Studying the diffusion mechanism of cosmic-ray particles

¹ Department of Physics, Xiangtan University, Xiangtan, Hunan 411105, PR China
² Key Laboratory of Stars and Interstellar Medium, Xiangtan University, Xiangtan 411105, China
³ Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540, USA

^⋆ Corresponding author: jfzhang@xtu.edu.cn

Received: 7 December 2024
Accepted: 17 June 2025

Abstract

Context. An increasing number of observations have indicated the existence of slow diffusion phenomena in astrophysical environments, such as around the supernova remnants and pulsar γ-ray halos, where the diffusion coefficient of cosmic rays (CRs) near the source region is significantly smaller than that far away from the source region. The inhomogeneous diffusion indicates the existence of multiple diffusion mechanisms.

Aims. Comparing the CR mirror diffusion with the scattering diffusion, our aim is to explore their diffusion characteristics in different magnetohydrodynamic (MHD) turbulence regimes and understand the effect of different MHD modes on mirror and scattering diffusion.

Methods. We performed numerical simulations with the test particle method. Within the global frame of reference, we first measured parallel and perpendicular CR diffusion and then determined the mean free path of CRs with varying energies.

Results. Our main results demonstrate that (1) CRs experience a transition from superdiffusion to normal diffusion; (2) mirror diffusion is more important than scattering diffusion in confining CRs; (3) CR diffusion strongly depends on the properties of MHD turbulence; and (4) magnetosonic and Alfvén modes respectively dominate the parallel and perpendicular diffusion of CR particles.

Conclusions. The diffusion of CRs is a complex problem of mixing the mirror diffusion and scattering diffusion. The property of turbulent magnetic fields influences CR diffusion. The CR slow diffusion due to the presence of magnetic mirrors in turbulence has important implications for explaining observations near a CR source.