Introduction

Recently analytic equilibrium and stability conditions were obtained for charged dust grains orbiting Saturn [1,2], including both positive and negatively charged grains in prograde or retrograde, equatorial or nonequatorial ('halo') orbits. The single particle Hamiltonian model included Keplerian gravity, co-rotating magnetic field (taken to be an aligned centered dipole), and corotational electric field. Planetary oblateness (J2), quadrupole magnetic field terms (<72) as well as non-axisymmetric effects such as plasma drag, radiation pressure, and time-dependent charging [3,4] were all neglected. The results gave simple existence conditions and stability bounds for arbitrary circular orbits. Equatorial orbits were parametrized by cylindrical radius (po) and charge-to-mass ratio (q/m) conveniently measured by the quantity $ = where $s is the surface po tential of the grain in Volts and a^ is its radius in microns. For nonequatorial orbits the spherical radius (r0) was employed. Here we extend this model to include planetary oblateness (J2), quadrupole magnetic field (<72), and radiation pressure. A well depth is defined, showing that halo orbits are as deeply trapped as their equatorial cousins. Consequently these grains are not greatly perturbed by J2 and their primary effect is to make the motion more ergodic and occasionally chaotic. Radiation pressure breaks the axisymmetry so that an effective potential no longer exists except in a average sense. Its effects are found to be much more pronounced for conducting than for dielectric grains. In general the relative strength of radiation pressure increases quadratically with distance from the planet, so that outer E-ring particles are most highly perturbed. As in our previous studies the surface potential is fixed at $s = ±10V; magnetospheric effects [5] are described elsewhere [6].

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