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Test Charge Response of a Dusty Plasma with Grain Size Distribution and Charging Dynamics

The response potential of a dusty (complex) plasma to a moving test charge strongly depends on its velocity. For a test charge moving with a velocity exceeding the dust-acoustic speed, a distinctive wake-field is produced trailing behind the test charge. Here the response to a fast moving test charge, when dispersion effects are small and the dust behaves as a cold plasma component, is considered. The effects of dynamical grain charging are included, and the cases with and without these effects are analyzed and compared. The plasma dielectric function is chosen assuming that all grains are of the same size and includes a response term for charging dynamics. The wake field potential is found either explicitly in terms of known functions or by using numerical methods for the integral expression. Maximum response is found on the wake cone with apex angle determined by the ratio between the dust acoustic velocity and the test charge velocity. The structure of the wake field stretches in the direction of the test charge velocity when this increases. The functional form of the field is given by separately changing the length scales parallel and perpendicular to the velocity. The potential on the axis gives an electric field close behind the test charge that can attract charges with the same sign. The grain charging dynamics leads to a spatial damping and a phase shift in the potential response.