Quasi-static Free-Boundary Equilibrium of Toroidal Plasma with CEDRES++: Computational Methods and Applications

Abstract : We present a comprehensive survey of the various computational methods in CEDRES++ for finding equilibria of toroidal plasma. Our focus is on free-boundary plasma equilib-ria, where either poloidal field coil currents or the temporal evolution of voltages in poloidal field circuit systems are given data. Centered around a piecewise linear finite element representation of the poloidal flux map, our approach allows in large parts the use of established numerical schemes. The coupling of a finite element method and a boundary element method gives consistent numerical solutions for equilibrium problems in unbounded domains. We formulate a new Newton method for the discretized non-linear problem to tackle the various non-linearities, including the free plasma boundary. The Newton method guarantees fast convergence and is the main building block for the inverse equilibrium problems that we can handle in CEDRES++ as well. The inverse problems aim at finding either poloidal field coil currents that ensure a desired shape and position of the plasma or at finding the evolution of the voltages in the poloidal field circuit systems that ensure a prescribed evolution of the plasma shape and position. We provide equilibrium simulations for the tokamaks ITER and WEST to illustrate the performance of CEDRES++ and its application areas.
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Holger Heumann, Jacques Blum, Cedric Boulbe, Blaise Faugeras, Gael Selig, et al.. Quasi-static Free-Boundary Equilibrium of Toroidal Plasma with CEDRES++: Computational Methods and Applications. Journal of Plasma Physics, Cambridge University Press (CUP), 2015, pp.35. ⟨10.1017/S0022377814001251⟩. ⟨hal-01088772⟩

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