  We calculate the low energy elementary excitations of a Bose-Einstein
Condensate in an effective magnetic field. The field is created by the
interplay between light beams carrying orbital angular momentum and the trapped
atoms. We examine the role of the homogeneous magnetic field, familiar from
studies of rotating condensates, and also investigate spectra for vector
potentials with a more general radial dependence. We discuss the instabilities
which arise and how these may be manifested.
