Coordinate transformation and construction of finite element mesh in a diverted tokamak geometry |
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Authors: | Y Nishimura JC Lyu FL Waelbroeck LJ Zheng CE Michoski |
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Institution: | 1. Institute of Space and Plasma Sciences, National Cheng Kung University, Tainan, Taiwan;2. Institute for Fusion Studies, University of Texas, Austin, Texas, USA;3. Institute for Computational Engineering and Sciences, University of Texas, Austin, Texas, USA |
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Abstract: | A coordinate transformation technique between straight magnetic field line coordinate system (Ψ, θ) and Cartesian coordinate system (R, Z) is presented employing a Solov'ev solution of the Grad-Shafranov equation. Employing the equilibrium solution, the poloidal magnetic flux Ψ(R, Z) of a diverted tokamak, magnetic field line equation is solved computationally to find curves of constant poloidal angle θ, which provides us with explicit relations R = R(Ψ, θ) and Z = Z(Ψ, θ). Correspondingly, conversion from one coordinate to the other along particle trajectories in the vicinity of separatrix is demonstrated. Based on the magnetic structure, a finite element mesh is generated in a diverted tokamak geometry to solve Poisson's equation. |
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Keywords: | coordinate transformation Poisson's equation Tokamak divertor |
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