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

Journal Article · · Physical Review. E
 [1];  [2]
  1. Univ. of Nebraska, Lincoln, NE (United States); OSTI
  2. Univ. of Nebraska, Lincoln, NE (United States)
+ Show Author Affiliations
Here, 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.
Research Organization:
Univ. of Nebraska, Lincoln, NE (United States)
Sponsoring Organization:
National Science Foundation (NSF); USDOE Office of Science (SC)
Grant/Contract Number:
SC0018363
OSTI ID:
2420774
Journal Information:
Physical Review. E, Journal Name: Physical Review. E Journal Issue: 6 Vol. 107; ISSN 2470-0045
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (5)

Plasma oscillations journal July 1959
On the theory of stationary waves in plasmas journal January 1955
An unconditionally stable, time-implicit algorithm for solving the one-dimensional Vlasov–Poisson system journal March 2022
Plasma oscillations journal January 1978
Longitudinal plasma oscillations journal January 1960

Figures / Tables (5)

FIG. 1(p. 3)figure FIG. 1
FIG. 2(p. 6)figure FIG. 2
FIG. 3(p. 6)figure FIG. 3
FIG. 4(p. 6)figure FIG. 4
FIG. 5(p. 7)figure FIG. 5

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Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Physics