| Gravity and a solar-wind electrostatic force are individually considered as perturbations to the Stormer problem, motion in a magnetic dipole field. The problems considered are conservative, Hamiltonian and either two or three degrees of freedom. Families of periodic orbits are calculated along with the linearized stability. The relationship between trajectories in the unaveraged and gyro-averaged (adiabatic) cases is considered. For low energy ions, gravity is shown to increase orbit stability and lead to trapping above or below the magnetic equator. The solar wind potential is shown to trap ions on the sun side of the dipole and to cause low energy ions to escape. For the Earth's magnetosphere the gravity result applies in the plasmasphere while the solar wind result applies in the Van Allen radiation belts. |
