the space-time region being large enough (and this is usually assumed when working in the context of the SME).

In what follows, we study the motion of an electron in an external magnetic field at the quantum level and obtain the characteristics of its electromagnetic radiation using the techniques of QED.

The model {#model}
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The Lagrangian obtained for an electron interacting with the electromagnetic field $ A^{\mu} $ and background constant condensate field $ b^{\mu} $ has the form: $$\label{model_L}
    {\cal L} =
        {\overline}{\psi} \left(
            i \gamma^{\alpha} D_{\alpha} - m
            + {{\textstyle}\frac{1}{2}} \mu \sigma^{\alpha \beta} F_{\alpha \beta}
            - \gamma^{5} \gamma^{\alpha} b_{\alpha}
        \right) \psi.$$ Here $ F_{\alpha \beta} $ is the electromagnetic field tensor; $ \mu $ is the electron anomalous (vacuum) magnetic moment [@Pauli_vmm], which we treat approximately as a constant quantity: $ \mu \simeq \mu_{0} \, \frac{e^{2}}{2\pi} $ where $ \mu_{0} = \frac{e}{2m} $ [@Schwinger_vmm]; $ \sigma^{\mu \nu} = \frac{i}{2} [ \gamma^{\mu}, \gamma^{\nu} ] $, $ \gamma^{5} = - i \gamma^{0} \gamma^{1} \gamma^{2} \gamma^{3} $. We accept $ e > 0 $ so that the electron charge $ q_{e} = -e $, and the covariant derivative is $ D_{\mu} = {\partial}_{\mu} - i e A_{\mu} $. We assume 