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Explicit solutions of the one‐dimensional Vlasov–Poisson system with infinite mass
Author(s) -
Pankavich Stephen
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.915
Subject(s) - charge (physics) , poisson's equation , plasma , electric field , poisson distribution , vlasov equation , dimension (graph theory) , ion , charge density , physics , mathematics , balance (ability) , mathematical analysis , mathematical physics , quantum mechanics , pure mathematics , statistics , medicine , physical medicine and rehabilitation
A collisionless plasma is modelled 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 | → ∞ is considered. 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 |. Copyright © 2007 John Wiley & Sons, Ltd.