Synchrotron radiation in nonuniform magnetic field

The distortion of the spectrum of synchrotron radiation received by a distant observer due to magnetic field inhomogeneity is discussed. It is shown that for single-particle radiation, a noticeable difference in the integrated spectrum from the case of a uniform magnetic field occurs only for observation times significantly exceeding the observer's departure from the beam pattern, and only for subrelativistic particles, when the radiation arrives from regions with significantly different magnetic fields during the observation time. For shorter observation times, field inhomogeneity leads only to small-scale distortions (smaller or comparable in frequency to the gyrofrequency) and does not manifest itself in the averaged spectrum. For the case of a particle ensemble, which is of interest for astrophysical applications, the difference in the integrated spectrum becomes negligible.