Gauss law constraints on Debye-Hückel screening

Abstract

We demand that the Gauss law at the edge must be obeyed by the electric potential φ(r) generated within a neutral plasma/electrolyte of strictly finite size by the introduction of a test charge q b . Our proposal has the nice features that total ionic numbers are conserved, the point-Coulomb behaviour of φ(r) is guaranteed at short-distance, and accumulation of induced charges near the centre and the surface can be demonstrated rigorously. In contrast, the standard Debye-Hückel potential φ D(r) applicable to unbounded plasma has the strange features that the Gauss law cannot be obeyed at the plasma's edge, total ionic numbers themselves are altered, the short-distance Coulomb behaviour has to be imposed by hand, and induced charge appearance at the surface cannot be built-in.