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Asymptotic solution of the Vlasov and Poisson equations for an inhomogeneous plasma

Published online by Cambridge University Press:  13 March 2009

Riccardo Croci
Affiliation:
Max-Planck-Institut für Plasmaphysik, EURATOM Association, D-8046 Garching, Germany

Abstract

The purpose of this paper is to derive the asymptotic solutions to a class of inhomogeneous integral equations that reduce to algebraic equations when a parameter ε goes to zero (the kernel becoming proportional to a Dirac δ function). This class includes the integral equations obtained from the system of Vlasov and Poisson equations for the Fourier transform in space and the Laplace transform in time of the electrostatic potential, when the equilibrium magnetic field is uniform and the equilibrium plasma density depends on εx, with the co-ordinate z being the direction of the magnetic field. In this case the inhomogeneous term is given by the initial conditions and possibly by sources, and the Laplace-transform variable ω is the eigenvalue parameter.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1991

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References

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