We investigate the diffusion of cosmic rays ( CR ) close to their sources .
Propagating individual CRs in purely isotropic turbulent magnetic fields with maximal scale of spatial variations l _ { \max } , we find that CRs diffuse anisotropically at distances r \raise 1.29 pt \hbox { $ < $ \kern - 7.5 pt \raise - 4.73 pt \hbox { $ \sim $ } } l _ { \max } from their sources .
As a result , the CR densities around the sources are strongly irregular and show filamentary structures .
We determine the transition time t _ { \ast } to standard diffusion as t _ { \ast } \sim 10 ^ { 4 } { yr } ( l _ { \max } / 150 { pc } ) ^ { \beta } ( E / { PeV } ) ^ { - % \gamma } ( B _ { rms } / 4 \mu G ) ^ { \gamma } , with \beta \simeq 2 and \gamma = 0.25 – 0.5 for a turbulent field with Kolmogorov power spectrum .
We calculate the photon emission due to CR interactions with gas and the resulting irregular source images .