  In this study, the Vlasov-Poisson equation with or without collision term for
plasma is solved by the unified gas kinetic scheme (UGKS). The Vlasov equation
is a differential equation describing time evolution of the distribution
function of plasma consisting of charged particles with long-range interaction.
The distribution function is discretized in discrete particle velocity space.
After the Vlasov equation is integrated in finite volumes of physical space,
the numerical flux across a cell interface and source term for particle
acceleration are computed to update the distribution function at next time
step. The flux is decided by Riemann problem and variation of distribution
function in discrete particle velocity space is evaluated with central
difference method. A electron-ion collision model is introduced in the Vlasov
equation. This finite volume method for the UGKS couples the free transport and
long-range interaction between particles. The electric field induced by charged
particles is controlled by the Poisson's equation. In this paper, the Poisson's
equation is solved using the Green's function for two dimensional plasma system
subjected to the symmetry or periodic boundary conditions. Two numerical tests
of the linear Landau damping and the Gaussian beam are carried out to validate
the proposed method. The linear electron plasma wave damping is simulated based
on electron-ion collision operator. Compared with previous methods, it is shown
that the current method is able to obtain accurate results of the
Vlasov-Poisson equation with a time step much larger than the particle
collision time. Highly non-equilibrium and rarefied plasma flows, such as
electron flows driven by electromagnetic field, can be simulated easily.
