Abstracts Brochure - CERN

WEPCH — Poster Session 28-Jun-06 16:00 - 18:00
High Order Aberration Correction
It is known that modern accelerators fall under
nonlinear aberrations influence. The
most of these aberrations have harmful character,
and their effect must be maximally de-
S.N. Andrianov (St. Petersburg State University, Applied Mathematics
& Control Processes Faculty) A.N. Chechenin (FZJ)
creased. There are a set of approaches and codes to solving this problem. In this paper, we consider an approach for
solving this problem using the matrix formalism for Lie algebraic tools. This formalism allows reducing the starting
problem to linear algebraic equations for aberration coefficients, which are elements of corresponding matrices.
There are discussed results evaluated using suggested approach and nonlinear programming tools. Some examples
of corresponding results are given.
On Optimization of Charged Particle Dynamics in Discrete Systems
Beam dynamics in accelerating and forming
structures are often described by discrete systems
of equations. In this paper optimization
problem for these systems are considered.
E.D. Kotina (St. Petersburg State University, Applied Mathematics
& Control Processes Faculty)
On trajectories of the system we consider functionals, characterizing the beam dynamics. Analytical expressions
of variation of the functionals are proposed.
The Models of Beam Dynamics Optimization in RFQ Structures
The beam dynamics optimization problems
attract the attention of numerous researches.
New approach for optimization of RFQ structures
was suggested in paper*. In this paper
new set of functionals is considered for opti-
D.A. Ovsyannikov (St. Petersburg State University) A.D. Ovsyannikov
(St. Petersburg State University, Applied Mathematics &
Control Processes Faculty)
mization of accelerating and focusing structures. It allows to solve problems of maximizing of longitudinal acceptance,
maximizing average rate of acceleration, minimizing length of structure and optimizing output beam parameters.
For suggested functionals corresponding algorithms, based on optimal control theory methods, were developed and
tested.
*A. D. Ovsyannikov. “New Approach to Beam Dynamics Optimization Problems”, Proceedings of the
6th International Computational Accelerator Physics Conference, Darmstadt, Germany, September 2000.
http://www.icap2000.de.
On a Problem of Beam Dynamics Optimization
Problem of joint optimization of program
motion and ensemble of disturbed by initial
states motions, arising with optimization
of parameters of charged particles beam dy-
A.D. Ovsyannikov (St. Petersburg State University, Applied Mathematics
& Control Processes Faculty)
namics, is considered. Analytical representation of variation of investigated functional and conditions of optimality
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