Luminosity Parameters Estimation (UNDER CONSTRUCTION)

Definitions

Emittance:

$ \sigma_{x,y}=\sqrt{\epsilon_{x,y}\beta_{x,y}} $

In the following we will define $ \epsilon= \sqrt{\epsilon_{x}\epsilon_{y}} $ and $ \beta= \sqrt{\beta_{x}\beta_{y}} $.

Geometric factor (including crossing angle $ \alpha $):

$ S= \sqrt{1+(\frac{\sigma_{z}}{\sigma_{x}})^2(\tan{\frac{\alpha}{2}})^2} $

Given that, the Luminosity is defined as:

$ L = \frac{n_{bb}\nu N_{i}N_{j} S}{4\pi \epsilon \beta^{*}} $

where $ \nu $ is the revolution frequency (well approximated by $ \nu=11245$ Hz), $ n_{bb} $ is the number of colliding bunch pairs, $ N_{i,j} $ 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.

$ \epsilon= \exp( - \frac{ (\bar{x}_1-\bar{x}_2 )^2 } {2(\sigma_{x1}^2+ \sigma_{x1}^2)} - \frac{ (\bar{y}_1-\bar{y}_2 )^2 } {2(\sigma_{y1}^2+ \sigma_{y1}^2)} ) $

(where $ \bar{x}_{1,2} $ and $ \bar{y}_{1,2} $ are the horizontal and vertical centroids of the beams at the IP) and therefore

$ L_{real} = \epsilon L$

Bunch intensities

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

Beam Profiles

Beam Instrumentation measurements

The profiles of the beams ($ \sigma_{x,y} $) are measured at P4 by:

  • BSRT: synchrotron light telescopes collecting light from the undulator(s) (for $ E \leq 2$ TeV) and the D3 (for $ E>1$ TeV). The measurements are taken at 0.1 Hz and therefore integrate the signal from all the bunches (and for several turns). During the 2009 LHC run, only one of the two undulators has been used (those for B2); for B1 only the fills at E=1.18 TeV had meaningful data recorded (thanks to the light produced by the D3).
  • Wire Scanner: the measurement is triggered by the LHC operator and therefore not always present. It usage is limited to operations at low intensities. Currently the reading of the signal is at higher frequency than the revolution (vector-numerical variable in the logging DB), though the signal is integrated for all the bunches (see below)

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).

BSRT

The useful variables can be found for B1 and B2 in LHC/Beam Instrumentation/Beam Profile/Synch Light Telescopes/:
  • BEAM_PROF_DATA_H/V are the actual data that can be used to fit the beam profile and extract the sigma
  • BEAM_SIGMA_H/V are the values for the sigma obtained online from the BSRT data

Wire Scan

The useful variables can be found in LHC/Beam Instrumentation/Beam Profile/Wire Scanners/. There are 2 sets of variable for each beam and each plane (why??). For each set:
  • SIGMA_IN and SIGMA_OUT (which should be the same) represent the result of the fit of the beam profile. The measurement are gathered at high frequency (see above), but only the first entry is meaningful and stands for the integrated profile of all the bunches.
  • PROF_DATA_IN and PROF_DATA_OUT are the data the values above are computed from

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 $ \beta $ at the level of the corresponding instrumentation. The values of $ \beta $ 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 $ \beta $ has to be taken from the position either of the undulator or of the D3 depending of the cases. The $ \beta^{*} $ at a given IP (if different from the nominal for a given energy) is normally logged.

External measurements

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:

  • The RMS of the beam-beam interaction points distribution
  • The RMS of the beam-gas interaction points distribution
together with the information recorded during a thorough VdM scan, can lead to a precise estimation of the beam sizes $ \sigma_{x,y} $. In the case of a non-zero crossing angle, an estimation of $ \sigma_{z} $ for both beams (aren't they the same to a good approximation?) is also needed. This can be achieved only by looking at the beam-beam interaction points distribution

Luminosity computation and Errors estimation

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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Topic revision: r5 - 2010-03-23 - MarcoZanetti
 
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