# Time dependent solar modulation of cosmic rays from solar minimum to solar maximum

## TL;DR

This paper models the time-dependent solar modulation of cosmic rays across solar activity cycles, deriving local interstellar spectra and analyzing the effects of heliospheric magnetic field variations.

## Contribution

It introduces a two-dimensional modulation model that accounts for temporal changes in the interplanetary environment and derives the LIS during different solar activity periods.

## Key findings

- Rigidity dependence of the diffusion coefficient is key during polarity reversal periods.
- A power law relates the diffusion coefficient to the heliospheric magnetic field strength.
- The model successfully fits experimental data from Voyager 1, PAMELA, BESS-POLARII, and ACE.

## Abstract

We study the time-dependent modulation effect and derive the local interstellar spectra (LIS) for the cosmic ray (CR) proton, helium, boron and carbon. A two-dimensional modulation model including the variation of the interplanetary environment with time is adopted to describe modulation process. The propagation equation of CRs in the heliosphere is numerically solved by the package Solarprop. We derive the LIS by fitting the latest results of several experiments, including Voyager 1, PAMELA, BESS-POLARII and ACE, during low solar activity periods. We further study the modulation in the polarity reversal periods with the PAMELA proton data. We find that the rigidity dependence of the diffusion coefficient is critical to explain the modulation effect during reversal periods. Our results also indicate a power law relation between the diffusion coefficient and the magnitude of the heliospheric magnetic field (HMF) at the Earth.