  A collisionless plasma is modeled by the Vlasov-Poisson system in one
dimension. We consider the situation in which mobile negative ions balance a
fixed background of positive charge, which is independent of space and time, as
x tends to positive or negative infinity. Thus, the total positive charge and
the total negative charge are both infinite. Smooth solutions with appropriate
asymptotic behavior are shown to exist locally in time, and criteria for the
continuation of these solutions are established.
