On the surface properties of a semi-infinite classical plasma model with permeable boundary

Abstract

We discuss the surface density profile and other surface properties of a classical plasma on a semi-infinite neutralizing background with a permeable boundary. The asymptotic behaviours of the charge density profile can be determined exactly to be of inverse-square-power form outside the boundary and of exponential form, with a switch-over to a damped oscillatory behaviour above a eritical value for the strength of the interactions, inside the boundary. In a local approximation for the free-energy density, instead, a regular solution for the profile has a monotonic behaviour and exists only over a finite range for the strength of the interactions once the known features of the equation of state of the homogeneous plasma are incorporated. Local approximations of increasing sophistication, starting from the simplest Debye-Hückel approximation, are then evaluated and their results compared.