Implementation of a 2D wave-solver using the Budé method with NGSolve: Initial validation without poloidal fields, with further investigation incorporating them

¹ Laboratory for Plasma Physics, LPP-ERM/KMS, 1000 Brussels, Belgium
² Department of applied physics, Ghent University, Belgium
³ Technical University of Denmark, Department of Physics, 2800 Lyngby, Denmark

^* Corresponding author: Vincent.Maquet@ulb.be

Published online: 7 January 2026

Abstract

This paper presents the first 2D implementation of the so-called Budé approach to solve the integro-differential wave equation as a high-order differential equation. The approach has the advantage that it can readily be implemented in standard FEM codes and has a fit superior to the traditionally adopted Taylor expansion of the dielectric tensor. The method was originally proposed and tested in 1D for radio-frequency waves in absence of poloidal fields. Using the open-source finite element software NGSolve, the Budé method is reproduced in 1D for benchmark purposes and validated up to sixth order. The work is then extended to 2D models, demonstrating the ability to simulate wave propagation in realistic geometries as well as linear wave transformation processes, e.g. the fast wave confluence to the ion Bernstein mode. Although still missing a fully convincing model to capture poloidal effects, this paper therefore advocates the use of a new open-source numerical tool to concentrate on physics development, and doing so presents a first step towards efficient full-wave computations for wave heating fusion applications.