Wednesday, July 06, 2005

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?

Wednesday, May 25, 2005

I originally posted this as a comment to Matt's blog, but given the lack of content on here lately (surprise!) I figured it deserved a wider (huh?) audience.

So, here's my ranking of all of the Cake songs I know. This includes all of Fashion Nugget, Prolonging the Magic, and Comfort Eagle; all of Motorcade of Generosity except "You Part the Waters", which my mental iPod couldn't come up with, and "No Phone", the only track I've heard off of Pressure Chief. Conveniently, this totals 50 in all.

Note that these rankings are off the top of my head and probably are highly mutable, given the interchangeability of so many of their songs.

1. Jolene (Motorcade of Generosity)
2. The Distance (Fashion Nugget)
3. I Will Survive (Fashion Nugget)
4. Cool Blue Reason (Prolonging the Magic)
5. Comfort Eagle (Comfort Eagle)
6. Friend Is a Four-Letter Word (Fashion Nugget)
7. When You Sleep (Prolonging the Magic)
8. Satan Is My Motor (Prolonging the Magic)
9. No Phone (Pressure Chief)
10. Rock 'n' Roll Lifestyle (Motorcade of Generosity)
11. Shadow Stabbing (Comfort Eagle)
12. Never There (Prolonging the Magic)
13. Short Skirt/Long Jacket (Comfort Eagle)
14. Ain't No Good (Motorcade of Generosity)
15. Open Book (Fashion Nugget)
16. You Turn the Screws (Prolonging the Magic)
17. Arco Arena (Comfort Eagle)
18. Mexico (Prolonging the Magic)
19. World of Two (Comfort Eagle)
20. Frank Sinatra (Fashion Nugget)
21. Pretty Pink Ribbon (Comfort Eagle)
22. Sheep Go to Heaven (Prolonging the Magic)
23. Opera Singer (Comfort Eagle)
24. Mr. Mastodon Farm (Motorcade of Generosity)
25. Stickshifts and Safetybelts (Fashion Nugget)
26. Commissioning a Symphony in C (Comfort Eagle)
27. Guitar (Prolonging the Magic)
28. Is This Love? (Motorcade of Generosity)
29. Daria (Fashion Nugget)
30. I Bombed Korea (Motorcade of Generosity)
31. Meanwhile, Rick James... (Comfort Eagle)
32. Where Would I Be? (Prolonging the Magic)
33. Haze of Love (Motorcade of Generosity)
34. Race Car Ya-Yas (Fashion Nugget)
35. Perhaps, Perhaps, Perhaps (Fashion Nugget)
36. Ruby Sees All (Motorcade of Generosity)
37. Long Line of Cars (Comfort Eagle)
38. She'll Come Back to Me (Fashion Nugget)
39. It's Coming Down (Fashion Nugget)
40. Up So Close (Motorcade of Generosity)
41. Love You Madly (Comfort Eagle)
42. Comanche (Motorcade of Generosity)
43. Walk on By (Prolonging the Magic)
44. Jesus Wrote a Blank Check (Motorcade of Generosity)
45. Let Me Go (Prolonging the Magic)
46. Sad Songs and Waltzes (Fashion Nugget)
47. Pentagram (Motorcade of Generosity)
48. Hem of Your Garment (Prolonging the Magic)
49. Nugget (Fashion Nugget)
50. Alpha Beta Parking Lot (Prolonging the Magic)

Thursday, March 10, 2005

Thought of the day

Think of as many temporally-based names as you can. These have to be names that you can think of actual people having, not just things that "could be" a name. Here's all of the names my coworkers and I could think up:

April, May, June, Summer, Autumn, Dawn, Sunrise, Sunset, Christmas (OK, I can only think of one example of this, but still, it counts), and Thursday (this one is kinda cheating).

Notice something they have in common? They're all female names. Can you think of any temporal names which are male? (And people actually have to have this name for it to count.) The only one I can think of is the knight January in one of the Canterbury Tales (damned if I can remember which one), but that's iffy at best.


Sunday, March 06, 2005

Oh, joy!

Of all the webcomics that have come and gone in the time that I was reading them, it was Nothing Nice to Say that I missed the most. Like Penny Arcade, Nothing Nice has an exceedingly rare trait: though 99% of the time Mitch Clem was referring to a band (or game, in Penny Arcade's case) that I had never heard of, or at least not heard enough of to get any inside references, it was still exceptionally, and consistently funny. The thing that made me saddest about the comic was all of the stupid mail that he received, which made me realize just what a thankless task nearly any webcartoonist has, but which also made me realize that he simply wouldn't be able to keep it up forever. And so it was no surprise when NN2S finally went away, but it was a sad event.

