Emittance:
In the following we will define and .
Geometric factor (including crossing angle ):
Given that, the Luminosity is defined as:
where is the revolution frequency (well approximated by Hz), is the number of colliding bunch pairs, the number of protons in the colliding bunches.
Another geometrical factor has to be introduced in order to take into account the not perfect superposition of the beams in the transverse plane at the IP. This parameter can be determined with a certain accuracy by means of a Van Der Meer scan.
(where and are the horizontal and vertical centroids of the beams at the IP) and therefore
The data are stored under LHC/Beam Instrumentation/Beam Intensity/Fast BCT Ring. For the sake of redundancy, there are 2 set of variables for each beam, they provide exactly the same information, one only has to pick up the only one of the two which is enabled for a given LHC fill. The variable to look at is (of course) BEAM_INTENSITY which is a vector with a number of values matching the maximum number of bunches in the machine. Those numbers carry an error of the order of 1 percent
The profiles of the beams () are measured at P4 by:
Both measurements are up to now (2009 LHC run) not fully calibrated.
The related data can be found in the logging database (e.g. by means of timber).
In order to compute the emittance(s) at the IP, one needs simply to compute them at P4 from the beam profiles measurements and the at the level of the corresponding instrumentation. The values of can be obtained from the LHC optics tables. They can be found here for the various running/energy scenarios. In the case of the synch light, the has to be taken from the position either of the undulator or of the D3 depending of the cases. The at a given IP (if different from the nominal for a given energy) is normally logged.
A more precise determination of the beams profiles can be achieved by means of the interactions vertex position measured by the experiments. More specifically, the use of:
TO BE WRITTEN
The filling scheme is fundamental for the Luminosity computation and is also normally manually logged by the operator. The filling schemes used so far are listed here.
-- MarcoZanetti - 12-Jan-2010
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