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.

14 pages