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

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.

References in corpus (3)

• Parametrization of gamma-ray production cross-sections for pp interactions in a broad proton energy range from the kinematic threshold to PeV energies
• Propagation of high-energy cosmic rays in extragalactic turbulent magnetic fields: resulting energy spectrum and composition
• Anisotropies of ultra-high energy cosmic rays diffusing from extragalactic sources

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