Screening in a one dimensional plasma

We investigate the screening behavior of a neutral one dimensional plasma made up by two types of charges not necessarily of equal values. The thermodynamic potential is given by the lowest eigenvalue of a generalized Mathieu equation. If the latter is interpreted as a Schrödinger equation, the dielectric constant is related in a simple manner to the band mass of the lowest energy band. We calculate this mass with the W.K.B. method and study the correlation function for a pair of test charges.