How to make a particle accelerator
(part two in an occasional series)
The two most important considerations in making a particle accelerator are (1) what particles you want to accelerate, and (2) what shape your accelerator will be. As it turns out, answering one of these questions will answer the other one for you, so let's consider (1) first.
Now, working from first principles, we can specify some limitations on what it's practical to accelerate. We'd like to accelerate stable particles, because it's rather a pain to have particles decaying when you're trying to accelerate them. (Though research on muon colliders is an active field, we're nowhere near actually building one.) Furthermore, we're pretty much limited to charged particles, as charged particles can be steered using magnetic fields and accelerated using electric fields, while neutral particles can't. (Neutrino beams do exist, but these are produced by steering and accelerating charged particles, which then decay to neutrinos.)
So, limiting ourselves to charged, stable particles, we're left with a very short list: protons and antiprotons, and electrons and positrons.
Considering all of the possibilities, colliding electrons with electrons will not produce very interesting results (the conservation laws in effect severely limit the possibilities of what you can get back), and positrons are easy to make anyway. Colliding electrons with protons can be done (and is done at HERA at DESY), but it's more of a specialized case (translation: I don't know that much about it), so I won't talk further about it. This leaves us with three interesting possibilities:
1) Protons and protons
2) Protons and antiprotons
3) Electrons and positrons
Now, our choice of geometry is pretty much determined by our choice of what to collide. If we choose electrons and positrons, a ring is pretty much ruled out, as the loss of energy via synchrotron radiation will prevent us from reaching interesting energies. So choice (3) leaves you with a linear collider. Conversely, if we choose protons, then there's no reason not to choose a ring over a linear collider, as the ring will allow us to reach higher energies (as the particles can be accelerated many times, rather than once).
The next obvious question is: why choose one over the other? Well, let's consider the advantages and disadvantages of each. Generally, for the reasons just mentioned above, a proton collider will allow us to reach higher energies. On the other hand, when a proton and an antiproton (or another proton) collide, only two of the six quarks (or antiquarks) involved actually interact, and they only have part of the total energy (and, worse yet, you don't know exactly how much that part is), while the other four will take some of the energy and do something uninteresting. Conversely, an electron-positron annihilation is much cleaner, conceptually speaking, and the entire energy goes into whatever they produced. So (and this is, of course, a drastic oversimplification, but good enough for my purposes), a proton collider will be better for producing new and interesting things, but a linear collider is better for making precision measurements of things. (Those of you paying attention might notice that my current project is trying to make a precision measurement using data from a proton-antiproton collider. That's part of the reason it's so difficult.)
How about choosing between options (1) and (2)? Well, the practical advantages and disadvantages are pretty straightforward. If you have protons and antiprotons in a ring, then you can use one set of magnets: the same magnetic field will bend protons one way and antiprotons the other way, so you're all set. On the other hand, having protons go in both directions requires two sets of magnets (and two separate tunnels for the separate beams), increasing your cost and complexity. However, the big disadvantage of using antiprotons is that they're hard to make. The efficiency of the antiproton-making process used at the Tevatron is about one one-millionth, so making antiprotons is a very slow process (and if the antiprotons are lost for any reason, as they not infrequently are, you can have hours of dead time while you wait for the antiproton stash to build up again). Ultimately, though, the decision is made on physics grounds: at the energies used at the Tevatron, top quarks are typically made by the interaction of a quark and an antiquark, so having an antiproton around greatly increases the number of top quarks (and other interesting stuff) produced; thus, the Tevatron uses protons and antiprotons. For the energies that will be used at the LHC, however, top quarks are more often made by the interaction of two gluons, and there are plenty of those in ordinary protons. Consequently the LHC can get away with being a proton-proton collider.
All right, now you've decided what you want to collide. Now, you want to make your collider the best damn collider it can be. How can you go about doing that? Well, there are two basic variables that determine how useful your collider is going to be: (1) energy -- the higher energy you have, the more interesting interactions you can produce; and (2) luminosity -- the number of interactions that take place per second. If you want a really good collider, you'll want to maximize both of these, given the constraints.
