Update: New record luminosity 876/μb/s in ATLAS and 800/μb/s in CMS using 768 bunches per beam. The total integrated luminosity delivered has now passed 300/pb
A couple of days ago we had some fun estimating how much integrated luminosity the Large Hadron Collider could collect this year. My estimate was 10/fb but a poll of readers favoured a more sober 5/fb-7/fb range. The official estimates shown at Chamonix said there would be about 2/fb – 4/fb collected in 2011. Following the comments I think it is worth going into a little more detail about how these calculations are done.
There are many factors involved but we can conveniently write an equation in terms of three factors
is the intgerated luminosity in inverse femtobarns.
is the number of running days for physics assuming no unplanned stoppages. If we allow for the build-up time this is going to be about 135 days this year.
is the peak luminosity in inverse microbarns per second. based on current luminosities and the assumption that they will increase bunch numbers to 1404 with most colliding we can estimate peak luminosity of 1600/μb/s. At Chamonix they estimated 2000/μb/s given the 50ns spacing being used so there may yet be room for improvement.
is the Hübner Factor which is the hardest part to estimate. It is the ratio of actual delivered luminosity to the amount you could collect by running continuously at the peak luminosity. This makes the equation above correct by definition. The official estimates for the Hübner Factor are about 0.2 or even just 0.15 for running at 50ns spacing. The actual Hübner Factor from the last few weeks has been in the range 0.3 to 0.4. To get my estimate of 10/fb they would need a factor of 0.53 for peak luminosity of 1600/μb/s or 0.43 for peak luminosity of 2000/μb/s. Obviously I am being optimistic but these numbers are not impossible.
The official estimates for the Hübner Factor are based on the observation the LEP realised a figure of 0.2 and the LHC might be expected to be similar. However, the LHC is very different from LEP and the Tevatron both of which required a store of anti-particles. I think there is good reason to expect a better result from the LHC especially given recent performance.
It is also possible to calculate theorectical values for the Hübner Factor given the luminosity half life for the beams and the mean cycle time between fills. The optimum time to keep each fill is then around . Assuming fills can always be kept for this time without an unplanned dump the value of the Hübner Factor is easily calculated. For example, taking the current half life of 20 hours and an average time between fills of 7 hours we find that fills of length 18 hours are about optimal and give as required! The minimum cycle time is even better at about 3 hours, but the real question is how much this will be extended due to failed injections and other faults.