IPAC2011 - List of Authors (Kosovtsov, M.)

Paper	Title	Page
WEPC115	A Global Optimization Approach Based on Symbolic Presentation of a Beam Propagator	2280
	S.N. Andrianov, A.N. Ivanov, M. Kosovtsov, E.A. Podzyvalov St. Petersburg State University, St. Petersburg, Russia
	It is known that modern systems of beam lines consist of huge control elements even in the case of small machines. The problem of the beam line design leads us to formulate this problem as a global optimization ones. This approach allows us defining a family of appropriate solutions. On the next steps a researcher should narrow this optimal solutions set using additional methods and concepts. The symbolic presentation of necessary information plays leading role on all steps of the suggested approach. The corresponding implementation presented in the paper allows us to find the optimal sets in parameters spaces in a proper way. The corresponding applied software was used for solution of some practical probems. The described ideology implies to use distributed and parallel technologies for necessary computing and will be integrated in the Virtual Accelerator concept.

WEPC116	A Matrix Presentation for a Beam Propagator including Particles Spin	2283
	M. Kosovtsov, S.N. Andrianov, A.N. Ivanov St. Petersburg State University, St. Petersburg, Russia
	Particles beam dynamics in magnetic and electrical fields with spin is discussed. This approach provides a constructive method of matrix presentation derivation for a beam propagator in magnetic and electrical fields. The beam propagator is evaluated in according to the well-known Lie algebraic tools. But in contrast to traditional approaches matrix presentation for Lie propagators bases on two-indexes matrices. This approach permit to apply all of matrix algebra opportunities and advantages in contrast with the tenzor presentation based on multi-indexes description. The necessary computation can be realized in symbolic (using computer algebra codes as Mathematica, Maple, Maxima and so on). The corresponding symbolic objects itself can be stored in special databases and used then in numerical computing. Parallel and distributed conception is well acceptable with the suggested matrix formalism. Some symbolic and numerical results are discussed for problems of long term evolution of particles with spin.

WEPC117	Symmetry Based Design for Beam Lines*	2286
	S.N. Andrianov, A.N. Ivanov, M. Kosovtsov St. Petersburg State University, St. Petersburg, Russia
	Usually, the beam line design problems are solved using numerical optimization methods (for example, in the frame of so called global optimization paradigm). But this approach demonstrates enough effectiveness only after sufficient reduction of a control parameters set. In this paper we present the symmetry design concept based on symbolic computations for the corresponding beam line propagator. The combination of symbolic algebra codes (such as Maple, Mathematica, Maxima and so on) with the matrix formalism for Lie algebraic tools enables us to carry out the entire theoretical and computing processes for design of the beam line under study. For this purpose some of necessary physical requirements are formulated in the terms of the corresponding symmetry conditions. The suggested approach can be realized in both exact and approximate forms of the symmetry terms. The found conditions can sufficiently reduce the number of control parameters for the next optimization step.

Paper

Title

Page

A Global Optimization Approach Based on Symbolic Presentation of a Beam Propagator

2280

S.N. Andrianov, A.N. Ivanov, M. Kosovtsov, E.A. Podzyvalov
St. Petersburg State University, St. Petersburg, Russia

It is known that modern systems of beam lines consist of huge control elements even in the case of small machines. The problem of the beam line design leads us to formulate this problem as a global optimization ones. This approach allows us defining a family of appropriate solutions. On the next steps a researcher should narrow this optimal solutions set using additional methods and concepts. The symbolic presentation of necessary information plays leading role on all steps of the suggested approach. The corresponding implementation presented in the paper allows us to find the optimal sets in parameters spaces in a proper way. The corresponding applied software was used for solution of some practical probems. The described ideology implies to use distributed and parallel technologies for necessary computing and will be integrated in the Virtual Accelerator concept.

WEPC116

A Matrix Presentation for a Beam Propagator including Particles Spin

2283

M. Kosovtsov, S.N. Andrianov, A.N. Ivanov
St. Petersburg State University, St. Petersburg, Russia

Particles beam dynamics in magnetic and electrical fields with spin is discussed. This approach provides a constructive method of matrix presentation derivation for a beam propagator in magnetic and electrical fields. The beam propagator is evaluated in according to the well-known Lie algebraic tools. But in contrast to traditional approaches matrix presentation for Lie propagators bases on two-indexes matrices. This approach permit to apply all of matrix algebra opportunities and advantages in contrast with the tenzor presentation based on multi-indexes description. The necessary computation can be realized in symbolic (using computer algebra codes as Mathematica, Maple, Maxima and so on). The corresponding symbolic objects itself can be stored in special databases and used then in numerical computing. Parallel and distributed conception is well acceptable with the suggested matrix formalism. Some symbolic and numerical results are discussed for problems of long term evolution of particles with spin.

WEPC117

Symmetry Based Design for Beam Lines*

2286

S.N. Andrianov, A.N. Ivanov, M. Kosovtsov
St. Petersburg State University, St. Petersburg, Russia

Usually, the beam line design problems are solved using numerical optimization methods (for example, in the frame of so called global optimization paradigm). But this approach demonstrates enough effectiveness only after sufficient reduction of a control parameters set. In this paper we present the symmetry design concept based on symbolic computations for the corresponding beam line propagator. The combination of symbolic algebra codes (such as Maple, Mathematica, Maxima and so on) with the matrix formalism for Lie algebraic tools enables us to carry out the entire theoretical and computing processes for design of the beam line under study. For this purpose some of necessary physical requirements are formulated in the terms of the corresponding symmetry conditions. The suggested approach can be realized in both exact and approximate forms of the symmetry terms. The found conditions can sufficiently reduce the number of control parameters for the next optimization step.