  The one-dimensional Vlasov-Poisson system is considered and a particle method
is developed to approximate solutions without compact support which tend to a
fixed background of charge as $| x | \to \infty$. Such a system of equations
can be used to model kinetic phenomena occurring in plasma physics, such as the
solar wind. The particle method is constructed, implemented, and used to
determine information regarding the time asymptotics of the electrostatic
field.
