Delayed shielding of a test charge due to dynamical grain charging in a dusty plasma

The dynamical charging of grains in a dusty plasma modifies the plasma dielectric response function and the nature of the electrostatic wave modes. The grain charging leads to an additional shielding effect that acts in the same way as Debye shielding. Both the additional shielding and the charging rate are important in determining the response of a dusty plasma to a moving test charge. The dynamics of the charging can be approximated by using a time delay. An alternative analysis of the potential of a slowly moving test charge is performed introducing a delay operator for the grain charge response. The terms in the potential that depend on the charging dynamics involve a spatial shift given by the test charge velocity and the charging time. This gives a physical interpretation of earlier results which are identical to first order in the test charge velocity.