  This paper derives a kinetic equation for a two-dimensional single species
point vortex system. We consider a situation (different from the ones
considered previously) of weak mean flow where the time scale of the
macroscopic motion is longer than the decorrelation time so that the trajectory
of the point vortices can be approximated by a straight line on the
decorrelation time scale. This may be the case when the number $N$ of point
vortices is not too large. Using a kinetic theory based on the Klimontovich
formalism, we derive a collision term consisting of a diffusion term and a
drift term, whose structure is similar to the Fokker-Planck equation. The
collision term exhibits several important properties: (a) it includes a
nonlocal effect; (b) it conserves the mean field energy; (c) it satisfies the H
theorem; (d) its effect vanishes in each local equilibrium region with the same
temperature. When the system reaches a global equilibrium state, the collision
term completely converges to zero all over the system.
