标题： 作为Hamilton系统的线性化Vlasov-Maxwell系统 显示英文标题

标题： The Linearized Vlasov-Maxwell System as a Hamiltonian System

摘要： 我们提出了一个用于线性化Vlasov-Maxwell系统的哈密顿表述，该系统具有麦克斯韦背景分布函数。 我们在连续级别上讨论了模型的几何特性，以及如何在GEMPIC框架下离散化该模型[1]。 此方法使我们能够在半离散水平上保留系统的结构。 为了在时间上整合模型，我们采用了泊松分裂，并讨论了如何分别积分每个子系统。 我们通过控制变量法来减少噪声，将模型与完整的Vlasov-Maxwell模型进行测试；所选的两个测试案例分别是弱朗道阻尼和伯恩斯坦波。 这两个测试案例在短时模拟中表现出相同的物理特性，但由于其几何构造，我们的模型在长时间稳定性及能量守恒方面表现更佳。 该模型已在开源Python库STRUPHY中实现[2, 3]。 显示英文摘要

摘要： We present a Hamiltonian formulation for the linearized Vlasov-Maxwell system with a Maxwellian background distribution function. We discuss the geometric properties of the model at the continuous level, and how to discretize the model in the GEMPIC framework [1]. This method allows us to keep the structure of the system at the semi-discrete level. To integrate the model in time, we employ a Poisson splitting and discuss how to integrate each subsystem separately. We test the model against the full Vlasov-Maxwell model with a control variate method for noise reduction; the two chosen test-cases are the weak Landau damping and the Bernstein waves. Both test-cases exhibit the same physical properties for short simulations but our model enjoys better long-time stability and energy conservation due to its geometric construction. The model is implemented in the open-source Python library STRUPHY [2, 3].