Having read lots of articles and questions about luminosity and luminance I will try to explain what I understood about it. Now that we have squeezed stable beams, this is becoming to be urgent.
The problem is that most of the articles use lots of math , and this scares away interested intelligent people who don't have enough math background . This article tries to fill the gap, starting as simple as possible and ending by actually computing the luminosity for the first squeezed run!.
Remember the "work" the LHC produces, is collisions between protons. We measure that like this:
- luminosity: how fast collisions are produced
- luminance or integrated luminosity: how many collisions are produced
You could compare this with rain: if you are waiting for the rain to give your plants enough water, one of these things will increase the amount of water for the plants:
- If it rains very hard
- If you collect the rain and give it to the plants directly
- only give water at the roots of the plants
- If you wait long enough
How much water your plants have got is called "luminance" or "integrated luminosity", and "luminosity" is how fast this is happening.
- Higher intensity (more bunches in the beam, and more protons per bunch) correspond to more rain;
- squeezing the beam makes it more narrow, corresponding to collecting the rain;
- making the bunches shorter is equivalent to watering at the root of the plants;
- waiting long enough is a matter of keeping the beam in for a long time (which is an art on itself
One page 2 http://op-webtools.web.cern.ch/op-webto ... p?usr=LHC3 the luminance is given in that unit.
If you don't want to do any maths, is suffices to know that the luminosity number will have to be above say 10 or so for a few days on end to get any useful results for the experiments, and that the record to date is about one hundredth (0.01 or 1e-2), so it is still going really slow.
If you like maths you can read on from here, and than you are set to read some of the more advanced articles elsewhere.
About the unit:
The "barn" is a (very tiny) measure of surface area; it is the area of a square with sides of 10 femtometers. In SI units, 1 barn = 1e-28 m^2.
Luminosity is be measured in "per barn per second", equivalent to 1e28 per square meter per second, but this enormous number is still too small too use. Now instead of adding a scale factor to the luminosity proper, like "mega-per barn per second", they scale down the area, so that they get "per microbarn". (Like speaking about "meter per millihour" instead of "kilometer per hour": it's the same thing, only more confusing )
In order for the physicists to be happy, the LHC will have to produce several "inverse femtobarn" of data, written as fb^-1. One "inverse femtobarn", which is anoter way of saying "one per femtobarn" is equal to 1 billion per microbarn: for example, a thousand per microbarn per second, for a million seconds. Currently the LHC does about .011 per microbarn per second (only at the beginning of a run), which totals to is about 950 per microbarn per day (and in practice more like a quarter of that number). So, to get to an inverse femtobarn, we'll have to run a million days at least. But, in the future, with at several thousand times higher luminosity, we could get there.
- the Tevatron produced about 8 inverse femtobarns of data to date (which is a lot, since Tevatron has high luminosity already).
- All the initial runs up to this week at ATLAS gave 200 inverse microbarns.
- The squeezed run gave 700 extra inverse microbarns! But still, were are only at .0000009 fb^-1, so there is still a long way to go.
If you want to calculate the luminosity yourself, don't forget to take into account that the protons are not equally distributed in the tube, but are bunched together, increasing the probabilty of interaction (as the physicists would say: "concentrated in the longitudinal direction".
Combining all this, luminosity is "effective proton passages per area per second":
<number of protons>/<area of contact>*<rotations per second>/<bunch length per tunnel length>
- Values during the first squeezed stable beams:
- Diameter of beam at area of contact: 15 microns (15e-6)
- Area of contact: pi/4*diameter squared = 1.77e-10
- Number of protons: 20 billion, or 2e10 (there were more, but at any point, this is how many actually contributed).
- Number of interactions per second: 11245 (rotations of the beam)
- Length of a bunch: 30 cm, or 30e-2 m
- Length of the tunnel: 27 km, or 27e6 m
(This post fixed; I confused femto and nano in earlier versions.)