Fluxes and Nuclear Abundances of Cosmic Rays inside the Magnetosphere using a Transmission Function Approach

At 1 AU and outside the Earth's magnetosphere, the relative abundances to protons for He (He/p), C (C/p) and Fe (Fe/p) nuclei were calculated using the observation-data of AMS-01 (for p and He) and HEAO-3 (for C and Fe) above 0.8 GeV/nucleon. In addition, the transmission function (TF) for the GCR propagation inside the magnetosphere was evaluated using the IGRF and T96 (introduced by Tsyganenko and Stern) models to obtain permitted and forbidden trajectories inside the magnetosphere. The TF allowed one to derive the primary He-nuclei fluxes in the same geomagnetic regions of AMS-01 observations. These fluxes were found in good agreement with the observation data. Furthermore inside the magnetosphere in addition to the flux of helium, it allowed one to obtain those of the primary p, C, and Fe nuclei and the relative abundances of He, C and Fe nuclei to protons from the same observation-data of AMS-01 and HEAO-3 above 0.8 GeV/nucleon. Up to a geomagnetic latitude of 45.84 deg, the relative isotopic abundances were found to depend on the mass number I_isot and, on average, range from a factor 2.31 up to 3.35 larger than those outside the magnetosphere at 1 AU. Thus, the magnetospheric isotopic/nuclear relative-abundances differ from those inside the solar cavity and those in the interstellar space. The usage of the TF approach can allow one to determine the nuclear abundances in the magnetosphere at any geomagnetic latitude and, thus, any orbit, provided that the CR spectra are determined at 1 AU.