CERN Accelerating science

c/o Frank Schmidt

One transparency (taken from Rogelio Tom�s's thesis) [ppt]. It shows how far the single particle approach can be taken to describe particle distributions:

Preconditions:

- In this example chromaticity has been well corrected. However, Rogelio has also treated the case with non-zero chromaticity in a independent study.

- 1000 turns, 2 pick-ups, medium strong kick (4 sigma), low intensity

Explanation:

The figure shows that the simulation of many single particles taken from a Gaussian distribution agree well with a model (left 2 figures) which uses just 3 fit parameters:

- tune at zero amplitude
- beam sigma
- just the dominant sextupole detuning (this could be refined)

The right figure is even more interesting: this model was used for fitting the three parameters for real pick-up data from the machine. Of course one could go the other way around by measuring them first to good precision and then predicting the tune distribution.

Note I: FFT analysis of pick-up data do not return single lines for simulation data but rather you get a distribution of lines which reflect the kicked particle distribution. Note II: This harmonic analysis actually can be used to measure beam emittances (too bad the wires scanner were not working at the time for comparisons!)

What does all that have to do with the LHC model? The LHC model will give you the detuning with amplitude which is more complicated than in the case of the SPS with a few strong test sextupoles. For a given tune and beam emittances one can model the tune distribution to be expected from beam. Of course, this is as far as single particle dynamics will go. After getting the LHC model and the real machine to agree on the detuning with amplitude one would then have a means to distinguish from collective effects.