Explicit Solutions of the One-dimensional Vlasov-Poisson System with Infinite Mass and Energy

Details Explicit Solutions of the One-dimensional Vlasov-Poisson System with Infinite Mass and Energy Explicit Solutions of the One-dimensional Vlasov-Poisson System with Infinite Mass and Energy

2010-02-26

arxiv.org/abs/1002.4927v1

Math. Meth. Appl. Sci. 31: 375-389, 2008

Mathematics

Analysis of PDEs

13-14 pages, no figures

Scientific paper

A collisionless plasma is modeled by the Vlasov-Poisson system in one-dimension. A fixed background of positive charge, dependent only upon velocity, is assumed and the situation in which the mobile negative ions balance the positive charge as x tends to positive or negative infinity. Thus, the total positive charge and the total negative charge are infinite. In this paper, the charge density of the system is shown to be compactly supported. More importantly, both the electric field and the number density are determined explicitly for large values of x.

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