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

Abstract : 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.
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https://hal.inria.fr/hal-03148534
Contributor : Nicolas Crouseilles Connect in order to contact the contributor
Submitted on : Wednesday, June 2, 2021 - 6:39:39 PM
Last modification on : Friday, May 20, 2022 - 9:04:53 AM

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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, Cambridge University Press (CUP), 2021, 87 (3), pp.article n° 825870301. ⟨10.1017/S0022377821000532⟩. ⟨hal-03148534v2⟩

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