Collisionless damping of oscillations in electrically supported dust rings

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Abstract
Low frequency density waves in a planetary ring, will be damped if there is a significant time delay in charging of dust particles. This damping can in many cases be more important than damping due to dust-dust and dust-plasma collisions. We have in this paper derived the response in plasma potential and dust particle charge when the dust density is varied periodically with frequency ω. This response is then applied to oscillations of dust particles in Jupiter's and Saturn's tenuous rings in the direction normal to the central plane of the rings. For tenuous rings we find analytically expressions which approximate the eigenfrequencies and timescales of damping for the oscillation. These expressions are compared with numerically solutions of the original set of equations.