  Transverse beam stability is strongly affected by the beam space charge.
Usually it is analyzed with the rigid-beam model. However this model is only
valid when a bare (not affected by the space charge) tune spread is small
compared to the space charge tune shift. This condition specifies a relatively
small area of parameters which, however, is the most interesting for practical
applications. The Landau damping rate and the beam Schottky spectra are
computed assuming that validity condition is satisfied. The results are applied
to a round Gaussian beam. The stability thresholds are described by simple fits
for the cases of chromatic and octupole tune spreads.
