A particle method for a collisionless plasma with infinite mass

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|→∞. Such a system of equations can be used to model kinetic phenomena occurring in plasma physics. A localized particle method is constructed and implemented using the fact that solutions to the Vlasov–Poisson system propagate at finite speeds. Finally, the numerical method is utilized to ascertain information regarding the time asymptotics of the generated electrostatic field.