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Explicit formula of energy-conserving, Fokker-Planck-type collision term for single-species point vortex system

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A kinetic equation for an unbounded two-dimensional point vortex system is considered. Similar to the Fokker-Planck equation, obtained collision term consists of a diffusion term and a drift (friction) term. It can be demonstrated that the collision term (a) conserves the system energy, (b) satisfies the H theorem that indicates the system temporally developing toward a thermal equilibrium state and (c) disappears locally in a locally equilibrium region with the same temperature. When system reaches a global equilibrium state, the collision term disappears all over the system.

Author(s):

Yuichi Yatsuyanagi    
Shizuoka University
Japan

Tadatsugu Hatori    
National Institute for Fusion Science
Japan