Instability in the 3rd dimension of the extended Stormer problem

The problem of motions of charged particles or charged grains of matter in the field of two magnetic dipoles in rotation about a common center are stu died by means of computing families of periodic solutions and their stabili ty. Ten such families are found and their stability study shows that only t wo out of the ten have short arcs of stable members, all with low inclinati on to the plane of the two dipoles, while the rest of the families consist exclusively of unstable solutions. Hence the impact of adding one dipole to the configuration of the Stormer problem, leads to the conclusion that in the modified system the three-dimensional motions are basically unstable un like those of the one-dipole case. The model magnetic field used in this st udy is a first approximation of the Z3 model of the magnetic field of Satur n as computed from the Pioneer 11 and Voyager 1 and 2 measurements.