Chocolate bar yardstick
Sorry about all the silence the last couple weeks. These days our day jobs are getting pretty busy.
After the question “what is 7 TeV?” came up in the comments on our imminent collisions post I though it would be fun to take a tour of some common quantities in energy physics. All of this appears in other sources such as “LHC: The Guide” (2008) and, many talks such as “LHC Status and Commission Plans”.
First of all, let’s stay humble. The size of the LHC and its experiments are often enumerated for dramatic effect with numbers like
- 27 km in circumference,
- 100 m underground,
- 8 stories high,
- 12,500 tons, etc.
But all this huge equipment is just support for the diminutive stars:
- bunches of 1011 protons,
- each 7 cm long and 1 mm in diameter (about the size of a mechanical pencil lead).
That really isn’t much stuff considering that macroscopic things contain around 1023 atoms. At rest this bunch of protons is just 1.6×10-13 g of matter. Given this tiny mass and the pencil-lead dimensions you end up with a density of roughly 4×10-7 g/m3, which is absolutely nothing considering that hydrogen gas is 200 million times denser at 90 g/m3 (the LHC can run for many months using the protons from one bottle of hydrogen gas). To increase the odds that these protons run into each other the bunches are focused to a diameter of about 16 μm just before they cross. Still, collisions are rare, with everything running well there will be at best 20 interactions per crossing (and only a tiny fraction of these interactions will be of any interest to scientists). On the otherhand, the LHC can be filled with 2808 bunches spaced about 7 m apart, and with all these bunches moving at just a hair under the speed of light we can end up with 600 million interactions each second.
So, what about this 7 TeV thing? A teraelectronvolt (TeV), or 1012 electronvolts (eV), is a unit of energy. What we are measuring is the energy available in individual proton interactions. The LHC was designed to operate up to 7 TeV per proton, or 14 TeV total. But, for the next couple years the protons will be accelerated up to a speed where each proton carries 3.5 TeV of energy, and for just a moment while two protons collide we will have 7 TeV of energy in one place ready to make new particles (a Higgs boson, dark matter, or maybe something completely new).
A TeV is actually a very tiny amount of energy. A popular analogy is to a flying mosquito, one proton has the same energy as a handful of mosquitoes,
|Kinetic energy of a flying mosquito||0.81 TeV||assuming a 1.5 mg mosquito moving at 1.5 kph|
On the other hand, we have to give these protons some credit. They are a lot smaller than a mosquito. In fact, if you consider energy density these interactions are record breaking. A simple way to look at this is in terms of energy per particle interaction. Chemical energy is what runs batteries, bombs, and us; but chemical reactions involve only around one electronvolt of energy per atom. Potentially, each of the LHC protons brings 7 trillion times more energy to their little party.
|Process||Energy per particle interaction|
|Nuclear fusion||~20000000 eV|
|LHC collision||7000000000000 eV|
Of course there can be quite a few protons spinning around the LHC at one time, and though only a few interact each time the bunches cross, we can wonder how much total energy is in the beam. This is important for two practical reasons that have nothing to do with the science:
- What would happen if the beam were to somehow go astray and hit the beam pipe and surrounding apparatus?
- How can we safely remove the beam in the normal course of work?
The short answer to the first question is pretty simple: bad things. The beam can punch through 2 meters of solid copper [slides 23-25]. But, it should be noted that it is essentially impossible for a person to be hit by a beam, even if they tried. This is because the beam travels in a vacuum pipe that does a very good job of keeping air out, not to mention human hands. In addition, no one can get anywhere close to tunnels with active beam without breaking safety interlocks that cause it to be dumped immediately. The danger is really only to the equipment. Of course they found exceptions to this in Soviet Russia.
When it’s time to inject a fresh beam of protons or the beam must be removed quickly for safety it is diverted toward a very large chunk of carbon that is liquid cooled and shielded in a 1000 tons of metal and concrete. A nice article about the beam dumps can be found in IEEE Spectrum.
So, to the energies…
|Energy in a head-on highway collision||1 MJ||cars each 1 metric ton moving at 115 kph|
|LHC: Energy in one beam||173 MJ||2808 bunches, 1.1×1011 p/bunch, 3.5 TeV|
|Energy in chocolate consumed by two Swiss people per year||244 MJ||22.4 lbs of chocolate / year / person in Switzerland|
|Energy required to melt 1 ton of copper from room temp.||620 MJ||Wikipedia: 63 g/mol, 24 J/mol/K, 13 kJ/mol|
|Kinetic energy of freight train moving at 60 kph||1400 MJ||100 cars, 100 tons each|
|LHC: Energy in the ATLAS’ toroidal magnetic field||1600 MJ||source: ATLAS e-News|
|Chemical energy in 1 metric ton of TNT||4600 MJ||Wikipedia: Trinitrotoluene|
|LHC: Energy in the magnetic field of all the LHC dipoles||11000 MJ||source: slide 12|
|Chemical energy in 1 metric ton of dark chocolate||24000 MJ||USDA: search for ‘chocolate 60-69%’|
You will notice that for all this crazy amount of energy in the beam (almost 200 car-accidents worth) there are even bigger energies lurking at the LHC. The magnetic field of the ATLAS toroid stores 10 times as much energy, and 10 times beyond that is the energy stored in all the LHC magnets. In fact, the average pair of Swiss people consume more energy every year in chocolate than our measly beams can provide.
(One thing I love about these numbers has nothing to do with high energy physics: you might have been surprised that there is over 5 times as much energy in chocolate as there is in TNT. What is important about an explosion is not as much that a lot of energy is released, but instead that it is released very quickly.)