# Interplanetary spread of solar energetic protons near a high-speed solar wind stream

## TL;DR

This study models how high-speed solar wind streams and CIR structures influence the interplanetary spread and acceleration of solar energetic protons, revealing complex effects on particle distribution and intensity profiles.

## Contribution

It introduces a combined modeling approach using a particle transport code and MHD simulations to analyze proton spread in structured solar wind conditions.

## Key findings

- Reverse shocks accelerate particles more efficiently than forward shocks.
- Particle intensity distribution width varies with heliocentric distance.
- IMF deflections and compressions deform particle distribution shapes.

## Abstract

We study how a high-speed solar wind stream embedded in a slow solar wind influences the spread of solar energetic protons in interplanetary space. To model the energetic protons, we used a recently developed particle transport code that computes particle distributions in the heliosphere by solving the focused transport equation in a stochastic manner. The particles are propagated in a solar wind containing a CIR, which was generated by the heliospheric magnetohydrodynamic model, EUHFORIA. We study four cases in which we assume a delta injection of 4 MeV protons spread uniformly over different regions at the inner boundary of the model. These source regions have the same size and shape, yet are shifted in longitude from each other, and are therefore magnetically connected to different solar wind conditions. The intensity and anisotropy profiles along selected IMF lines vary strongly according to the different solar wind conditions encountered along the field line. The IMF lines crossing the shocks bounding the CIR show the formation of accelerated particle populations, with the reverse shock wave being a more efficient accelerator than the forward shock wave. Moreover, we demonstrate that the longitudinal width of the particle intensity distribution can increase, decrease, or remain constant with heliographic radial distance, reflecting the underlying IMF structure. Finally, we show how the deflection of the IMF at the shock waves and the compression of the IMF in the CIR deforms the three-dimensional shape of the particle distribution in such a way that the original shape of the injection profile is lost.