  We obtain a system of exact solutions of the Dirac equation for an electron
moving in a constant homogeneous external magnetic field with account of its
vacuum magnetic moment and assumed Lorentz invariance violation in the minimal
CPT-odd form in the framework of the Standard Model Extension. Using these
solutions, characteristics of the particle synchrotron radiation are
calculated, and possible observable effects caused by the Lorentz non-invariant
interaction are described. We demonstrate that the angular distribution of the
radiation has specific asymmetry, which can be explained as a consequence of
non-conservation of transversal electron polarization in the presence of a
background Lorentz non-invariant condensate field.
