Chaotic and hyperchaotic motion of a charged particle in a magnetic dipolefield

The motion of a charged particle in the field of a magnetic dipole is studi ed 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 th e energy of the particle, but whatever the energy this picture is not obser ved. For low energies the particle will corkscrew towards the poles, while at the same time drifting laterally with a variable speed in a quasiperiodi c 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 var ying, the particle undergoes chaotic motion even in the equatorial plane, b ut only for high energies.