Screening of point charges by an ideal plasma in two and three dimensions

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Abstract
It is proven, using the Poisson-Boltzmann equation, that a point charge held fixed in an ideal ‘‘jellium’’ plasma attracts a finite amount of opposite charge arbitrarily close to itself. In two dimensions this condensate is insufficient to neutralize the charge completely; in three or more dimensions neutralization is complete. The proof, which extends and simplifies older results, is based on the idea that the concentration exp(-qφ/kT)/F dr exp(-qφ/kT) is a δ function when φ(r) is such that exp(-qφ/kT) has a nonintegrable singularity. It is also proven that the species in the plasma of opposite polarity to the immersed charge condense onto it in strict order of charge, largest first.