Fast symplectic mapping and quasi-invariants for the Large Hadron Collider

Author

Warnock, R.L. ; Berg, J.S. ; Forest, É

Author_Institution

Stanford Linear Accel. Center, Stanford Univ., CA, USA

Volume

5

fYear

1995

fDate

1-5 May 1995

Firstpage

2804

Abstract

Beginning with a tracking code for the LHC, we construct the canonical generator of the full-turn map in polar coordinates. For very fast mapping we adopt a model in which the momentum is modulated sinusoidally with a period of 130 turns (very close to the synchrotron period). We achieve symplectic mapping of 10⁷ turns in 3.6 hours on a workstation. Quasi-invariant tori are constructed on the Poincare section corresponding to multiples of the synchrotron period. The possible use of quasi-invariants in deriving long-term bounds on the motion is discussed

Keywords

colliding beam accelerators; high energy physics instrumentation computing; particle beam dynamics; proton accelerators; storage rings; synchrotrons; LHC; Large Hadron Collider; Poincare section; canonical generator; fast symplectic mapping; full-turn map; long-term motion bounds; polar coordinates; quasiinvariants; synchrotron period; tracking code; very fast mapping; Fourier series; Laboratories; Large Hadron Collider; Lattices; Linear accelerators; Orbits; Resonance; Spline; Synchrotrons; Workstations;

fLanguage

English

Publisher

ieee

Conference_Titel

Particle Accelerator Conference, 1995., Proceedings of the 1995

Conference_Location

Dallas, TX

Print_ISBN

0-7803-2934-1

Type

conf

DOI

10.1109/PAC.1995.505699

Filename

505699