Electric field dynamics at a charged point

The autocorrelation function for the electric field at an impurity ion in a plasma is considered. A simple model is constructed that preserves the exact short time dynamics and the long time global constraint of a given self-diffusion coefficient. The input required is the initial value of the autocorrelation function and its derivatives, and the self-diffusion coefficient. These are calculated from the hypernetted chain equations for correlation functions and a ''disconnected'' approximation for the self-diffusion coefficient. A comparison of the predictions of the model for the electric field autocorrelation function with results from molecular dynamics simulation shows good agreement over a wide range of plasma coupling, impurity ion charge, and impurity ion mass. This provides justification for a simple interpretation of electric field dynamics in terms of three collective modes.