Vlasov–Maxwell equations with spin effects. (27th April 2023)

• Record Type: Journal Article
• Authors: Crouseilles, Nicolas; Hervieux, Paul-Antoine; Hong, Xue; Manfredi, Giovanni
• Is Part Of: Journal of plasma physics. Volume 89:Number 2(2023)
• Publication Date: 2023-04-27
• Subjects: plasma simulation -- quantum plasma -- plasma dynamics; Plasma (Ionized gases) -- Periodicals; 530.4405
• DOI: 10.1017/S0022377823000314
• Languages: English
• ISSNs: 0022-3778

Abstract

Abstract : We present a numerical method to solve the Vlasov–Maxwell equations for spin-1/2 particles, in a semiclassical approximation where the orbital motion is treated classically while the spin variable is fully quantum. Unlike the spinless case, the phase-space distribution function is a $2\times 2$ matrix, which can also be represented, in the Pauli basis, as one scalar function $f_0$ and one three-component vector function $\boldsymbol f$ . The relationship between this 'vectorial' representation and the fully scalar representation on an extended phase space first proposed by Brodin et al. ( Phys. Rev. Lett., vol. 101, 2008, p. 245002) is analysed in detail. By means of suitable approximations and symmetries, the vectorial spin-Vlasov–Maxwell model can be reduced to two-dimensions in the phase space, which is amenable to numerical solutions using a high-order grid-based Eulerian method. The vectorial model enjoys a Poisson structure that paves the way to accurate Hamiltonian split-time integrators. As an example, we study the stimulated Raman scattering of an electromagnetic wave interacting with an underdense plasma, and compare the results with those obtained earlier with the scalar spin-Vlasov–Maxwell model and a particle-in-cell code.