Shielding of a slowly moving test charge in a dusty plasma with dynamical grain charging

Abstract

The dynamical charging of grains in a dusty plasma enhances the shielding of test charges. Time scales for charging are determined by the ambient plasma parameters and the grain dimensions. They can be very short, approaching the ion plasma period for grain sizes of the order of an electron Debye length. For a slowly moving test charge the response potential is found as a power series in the test charge velocity. Collisional effects are included. Analytical expressions for the response potential, valid for all radial distances, are found up to second order in the test charge velocity. The first-order dynamical charging term is shown to be the consequence of the delay in the shielding due to the dynamics of the charging process. The remaining first-order terms are given by analytical expressions that yield the well known asymptotic power law forms for large distances.