The dynamics of weakly charged dust: Motion through Jupiter's gravitational and magnetic fields

Abstract

We derive perturbation equations for the motion of weakly charged dust grains (q/M1→0, where q is the grain's electric charge and M1 its mass) in planetary rings, with emphasis on the Jovian ring system. Our analysis includes the effects of planetary oblateness and an arbitrarily complex magnetic field expressed in terms of spherical harmonics. The perturbation solutions are shown to agree with numerical integrations for most initial conditions, and to provide a simple means of understanding the nature of charged grain trajectories in terms of forced oscillator models. We identify “Lorentz resonances” where a frequency of the perturbing Lorentz force matches a natural orbital frequency of the grain. The resonances come in pairs, with one on either side of the synchronous orbit rs; as rs is approached, resonances are more closely spaced, and their zones become narrower. Large vertical and horizontal excursions from planar circular orbits are predicted at these locales, and this is confirmed in numerical simulations. The amplitudes of the vertical oscillations at resonance can be 1–2 orders of magnitude larger than those outside such zones. The enhanced vertical excursions mean that for shallow viewing angles the optical depth will decrease as lines of sight approach the Lorentz resonance radii. This then provides a mechanism for explaining some apparent boundaries in dusty rings, such as those of the Jovian halo and, less likely, the outer edges of the Jovian main ring and the gossamer ring. For future use, we list the low‐order resonances that lie at or near several features in the Voyager images. Theoretical ring cross sections and overall ring topology are obtained from averages of the analytical solutions over initial conditions. We find that because of the forced response to perturbations, short time solutions predict a warping of the halo out of the equatorial plane that is not seen in the available images. We then point out the significance of including a slow evolutionary process, such as plasma drag, in the dynamical model. Since the large vertical excursions produced as grains drift through Lorentz resonances apparently survive over the radial evolution time scale, the natural response will dominate the motion in the halo region, and the halo will not be appreciably warped.