  The behavior of K-V, waterbag, parabolic, conical and Gaussian distributions
in periodic quadrupole channels is studied by particle simulations. It is found
that all these different distributions exhibit the known K-V instabilities. But
the action of the K-V type modes becomes more and more damped in the order of
the types of distributions quoted above. This damping is so strong for the
Gaussian distribution that the emittance growth factor after a large number of
periods is considerably lower than in the case of an equivalent K-V
distribution. In addition, the non K-V distributions experience in only one
period of the channel a rapid initial emittance growth, which becomes very
significant at high beam intensities. This growth is attributed to the
homogenization of the space-charge density, resulting in a conversion of
electric-field energy into transverse kinetic and potential energy. Two simple
analytical formulae are derived to estimate the upper and lower boundary values
for this effect and are compared with the results obtained from particle
simulations.
