  We consider the radiation emitted by an ultrarelativistic charged particle
moving in a magnetic field, in the presence of an additional Lorentz-violating
interaction. In contrast with prior work, we treat a form of Lorentz violation
that is represented by a renormalizable operator. Neglecting the radiative
reaction force, the particle's trajectory can be determined exactly. The
resulting orbit is generally noncircular and does not lie in the place
perpendicular to the magnetic field. We do not consider any Lorentz violation
in the electromagnetic sector, so the radiation from the accelerated charge can
be determined by standard means, and the radiation spectrum will exhibit a
Lorentz-violating directional dependence. Using data on emission from the Crab
nebula, we can set a bound on a particular combination of Lorentz-violating
coefficients at the $6\times10^{-20}$ level.
