Method of Reconstruction of Unidirectional Flux in the Earth’s Radiation Belts in Gyrocenter Approximation

Abstract

We presented an extension of our method of reconstruction of anisotropic fluxes in the Earth’s radiation belts (ERB) to the gyrocenter approximation, which is necessary to calculate fluxes using geomagnetic parameters measured at the gyrocenter of registered particles. The main issue of such an analysis is to find the connection between coordinate grids of local observable parameters and gyrocenter ones defining the fluxes in the ERB. The main complication here compared to the local case is that the observable range of local parameters (pitch- and gyro-angles) depends on three parameters (L-shell and equatorial pitch angle at gyrocenter, and particles’ energy), which leads to the regular rectangular coordinate grid of geomagnetic parameters at gyrocenter converting into an irregular nonrectangular grid of local observable geomagnetic parameters. In the article, we describe in detail the developed algorithm for establishing such a connection for any point of near-Earth space and any orientation of an instrument with a known field of view (FoV) cone. We reconstructed a set of local grids corresponding to a fixed gyrocenter parameters grid along the trajectory of the PAMELA spectrometer in the ERB and showed a great variability of observable parameter space at the gyrocenter. Our analysis demonstrated that using local geomagnetic parameters for the calculation of proton fluxes with energies higher than 100 MeV in the ERB can significantly distort measured fluxes and might be one of the reasons for discrepancies between different measurements in this area.