Solar Modulation of Galactic Cosmic-Ray Protons Based on a Modified Force-field Approach

In this work, a modified force-field approach is established to investigate the long-term solar modulation of galactic cosmic-ray (GCR) protons. In this approach, the solar modulation potential ϕ is assumed to be energy dependent. As ϕ also depends on the local interstellar spectrum (LIS), a new proton LIS model is first presented based on data from Voyager 1 and 2, PAMELA, and AMS-02. Then, a double power-law expression is proposed to model ϕ as a function of proton energy. By fitting to the selected GCR measurements, the solar cycle variation characteristics of parameters in the expression of ϕ are obtained, and these parameters are reconstructed using the sunspot number, the heliospheric current sheet tilt angle, and the polarity of heliospheric magnetic field. Finally, a new analytical predictive model for GCR protons is established. It is shown that the 11 and 22 yr cyclic variations of GCRs are reproduced, and the computed proton intensities are in good agreement with GCR measurements at various energies since 1954.