In this article, we discuss the modifications that occur in
the brightness and gain of a longitudinal wiggler-free electron
laser with the aid of induced betatron oscillation. Two novel
approaches have been discussed to improve the gain of the system.
In the first scheme, an auxiliary undulator field with betatron
oscillations brings in additional bunching and results in enhanced
gain. In the second scheme, an axial magnetic field is tuned
to provide additional bunching for gain enhancement.