temperature [@Ebert_Zhukovsky_Razumovsky]; various astrophysical manifestations [@Andrianov_Giacconi_Soldati], [@sme_eff_astro], [@Altschul]; etc. In the present work, we shall actually consider a very particular limit of the SME related to the minimal Lorentz and CPT-symmetry breaking in the electron sector of the theory (the reasons for making this approximation are discussed further in the paper in more detail); it is described by means of the additional (to the standard fermion Lagrangian) term $ -{\overline}{\psi} \gamma^{5} \gamma^{\mu} b_{\mu} \psi $, where $ b^{\mu} $ is a pseudovector quantity independent of the space-time coordinates $ x^{\mu} $ in every fixed reference frame, regarded as a vacuum expectation value of some object of a more fundamental theory.

We shall study the synchrotron radiation of a high-energy electron supposing (in the same way as it was done in [@Zhukovsky_Lobanov_Murchikova]) that $ | b^{0} | \gg | {\bf b} | $; such assumption does not contradict most of the estimates available at present (see, e.g., [@sme_reviews], [@Andrianov_Giacconi_Soldati]). So we consider the interaction of the fermion field $ \psi $ with the condensate $ b^{\mu} $ as the only type of Lorentz invariance violation present in our theory, neglecting other possible types (in particular, referring to the photon sector).

In 