# Tutorial: Introduction to the Large Hadron Collider

What if you want to build the most energetic particle accelerator in the world and you want it to fit into a pre-existing 27 km circumference tunnel?

Parts list:

• Source of particles (in this case, protons)
• Pre-accelerators
• Shovel (understatement)
• Lots of helium (why?)
• What else?

Let's get at one aspect of the problem:

How do we keep protons at 7 TeV (max design energy) running around in a 27 km circle?

Let's do the simplest possible classical calculation, imagining the LHC is a big cyclotron in a uniform magnetic field with no need to worry about relativity (that is, model it as what it really isn't). Here are some notes:

Try this calculation out and see what you get!

This may seem like a small field...because it is. We need to take into account the relativistic momentum of the protons (max 7 TeV/c = 7000 GeV/c):

Do the calculation: it will still understate the magnetic fields needed by more than an order of magnitude. The reason is that we cannot have a single uniform magnetic field. Rather, the proton paths are bent by over 1000 dipole magnets placed around the ring

Let's bring in somre resources:

Now what if the dipoles each runs with an 8 Tesla magnetic field and we imagine it is basically a powerful electromagnet made from #8 gauge wire? (It isn't, of course.) What current would it run?

More notes:

(You can find out how to get the diameter of a particular gauge of wire here.)

This puts us in the ballpark...and it is a lot of current. So why do we need all that helium again?

Here is what we do with all those high-energy, high-momentum protons:

• We collide them for a maximum collision energy of 14 TeV.
• We use large detectors to measure what comes out of the collisions.
• We use conservation laws to work backwards from those measurements to understand their parent particles that were made in the collisions.
• We use triggering to look for the most interesting physics.
• We send the data out for analysis to a worldwide grid.

Speaking of detectors...