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Journal Articles Journal of Plasma Physics Year : 2021

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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Dates and versions

hal-03148534 , version 1 (22-02-2021)
hal-03148534 , version 2 (02-06-2021)

Identifiers

Cite

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⟩
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