What are the constraints on energy? Let's consider a linear collider first. Well, a linear collider has a bunch of RF generators (called "klystrons") which pump energy into the electron beam. So, it should be pretty clear that the two ways to get more energy out of a linear collider are to (1) inject more energy in each klystron, and (2) have more klystrons. The latter means a longer linear accelerator, and so there the main constraint is cost (not only in building, but also in running, since each klystron is going to take a prodigious amount of power). The former is limited by technological constraints on how much power you can produce (given the stringent timing requirements necessary in any accelerator).
As for a circular collider, the injection of energy is no longer a major problem -- since the beam can travel around the ring as often as necessary, the RF generators are not the limiting factor. Rather, the trick is building magnets strong enough to hold them in the ring, since the magnetic field required to get a particle to travel in a circular path is dependent on the particle energy. Again, there are two possible ways to deal with the problem: (1) build stronger magnets, or (2) build a bigger ring (which reduces the force needed), and again, the former is a technological issue, while the latter is cost-constrained.
Now for the luminosity side of things. First, I'll need to define some terms. Suppose you have an object, and you fire a wide stream of bullets at it (where the width of the stream is much bigger than the object). It should be obvious that the number of bullets that hit the object is going to be dependent on (a) the rate of bullet-firing and (b) the cross-sectional area of the object. For particle physics, the story is much the same. We define a quantity called the "cross section" which is essentially the probability of a given interaction occurring, and then the total number of that interaction we would expect is given by the "rate" (which is called the luminosity) times the cross section. The cross section is usually expressed in units of "barns" (a particle physics joke derived from the expression "as easy to hit as the broad side of a barn"), and typically the luminosity is expressed in units of inverse cross section per time. So, if my accelerator has a luminosity of 5 inverse picobarns per second, that means if I have a particular interaction with a cross section of 2 picobarns, that means I would expect to see 10 of that interaction per second.
All right, hopefully you understood most of that. (If not, don't worry too much; the rest of this article doesn't depend that much on it.) Now, for a wide variety of practical reasons, a typical beam in a particle accelerator is not a continuous stream of particles, but rather a series of bunches -- you have a bunch of particles, then a gap, then another bunch, and so forth. So, it should be clear that if you want to increase the luminosity, you have (once again) two options: (1) increase the number of particles in each bunch, or (2) decrease the spacing between bunches.
Option (2) seems like the simpler one. It is primarily limited by the speed of your readout electronics -- you need to be able to finish reading out one event before the next one comes. As you might expect, this is one area where there's been a lot of progress in recent years. The electronics used in ATLAS, for example, will be so fast that the particles from one interaction won't have even finished travelling through the detector before the next interaction happens. But the electronics are fast enough to handle this, so it's OK. (You might worry that a faster particle from a later interaction might "catch up", but since all of the particles, even the lowest-energy ones, are travelling very near the speed of light, this is not a big concern.)
Option (1) has a few drawbacks as well. For a proton-antiproton collider, like the Tevatron, the obvious disadvantage is that you have to have the particles in the first place -- you can't stuff more antiprotons in each bunch if you don't have any more antiprotons to begin with. This is not a problem for proton-proton or electron colliders, since protons and electrons are easy to make, and positrons are much easier to make than antiprotons. Another issue is that the more particles you stuff into a single bunch, the more likely you'll get multiple interactions in a single bunch crossing; this is not the end of the world (especially since most of them are likely to be uninteresting); indeed, ATLAS plans to typically have (if I recall correctly) about seven interactions in every bunch crossing, but it does make your reconstruction task more difficult (and thus makes greater demands on your detector, since it needs to be able to distinguish these different interactions). Finally, more particles in a bunch makes them harder to focus, since these particles (all having the same charge) will naturally tend to repel each other, so keeping them in a confined volume becomes trickier the more of them you have.
Anyway, those are all of the "big picture" issues I can think of an an accelerator. Of course there are hundreds of tinier issues that I've glossed over or not mentioned at all, as I'm sure you'll rapidly discover when you try to build your own particle accelerator. What do you mean, you weren't planning on doing that?