A Novel Method for Solving the Linearized 1D Vlasov--Poisson Equation
Plasma Physics
2023-07-05 v1 Mathematical Physics
math.MP
Abstract
We present a novel 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.
Keywords
Cite
@article{arxiv.2305.03896,
title = {A Novel Method for Solving the Linearized 1D Vlasov--Poisson Equation},
author = {Frank M. Lee and B. A. Shadwick},
journal= {arXiv preprint arXiv:2305.03896},
year = {2023}
}
Comments
Accepted for publication as a letter at PRE