The behaviour of betatron oscillations in the vicinity of half-integral structure resonances
In order to achieve a good luminosity in storage rings the beam--beam collisions take place in a small number of low-..beta.. insertions where the betatron functions are smaller than in the rest of the machine. As a consequence, the number of superperiods S which is assumed to be equal to the number of insertions becomes much smaller than in the first generation of alternating gradient synchrotrons. Structure resonances of order n occurs whenever n..nu.. = pS, where p is an integer. For small S, these resonances are not easy to avoid. In the following, the effects of a half-integral structure resonance (n =2) on the behavior of betatron oscillations shall be studied. It is assumed that the chromaticities xi/sub x/ and xi/sub y/ are made to vanish by an appropriate distribution of sextupoles. This should remove the linear variations of tunes and betatron functions with the momentum error but not the higher-order variations. It will be shown that these variations can be influenced by changing the driving term for the 2 ..nu.. = pS resonance for off-momentum particles, using SPEAR as an example. 6 refs., 5 figs., 3 tabs.
- Research Organization:
- Stanford Linear Accelerator Center, Menlo Park, CA (USA)
- DOE Contract Number:
- AC03-76SF00515
- OSTI ID:
- 6955657
- Report Number(s):
- SLAC-PEP-NOTE-121; ON: DE88014849
- Country of Publication:
- United States
- Language:
- English
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