  We consider space-charge dominated beam transport systems, where space-charge
forces are the same order as external focusing forces and dynamics of the
corresponding emittance growth. We consider the coherent modes of oscillations
and coherent instabilities both in the different nonlinear envelope models and
in initial collective dynamics picture described by Vlasov system. Our
calculations are based on variation approach and multiresolution in the base of
high-localized generalized coherent states/wavelets. We control contributions
to dynamical processes from underlying multiscales via nonlinear high-localized
eigenmodes expansions in the base of compactly supported wavelet and wavelet
packets bases.
