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Michael G. Zeitlin

Publications and source records attributed to Michael G. Zeitlin.

At least 37 records · Page 2Linked to original sources
arXiv2002

Fast Calculations in Nonlinear Collective Models of Beam/Plasma Physics

We consider an application of variational-wavelet approach to nonlinear collective models of beam/plasma physics: Vlasov/Boltzmann-like reduction from general BBGKY hierachy. We obtain fast convergent multiresolution representations for solutions which allow to consider polynomial and rational type of nonlinearities. The solutions are represented via the multiscale decomposition in nonlinear high-localized eigenmodes (waveletons).

physics.plasm-ph↗
arXiv2002

BBGKY Dynamics: from Localization to Pattern Formation

A fast and efficient numerical-analytical approach is proposed for modeling complex behaviour in the BBGKY--hierarchy of kinetic equations. Our calculations are based on variational and multiresolution approaches in the basis of polynomial tensor algebras of generalized coherent states/wavelets. We construct the representation for hierarchy of reduced distribution functions via the multiscale decomposition in highly-localized eigenmodes. Numerical modeling shows the creation of various internal structures from localized modes, which are related to localized or chaotic type of behaviour and the corresponding patterns (waveletons) formation. The localized pattern is a model for energy confinement state (fusion) in plasma.

physics.plasm-ph↗
arXiv2002

From Localization to Stochastics in BBGKY Collective Dynamics

Fast and efficient numerical-analytical approach is proposed for modeling complex collective behaviour in accelerator/plasma physics models based on BBGKY hierarchy of kinetic equations. Our calculations are based on variational and multiresolution approaches in the bases of polynomial tensor algebras of generalized coherent states/wavelets. We construct the representation for hierarchy of reduced distribution functions via the multiscale decomposition in high-localized eigenmodes. Numerical modeling shows the creation of different internal coherent structures from localized modes, which are related to stable/unstable type of behaviour and corresponding pattern (waveletons) formation.

physics.acc-ph↗
arXiv2002

Fast Calculation Methods in Collective Dynamical Models of Beam/Plasma Physics

We consider an application of modification of our variational-wavelet approach to some nonlinear collective model of beam/plasma physics: Vlasov/Boltzmann-like reduction from general BBGKY hierachy related to modeling of propagation of intense charged particle beams in high-intensity accelerators and transport systems. We use fast convergent multiscale variational-wavelet representations for solutions which allow to consider polynomial and rational type of nonlinearities. The solutions are represented via the multiscale decomposition in nonlinear high-localized eigenmodes (waveletons). In contrast with different approaches we do not use perturbation technique or linearization procedures.

physics.acc-ph↗
arXiv2002

Multiscale Decomposition for Vlasov-Poisson Equations

We consider the applications of a numerical-analytical approach based on multiscale variational wavelet technique to the systems with collective type behaviour described by some forms of Vlasov-Poisson/Maxwell equations. We calculate the exact fast convergent representations for solutions in high-localized wavelet-like bases functions, which correspond to underlying hidden (coherent) nonlinear eigenmodes. This helps to control stability/unstability scenario of evolution in parameter space on pure algebraical level.

physics.acc-ph↗
arXiv2002

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 procedures.

physics.acc-ph↗
arXiv2002

Nonlinear Localized Coherent Spectrum of Beam-Beam Interactions

We consider modeling for strong-strong beam-beam interactions beyond preceding linearized/perturbative methods such as soft gaussian approximation or FMM (HFMM) etc. In our approach discrete coherent modes, discovered before, and possible incoherent oscillations appear as a result of multiresolution/multiscale fast convergent decomposition in the bases of high-localized exact nonlinear modes represented by wavelets or wavelet packets functions. The constructed solutions represent the full multiscale spectrum in all internal hidden scales from slow to fast oscillating eigenmodes. Underlying variational method provides algebraical control of the spectrum.

physics.acc-ph↗
arXiv2002

Nonlinear Motion in Electromagnetic Fields via Multiscale Expansions

The consideration of dynamics of relativistic beams/particles is based on variational approach to rational (in dynamical variables) approximation for equations of motions. 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.

physics.acc-ph↗
arXiv2001

The Short-Term Dynamical Aperture via Variational-Wavelet Approach with Constraints

We present the applications of wavelet analysis methods in constrained variational framework to calculation of dynamical aperture. We construct represention via exact nonlinear high-localized periodic eigenmodes expansions, which allows to control contribution to motion from each scale of underlying multiscale structure and consider qualitative approach to the problem.

physics.acc-ph↗
arXiv2001

Quasiclassical Calculations of Wigner Functions in Nonlinear Beam Dynamics

We present the application of variational-wavelet analysis to numerical/analytical calculations of Wigner functions in (nonlinear) quasiclassical beam dynamics problems. (Naive) deformation quantization and multiresolution representations are the key points. We construct the representation via multiscale expansions in generalized coherent states or high-localized nonlinear eigenmodes in the base of compactly supported wavelets and wavelet packets.

physics.acc-ph↗
arXiv2001

Modelling of Beam-Beam Effects in Multiscales

We present the applications of nonlinear local harmonic analysis methods to the modelling of beam-beam interaction. Our approach is based on methods provided the possibility to work with dynamical beam localization in phase space. The consideration of Fokker-Planck or Vlasov-Maxwell models is based on a number of anzatzes, which reduce initial problems to a number of dynamical systems (with constraints) and on variational-wavelet approach to polynomial/rational approximations for reduced nonlinear dynamics. We calculate contribution to full dynamics (partition function) from all underlying subscales via nonlinear eigenmodes decomposition.

physics.acc-ph↗
arXiv2001

Coherent Structures and Pattern Formation in Vlasov-Maxwell-Poisson Systems

We present the applications of methods from nonlinear local harmonic analysis for calculations in nonlinear collective dynamics described by different forms of Vlasov-Maxwell-Poisson equations. Our approach is based on methods provided the 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. The consideration is based on a number of anzatzes, which reduce initial problems to a number of dynamical systems and on variational-wavelet approach to polynomial approximations for nonlinear dynamics. This approach allows us to construct the solutions via nonlinear high-localized eigenmodes expansions in the base of compactly supported wavelet bases and control contribution from each scale of underlying multiscales. Numerical modelling demonstrates formation of coherent structures and stable patterns.

physics.acc-ph↗
arXiv2001

Space-Charge Dominated Beam Transport via Multiresolution

We consider space-charge dominated beam transport systems, where space-charge forces are the same order as external focusing forces and dynamics of the corresponding emittance growth. We consider the coherent modes of oscillations and coherent instabilities both in the different nonlinear envelope models and in initial collective dynamics picture described by Vlasov system. Our calculations are based on variation approach and multiresolution in the base of high-localized generalized coherent states/wavelets. We control contributions to dynamical processes from underlying multiscales via nonlinear high-localized eigenmodes expansions in the base of compactly supported wavelet and wavelet packets bases.

physics.acc-ph↗
arXiv2001

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.

physics.acc-ph↗
arXiv2001

Orbital Beam Dynamics in Multipole Fields via Multiscale Expansions

We present the applications of methods from nonlinear local harmonic analysis in variational framework to calculations of nonlinear motions in polynomial/rational approximations (up to any order) of arbitrary n-pole fields. Our approach is based on the methods provided possibility to work with dynamical beam/particle localization in phase space, which gives representions via exact nonlinear high-localized eigenmodes expansions and allows to control contribution to motion from each scale of underlying multiscale structure.

physics.acc-ph↗
arXiv2001

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.

physics.acc-ph↗