A Coupled FEM-BEM Approach for the Solution of the Free-Boundary Axi-Symmetric Plasma Equilibrium Problem

Abstract

In this paper we present a coupled Finite Element Method -Boundary Element Method (FEM-BEM) approach for the solution of the free-boundary axi-symmetric plasma equilibrium problem. The proposed method, obtained from an improvement of the Hagenow-Lackner coupling method, allows to efficiently model the equilibrium problem in unbounded domains by discretizing only the plasma region; the external conductors can be modelled either as 2D or 3D models, according to the problem of interest. The paper explores different iterative methods for the solution of the nonlinear Grad-Shafranov equation, such as Picard, Newton-Raphson and Newton-Krylov, in order to provide a robust and reliable tool, able to handle large-scale problems (e.g. high resolution equilibria). This method has been implemented in the FRIDA code (FReeboundary Integro-Differential Axisimmetric -ØØÔ× »» Ø Ù ºÓÑ»Ñ ØØ Ó ÓÒÓØØÓ» ÊÁ ), together with a suitable Adaptive Integration Technique (AIT) for the computation of the source term. FRIDA has been successfully tested and validated against experimental data from RFX-mod device, and numerical equilibria of an ITER-like device.

Efficient Numerical Solution of Coupled Axisymmetric Plasma Equilibrium and Eddy Current Problems

“…This peculiar feature of the jacobian was also typical of the formulation at the basis of FRIDA code, described in detail in Ref. [8]. Thus, also for this problem, the fixed term J ′ F (x 0 ) depends only on the geometry of the triangulation, and it is always the same if the same mesh is considered.…”

“…In order to solve the FB-PEP in axisymmetric geometry, the FRIDA (FRee-boundary Integro-Differential Axi-symmetric) code has been recently developed [8]. The proposed method is based on a novel Finite Element Method -Boundary Element Method (FEM-BEM) scheme, obtained from an improvement of the Hagenow-Lackner (HL) coupling method [13], and is able to efficiently model the equilibrium problem in unbounded domains by discretizing only the plasma region.…”

“…As pointed out in detail in Ref. [8], the FRIDA code has several advantages. At first, it overcomes the convergence limitations of the original HL scheme, providing a FEM-BEM coupling scheme that has an optimal convergence rate.…”

“…In Ref. [8], a detailed comparison of these two methods is also reported. VOLUME 10, 2022 3) Boundary conditions…”

“…This paper aims to present an extension of the existing FRIDA (FRee-boundary Integro-Differential Axisymmetric) code [8], which solves the static free-boundary plasma equilibrium problem. This novel tool, named FRIDA-TD, which stands for FRIDA-Time Domain, exploits the same strengths of the FRIDA code: (i) two different approaches for solving the elated nonlinear system of Partial Differential Equations (PDE), that are Finite Element Method -Boundary Element Method (FEM-BEM) for plasma equilibrium, and Axisymmetric Volume Integral (AVI) formulation for eddy currents, requiring to mesh only the conductors and the vacuum chamber; (ii) it is based on a novel FEM-BEM coupling scheme which has been proven to have optimal convergence rate and is efficient concerning the computation of the Green matrix needed for FEM-BEM coupling [8]; (iii) an Adaptive Integration Technique (AIT) for the computation of the plasma source term has been implemented, to treat the problem of mismatching between plasma domain, whose boundary is not known a priori, and the mesh elements.…”