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Study of betatron oscillations in a constant field and alternating gradient accelerator; Etude des oscillations betatron dans l'accelerateur a champ fixe et a gradient alterne

Abstract

The conditions for the stability of a constant energy particle beam circulating in the magnetic field of the F.F.A.G. accelerator are studied. By a mathematical study it is possible to derive the equations for the equilibrium orbit and for the low amplitude oscillations, and the expressions for the amplitude stability limits of the beam. For this, approximation methods are used, in particular the linearization of the differential equations of the movement, and the method of gradual approximation. Numerical investigations carried out with the help of the IBM 7090 computer make it possible to judge the precision of the results given by the theory. A systematic variation of the parameters makes it possible to understand more clearly the mechanism of the amplitude variations of the trajectories. Finally, for the radial sector model, the possibility of introducing zones free from the magnetic field is considered. The case of short straight sections, respecting the field periodicity, and of that of long straight sections creating super-periods are considered. For the two cases are given solutions which should lead to a practical machine. (author) [French] On etudie les conditions de stabilite d'un faisceau de particules circulant a energie constante dans le champ magnetique de l'accelerateur  More>>
Authors:
Lauzanne, C [1] 
  1. Commissariat a l'Energie Atomique, Saclay (France). Centre d'Etudes Nucleaires
Publication Date:
Jul 01, 1963
Product Type:
Thesis/Dissertation
Report Number:
CEA-R-2279
Resource Relation:
Other Information: TH: These sciences physiques; 8 refs
Subject:
43 PARTICLE ACCELERATORS; BEAM DYNAMICS; BETATRON OSCILLATIONS; BETATRONS; HARMONICS; MAGNETIC FIELDS; NONLINEAR PROBLEMS; ORBIT STABILITY; PARTICLE BEAMS; PERIODICITY; RESONANCE
OSTI ID:
20808533
Research Organizations:
CEA Saclay, 91 - Gif-sur-Yvette (France); Feculte des Sciences de l'Universite de Paris, 75 (France)
Country of Origin:
France
Language:
French
Other Identifying Numbers:
TRN: FR06R2279110038
Availability:
Available from INIS in electronic form
Submitting Site:
FRN
Size:
143 pages
Announcement Date:
Dec 23, 2006

Citation Formats

Lauzanne, C. Study of betatron oscillations in a constant field and alternating gradient accelerator; Etude des oscillations betatron dans l'accelerateur a champ fixe et a gradient alterne. France: N. p., 1963. Web.
Lauzanne, C. Study of betatron oscillations in a constant field and alternating gradient accelerator; Etude des oscillations betatron dans l'accelerateur a champ fixe et a gradient alterne. France.
Lauzanne, C. 1963. "Study of betatron oscillations in a constant field and alternating gradient accelerator; Etude des oscillations betatron dans l'accelerateur a champ fixe et a gradient alterne." France.
@misc{etde_20808533,
title = {Study of betatron oscillations in a constant field and alternating gradient accelerator; Etude des oscillations betatron dans l'accelerateur a champ fixe et a gradient alterne}
author = {Lauzanne, C}
abstractNote = {The conditions for the stability of a constant energy particle beam circulating in the magnetic field of the F.F.A.G. accelerator are studied. By a mathematical study it is possible to derive the equations for the equilibrium orbit and for the low amplitude oscillations, and the expressions for the amplitude stability limits of the beam. For this, approximation methods are used, in particular the linearization of the differential equations of the movement, and the method of gradual approximation. Numerical investigations carried out with the help of the IBM 7090 computer make it possible to judge the precision of the results given by the theory. A systematic variation of the parameters makes it possible to understand more clearly the mechanism of the amplitude variations of the trajectories. Finally, for the radial sector model, the possibility of introducing zones free from the magnetic field is considered. The case of short straight sections, respecting the field periodicity, and of that of long straight sections creating super-periods are considered. For the two cases are given solutions which should lead to a practical machine. (author) [French] On etudie les conditions de stabilite d'un faisceau de particules circulant a energie constante dans le champ magnetique de l'accelerateur F.F.A.G. Une etude mathematique permet d'etablir les equations de l'orbite d'equilibre et des oscillations de faible amplitude, les expressions des limites de stabilite en amplitude du faisceau. On emploie a cet effet des methodes d'approximation, essentiellement la linearisation des equations differentielles du mouvement et la methode de l'approximation douce. Des investigations numeriques effectuees a l'aide de la calculatrice IBM 7090 permettent d'apprecier l'exactitude des resultats fournis par la theorie. Une variation systematique des parametres permet de mieux comprendre le mecanisme des variations d'amplitude des trajectoires. On etudie enfin, pour le modele a secteur radial, la possibilite d'intercaler des zones non soumises au champ magnetique. On envisage les cas de sections droites courtes, respectant la periodicite du champ, et de sections droites longues qui creent des superperiodes. On indique dans les deux cas quelles solutions semblent conduire a des machines viables. (auteur)}
place = {France}
year = {1963}
month = {Jul}
}