Tokamak free-boundary plasma equilibrium computation using finite elements of class C0 and C1 within a mo

Abstract

The numerical simulation of the equilibrium of the plasma in a tokamak as well as its self-consistent coupling with resistive diusion should benet from higher regularity of the approximation of the magnetic ux map. In this work, we propose a nite element approach on a triangular mesh of the poloidal section, that couples piece-wise linear nite elements in a region that does not contain the plasma and reduced Hsieh-Clough-Tocher nite elements elsewhere. This approach gives the exibility to achieve easily and at low cost higher order regularity for the approximation of the ux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details in the rest of the computational domain. The continuity of the numerical solution at the coupling interface is weakly enforced by mortar projection. A new technique for the computation of the geometrical coecients is also presented.

First equilibrium reconstruction for ITER with the code NICE

“…It can also be used to solve the inverse problems consisting in finding the currents or voltages in the poloidal field coils which enable to have a desired plasma shape [9]. Finally the code NICE can be used with high order finite elements providing a smooth representation of the magnetic flux and field in the plasma [7,32].…”

Coupling finite elements of class C1 on composite curved meshes for second order elliptic problems

“…We denote by $$$ {\left\{{\phi}_i\right\}}_{i=1,3{N}_h} $$$ the basis of in duality with the dofs of Definition 1 associated with the $$$ {N}_h $$$ nodes of $$$ {\tau}_h $$$ and we refer to 12 for its detailed construction. See Reference 13 for application of these FEs in the context of plasma equilibrium simulations.…”

Tokamak Free-Boundary Plasma Equilibrium Computations in Presence of Non-Linear Materials

“…In this work, we are interested in simulating the equilibrium of a plasma for fusion reaction in a tokamak [4]. We push forward the method proposed in [10] to compute a plasma equilibrium in tokamak devices that include ferromagnetic parts. The choice of an iron-transformer tokamak is due to Paul-Henri Rebut, a French physicist, working on nuclear fusion.…”

“…In this work, we rely on the existing literature (see, e.g., [4,5,10,11,16,17]) to make some steps forwards. We approximate the solution of both the static and quasi-static evolution problems by adopting a non-overlapping domain decomposition mortar-like approach, coupling C 0 -C 1 finite elements, on a triangular mesh of the poloidal section of a iron tokamak.…”

“…We start in Section 2 by recalling from books such as [4,18] how to derive the famous Grad-Shafranov-Schlüter equation [14,19,26], to solve for the numerical simulation of the axisymmetric equilibrium of the plasma. Then, in Section 3, we treat the static case: we adapt the finite element approach proposed in [10] involving highly regular approximations of the poloidal magnetic flux field ψ, to the iron case. Already in [17], it has been remarked that finite elements providing piece-wise polynomial approximations of ψ that are only C 0 have two main drawbacks: 1.)…”