Chaotic and hyperchaotic motion of a charged particle in a magnetic dipole field

The motion of a charged particle in the field of a magnetic dipole is studied by numerically integrating the equations of motion. The widely believed picture in which a bound particle corkscrews about a line of magnetic flux, bouncing back along the same line as it nears the poles, is shown to be a substantial over-simplification. The nature of the trajectory depends on the energy of the particle, but whatever the energy this picture is not observed. For low energies the particle will corkscrew towards the poles, while at the same time drifting laterally with a variable speed in a quasiperiodic fashion. For intermediate energies the motion is found to be chaotic, and for higher energies it becomes hyperchaotic. In the equatorial plane only quasiperiodic orbits can occur. If the magnetic dipole moment is slowly varying, the particle undergoes chaotic motion even in the equatorial plane, but only for high energies.