  We examine the stability of intense flat bunches in barrier buckets used in
the Recycler. We consider some common stationary distributions and show that
they would be unstable against rigid dipole oscillations. We then discuss an
analytical model for the line density that best describes measured bunch
profiles. We include space charge in this model to predict the bunch intensity
at which Landau damping would be lost. The dependence of this threshold on the
bunch length is studied and related to the results of an experimental study
with shorter bunch lengths. The threshold for the microwave instability is
estimated. These studies will be followed by more detailed numerical studies.
