Equatorial dynamics of charged particles in planetary magnetospheres

The dynamics of a charged particle under axisymmetric gravitational and electromagnetic forces is studied. The symmetry allows a phase space reduction from three to two degrees of freedom. The reduced system is a function of two parameters (essentially: the ratio “charge to mass” and the z -component of the angular momentum) and it has an invariant plane associated to the equatorial motion. This paper contains: a global bifurcation chart of equatorial phase-portraits, including stability of equilibria with respect to out of equatorial plane perturbations; an analysis of stability of separatrices and nearby periodic orbits with respect to out of equatorial plane perturbations; an explanation for a lower bound found on the size of particles in the so called “spokes” in Saturn’s B ring; and the new concept of “Kepler caustic”, which is a distinguished curve in the two-parameter space related to the way dust is generated in real planetary rings.