Solar Cycle Modulation of Galactic Cosmic Rays Using a Generalized Force-Field Approximation

Galactic cosmic rays entering the heliosphere are modulated by the magnetized solar wind plasma, resulting in temporal intensity variations that closely follow the 11-year solar activity cycle. In this work, we present a generalized force-field approximation (FFA) for modeling the solar cycle modulation of galactic cosmic rays (GCRs), in which the diffusion coefficient is expressed as κ∝β κ2(P), with β = v/c and P the particle rigidity in gigavolts (GV). Unlike the conventional assumption of a linear rigidity dependence, we parameterize κ2(P) as a triple power-law in rigidity. Our analysis suggests that while the overall rigidity dependence of κ2(P) is fundamentally shaped by diffusion, particle drifts introduce a significant modification at rigidities below ~4 GV. Using Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) and Alpha Magnetic Spectrometer-02 (AMS-02) proton flux data, we determine three key model parameters. These parameters are time-dependent, and capture variations in the modulation strength throughout the solar cycle. Applying the same parameter set accurately reproduces the temporal evolution of helium fluxes and the He/p ratio, providing a unified and compact framework for describing GCR modulation across different nuclear species.