Particle motion in the equatorial plane of a dipole magnetic field

An exact relation is derived describing bound-particle orbits in the equatorial plane of a dipole magnetic field. An exact expression is then obtained for the average angular velocity of the particle about the dipole axis. The corresponding drift velocity is compared with the usual first-order expression based on a constant local field gradient. It is shown that the first- order expression for the drift velocity can be considerably in error when the particle loops are not small compared with the mean distance from the dipole axis.