  In the framework of the classical effective Lorentz invariance violating
(LIV) model of Myers-Pospelov, we present a complete calculation of the
synchrotron radiation produced by a circularly moving charge in the rest frame
of the model. Within the full far-field approximation we compute exact
expressions for the electric and magnetic fields, the angular distribution of
the power spectrum and the total emitted power in the m-th harmonic. We also
perform an expansion of the latter quantity in terms of the electromagnetic LIV
parameter and calculate the average degree of circular polarization to first
order in such a parameter. In both cases we find, under adequate circumstances,
the appearance of rather unexpected and large amplifying factors, which go
together with the otherwise negligible naive expansion parameter. This opens up
the possibility of selecting astrophysical sources where these amplifying
factors are important, to explore further constraints imposed upon the LIV
parameters by synchrotron radiation measurements.
