Nonlinear Reduced Hamiltonian and Collisional Gyrokinetic Plasma Transport Models

该项目的主要目的是推导出易于处理的数学上精确的等离子体物理模型，该模型适用于等离子体模拟代码中的数值实现。物理世界的压倒性的复杂性使得它很难进行精确的计算机模拟忠实于它。幸运的是，支配这个世界的物理定律具有数学性质和结构，可以保证重要的守恒定律的存在，比如能量守恒定律。等离子体物理学一直处于几个动力学模型推导的前沿，例如等离子体回旋动力学模型，这些模型已成功地在美国领先大学和国家实验室开发的高性能计算机算法中实现。然而，开发快速高效的模拟算法必须依赖于我们推导简化物理模型的能力，这些模型保留了原始物理定律的性质和结构。该项目的目标是开发和实现保持结构的哈密顿和碰撞回旋动力学模型，以研究强磁化等离子体中湍流无碰撞和不可逆碰撞输运过程。这些简化的回旋动力学模型为未来设计用于实验室和空间等离子体高级等离子体模拟的几何和三聚体算法的发展提供了理论基础。在推导过程中应用lie变换方法，保证了约简Vlasov-Maxwell括号的性质。然而，由于有限阶截断和陀螺角平均运算对于简化的Vlasov-Maxwell括弧的任何实际应用都是必需的，因此必须确定这些运算是否保留括弧的性质。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.