Nonlinear Reduced Hamiltonian and Collisional Gyrokinetic Plasma Transport Models

这个项目的主要目的是推导出易于处理的、数学上准确的、适合于在等离子体模拟程序中数值实现的等离子体物理模型。物理世界极其复杂，很难进行忠实于它的准确的计算机模拟。幸运的是，支配这个世界的物理定律具有保证存在重要守恒定律的数学性质和结构，例如能量守恒定律。等离子体物理学一直处于几个动力学模型推导的前沿，例如等离子体陀螺动力学模型，这些模型已成功地在美国顶尖大学和国家实验室开发的高性能计算机算法中实现。然而，开发快速有效的模拟算法的需要必须依赖于我们推导出保留原始物理定律的属性和结构的简化物理模型的能力。该项目的目标是发展和实施结构保持哈密顿和碰撞回转动力学模型，目的是研究强磁化等离子体中的湍流无碰撞和不可逆碰撞输运过程。这些简化的回转动力学模型为未来发展为实验室和空间等离子体的高级等离子体模拟而设计的几何和度量算法提供了理论基础。简化的Vlasov-Maxwell括号的性质通过在其推导过程中使用的Lie变换方法来保证。由于任何简化的Vlasov-Maxwell括号的实际应用都需要有限阶截断和回转平均运算，因此必须确定这些运算是否保留了括号的属性。该奖项反映了NSF的法定使命，并已通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.