Data-driven discovery of heat-flux closures for collisionless electrostatic plasma phenomena

Global modeling of multi-scale collisionless plasma phenomena is a long-standing computational challenge. Collisionless fluid models offer an approximate but more tractable alternative to fully kinetic modeling, calling for a systematic approach to constructing accurate closures that capture the essence of the kinetic physics. We employ data-driven methods [E.P. Alves and F. Fiuza 2022 Phys. Rev. Res. 4, 033192] based on the SINDy algorithm [S.L. Brunton et al. 2016 PNAS 113, 3932], to obtain a fluid closure in two-stream unstable and Landau-damped plasmas. More specifically, using OSIRIS particle-in-cell simulation data, we search for expressions for the heat flux in terms of lower order moments, which are optimally accurate at each given model complexity. Besides a local approximation of the Hammett-Perkins closure [P. Sharma et al. 2006 Astrophys. J. 637, 952; G.W. Hammett and F.W. Perkins 1990 Phys. Rev. Lett. 64, 3019], we find several additional closure terms - largely the same set in both the two-stream unstable and Landau-damped scenarios. Some terms are present only when wave propagation or beam asymmetry breaks isotropy. The generality of the found closures with respect to parameter variations is explored.