Lorentz resonances and the vertical structure of dusty rings: Analytical and numerical results

摘要: Dust grains orbiting the giant outer planets carry a weak and nearly constant electrical charge. Through interaction with planet's irregular magnetic field, inclinations i eccentricities e of these charged can be pumped up significantly. This occurs especially when period Lorentz force matches radial or out-of-plane epicyclic periods. Since particles sample spatial structure planetary field at differing rates depending on their mean orbital radius a, resonances (LR) occur specific radii. Several strongest LR have been related to structural features Jovian dust ring system. In this paper we use combination analytical numerical techniques in order understand nature resonances. A simple extension perturbation theory for LRs yields charge-to-mass ratio (q/m) corrections periods in-plane motion, thus allowing an accurate determination resonance locations. The analysis also indicates that two modes oscillation are weakly coupled. We then show assumed previous developments, undergoes small but significant resonant forcing as well, resulting shifts which break exact linear condition. An energy grain's orbit - values eccentricity inclination shows it decomposed into three parts: energies vertical horizontal oscillators, circular equatorial from perturbed by force. In reference frame corotating planet where no electric is present, cannot do work exert torque; hence transfer between oscillators. Numerical integrations zones support view dynamical interaction, confirm existence range ratios overlap, thereby producing what appears chaotic motion. Resonance traversed orbits evolve semimajor axis, e.g., due plasma drag. Using simulations study passage through resonance, find elements undergo large jumps, determine size jumps function drag evolution rates. ascertain distribution final parameters, after passage, initial launch longitudes. particular longitude nodes, Ω, uniformly distributed over interval 0 < Ω 2π. case, cross-section halo would predicted symmetry about plane, confirmed Voyager data Showalter et al. (1987, Icarus, 69, 458–498). adiabatic invariants induced passing one survive during excursion next encounter. Thus many explained mechanism.