A Stupid Thing to do at the LHC

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This is a comment I originally made on Metafilter, in response to the question "what would happen if you stuck your head into the LHC beam." I checked and discovered that there were a lot of responses by physicists to this, but felt the need to add my 2 cents.

First, take at look at these two videos of other physicists' opinions.

I really don't know what would happen if you put your head (or hand) into the LHC beam, and  the Anatoli Bugorski incident only gives us a vague sense of what would happen in the much more powerful LHC. So let's do a Fermi-style thought experiment. Also known as writing down a bunch of numbers and then guessing from that.

Let's ignore the fact that you physically can't do this, since the LHC beam requires a very good vacuum in the beam pipe, so there are no gaps where you can stick your head. This vacuum is because Bad Things will happen if the beam hits free-floating particles (mostly to the beam itself, which must be very well collimated and have regular physical properties otherwise the experiments cannot extract as much useful data). Let's also ignore the radiation around the beam, which is so intense that you are not allow to go near the experiment at all while it is operating (or indeed, for many days afterwards due to activation of radioactive isotopes. Fire-fighting mechanisms for the LHC are automated, as if something bad happened, CERN would not be able to send humans in until the radiation levels dropped). We want a pure LHC-kill-beam thought experiment here.

In that case, we have two antiparallel beams of protons, each with 3.5, 4, or 6.5 TeV, depending on which run of the LHC we are discussing (3.5 and 4 are the Run I numbers, Run II starts in the late winter/early spring with 13 TeV beam-to-beam energy, so 6.5 TeV in each beam). The protons are organized in bunches, with a 50 ns spacing between bunches, moving down to 25 ns in each bunch (this means each bunch of protons is separated by about 7.5 meters in the 25 ns configuration). I'm now going to use nominal LHC beam parameters (as my dedication to this thought experiment is not great enough to sift through all the papers written on what the LHC was expected to do before turn-on, versus the parameters we are actually running with). There are 2808 bunches in each beam, and 1.15e11 protons in each bunch. Since the LHC ring is 27 km around, once you stick your head in the beam you will have 0.0001 seconds until the entire circulating beam piles into you, so all in all, your head will get to enjoy the presence of 3.3e14 protons, each with 6.5 TeV of kinetic energy (the protons only weigh a billionth of a gram, though adding in their kinetic energy it's about 7 millionths). Total energy of both beams I get as 670 MJ. The beams are separated though (until they reach the crossing points where the experiments are: CMS, ATLAS, ALICE, and LHC-b), and the beams are further apart than one human head usually (which means that the dipole magnet configuration is pretty nifty; its hard to get two beams of positive charge rotating in opposite directions with a single magnet). So we can only access half that energy to cause your head to explode, unless CMS or ATLAS lets you do this in their hall. 

Now, what happens to that energy? Let's take the mm value as the width w of the beams at the point in which your head is inserted. We'll estimate the depth of head (d_h) as 30 cm, with a density of water -- this gives approximately the right mass for a human head, which should be about 20 lbs for an average man. This means that the mass in the way of the beam is approximately:

latex-image-1.jpeg


 

so there are about 1e23 target nucleons whose day this beam is about to ruin. 

The total inelastic cross section of proton-proton collisions at 14 TeV center of mass energy is 85 mbarn (mbarn = 1e-3 barn, the barn = 1e-24 cm^2 being the unit of area -- "size" -- that we use in particle physics. As in, "broad side of a"). However, the correct cross section should be at a lower energy, since the target head-nucleons are at rest. Eyeballing some plots of cross section versus energy, I estimate the appropriate cross section here is 40 mb. This makes the probability of a single beam proton hitting a single target nucleon the ratio of cross section to beam size, which works out to be about 1.3e-24. As there are 1e23 target nucleons, the probability for each beam proton to hit something in your head is about 13%.

Now, the big question, what does 13% of a 335 MJ beam do to your head? The beam will impart 43 MJ of energy in that mm wide beam, so I'm going to state with pretty high certainty that every atom in that beam is completely gone. Just totally vaporized. This is in contrast to the mere neuron-killing beam that Bugorski received. Two things go into this: the higher energy per proton for one, but also the much higher luminosity of the LHC compared to every other accelerator beam ever built. There's just more energy in the beam. 

What about the rest of your head? Sadly after all the work that went into this, I don't know for sure. There are several considerations. First, most of the energy deposited will go into accelerating your ex-head nucleons in the direction of the beam, so to first order you might say that the surrounding tissue is not affected: the beam just removes a cylinder through your brain at nearly the speed of light. Downstream there's going to be a problem for the beam physicists, as they now have to deal with entirely too much radiation from your ex-head particles, which are now mostly ex-nucleons. The second consideration though is two-fold: first, there will be some scattering of energy transverse to the beam, which will deposit energy into the rest of your head. Too much energy and the rest of your head will either explode, vaporize, or just catch on fire. This is exacerbated by the 2nd effect, which is that collisions in the front of your head will have secondary interactions down-stream in your brain, which will likely increase the energy moving out of the beam path into the rest of your head.

It takes 18 MJ of energy to vaporize an 8 kg ball of water (ignoring the fact that said head of water is in a vacuum for the LHC beam to hit it). So I'm going to rule out complete vaporization the head, there's enough energy deposited, but too much of it would have to move transversely by my estimation. My best guess then is that -- in addition to your new mm sized hole -- you are probably going to get a region around that which gets to boiling or near boiling, which will likely kill you, but that your head won't spontaneously combust. You are certainly going to get a lethal dose of radiation from this, so regardless of physical damage, death is imminent. All this said, I think the only sure way to know is A) stick a head in the LHC, which sounds expensive and I'm sure some committee would nix it for the low scientific value, or B) we find an experimentalist with a copy of GEANT or similar code that simulates (among other things) the propagation of proton beams in matter, and ask them to mock up a head and hit it with simulated protons. You know, For Science.