Minimizing proton displacement damage dose during electric orbit raising of satellites

A formulation was developed to determine orbit-raising trajectories that minimize the radiation damage dose incurred by a satellite during electric orbit raising to the geosynchronous equatorial orbit. The proposed formulation considers the discretization of the spacecraft trajectory as well as the energy levels for the protons in the Van Allen belts, and the resulting nonlinear programming problem is solved using the solver LOQO. Furthermore, analytical models of the radiation flux of protons in the Van Allen belts, based on AP8MIN models, is used to facilitate the optimization process. The slowing down of the proton spectrum, that is the effect of shielding, is ignored in the computation of the displacement damage dose. At the beginning of the transfer, the satellite stays in the lower regimes of radiation flux and thereby restricts doing as much plane change as a minimum-time transfer.