Finite element methods on composite meshes for tuning plasma equilibria in tokamaks View Full Text


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Article Info

DATE

2018-12

AUTHORS

Holger Heumann, Francesca Rapetti, Xiao Song

ABSTRACT

The fundamental concept of magnetically confined nuclear fusion devices is the magnetohydrodynamic (MHD) equilibrium: the pressure gradient due to highly energetic charged particles is balanced by the Lorenz force due to strong magnetic fields. Hence, numerical methods for MHD equilibria are also fundamental for fusion engineering applications. We rely here on a finite element method on composite meshes for the simulation of axisymmetric equilibria in tokamaks, torus-shaped nuclear fusion devices. One mesh with Cartesian quadrilaterals covers the domain accessible by the plasma and one mesh with triangles discretizes the region outside the chamber. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the principal unknown, the poloidal magnetic flux, while preserving accurate meshing of the geometric details in the exterior. We show that higher order regularity allows to formulate appropriate optimal control problems that help to find a special type of equilibria, called snowflake equilibria, that are a very promising concept to mitigate high heat loads due to plasma escaping particles. More... »

PAGES

8

References to SciGraph publications

  • 2009. Numerical Zoom and the Schwarz Algorithm in DOMAIN DECOMPOSITION METHODS IN SCIENCE AND ENGINEERING XVIII
  • 1977-06. Composite mesh difference methods for elliptic boundary value problems in NUMERISCHE MATHEMATIK
  • 1987. Ideal Magnetohydrodynamics in NONE
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