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

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. Stand...

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Bibliographic Details
Published in:Physical review. E 2023-06, Vol.107 (6), p.L063201-L063201, Article L063201
Main Authors: Lee, Frank M, Shadwick, B A
Format: Article
Language:English
Subjects:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Physics
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Summary: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.
ISSN:2470-0045
2470-0053
DOI:10.1103/PhysRevE.107.L063201