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L H C

LHC is the most powerful particle accelerator in the world and it´s located in CERN on the France-Swiss border.

It uses part of the same structure as the former accelerator (LEP), and it has a circumference of 27 km long and runs 100 m underground.

L A R G E :

The size of an accelerator is related to the maximum energy obtainable. In the case of a collider or storage ring, this is a function of the radius of the machine and the strength of the dipole magnetic field that keeps particles on their orbits. The LHC uses some of the most powerful dipoles and radiofrequency cavities in existence. The size of the tunnel, magnets, cavities and other essential elements of the machine, represent the main constraints that determine the design energy of 7 TeV per proton.
    

H A D R O N:

The LHC will accelerate two beams of particles of the same kind, either protons or lead ions, which are hadrons.

A hadron, in particle physics, is any strongly interacting composite subatomic particle. All hadrons are  composed of quarks  (i.e.: protons and neutrons).

   

C O L L I D E R:

A collider (that is a machine where counter-circulating beams collide) has a big advantage over accelerators where a beam collides with a stationary target.

When two beams collide, the energy of the collision is the sum of the energies of the two beams:

E =2·Ebeam

    

In the pipes where protons will travel a high vacuum is required. The pressure will be over one billionth of a bar.

The two beams will be made up of cylinder-like bunches 7,48 cm long  and ~16x16 micras SECTION (1 millimetre wide when they are far from a collision point).
   
Between each consecutive bunch there will be 7,5 m. So, with a circumference of 27 km there should be:

26659 / 7,5 ~ 3550  bunches.

To be able to insert new bunches when non-useful ones are extracted it´s necessary to allow enough space for that.

The effective number of bunches is 2808.

So the rate of "bunches with protons" is: f = (2808/3550) ~ 0,8

Each bunch has 1,15·1011 protons (1 cm3 of hydrogen has ~1019 protons).

Each bunch gets squeezed down (using magnetics lenses) to 16 x16 μm section at an interaction point, where collisions take place.

The "volume occupied" for each proton in the inteaction point is: (74800x16x16) / (1,15·1011) ~ 10-4 μm3

That’s much bigger than an atom!, so a collision is still rare.

The probability of one particular proton in a bunch coming from the left hitting a particular proton in a bunch coming from the right depends roughly on the rate of proton size (d2 with d~1 fm) and the cross-sectional size of the bunch (σ2, with σ =16 microns) in the interaction point.

Then:         Probability ≈ (dproton)2/(σ2) ⇒ Probability ≈ (10-15)2/(16·10-6) ≈ 4 ·10-21

But with 1,15·1011 protons/bunch a good number of interactions will be possible every crossing.

Now, the number of interactions will be:   Probability x N2   (with N = number of protons per bunch)

So,        (4·10-21) x ( 1,15·1011)2   ⇒   ~ 50 interactions every crossing

But just a fraction of these interactions (~50 %) are inelastic scatterings that give rise to particles at sufficient high angles with respect to the beam axis.

Therefore, there are about 20 "effective" collisions every crossing.

With 11245 crosses per second we get:

11245 x 2808 = 31,6 millions crosses , the average crossing rate

(31,6·106crosses/s) x (20 collisions/cross) ⇒ 600 millions collision/s

If we consider 3550 bunches: 11245 x 3550 = 40 millions crosses  ⇒ 40 MHz