A nonlocal electron transport model in the diffusion scaling of hydrodynamics

Abstract

We analyze a model of nonlocal electron transport named P1-diffusion based on a spherical harmonic expansion in velocity space and a diffusion scaling, which makes it compatible with assumptions from magneto-hydrodynamics (MHD). An iterative, fully implicit (CFL-free, as defined by the Courant Friedrich Levy condition) and asymptotic preserving discretization is proposed, which necessitates the inversion of a possibly large number of—but small—linear systems. It is found accurate with respect to reference solutions from a Vlasov–Fokker–Planck–Maxwell code (based on a Polynomial expansion of order N, or PN expansion) on a series of tests, which are representative of the conduction zone in laser-created plasmas. Thereby, the present approach is a good candidate for being embedded in multi-D MHD codes.

Electron kinetics in a positive column of AC discharges in a dynamic regime

“…The kinetic equation ( 6) has been used (in 2D phase space) for the analysis of the axial and radial structure of DC discharges and plasma stratification [16]. It has also appeared in the study of fully-ionized plasma [17].…”

“…We aim to clarify the nature of these fluxes under nonlocal electron kinetics conditions. Specific source terms S 0 for quasi-elastic, inelastic, and Coulomb collisions can be found in [11,17,18]. The quasielastic collisions and Coulomb interactions contribute a differential (Fokker-Planck) term to the energy flux Γ (see below).…”

The fastVFP code for solution of the Vlasov–Fokker–Planck equation

“…VFP simulation until a decade ago was reviewed by Thomas et al (2012). Codes such as IMPACT Bell 2004, Thomas et al 2009), KALOS (Bell et al 2006), OSHUN (Tzoufras et al 2011(Tzoufras et al , 2013, (Nikl et al 2021), K2 (Sherlock et al 2017) and P1-diffusion (Michel et al 2023) have been a significant improvement on the first VFP code for laser-plasmas of Bell et al (1981) and its variants (Matte and Virmont 1982). A VFP model has been coupled to 1D hydro models of IFE implosions by Nishiguchi et al (1992) and Sunahara et al (2003).…”