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This paper derives a kinetic equation for a two-dimensional single speciespoint vortex system. We consider a situation (different from the onesconsidered previously) of weak mean flow where the time scale of themacroscopic motion is longer than the decorrelation time so that the trajectoryof the point vortices can be approximated by a straight line on thedecorrelation time scale. This may be the case when the number $N$ of pointvortices is not too large. Using a kinetic theory based on the Klimontovichformalism, we derive a collision term consisting of a diffusion term and adrift term, whose structure is similar to the Fokker-Planck equation. Thecollision term exhibits several important properties: (a) it includes anonlocal effect; (b) it conserves the mean field energy; (c) it satisfies the Htheorem; (d) its effect vanishes in each local equilibrium region with the sametemperature. When the system reaches a global equilibrium state, the collisionterm completely converges to zero all over the system.

Explicit formula of energy-conserving Fokker-Planck type collision term for single species point vortex systems with weak mean flow