Where the "needles" collide

14 June 2010

Evolution of the measured beam spot size during a fill and comparison to the size expected from machine parameters

On March 30, in a widely quoted remark, Steve Myers likened colliding the particle beams in the LHC to shooting needles across the Atlantic and getting them to collide halfway. So where exactly do these collisions take place inside the comparatively vast beam pipe? Finding this out is the task of beam spot determination. Both beam spot position and size can change quite a bit even during a single fill. Because almost every physics analysis in ATLAS uses the beam spot either directly or indirectly (as a constraint for primary vertex finding), it must be measured continually as precisely as possible.

Actually, the term beam ‘spot’ is a bit of a misnomer, since the luminous region, i.e. the spatial region where collisions take place, has rather the dimensions of a thin hair: along the beam direction it is a few centimeters long, while in the transverse direction the size has varied from initially about 200 µm at √s = 900 GeV to about 30 µm (1000 times smaller than its length) at the beginning of recent runs at 7 TeV. Ultimately the transverse luminous size (or beam spot size) will be even smaller: at 14 TeV with a β* of 0.55 m it will be only 12 µm, thus providing an even better constraint on the spatial origin of primary particles.

Where does this large variation of the luminous size come from, and what's the β* that's always quoted in this context? Obviously, the luminous region is defined by the volume where the proton bunches of the two beams cross through each other. The shape of the particle bunches in the LHC beams can be described by a 3-dimensional Gaussian distribution whose width in the transverse direction is given by the square root of the product of the transverse emittance and the amplitude function β. While emittance is a measure of the intrinsic spread of the particles within a bunch that scales inversely with the beam energy Ebeam, β describes the beam optics and is determined by the accelerator magnet configuration. The value of the β function at the interaction point is called β*. For two Gaussian beams with equal transverse size, the transverse size of the luminous region is simply the beam size divided by √2. Thus the beam spot size should scale with √β*/√ Ebeam. Indeed, from the increase in beam energy and the change of β* from 11m to 2m we expect the observed decrease of the beam spot size from 200 µm to 30 µm.

The method used in ATLAS for measuring the beam spot parameters is based on the distribution of the position of reconstructed primary vertices collected from many events. The High-Level Trigger gets a first stab at this by collecting histograms of the position of vertices reconstructed by a fast tracking and vertexing algorithm. The final beam spot reconstruction using an unbinned maximum-likelihood fit to primary vertices reconstructed using the full ATLAS reconstruction chain takes place shortly afterwards during the Tier-0 processing of the express stream as part of the prompt calibration loop.

Even with the relatively small statistics (compared to the level 2 trigger) available on the express stream, the precision of the measured beam spot parameters is in most cases already limited by systematic errors and not by the available statistics. This is particularly true for the measurement of the transverse luminous size, which requires the subtraction of the primary vertex resolution from the observed distribution of vertices. With the selection made for beam spot reconstruction, the most probable transverse vertex error is about 25 µm in recent 7 TeV runs (due to the asymmetric distribution of vertex errors the mean error is about twice as high). Thus the vertex resolution is similar to the beam spot size and contributes significantly to the observed distribution of primary vertices. As the beam spot size will become smaller, the extraction of the transverse size will become increasingly difficult since the vertex resolution must be known more and more precisely.

In order to cross-check the beam spot size determined by the maximum likelihood fit, a vertex-splitting method is used to determine the vertex resolution independently. In this method tracks are randomly assigned to two half-vertices instead of a single primary vertex. Since the two half-vertices represent two independent measures of the position of the same primary vertex, their average distance should depend only on the vertex resolution.

Following our earlier discussion on how the beam spot size depends on LHC machine parameters, we can compare the measured beam spot size to the size expected from measurements of emittance and β*. Such a comparison is shown in the figure above. No error bars are shown on the luminous size inferred from emittance and β* since the corresponding systematic effects have not yet been fully analyzed (they are expected to be about 10% each on emittance and β*). The agreement between the two very different methods of determining the beam spot size is excellent, particularly at this early stage (the outliers between 18:00 and 19:00 UTC are an artifact of luminosity scans carried out at that time). The figure also shows an increase of the luminous size over the course of the fill due to an emittance increase (see blue open symbols). While some growth of the transverse emittance over the course of a fill is expected, the observed growth rate appears larger than expected. These kinds of comparisons and other feedback from the ATLAS Beam Spot Group have been highly appreciated by our colleagues from LHC.

The need to continuously determine and monitor the beam spot makes it necessary to automatically run a large number of jobs. In order to keep track of these jobs and to give immediate and convenient access to the fit results and various history and validation plots even before the final beam spot results are uploaded into COOL, a web-based monitoring system was developed. It allows beam spot experts and shifters alike to easily spot any problems and gives detailed access to job parameters, log files and results of each beam spot job. Even earlier, beam spot and primary vertex monitoring displays from ATLAS Global Monitoring in the ATLAS Control Room give a first glimpse at the results from the offline primary vertex reconstruction. Eventually, a summary of the beam spot results can be obtained from Run Query or the ATLAS Data Summary pages.

Since the early beginnings of offline beam spot reconstruction in ATLAS at the time of the Ringberg workshop in 2008, beam spot determination has become a mature and indispensable part of the ATLAS data processing chain that has worked very well since the exciting moments when the very first collisions arrived in ATLAS. Last fall the beam spot effort became an official ATLAS working group under Data Preparation. If this article made you curious to learn more about the beam spot, please join us at one of our next Beam Spot Group meetings!


 

 

Juerg Beringer

Lawrence Berkeley
National Laboratory