On the location of trapped particle populations in quadrupole magnetospheres

Populations of trapped particles in Earth's magnetic field are intimately l inked to prominent magnetospheric phenomena, for example, to the radiation belts and the ring current. Particles are forced to bounce between both hem ispheres because field lines converge from the magnetic equatorial region t oward the poles owing to the dominating dipolar component. The scenario may change essentially if the so-called paleomagnetosphere is considered, that is, the terrestrial magnetosphere during apolarity reversal period. This r eport deals with particle trapping in general field configurations and conc entrates on the quadrupole case as a potential scenario for paleomagnetosph eric studies. By using the tensor representation of the quadrupole field, w e show that its topology is controlled by a single "shape" parameter which is a measure for the relative strength of quadrupole tensor components, or equivalently, coefficients in the spherical harmonics expansion of the pote ntial. In order to locate centers of particle bounce motion the concept of a magnetic equatorial surface is extended to a more general type of "trappi ng center surface" by means of geometrical criteria such as B . del B = 0. The quadrupole case yields two such surfaces. As does the field line topolo gy, those surfaces and the resulting drift orbits vary strongly with the qu adrupole shape parameter.