The transport of galactic cosmic rays in heliosphere: The HELMOD model compared with other commonly employed solar modulation models

HELMOD model allows one to describe how solar modulation affects the propagation of galactic cosmic rays (GCRs) through the heliosphere by solving the Parker transport equation. HELMOD provides modulated spectra for protons and nuclei during high and low solar activity periods, in the inner and outer heliosphere, at Earth location and outside the ecliptic plane, as well as at different distances from Sun in the inner and outer heliosphere. The GCRs mainly constitute the high-energy population of the so-called space radiation environment. Modulated cosmic-ray spectra of protons and nuclei, obtained from HELMOD and other solar modulation codes were compared to the AMS–02 spectra ranging from GeV up to TeV energies. Concerning other commonly used solar modulation models, HELMOD modulated spectra are available over the entire rigidity range and observation period of AMS–02 mission. A quantitative comparison among models was carried out using ΔΦ, i.e., the relative difference between the experimental and simulated fluences, and ηRMS, i.e., the error-weighted root mean square of the relative difference between AMS–02 experimental data and simulated differential intensities. HELMOD was found to achieve a good agreement over the full set of experimental data with, typically, ΔΦ within ±2.5% and ηRMS within 5%. Usually larger or, in a few cases, much larger values for ΔΦ and ηRMS were found for the other models.