Cauchy-type integral method for solving the linearized one-dimensional Vlasov-Poisson equation
Cauchy-type integral method for solving the linearized one-dimensional Vlasov-Poisson equation
复制标题
求解线性化一维 Vlasov-Poisson 方程的柯西型积分法
DOI：
10.1103/physreve.107.l063201
复制
发表时间：
2023
影响因子：
2.4
通讯作者：
Shadwick, B. A.
中科院分区：
文献类型：
--
作者：
Lee, Frank M.;Shadwick, B. A.
基于平衡和初始条件的解析性，通过柯西型积分，给出了线性化的Vlasov-Poisson方程的一种求解方法，给出了分布和场的代数表达式，即解不用积分表示。现有的标准方法包括对Bromwich轮廓的变形，对于某些物理上合理的构型给出错误的结果，或者对于解的时间结构给出误导的本征函数展开式。我们的方法更透明，没有这些缺陷，并预测了以前未被识别的行为。
We present a method for solving the linearized Vlasov-Poisson equation, based on analyticity properties of the equilibrium and initial condition through Cauchy-type integrals, that produces algebraic expressions for the distribution and field, i.e., the solution is expressed without integrals. Standard extant approaches involve deformations of the Bromwich contour that give erroneous results for certain physically reasonable configurations or eigenfunction expansions that are misleading as to the temporal structure of the solution. Our method is more transparent, lacks these defects, and predicts previously unrecognized behavior.