The paper presents a method for numerically simulating the synchrotron radiation of relativistic electrons in a turbulent, inhomogeneous galactic magnetic field. Using the developed software, maps of the synchrotron background distribution on the celestial sphere are constructed. Particular attention is paid to a multipole analysis of the obtained maps, which make it possible to investigate the influence of the distributed source generation depth on the formation of the angular structure of radiation. It is shown that at shallow generation depths, low-frequency harmonics dominate the multipole decomposition spectrum. A pronounced anisotropy is observed, due to the limited spatial scales. With increasing depth, the multipole decomposition spectra become smoother and closer to isotropic, reflecting the averaged nature of the turbulent medium. It is found that for deep generation of the spatial structure of distributed sources, changes in the turbulence spectrum slope significantly affect the shape of the angular power distribution, leading to a redistribution of energy between large-scale and small-scale components. The results highlight the importance of scaling parameters in simulating the structure of the synchrotron background and may be useful for interpreting radio astronomical observations.
Batrakov et al. (Mon,) studied this question.