Asymptotically preserving particle methods for strongly magnetized plasmas in a torus

• Published in: Journal of computational physics Vol. 480; p. 112015
• Main Authors: Filbet, Francis, Rodrigues, Luis Miguel
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.05.2023
• Subjects: High-order time discretization; Particle methods; Strong magnetic field; Vlasov equation; High-order time discretization; Strong magnetic field; Vlasov equation; Particle methods
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2023.112015

We propose and analyze a class of particle methods for the Vlasov equation with a strong external magnetic field in a torus configuration. In this regime, the time step can be subject to stability constraints related to the smallness of Larmor radius. To avoid this limitation, our approach is based on higher-order semi-implicit numerical schemes already validated on dissipative systems [3] and for magnetic fields pointing in a fixed direction [10,11,13]. It hinges on asymptotic insights gained in [12] at the continuous level. Thus, when the magnitude of the external magnetic field is large, this scheme provides a consistent approximation of the guiding-center system taking into account curvature and variation of the magnetic field. Finally, we carry out a theoretical proof of consistency and perform several numerical experiments that establish a solid validation of the method and its underlying concepts. •We propose a new algorithm, inspired by our previous work in two dimension, to treat a torus geometry in 3D.•The numerical scheme is uniformly consistent and stable with respect to the intensity of the magnetic field.•Numerical simulations illustrate the efficiency of this approach.