Solar cycle modulation of galactic cosmic rays using a generalized force-field approximation

ABSTRACT Galactic cosmic rays (GCRs) entering the heliosphere are modulated by the magnetized solar wind plasma, resulting in temporal intensity variations that closely follow the 11-yr solar activity cycle. In this work, we present a generalized force-field approximation for modelling the solar cycle modulation of GCRs, in which the diffusion coefficient is expressed as $\kappa \propto \beta \, \kappa _2(P)$, with $\beta = v/c$ and P the particle rigidity in GV (gigavolts). Unlike the conventional assumption of a linear rigidity dependence, we parametrize $\kappa _2(P)$ as a triple power law in rigidity. Our analysis suggests that while the overall rigidity dependence of $\kappa _2(P)$ is fundamentally shaped by diffusion, particle drifts introduce a significant modification at rigidities below ${\sim} 4 \, \mathrm{GV}$. Using PAMELA (Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics) and AMS-02 (Alpha Magnetic Spectrometer-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.