RESUMO
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.
RESUMO
In this work, we study the gapped surface electrode (SE), a planar system composed of two-conductor flat regions at different potentials with a gapGbetween both sheets. The computation of the electric field and the surface charge density requires solving Laplace's equation subjected to Dirichlet conditions (on the electrodes) and Neumann boundary conditions over the gap. In this document, the gapless surface electrode is modeled as a two-dimensional classical Coulomb gas having punctual charges +qand -qon the inner and outer electrodes, respectively, interacting with an inverse power law 1/r-potential. The coupling parameter Γ between particles inversely depends on temperature and is proportional toq2. Precisely, the density charge arises from the equilibrium states via Monte Carlo (MC) simulations. We focus on the coupling and the gap geometry effect. Mainly on the distribution of particles in the circular and the harmonically-deformed gapped SE. MC simulations differ from electrostatics in the strong coupling regime. The electrostatic approximation and the MC simulations agree in the weak coupling regime where the system behaves as two interacting ionic fluids. That means that temperature is crucial in finite-size versions of the gapped SE where the density charge cannot be assumed fully continuous as the coupling among particles increases. Numerical comparisons are addressed against analytical descriptions based on an electric vector potential approach, finding good agreement.