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Asymptotically preserving particle-in-cell methods for inhomogeneous strongly magnetized plasmas. (English) Zbl 1422.82006

Summary: We propose a class of particle-in-cell (PIC) methods for the Vlasov-Poisson system with a strong and inhomogeneous external magnetic field with fixed direction, where we focus on the motion of particles in the plane orthogonal to the magnetic field (so-called poloidal directions). In this regime, the time step can be subject to stability constraints related to the smallness of Larmor radius and plasma frequency. To avoid this limitation, our approach is based on first- and higher-order semi-implicit numerical schemes already validated on dissipative systems [S. Boscarino et al., J. Sci. Comput. 68, No. 3, 975–1001 (2016; Zbl 1353.65075)] and for homogeneous magnetic fields [the authors, SIAM J. Numer. Anal. 54, No. 2, 1120–1146 (2016; Zbl 1342.35392)]. Thus, when the magnitude of the external magnetic field becomes large, this method provides a consistent PIC discretization of the guiding-center system taking into account variations of the magnetic field. We carry out some theoretical proofs and perform several numerical experiments that establish a solid validation of the method and its underlying concepts.

MSC:

82-08 Computational methods (statistical mechanics) (MSC2010)
35Q83 Vlasov equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
82D10 Statistical mechanics of plasmas
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References:

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