Comparative analysis of molecular dynamics and method of moments in two-dimensional concentric circular layers

In this manuscript, we undertake an examination of a classical plasma deployed on two finite co-planar surfaces: a circular regionΩininto an annular regionΩoutwith a gap in between. It is studied both from the point of view of statistical mechanics and the electrostatics of continua media. We employ a dual perspective: the first one is by using molecular dynamics (MD) simulations to find the system's positional correlation functions and velocity distributions. That by modeling the system as a classical two-dimensional Coulomb plasma of point-like charged particlesq₁andq₂on the layersΩinandΩoutrespectively with no background density. The second one corresponds to a finite Surface Electrode (SE) composed of planar metallic layers displayed on the regionsΩin,Ωoutat constant voltagesVin,Voutconsidering axial symmetry. The surface charge density is calculated by the Method of Moments (MoM) under the electrostatic approximation. Point-like and differential charges elements interact via a1/r-electric potential in both cases. The thermodynamic averages of the number density, and electric potential due to the plasma depend on the coupling and the charge ratioξ=q1/q2once the geometry of the layers is fixed. On the other hand, the fields due to the SE depend on the layer's geometry and their voltage. In the document, is defined a protocol to properly compare the systems. We show that there are values of the coupling parameter, where the thermodynamic averages computed via MD agree with the results of MoM for attractiveξ=-1and repulsive layersξ = 1.