Title :
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
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;
Conference_Titel :
Particle Accelerator Conference, 1995., Proceedings of the 1995
Conference_Location :
Dallas, TX
Print_ISBN :
0-7803-2934-1
DOI :
10.1109/PAC.1995.505699
