  A collisionless plasma is modeled by the Vlasov-Poisson system in three space
dimensions. A fixed background of positive charge, which is independent of time
and space, is assumed. The situation in which mobile negative ions balance the
positive charge as x tends to infinity is considered. Hence the total positive
charge, total negative charge, and total energy are all infinite. Smooth
solutions with appropriate asymptotic behavior for large x, which were
previously shown to exist locally in time, are continued globally for
spherically symmetric data. This is done by showing that the charge density
decays at least as fast as x^{-4}. Finally, an increased decay rate of x^{-6}
is shown in the general case without the assumption of spherical symmetry.
