  The behavior of mismatched intense charged-particle beams in periodic
transport channels of the solenoid and quadrupole type is studied
theoretically. The envelope-oscillation frequencies of the mismatched beam are
obtained by the smooth-approximation method and by numerical evaluation of the
linearly perturbed K-V envelope equations. Phase shifts of the envelope
oscillations and growth rates in the case of instability are calculated for a
solenoid and a magnetic quadrupole (FODO) channel using the parameters of the
Maryland and GSI beam transport experiments. For comparison and the purpose of
illustration, the K-V equations are integrated numerically, and envelope curves
as well as single-particle trajectories for for mismatched beams are shown in
graphical form. In addition, computer simulation studies with the PARMILA code
were performed, and results are presented both for K-V and a Gaussian
distribution in transverse phase space.
