Solar origin iron ions in the Earth's radiation belts: Multi-dimensional equilibrium configuration modeling with charge states 1 through 12

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We have developed the first 3+1 dimensional model for energetic atomic iron (Ferrum) ions in the Earth's radiation belts taking into account also the angular anisotropy. The multi-dimensional iron ion model is parameterized with five free variables: geomagnetic L-shell, the ion magnetic moment, M, the second adiabatic invariant, J, the discrete charge state number, i, and time, t. This extends the earlier work on iron ions that was restricted to equatorially mirroring iron ions (Spjeldvik, 1996). In this work, quite time, steady state ion distributions have been obtained numerically from an assumed outer radiation zone boundary condition imposed at L=7, average values of the radial diffusion coefficients, D LL i , and standard values for the exospheric neutral densities due to the MSIS-86 upper atmosphere and exosphere neutral thermal particle density model. The plasmasphere was assumed to have a mean plasmapause location just beyond L=4. We included the twelve lowest charge states of atomic iron ions ( 56 26Fe). The results demonstrate that iron ions have a rather shallow penetration depth into the inner magnetosphere, even at MeV energies, but are distributed over a substantial angular domain. The penetration depth feature is, in part, due to the higher charge state reducing cross sections at these energies, substantially higher cross sections that those of the lighter ion species.