Exact Correlation Function of Electric Fields in a One-Dimensional Plasma

Abstract

Exact correlation function of electric fields of the ion-electron sheet model is obtained using Lenard’s method. The result is an infinite series including the Fourier coefficients of the even Mathieu function of the zeroth order. The spectrum I_k with respect to the wave number k is shown to be proportional k⁻². This fact suggest that this model plasma lacks an important nature of plasma—the Debye shielding. The limits in which the plasma parameter tends to zero or also investigated.