The self-consistent equilibrium and diffusion code sced

Blum, Jacques; Foll, J. Le; Thooris, B.

doi:10.1016/0010-4655(81)90149-1

Cited by 76 publications

(60 citation statements)

References 14 publications

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“…Because of the presence of ψ on both sides of the equality, the GSh equation is classified as a nonlinear elliptic partial differential equation. In general, this type of equation can only be solved via iterative methods, such as a Picard iteration scheme [6]. The flux ψ n-1 at iteration step n-1 is used to find the flux ψ n at step n,…”

Section: General Mhd Equilibriummentioning

confidence: 99%

“…There exist two distinct classes of numerical techniques: Lagrangian schemes that use curvilinear flux coordinates to map plasma geometry and which involve adaptive grid [2], variational [3], perturbative [4] or inverse coordinates [5] methods. The second class of techniques is based on an Eulerian scheme, relying on a twodimensional (2D) mesh without any direct link to plasma shape [6,7]. We will use a direct approach, where the geometric space is meshed instead of the flux space [8], so plasma with diverted configurations, i.e.…”

Section: Introductionmentioning

confidence: 99%

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High-resolution magnetohydrodynamic equilibrium code for unity beta plasmas

Gourdain¹,

Leboeuf²,

Neches³

2006

Journal of Computational Physics

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There is great interest in the properties of extremely high-beta magnetohydrodynamic equilibria in axisymmetric toroidal geometry and the stability of such equilibria. However, few equilibrium codes maintain solid numerical behavior as beta approaches unity. The free-boundary algorithm presented herein utilizes a numerically stabilized multigrid method, current density input, position control, magnetic axis search, and dynamically adjusted simulated annealing. This approach yields numerically robust behavior in the spectrum of cases ranging from low to very high beta configurations. As the convergence time depends linearly on the total number of grid points, the production of extremely fine, low-error equilibria becomes possible. Such a code facilitates a variety of intriguing applications which include the exploration of the stability of extreme Shafranov shift equilibria.

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Section: General Mhd Equilibriummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

High-resolution magnetohydrodynamic equilibrium code for unity beta plasmas

Gourdain¹,

Leboeuf²,

Neches³

2006

Journal of Computational Physics

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show abstract

“…The first sort is based on an Eulerian scheme, relying on a twodimensional (2D) mesh without any direct link to plasma shape or properties. 4,5 The second one is based on a Lagrangian scheme using curvilinear flux coordinates to map plasma geometry, 6 involving adaptive grid, 7 variational, 8 or perturbative approaches, 9 or inverse coordinates 10 methods. Nevertheless, many of these excellent methods cannot compute asymptotic high beta equilibria such as the one presented at the end of this paper.…”

Section: Introductionmentioning

confidence: 99%

Contour dynamics method for solving the Grad–Shafranov equation with applications to high beta equilibria

Gourdain

Leboeuf

2004

Physics of Plasmas

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Numerous methods exist to solve the Grad-Shafranov equation, describing the equilibrium of a plasma confined by an axisymmetric magnetic field. Nevertheless, they are limited to low beta or small plasma pressure. Combining a nonconservative variational principle with a contour dynamics approach, the approach presented in this paper converges for extreme high beta configurations. By reducing the dimension of the problem from two to one, a compact and efficient numerical algorithm can be developed, and a wide range of boundary shapes can be utilized. Furthermore, the iterative nature of this technique greatly facilitates convergence at high beta while minimizing computation times.

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“…We are solving this FBE problem by the numerical methods outlined in [8,17]. The poloidal flux is approximated by a finite dimensional function that is piecewise linear with respect to an unstructured triangular mesh.…”

Section: Free Boundary Equilibrium Computationmentioning

confidence: 99%

“…the magnetic field lines, for a given current configuration. We are using an implementation of the numerical methods described in [8,17] to find approximate solutions of the FBE problem.…”

Section: Introductionmentioning

confidence: 99%

Towards Automated Magnetic Divertor Design for Optimal Heat Exhaust

et al. 2016

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Abstract. Avoiding excessive structure heat loads in future fusion tokamaks is regarded as one of the greatest design challenges. In this paper, we aim at developing a tool to study how the severe divertor heat loads can be mitigated by reconfiguring the magnetic confinement. For this purpose, a free boundary equilibrium code is integrated with a plasma edge transport code to work in an automated fashion. Next, a practical and efficient adjoint based sensitivity calculation is proposed to evaluate the sensitivities of the integrated code. The sensitivity calculation is finally applied to a realistic test case and compared with finite difference sensitivity calculations.

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The self-consistent equilibrium and diffusion code sced

Cited by 76 publications

References 14 publications

High-resolution magnetohydrodynamic equilibrium code for unity beta plasmas

High-resolution magnetohydrodynamic equilibrium code for unity beta plasmas

Contour dynamics method for solving the Grad–Shafranov equation with applications to high beta equilibria

Towards Automated Magnetic Divertor Design for Optimal Heat Exhaust

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