# Modulation of Galactic Cosmic Rays in the Inner Heliosphere, Comparing with PAMELA Measurements

## TL;DR

This paper presents a numerical model for the time-dependent modulation of galactic cosmic rays in the inner heliosphere, incorporating a modified magnetic field, a new diffusion coefficient, and observationally-based turbulence dependencies, successfully matching PAMELA data.

## Contribution

The study introduces a comprehensive numerical model with a modified Parker magnetic field and a novel diffusion coefficient, improving the understanding of cosmic ray modulation in the heliosphere.

## Key findings

- Model reproduces PAMELA proton spectra during solar minimum.
- Analytical turbulence variation matches spacecraft observations.
- Radial dependence of turbulence aligns with empirical data.

## Abstract

We develop a numerical model to study the time-dependent modulation of galactic cosmic rays (GCRs) in the inner heliosphere. In the model a time-delayed modified Parker heliospheric magnetic field (HMF) and a new diffusion coefficient model, NLGCE-F, from Qin \& Zhang (2014), are adopted. In addition, the latitudinal dependence of magnetic turbulence magnitude is assumed as $\sim (1+\sin^2\theta)/2$ from the observations of Ulysses, and the radial dependence is assumed as $\sim r^S$, where we choose an expression of $S$ as a function of the heliospheric current sheet (HCS) tilt angle. We show that the analytical expression used to describe the spatial variation of HMF turbulence magnitude agrees well with the Ulysses, Voyager 1, and Voyager 2 observations. By numerically calculating the modulation code we get the proton energy spectra as a function of time during the recent solar minimum, it is shown that the modulation results are consistent with the PAMELA measurements.