Collisionless braking of dust particles in the electrostatic field of planetary dust rings

We show that a dust test particle moving in a periodic orbit in electrostatic fields, as those due to planetary rings, will experience a net deceleration also in the absence of any dust-dust collisions. The varying charge on the moving dust, as it moves in and out of regions of differing electron and ion densities (due to changes in the ring electrostatic potential), will be out of phase with the equilibrium charge in a way which leads to a net braking of the particle. This effect has been shown to damp the coherent oscillations of electrostatically supported dust rings [1] and to damp the oscillatons of levitated dust particles in plasma sheaths at surfaces of solid bodies [2]. We show that this effect will lead to a damping of internal random velocities in a planetary ring, at a rate which in many cases can be much faster than that due to dust-dust collisions. For moderate radial motions of dust test particles relative to a ring we also find that there can be an efficient braking and pick-up of particles already at the ring edges.