Instability in the 3rd Dimension of the Extended Störmer Problem

ISSN： 0167-9295

Source： Earth, Moon, and Planets, Vol.84, Iss.2, 1999-03, pp. : 63-79

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Abstract

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 studied by means of computing families of periodic solutions and their stability. Ten such families are found and their stability study shows that only two out of the ten have short arcs of stable members, all with low inclination 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 Störmer problem, leads to the conclusion that in the modified system the three-dimensional motions are basically unstable unlike those of the one-dipole case. The model magnetic field used in this study is a first approximation of the Z3model of the magnetic field of Saturn as computed from the Pioneer 11 and Voyager 1 and 2 measurements.