytical solution is discussed for several test examples such as small size Damavand tokamak, ITER-like equilibrium, NSTX-like equilibrium, and typical Spheromak.

Authors:
;  [1];  [2]
  1. Radiation Application Department, Shahid Beheshti University, Tehran (Iran, Islamic Republic of)
  2. Nuclear Safety and Radiological Protection Group, Nuclear Science and Technology Research Institute, Tehran (Iran, Islamic Republic of)
Publication Date:
OSTI Identifier:
22599941
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 8; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; ANALYTICAL SOLUTION; CALCULATION METHODS; COMPARATIVE EVALUATIONS; EQUILIBRIUM; ERRORS; GRAD-SHAFRANOV EQUATION; INTERPOLATION; ITER TOKAMAK; MAGNETIC FIELDS; NONLINEAR PROBLEMS; NSTX DEVICE; PLASMA; PLASMA CONFINEMENT; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Rasouli, C., Abbasi Davani, F., and Rokrok, B.. Study of plasma equilibrium in toroidal fusion devices using mesh-free numerical calculation method. United States: N. p., 2016. Web. doi:10.1063/1.4960680.
Rasouli, C., Abbasi Davani, F., & Rokrok, B.. Study of plasma equilibrium in toroidal fusion devices using mesh-free numerical calculation method. United States. doi:10.1063/1.4960680.
Rasouli, C., Abbasi Davani, F., and Rokrok, B.. 2016. "Study of plasma equilibrium in toroidal fusion devices using mesh-free numerical calculation method". United States. doi:10.1063/1.4960680.
@article{osti_22599941,
title = {Study of plasma equilibrium in toroidal fusion devices using mesh-free numerical calculation method},
author = {Rasouli, C. and Abbasi Davani, F. and Rokrok, B.},
abstractNote = {Plasma confinement using external magnetic field is one of the successful ways leading to the controlled nuclear fusion. Development and validation of the solution process for plasma equilibrium in the experimental toroidal fusion devices is the main subject of this work. Solution of the nonlinear 2D stationary problem as posed by the Grad-Shafranov equation gives quantitative information about plasma equilibrium inside the vacuum chamber of hot fusion devices. This study suggests solving plasma equilibrium equation which is essential in toroidal nuclear fusion devices, using a mesh-free method in a condition that the plasma boundary is unknown. The Grad-Shafranov equation has been solved numerically by the point interpolation collocation mesh-free method. Important features of this approach include truly mesh free, simple mathematical relationships between points and acceptable precision in comparison with the parametric results. The calculation process has been done by using the regular and irregular nodal distribution and support domains with different points. The relative error between numerical and analytical solution is discussed for several test examples such as small size Damavand tokamak, ITER-like equilibrium, NSTX-like equilibrium, and typical Spheromak.},
doi = {10.1063/1.4960680},
journal = {Physics of Plasmas},
number = 8,
volume = 23,
place = {United States},
year = 2016,
month = 8
}
  • This paper attempts to study the application of mesh-free method in the numerical simulations of the higher-order continuum structures. A high-order bending beam considers the effect of the third-order derivative of deflections, and can be viewed as a one-dimensional higher-order continuum structure. The moving least-squares method is used to construct the shape function with the high-order continuum property, the curvature and the third-order derivative of deflections are directly interpolated with nodal variables and the second- and third-order derivative of the shape function, and the mesh-free computational scheme is establish for beams. The coupled stress theory is introduced to describe themore » special constitutive response of the layered rock mass in which the bending effect of thin layer is considered. The strain and the curvature are directly interpolated with the nodal variables, and the mesh-free method is established for the layered rock mass. The good computational efficiency is achieved based on the developed mesh-free method, and some key issues are discussed.« less
  • The equilibrium condition for a toroidal pinch is formulated as a nonlinear operator equation for the parameter functions representing the plasma boundary. This operator equation is transformed into an optimization problem, and a finite-dimensional approximation to the optimization problem is given which is treated by an algorithm proposed by Brent (''Algorithms for Minimization without using Derivatives,'' Prentice-Hall, Englewood Cliffs, N.J., 1973). This procedure turns out to be numerically stable and reasonably fast. This approach may easily be generalized to treat a variety of free boundary problems in two and three dimension.
  • Controlling the boundary layer in fusion-grade, high-performance, plasma discharges is essential for the successful development of toroidal magnetic confinement power generating systems. A promising approach for controlling the boundary plasma is based on the use of small, externally applied, edge resonant magnetic perturbation (RMP) fields (δmore » $$b_⊥^{ext}$$ ≈ $$10^{-4}$$ → $$10^{-3}$$ T). A long-term focus area in tokamak fusion research has been to find methods, involving the use of non-axisymmetric magnetic perturbations to reduce the intense particle and heat fluxes to the wall. Experimental RMP research has progressed from the early pioneering work on tokamaks with material limiters in the 1970s, to present day research in separatrix-limited tokamaks operated in high-confinement mode, which is primarily aimed at the mitigation of the intermittent fluxes due edge localized modes. At the same time the theoretical research has evolved from analytical models to numerical simulations, including the full 3D complexities of the problem. Following the first demonstration of ELM suppression in the DIII-D tokamak during 2003, there has been a rapid worldwide growth in theoretical, numerical and experimental edge RMP research resulting in the addition of ELM control coils to the ITER baseline design [A. Loarte, et al., Nucl. Fusion 54 (2014) 033007]. This review provides an overview of edge RMP research including a summary of the early theoretical and numerical background along with recent experimental results on improved particle and energy confinement in tokamaks triggered by edge RMP fields. The topics covered make up the basic elements needed for developing a better understanding of 3D magnetic perturbation physics, which is required in order to utilize the full potential of edge RMP fields in fusion relevant high performance, H-mode, plasmas.« less