HEACC-2001, Abstract 3

Fedorova A.N., Zeitlin M.G.

NONLINEAR EIGENMODE EXPANSION FOR NONLINEAR RMS ENVELOPE DYNAMICS

We present applications of methods from nonlinear (local) harmonic analysis or wavelet analysis to a number of nonlinear accelerator physics problems. This is continuation of our results which were presented on PAC97/99, EPAC98/00. Our approach is based on methods provided possibility to work with well-localized bases in phase space and good convergence properties of corresponding expansions. Consideration of transverse dynamics of relativistic, space-charge dominated beams is based on variational approach to rational (in dynamical variables) approximation for rms envelope equations and allows us to control contribution from each scale of underlying multiscales and represent the solutions via exact nonlinear (eigen)mode expansions (Courant-Snyder equation is a particular case for our general approach).