# Abstracts

## XX International Linac Conference

## MOE14 (Poster)

**Presenter: **Michael Zeitlin (IPME RAS)

** email: **zeitlin@math.ipme.ru

**Status: **Complete

**FullText: **
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**Eprint:** physics/0008043
# Multiscale Analysis of RMS Envelope Dynamics

A. FEDOROVA, M. ZEITLIN* (IPME RAS)

We present applications of methods from nonlinear(local) Fourier 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[1]. Our
approach is based on methods provided possibility to work with well-localized in
phase space bases, which gives the most sparse representation for the general type of
operators and good convergence properties[2]. 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 multiresolution expansion
both for dynamical variables and for energy spectrum[3].

[1] Nonlinear Accelerator Problems via Wavelets, parts 1-8, Proc.PAC99,
IEEE, 1614,1617,1620,2900,2903,2906,2909,2912.

[2] American Institute of Physics, Conf. Proc., vol. 468, Nonlinear and
Collective Phenomena in Beam Physics, pp. 48-68, 69-93, 1999

[3] Variational-Wavelet Approach to RMS Envelope Equations Los Alamos,
physics/0003095

*e-mail: zeitlin@math.ipme.ru,
http://www.ipme.ru/zeitlin.html

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