Abstract
We describe a new semi-phenomenological approach to estimate the internal energy of the classical one-component-plasma in two dimensions. This approach reproduces the Debye-Hückel asymptote in the limit of weak coupling, the ion disc asymptote in the limit of strong coupling, and provides reasonable interpolation between these two limits. The present analytic results are compared with those from other approximations as well as with existing data from numerical simulations.
Highlights
We describe a new semi-phenomenological approach to estimate the internal energy of the classical one-component-plasma in two dimensions
Thermodynamic properties of the OCP have been extensively studied over decades, simple physically motivated approaches are still of considerable interest.[4,6,7]
The first is characterized by the conventional 3D Coulomb interaction potential (∝ r−1), but the particle motion is restricted to a 2D surface
Summary
The one-component-plasma (OCP) is an idealized system of identical point-like particles of charge e immersed in a uniform neutralizing background of opposite charge.[1,2,3] This model is of considerable interest from the fundamental point of view and has wide interdisciplinary applications, including ionized matter in white dwarfs, interiors of heavy planets, alkali metals, colloidal suspensions, and complex (dusty) plasmas.[3,4,5] thermodynamic properties of the OCP have been extensively studied over decades, simple physically motivated approaches are still of considerable interest.[4,6,7] The purpose of this paper is to discuss a simple approach to estimate the internal energy of two dimensional (2D) classical OCP in a wide parameter regime. The first is characterized by the conventional 3D Coulomb interaction potential (∝ r−1), but the particle motion is restricted to a 2D surface This system has been used as a first approximation for the description of electron layers bound to the surface of liquid dielectrics and of inversion layers in semi-conductor physics.[2] It is relevant to colloidal and complex (dusty) plasma mono-layers in the regime of week screening.[3,5,8] In the second system, the interaction potential is defined via the 2D Poisson equation and scales logarithmically with distance (∝ − ln(r)). The reduced excess (that over non-charged particles) energy of the systems can be evaluated from uex
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