论文标题
深入研究分布函数：使用连续vlasov-Maxwell模拟理解相空间动力学
A Deep Dive into the Distribution Function: Understanding Phase Space Dynamics with Continuum Vlasov-Maxwell Simulations
论文作者
论文摘要
在无碰撞和弱碰撞等离子体中，粒子分布函数是基础物理学的丰富挂毯。但是，实际上利用粒子分布函数了解弱碰撞等离子体的动力学是具有挑战性的。相关的方程式系统，即vlasov-Maxwell-Fokker-Planck（VM-FP）方程系统，很难数值集成，而传统方法（例如粒子中的方法）将计数噪声引入分布函数。 在本论文中，我们提出了一种新算法，用于离散VM-FP方程系统，以研究动力学制度中的等离子体。使用不连续的Galerkin（DG）有限元方法进行空间离散化，并为时间离散化的三阶稳定性保留runge-kutta，我们获得了在时空中等离子体分布函数的准确解决方案。 我们都证明了数值方法保留了VM-FP系统的关键物理特性，例如能量保存和第二种热力学定律，并以数值证明了这些特性。这些结果在DG方法的历史中被背景化。我们讨论算法是无别名的重要性，这是得出动力学方程的稳定DG方案的必要条件，以保留嵌入在粒子分布函数中的隐式保护关系，以及使用模态，正常基础的计算有利实现，与传统的DG方法相比，将其用于计算动力学中的传统DG方法。最后，我们证明了分布函数的高保真度表示如何结合新的诊断，可以详细分析基本等离子体过程中的能量机制，例如无碰撞冲击。
In collisionless and weakly collisional plasmas, the particle distribution function is a rich tapestry of the underlying physics. However, actually leveraging the particle distribution function to understand the dynamics of a weakly collisional plasma is challenging. The equation system of relevance, the Vlasov-Maxwell-Fokker-Planck (VM-FP) system of equations, is difficult to numerically integrate, and traditional methods such as the particle-in-cell method introduce counting noise into the distribution function. In this thesis, we present a new algorithm for the discretization of VM-FP system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin (DG) finite element method for the spatial discretization and a third order strong-stability preserving Runge-Kutta for the time discretization, we obtain an accurate solution for the plasma's distribution function in space and time. We both prove the numerical method retains key physical properties of the VM-FP system, such as the conservation of energy and the second law of thermodynamics, and demonstrate these properties numerically. These results are contextualized in the history of the DG method. We discuss the importance of the algorithm being alias-free, a necessary condition for deriving stable DG schemes of kinetic equations so as to retain the implicit conservation relations embedded in the particle distribution function, and the computational favorable implementation using a modal, orthonormal basis in comparison to traditional DG methods applied in computational fluid dynamics. Finally, we demonstrate how the high fidelity representation of the distribution function, combined with novel diagnostics, permits detailed analysis of the energization mechanisms in fundamental plasma processes such as collisionless shocks.
