Analytical model of Van Allen proton radiation flux for trajectory optimization solvers
Foster, Alexander T.; Dutta, Atri. 2015. Analytical model of Van Allen proton radiation flux for trajectory optimization solvers. Advances in the Astronautical Sciences Spaceflight Mechanics, vol. 155:pp 473-486
Radiation damage is a concern for electric orbit-raising of spacecraft to the Geostationary orbit because the spacecraft spends a lot of time in the Van Allen radiation belts. Trajectory optimization solvers are required to compute the solar array degradation during orbit-raising because the loss of power generation capability of the solar array impacts the thrust generated by the electric propulsion devices. Considering that the charged protons in the Van Allen belts cause the majority of damage to the spacecraft solar array, this paper proposes to develop approximate analytical models of the flux of protons in the radiation belts using the recently released AP-9 data. The analytical functions can be used within optimization solvers for improving convergence characteristics and computational time for generating low-thrust trajectories. This paper compares different approximate analytical models for the proton radiation flux.