Bridging Kinetic and Fluid Scales: A GLE-FDT Framework for Coarse-Graining Electron Kinetic Physics

This award supports development of a novel numerical method to model shocks in a plasma. Most visible matter in the universe exists in the plasma state. When stars explode or our Sun blows wind towards Earth, powerful shock waves are driven through the plasma of space. These shocks are believed to be nature’s most powerful particle accelerators, and similar shocks shape the space weather that can damage satellites, disrupt GPS signals, and threaten power grids. Modeling these shocks requires simultaneously tracking physics on scales ranging from the width of a human hair to thousands of miles, a task beyond even the most powerful supercomputers. In this project, a new simulation method will be developed to capture the effects of the small-scale physics within large scale computer models without tracking every microscopic detail. The resulting tools may help to unlock the origin of cosmic rays, as well as strengthen the nation’s capabilities in fusion energy research and space-weather prediction. A graduate student and a postdoctoral researcher will be trained, new materials will be integrated into the graduate curriculum at the University of Rochester, and research opportunities will be provided to undergraduate students, helping to prepare the next generation of the American scientific workforce. This project aims to develop a multiscale simulation framework in which the effects of electron kinetic physics are systematically incorporated into hybrid plasma models. Conventional hybrid codes, which treat ions kinetically and electrons as a fluid, rely on collisional or ad hoc closures that fail in collisionless environments where dissipation is mediated by micro-instabilities and wave-particle interactions. Instead, the project will encode the influence of unresolved electron-scale dynamics into non-Markovian memory kernels and a correlated stochastic forcing term. A library of state-dependent kernels will be constructed from the fluctuation spectra of first-principle particle-in-cell simulations, validated against analytical kinetic theory, and used to derive effective non-collisional transport coefficients. A generalized, non-Markovian Ohm’s law will then be implemented through an efficient auxiliary-differential-equation formulation, allowing the growth and saturation of instabilities to be captured at a computational cost comparable to that of conventional fluid models. The framework will be applied to the long-standing problem of ion-electron temperature equilibration in collisionless shocks, culminating in predictive simulations at the realistic proton-electron mass ratio with broad applicability to multi-scale plasma physics problems. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.