Data-driven discovery of a heat flux closure for electrostatic plasma phenomena

Abstract: Progress in understanding multi-scale collisionless plasma phenomena requires employing tools which balance computational efficiency and physics fidelity. Collisionless fluid models are able to resolve spatio-temporal scales that are unfeasible with fully kinetic models. However, constructing such models requires truncating the infinite hierarchy of moment equations and supplying an appropriate closure to approximate the unresolved physics. Data-driven methods have recently begun to see increased application to this end, enabling a systematic approach to constructing closures. Here, we utilise sparse regression to search for heat flux closures for one-dimensional electrostatic plasma phenomena. We examine OSIRIS particle-in-cell simulation data of Landau-damped Langmuir waves and two-stream instabilities. Sparse regression consistently identifies six terms as physically relevant, together regularly accounting for more than 95% of the variation in the heat flux. We further quantify the relative importance of these terms under various circumstances and examine their dependence on parameters such as thermal speed and growth/damping rate. The results are discussed in the context of previously known collisionless closures and linear collisionless theory.