NSF-BSF: Collaborative Research: Rankine-Hugoniot Conditions Relating the Gyrotropic Regions of Collisionless Shocks in Non-Thermal Plasma

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This project will develop a new and more accurate model of shock waves in rarefied plasmas in space and laboratory environments. So-called collisionless shock waves belong to the most fundamental phenomena occurring in hot and rarified plasmas. Astrophysical waves accelerate particles, dissipate energy, and strongly perturb the environment they propagate through by converting dynamic pressure of a plasma flow into thermal energy. One of the central theoretical issues in modern plasma physics is a quantitative prediction of the plasma state behind a shock wave (downstream) for given parameters in front of it (upstream). The majority of directly observed collisionless shocks are in the heliosphere; however, they can also be created in a laboratory. The grand challenge of this project is to develop a new theoretical approach that would, on the one hand, account for the details of how individual particles interact with shock waves in collisionless plasma, but on the other hand, identify easy-to-use relationships between upstream and downstream conditions, similar to those widely used for shock waves in aerodynamics. The project will train students and postdocs in computational science and plasma physics, as well as expose them to international science cooperation via collaboration with Ben Gurion University supported by the U.S. - Israel Binational Science Foundation.Collisionless shocks (CSs) are ubiquitous in many space physics, astrophysics, and laboratory settings. Despite more than six decades of CS research, the present status of the problem remains essentially unchanged in comparison to the early advances. Application of standard Rankine–Hugoniot conditions to CSs is either invalid or highly inaccurate. The objective of this research is to incorporate the essential ion dynamics at shock fronts into a statistical description which would make it possible, on the one hand, to avoid going into details of ion motion and, on the other hand, abandon ad hoc assumptions related to the equations of state. Local hybrid and fully-kinetic PIC simulations will be used to validate and improve on the probabilistic, test-particle approach. This research will ensure a substantial step forward in the CS physics by providing a theory which can be compared quantitatively with real observations. The probabilistic approach is expected to be efficient for other problems of plasma physics, where the full kinetic approach is currently impossible, while the assumptions based on the fluid approximation are not valid. Its relative simplicity and ability to cover a wide range of shock parameters makes it possible to create convenient analytic formulae and/or lookup tables to be used by a wide range of plasma physicists. These will also be useful for the development of global magnetohydrodynamic models involving collisionless shocks enabling, in particular, more accurate forecasting of space weather.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.