Abstract
We consider a two dimensional collisionless plasma interacting with a fixed background of positive charge, the density of which depends only upon velocity variable $v$ and decays as $|v| \to \infty $. Suppose that mobile negative ions balance the positive charge as spatial variable $|x|\to \infty $, then on the mesoscopic level the system is characterized by the two dimensional Vlasov-Poisson system with steady spatial asymptotics, whose total positive charge and total negative charge are both infinite. Smooth solutions with appropriate asymptotic behavior are shown to exist locally in time, and an 'almost optimal' criterion for the continuation of these solutions is established.
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