Renormalization group reduction of the Henon map and application to the transverse betatron motion in cyclic accelerators

Tsenov, S.I.; Davidson, R.C.

doi:10.1088/1367-2630/5/1/367

Renormalization group reduction of the Henon map and application to the transverse betatron motion in cyclic accelerators

2003

13 pages

Published in:

New J.Phys. 5 (2003) 67

e-Print:

nlin/0302031 [nlin.SI]

DOI:

10.1088/1367-2630/5/1/367

View in:

reference search0 citations

Citations per year

0 Citations

Abstract: (IOP)

The renormalization group?(RG) method is applied to the study of discrete dynamical systems. As a particular example, the H?non map is considered as being applied to describe the transverse betatron oscillations in a cyclic accelerator or storage ring possessing a FODO-cell structure with a single thin sextupole. A powerful RG method is developed that is valid correct to fourth order in the perturbation amplitude, and a technique for resolving the resonance structure of the H?non map is also presented. This calculation represents an application of the RG method to the study of discrete dynamical systems in a unified manner capable of reducing the dynamics of the system both far from and close to resonances, thus preserving the symplectic symmetry of the original map.

Note:

LaTeX, 18 pages, 4 figures

synchrotron: beam dynamics
beam dynamics: nonlinear
beam dynamics: transfer matrix
transfer matrix: symplectic
quadrupole lens: special focusing
renormalization group

References(24)

Figures(0)

[1]

Physics of collective beam instabilities in high-energy accelerators

Chao A. W

[2]

An Introduction to the physics of high-energy accelerators

Edwards D. A
,
Syphers M. J

[3]

Physics of intense charged particle beams in high energy accelerators

Davidson R. C
,
Qin H

[4]

Principles of Circular Accelerators and Storage Rings (Cambridge: Cambridge University Press)

Bryant P. J
,
Johnsen K

[5]

Nonlinear Dynamics in Particle Accelerators: Theory and Experiments (Arcidosso, 1994) (AIP Conf. Proc. vol 344) (New York: American Institute of Physics)

Chattopadhyay S

[6]

Nonlinear and Collective Phenomena in Beam Physics (Arcidosso, 1996) (AIP Conf. Proc. vol 395) (New York: American Institute of Physics)

Chattopadhyay S

[7]

Regular and Stochastic Motion (Berlin:

Lichtenberg A. J
,
Lieberman M. A

[8]

Introduction to Perturbation Techniques (New York:

Nayfeh A. H

[9]

1982 Physics of High Energy Particle Accelerators. Lectures on Nonlinear Orbit Dynamics Summer School,) (AIP Conf. Proc. vol 87) R A Carrigan et al. (eds.) (New York: American Institute of Physics) pp 147-313

Dragt A. J

[10]

Perturbation Methods in Nonlinear Systems (Appl. Math. Sci. No 8) (Berlin:

Giacaglia G.E. O

[11]

Cary J. R

- Phys.Rept. 79 (1981) 129

[12]

The Renormalization group and singular perturbations: Multiple scales, boundary layers and reductive perturbation theory

Lin-Yuan Chen
(
- Illinois U., Urbana and
- Santa Barbara, KITP
)
,
Nigel Goldenfeld
(
- Illinois U., Urbana
)
,
Y. Oono
(
- Illinois U., Urbana
)

- Phys.Rev.E 54 (1996) 376-394
•
e-Print:
- hep-th/9506161
•
DOI:
- 10.1103/PhysRevE.54.376

[13]

Nozaki K
,
Oono Y

- Phys.Rev.E 63 (2001) 046101-1

[14]

Renormalization group method for reduction of evolution equations: Invariant manifolds and envelopes

- Annals Phys. 280 (2000) 236-298
•
e-Print:
- hep-th/9905088
•
DOI:
- 10.1006/aphy.1999.5989

[15]

Goto S-I
,
Nozaki K

- J.Phys.Soc.Jap. 70 (2001) 49

[16]

Kunihiro T
,
Matsukidaira J

- Phys.Rev.E 57 (1998) 4817

[17]

Goto S-I
,
Nozaki K
,
Yamada H

- Prog.Theor.Phys. 107 (2001) 637

[18]

Ergodic Problems of Classical Mechanics (New York:

Arnold V. I
,
Avez A

[19]

Lectures in Theoretical Physics vol 3, W E Brittin (eds.) (New York:

Zwanzig R. W

[20]

Renormalization group reduction of nonintegrable Hamiltonian systems

Stephan I. Tzenov
(
- Princeton U., Plasma Physics Lab.
)

- New J.Phys. 4 (2002) 6
•
e-Print:
- physics/0107065
•
DOI:
- 10.1088/1367-2630/4/1/306

[21]

Q

Hénon M

- J.Appl.Math. 27 (1969) 291

[22]

Hénon M

- Commun.Math.Phys. 50 (1976) 69

[23]

Contemporary Accelerator Physics (Singapore:

Tzenov S. I

[24]

Theory of the alternating gradient synchrotron

E.D. Courant
(
- Brookhaven
)
,
H.S. Snyder
(
- Brookhaven
)

- Annals Phys. 3 (1958) 1-48,
- Annals Phys. 281 (2000) 360-408
•
DOI:
- 10.1016/0003-4916(58)90012-5