Nonlinear Dynamics of High-Brightness Beams

The consideration of transverse dynamics of relativistic space-charge dominated beams and halo growth due to bunch oscillations is based on variational approach to rational (in dynamical variables) approximation for rms envelope equations. It allows to control contribution from each scale of underlying multiscales and represent solutions via exact nonlinear eigenmodes expansions. Our approach is based on methods provided possibility to work with well-localized bases in phase space and good convergence properties of the corresponding expansions.