Abstracts Brochure - CERN

WEPCH085
WEPCH086
WEPCH087
28-Jun-06 16:00 - 18:00 WEPCH — Poster Session
Algorithms for Chromatic Sextupole Optimization and Dynamic Aperture Increase
Strong chromatic sextupoles compensating
E. Levichev, P.A. Piminov (BINP SB RAS)
natural chromaticity of a storage ring may
reduce dynamic aperture drastically. In the
case of several sextupole families, one can find a lot of ways to correct chromaticity, which provides different sizes of
the dynamic aperture. Finding a solution that gives the largest dynamic aperture is an important task for the storage
ring design and operation. The paper discusses several approaches to sextupole arrangement optimization in order
to obtain a large dynamic aperture.
Adiabatic Theory of Slow Extraction from Synchrotron
An analytical approach is developed to de-
S.A. Nikitin (BINP SB RAS)
scribe the process of slow extraction of particles
from a synchrotron based on adiabatic
crossing of the betatron resonance of the third order. An exact expression for the phase integral is found to analyze
the conditions of oscillation amplitude growth near the resonance band. It allows one to directly define the interval
of adiabatic motion from the start of decreasing the resonant tune to the beginning of fast increase of the oscillation
amplitude. The interval distribution function is constructed for the cases of zero momentum spread and zero machine
chromaticity as well as for the general case, taking into account non-zero momentum spread, non-zero chromaticity
and synchrotron oscillations. Some numeric calculations of the time dependence of the extracted particle current are
presented. It is shown that the momentum spread in the extracted beam can be minimized with the use of additional
RF acceleration of particles during the slow extraction procedure.
Normal Form for Beam Physics in Matrix Representation
S.N. Andrianov (St. Petersburg State University, Applied Mathematics
& Control Processes Faculty) A.N. Chechenin (FZJ)
296
The modeling of long beam evolution dynamics
in nonlinear accelerator structures
has raised new interest in the effective methods
of nonlinear effects calculation. More-
over, it is preferably to use both analytical tools and numerical methods for evolution modeling. Usually the standard
numerical methods and computer codes are based on the concept of symplectic transfer maps, whereas the analytical
tool is the theory of normal forms. The method of normal forms can be realized in symbolic and numerical modes
easily enough. In this paper, we discuss the normal form theory based on the matrix formalism for Lie algebraic tools.
This approach allows using well known methods of matrix algebra. This permits to compute necessary matrices stepby-step
up to desired order of approximation. This procedure leads to more simple structure of matrix representation
for very complicated structure of this map does not allow using this map for practical computing. Therefore, it is
necessary to transform this map in more appropriate form. In another words the new matrix representation for the
map is particularly simple and has explicit invariants and symmetries.