New systematic expansion of the electric field distribution in plasmas

We derive a new systematic expansion of the electric field distribution at a test charge immersed in an infinite two- or three-dimensional one-component plasma. The lowest-order truncation of this expansion leads to a mean-field theory very similar to the adjustable-parameter exponential approximation (APEX). The next-order corrections to this mean-field theory are explicitly computed in terms of the distribution functions of the plasma particles. All these approximations are compared to the Monte Carlo results for a two-dimensional system at Γ=2 and various test charges. The systematic approximations appear to be useful. Even the zeroth-order approximation is quite accurate for large test charges or strongly coupled systems and the next order improves on it. Still, APEX is found to be most reliable (as it is also in three dimensions) and remains accurate in the practical interesting limit where the test charge vanishes, i.e., at a neutral atom.