Gauss law constraints on Debyea€“H??ckel screening

摘要

We demand that the Gauss law at the edge must be obeyed by the electric potential e???(e?‘?) generated within a neutral plasma/electrolyte of strictly ???nite size by the introduction of a test charge e?‘?b. Our proposal has the nice features that total ionic numbers are conserved, the point-Coulomb behaviour of e???(e?‘?) is guaranteed at short-distance, and accumulation of induced charges near the centre and the surface can be demonstrated rigorously. In contrast, the standard Debyea€“H??ckel potential e???D(e?‘?) 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.