Cauchy-type integral method for solving the linearized one-dimensional Vlasov-Poisson equation

Authors

Frank M. Lee, University of Nebraska–LincolnFollow
Bradley A. Shadwick, University of Nebraska - LincolnFollow

Date of this Version

6-23-2023

Citation

PHYSICAL REVIEW E 107, L063201 (2023). DOI: 10.1103/PhysRevE.107.L063201

Comments

Used by permission.

Abstract

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.