Mathematics – Logic
Scientific paper
Sep 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999dda....31.0505h&link_type=abstract
American Astronomical Society, DDA meeting #31, #05.05
Mathematics
Logic
Scientific paper
We study the global stability of charged dust grains orbiting an axisymmetric planet with co-rotating magnetic field. The magnetic field and induced electric field are described in an inertial frame using the magnetic stream function Psi . The combined gravitational, magnetic, and electric forces are modelled by a two-dimensional effective potential U(e(rho ,z)) , parametrized by the conserved angular momentum p_φ. The critical points of U(e) then locate the equilibrium circular orbits, nonequatorial as well as equatorial. The stable equilibria form the nuclei of potential wells, which can contain large populations of dust grains. These potential wells have their own topological structure, so that a particle which loses local stability can still be trapped globally. Explicit Lyapunov stability boundaries ar derived for both positive and negative charges in both prograde and retrograde orbits. Thus, radial stability is lost when a critical point undergoes a tangent bifurcation, while transverse stability is lost via a pitchfork bifurcation. For a given position near a given planet stability depends only on the charge-to-mass-ratio q/m, which for a spherical dust grain is proportional to Phi /a(2) , where Phi is the ambient plasma potential and a is the grain radius. The results are applied to Saturn and Jupiter.
Horanyi Mihaly
Howard James E.
Stewart Glen Robert
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