Geometric particle-in-cell methods for the Vlasov-Maxwell equations with spin effects
Nicolas Crouseilles, Paul-Antoine Hervieux, Yingzhe Li, Giovanni Manfredi, Yajuan Sun
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 $f(t,{\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ that evolves in an extended 9-dimensional phase space $({\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ , where $\boldsymbol s$ represents the spin vector. Using suitable approximations and symmetries, the extended phase space can be reduced to five dimensions: $(x,{{p_x}}, {\boldsymbol s})$ . 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. Total energy conservation is very well satisfied, with a relative error below $0.05\,\%$ . 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.
BibTeX
@article{Crouseilles_2021,
title={Geometric particle-in-cell methods for the Vlasov–Maxwell equations with spin effects},
volume={87},
ISSN={1469-7807},
url={http://dx.doi.org/10.1017/s0022377821000532},
DOI={10.1017/s0022377821000532},
number={3},
journal={Journal of Plasma Physics},
publisher={Cambridge University Press (CUP)},
author={Crouseilles, Nicolas and Hervieux, Paul-Antoine and Li, Yingzhe and Manfredi, Giovanni and Sun, Yajuan},
year={2021},
month=May }