| Paper |
Title |
Page |
| WEPSB019 |
Orbital Motion in Multipole Fields via Multiscale Decomposition |
404 |
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- A.N. Fedorova, M.G. Zeitlin
RAS/IPME, St. Petersburg, Russia
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We present applications of methods of nonlinear local harmonic analy- sis in variational framework for a description of multiscale decomposition in polynomial/rational approximations (up to any order) for nonlinear motions in arbitrary n-pole fields. Our approach is based on the methods allowed to consider dynamical beam/particle localization in phase space and provided exact multiscale representations via nonlinear high-localized eigenmodes for observables with exact control of contributions to motion from each underlying hidden scale.
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| WEPSB026 |
Dynamical Aperture Beyond Perturbations: From Qualitative Analysis to Maps |
419 |
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- A.N. Fedorova, M.G. Zeitlin
RAS/IPME, St. Petersburg, Russia
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We start with a qualitative approach based on the detailed analysis of smoothness classes of the underlying functional spaces provided possible evaluation of the dynamical aperture in general nonlinear/polynomial models of particle/beam motion in accelerators. We present the applications of discrete multiresolution analysis technique to the maps which arise as the invariant discretization of continuous nonlinear polynomial problems. It provides a generalization of the machinery of local nonlinear harmonic analysis, which can be applied for both discrete and continuous cases and allows to construct the explicit multiresolution decomposition for solutions of discrete problems which are the correct discretizations of the corresponding continuous cases.
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