Statistical equilibrium of the Coulomb vortex gas on the unbounded 2-dimensional plane

This paper presents the statistical equilibrium distributions of single-species vortex gas and cylindrical electron plasmas on the unbounded plane obtained by Monte Carlo simulations. We present detailed numerical evidence that at high values of beta > 0 and mu > 0, where beta is the inverse temperature and mu is the Lagrange multiplier associated with the conservation of the moment of vorticity, the equilibrium vortex gas distribution is centered about a regular crystalline distribution with very low variance. This equilibrium crystalline structure hag the form of several concentric nearly regular polygons within a bounding circle of radius R. When beta similar to O(1), the mean vortex distributions have nearly uniform vortex density inside a circular disk of radius R. In all the simulations, the radius R = rootbetaOmega/(2mu) where Omega is the total vorticity of the point vortex gas or number of identical point charges. Using a continuous vorticity density model and assuming that the equilibrium distribution is a uniform one within a bounding circle of radius R, we show that the most probable value of R scales with inverse temperature beta > 0 and chemical potential mu > 0 as in R = rootbetaOmega/(2mu).