Nonlinear Reduced Hamiltonian and Collisional Gyrokinetic Plasma Transport Models

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The primary purpose of this project is to derive tractable mathematically accurate plasma physics models that are suitable for numerical implementation in plasma simulation codes. The overwhelming complexity of the physical world makes it very difficult to carry out accurate computer simulations that are faithful to it. Fortunately, the physical laws that govern this world have mathematical properties and structures that guarantee the existence of important conservation laws, such as conservation of energy. Plasma physics has been at the cutting edge of the derivation of several dynamical models, such as plasma gyrokinetic models, that are successfully implemented in high-performance computer algorithms developed at leading US universities and national laboratories. The need to develop fast and efficient simulation algorithms must rely, however, on our ability to derive reduced physical models that preserve the properties and structures of the original physical laws. The goal of the project is to develop and implement structure-preserving Hamiltonian and collisional gyrokinetic models for the purpose of studying turbulent collisionless and irreversible collisional transport processes in strongly magnetized plasmas. These reduced gyrokinetic models provide a theoretical foundation for the future development of geometric and metriplectic algorithms designed for advanced plasma simulations of laboratory and space plasmas. The bracket properties of a reduced Vlasov-Maxwell bracket are guaranteed by the application of Lie-transform methods used in its derivation. Since the operations of truncation at finite order and gyroangle averaging are required for any practical application of a reduced Vlasov-Maxwell bracket, however, it is imperative to determine whether these operations preserve the brackets properties.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.