Symplectic tracking using point magnets and a reference orbit made of circular arcs and straight lines
In order to study long term stability, it appears desirable that the particle tracking by symplectic. One way to achieve symplectic tracking is to replace the magnets by a series of point magnets and drift spaces. This approach is modified here by using a reference orbit that is made up of arcs of circles and straight lines which join smoothly with each other. This make sthe symplecticity more evident, and simplifies in some way the particle tracking, as the coordinate system based on this reference orbit is not changing discontinuously between elements. It also allows the use of transfer matrices to find the linear orbit parameters. For this choice of reference orbit, the required ersults are obtained to track particles, which are the transfer functions, the transer matrices and the transfer time, for the different elements present in the accelerator. It is shown that, in the absence of longitudinal magnetic fields these results provide a symplectic, second order itnegrator. Existing tracking programs that use a reference orbit, made up of arcs of circles and straight lines, can be modified, using the results given here to do symplectic tracking with point magnets. The results have been used to modify the ORBIT tracking program. The ORBIT program will now, by changing an indicator, either track using the usual large accelerator approximation for the transfer functions or do symplectic tracking with ponit magnets, and will use the same reference orbit in both cases.
- Research Organization:
- Brookhaven National Lab. (BNL), Upton, NY (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC02-76CH00016
- OSTI ID:
- 10178232
- Report Number(s):
- BNL-49212; AD/RHIC-120; ON: DE93019924; TRN: 93:019184
- Resource Relation:
- Other Information: PBD: Jun 1993
- Country of Publication:
- United States
- Language:
- English
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Symplectic tracking using point magnets and a reference orbit made of circular arcs and straight lines
Symplectic tracking using point magnets and a reference orbit made of circular arcs and straight lines