Construction of Large Period Symplectic Maps by Interpolative Methods
The goal is to construct a symplectic evolution map for a large section of an accelerator, say a full turn of a large ring or a long wiggler. We start with an accurate tracking algorithm for single particles, which is allowed to be slightly non-symplectic. By tracking many particles for a distance S one acquires sufficient data to construct the mixed-variable generator of a symplectic map for evolution over S, given in terms of interpolatory functions. Two ways to find the generator are considered: (1) Find its gradient from tracking data, then the generator itself as a line integral. (2) Compute the action integral on many orbits. A test of method (1) has been made in a difficult example: a full turn map for an electron ring with strong nonlinearity near the dynamic aperture. The method succeeds at fairly large amplitudes, but there are technical difficulties near the dynamic aperture due to oddly shaped interpolation domains. For a generally applicable algorithm we propose method (2), realized with meshless interpolation methods.
- Research Organization:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC02-76SF00515
- OSTI ID:
- 969221
- Report Number(s):
- SLAC-PUB-13867; TRN: US1000212
- Resource Relation:
- Conference: Invited talk at 10th International Computational Accelerator Physics Conference, San Francisco, Aug 31 - Sep 4, 2009
- Country of Publication:
- United States
- Language:
- English
Similar Records
Fast symplectic mapping, quasi-invariants, and long-term stability in the LHC
Fast symplectic mapping and long-term stability near broad resonances