Geometric Particle-in-Cell methods for the Vlasov-Maxwell equations with spin effects

Nicolas Crouseilles (1, 2, 3) , Paul-Antoine Hervieux (4, 5) , Yingzhe Li (6) , Giovanni Manfredi (4, 5, 7) , Yajuan Sun (8)

1 MINGUS - Multi-scale numerical geometric schemes
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 UR - Université de Rennes
4 IPCMS - Institut de Physique et Chimie des Matériaux de Strasbourg
5 UNISTRA - Université de Strasbourg
6 IPP - Max-Planck-Institut für Plasmaphysik [Garching]
7 CNRS - Centre National de la Recherche Scientifique
8 AMSS - Academy of Mathematics and Systems Science

We propose a numerical scheme to solve the semiclassical Vlasov-Maxwell equations for electrons with spin. The electron gas is described by a distribution function f (t, x, p, s) that evolves in an extended 9-dimensional phase space (x, p, s), where s represents the spin vector. Using suitable approximations and symmetries, the extended phase space can be reduced to 5D: (x, p x , s). It can be shown that the spin Vlasov-Maxwell equations enjoy a Hamiltonian structure that motivates the use of the recently developed geometric particle-in-cell (PIC) methods. Here, the geometric PIC approach is generalized to the case of electrons with spin. As a relevant example, we study the stimulated Raman scattering of an electromagnetic wave interacting with an underdense plasma, where the electrons are partially or fully spin polarized. It is shown that the Raman instability is very effective in destroying the electron polarization.

Domaines: Physique Numérique [physics.comp-ph]; Analyse numérique [math.NA]

Nicolas Crouseilles, Paul-Antoine Hervieux, Yingzhe Li, Giovanni Manfredi, Yajuan Sun. Geometric Particle-in-Cell methods for the Vlasov-Maxwell equations with spin effects. Journal of Plasma Physics, 2021, 87 (3), pp.article n° 825870301. ⟨10.1017/S0022377821000532⟩. ⟨hal-03148534v2⟩