  This paper considers a kinetic equation for an unbounded two-dimensional
single species point vortex system. No axisymmetric flow is assumed. Using the
kinetic theory based on the Klimontovich formalism, we derive a collision term
consisting of a diffusion 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 converge to zero all over the
system.
