On transition of propagation of relativistic particles from the ballistic to the diffusion regime

TL;DR

This paper develops a comprehensive stationary distribution function for relativistic particle propagation that captures the transition from ballistic to diffusion regimes, improving modeling of gamma-ray emissions near accelerators.

Contribution

It introduces a novel distribution function that accurately describes the entire propagation process, including the transition regime, and applies it to gamma-ray imaging near particle accelerators.

Findings

Gamma-ray morphology and spectra deviate from standard diffusion models.

The new function accurately captures the transition regime.

Results improve understanding of particle propagation near accelerators.

Abstract

A stationary distribution function that describes the entire processes of propagation of relativistic particles, including the transition between the ballistic and diffusion regimes, is obtained. The spacial component of the constructed function satisfies to the first two moments of the Boltzmann equation. The angular part of the distribution provides accurate values for the angular moments derived from the Boltzmann equation, and gives a correct expression in the limit of small-angle approximation. Using the derived function, we studied the gamma-ray images produced through the $pp$ interaction of relativistic particles with gas clouds in the proximity of the accelerator. In general, the morphology and the energy spectra of gamma-rays significantly deviate from the "standard" results corresponding to the propagation of relativistic particles strictly in the diffusion regime.