Variational-Wavelet Approach to RMS Envelope Equations

Multiscale Analysis of RMS Envelope Dynamics

We present applications of variational -- wavelet approach to different forms of nonlinear (rational) rms envelope equations. We have the representation for beam bunch oscillations as a multiresolution (multiscales) expansion in the base of compactly supported wavelet bases.

Local Analysis of Nonlinear RMS Envelope Dynamics

We present applications of variational -- wavelet approach to nonlinear (rational) rms envelope dynamics. We have the solution as a multiresolution (multiscales) expansion in the base of compactly supported wavelet basis.

Finding matched rms envelopes in rf linacs: A Hamiltonian approach

We present a new method for obtaining matched solutions of the rms envelope equations. In this approach, the envelope equations are first expressed in Hamiltonian form. The Hamiltonian defines a nonlinear mapping, $\cal M$, and for periodic transport systems the fixed points of the one-period map are the matched envelopes. Expanding the Hamiltonian around a fiducial trajectory one obtains a linear map, $M$, that describes trajectories (rms envelopes) near the fiducial trajectory. Using $\cal M$ and $M$ we construct a contraction mapping that can be used to obtain the matched envelopes. The alg…

RMS/Rate Dynamics via Localized Modes

We consider some reduction from nonlinear Vlasov-Maxwell equation to rms/rate equations for second moments related quantities. Our analysis is based on variational wavelet approach to rational (in dynamical variables) approximation. It allows to control contribution from each scale of underlying multiscales and represent solutions via multiscale exact nonlinear eigenmodes (waveletons) expansions. Our approach provides the possibility to work with well-localized bases in phase space and best convergence properties of the corresponding expansions without perturbations or/and linearization proced…

Localized Coherent Structures and Patterns Formation in Collective Models of Beam Motion

We present applications of variational -- wavelet approach to three different models of nonlinear beam motions with underlying collective behaviour: Vlasov-Maxwell-Poisson systems, envelope dynamics, beam-beam model. We have the representation for dynamical variables as a multiresolution (multiscales) expansion via high-localized nonlinear eigenmodes in the base of compactly supported wavelet bases. Numerical modelling demonstrates formation of coherent structures and stable patterns.

使用 Fokker-Planck 方法改进粒子束的包络和发射度描述

Improved envelope and emittance description of particle beams using the Fokker-Planck approach

针对 Vlasov 方程无法处理随机现象的问题，提出基于 Fokker-Planck 方程推导束流包络和发射度运动方程，包含温度平衡附加项，可估算储存环中束内散射导致的发射度增长率。