High-precision cosmic ray measurements from both space-based and balloon-borne experiments have revealed a variety of spectral features. Primary nuclei and their secondaries produced during propagation exhibit spectral hardening above ~200 GV. Proton-spectrum softening has been observed at ~10 TeV. Helium-spectrum softening has been observed at slightly higher energies. A positron excess above ~25 GeV has also been observed. The cosmic-ray propagation code GALPROP v57 was utilized to study these features. GALPROP v57's parameter optimization module, utilizing the minimization library MINUIT2, was applied to find the best fit to the experimental data. As a baseline, the plain diffusion model with reacceleration and convection effects is employed. To study the hardening, three cases were explored: (1) a break in the diffusion coefficient, (2) breaks in the injection spectra, and (3) a combination of both. To account for the proton and helium spectra softening, an additional source break was introduced. A charge-symmetric primary positron source was introduced for the positron excess. Results are compared for the elemental spectra and ratios, as well as the all-particle spectrum, to compiled cosmic-ray data. Implications of these findings are discussed.
Chen et al. (2025) studied this question.