I still kept it in my bookmarks, and in those days when I was really, really bored I'd go to visit again, in the hopes that it would be back. But no, it never was; for a while the domain name had even expired, but I still couldn't bring myself to delete the bookmark, and eventually the domain came back but there was nothing there...

And today, I was reading Questionable Content (my best recent webcomic discovery), and it mentioned Nothing Nice to Say, and I did a double-take, and I clicked the link, and it was back! Yay! And has been back for a month! I have no idea how long this will last, but I'll be glad as long as it's still around.

Friday, February 11, 2005

How to build a particle detector
(also part 1 in an occasional series)

Why am I writing this? Well, I've learned quite a bit on the subject in the last couple of years, and I wanted to share that knowledge in a simple, easy-to-read form. If this fails to interest you, feel free to ignore it.

Anyway, let's consider the purpose of a particle detector. You have one beam of particles coming in from one side, another beam (usually of antiparticles) coming in from the other side, and they collide, hopefully producing new and interesting particles. Your job is to detect as many of these new particles as possible, measuring their properties as completely as you can.

The first consideration is the overall shape. Obviously, when an interesting collision occurs, the new particles will fly off (more or less) randomly in all directions. So, your first thought would be that you want your detector to be a sphere, centered around the point of interaction. This would be true, if collisions only occurred in one solitary point. However, for a variety of reasons, collisions typically occur in an "interaction region" along the beamline a couple of meters long. (To briefly summarize, this increases the number of collisions and thus the odds of actually getting something interesting.) So, your typical particle detector is actually mostly cylindrical centered around this interaction region (usually with caps on the end to catch any stray particles).

The four detectors I know the most about (CDF and D0, the two detectors at Fermilab, the world's current highest-energy collider, and ATLAS and CMS, the two detectors at LHC, which will be the world's highest-energy collider when it opens) all follow the same basic pattern (more or less). If you want to see some layouts, you can see them here:

CDF (or a much nicer PostScript version), D0 (only PostScript, sorry), ATLAS, CMS.

In any case, the general layout in all cases is as follows:

* Closest to the beamline is a silicon detector. The silicon detector is designed for very-high-resolution tracking. This is extremely important to the physics, since some of the particles produced in the initial interaction have very short lifetimes and will thus travel a short distance before decaying again. Identifying the location of the secondary decays ("secondary vertices" in the parlance) allows us to see the presence of these short-lived particles.

The technology used in these silicon detectors is not too different from the technology used in ordinary digital cameras. The detector is made of several layers, each containing a large number of appropriately-prepared silicon strips or pixels. When a particle hits a strip, it knocks off some electrons. By applying a voltage to the strip, these electrons will move to one end, where they can be collected and measured. The big difference between this and your digital camera, of course, is that these detectors operate in an extremely demanding environment. In order to operate at the necessary speeds, very high voltages are are used (typically a few thousand volts), which in turn generates a lot of heat (the silicon can literally melt within minutes if the cooling system fails). Furthermore, the high dose of radiation received this close to the interactions puts a high strain on the electronics used. All in all, it's not an easy job.

The silicon detector is typically not very large. The original CDF silicon detector used is maybe the size of two coffee cans on top of each other; the current one is approximately a foot in diameter and three feet in length (about the size of a large trash can), with some additional layers further out. This is partially because most of these secondary vertices are very close to the interaction point, and partially because the silicon is very expensive.

In general, the amount of silicon is usually limited by cost considerations; over the past 10 years, technology improvement has allowed most detectors to considerably expand their silicon coverage. CMS, in fact, uses silicon for all of their tracking (so they don't have a general-purpose tracker as described below).

* Outside of the silicon tracker is a larger, general-purpose tracker. This is typically a few meters in diameter and a few meters in length. The details vary from detector to detector, but the basic principle is almost always a "drift chamber": you have a large cylinder filled with gas (usually argon or some mix), and some wires running along the length of a cylinder. You apply a positive voltage to some of the wires and a negative voltage to some of the other wires. Again, particles passing through the gas will create some ions, which will drift toward the wires (hence the name) where they can be measured. In CDF, many wires are present in a "cell", while in ATLAS, each wire is isolated in its own "straw".

Drift chambers are a sturdy, (relatively) simple, and (relatively) cheap technology, and they provide good resolution, though obviously not as good as the silicon detectors.

The tracking chambers are typically enclosed in a powerful magnetic field. This magnetic field bends the path of charged particles, so that their momenta can be measured by how much the track is curved (higher-momentum particles will curve less).

* Calorimetry: In contrast to the trackers, where a goal is to disturb the particles as little as possible so that their track can be measured as accurately as possible, the calorimeters have the exact opposite goal: to absorb all of the energy of the particle so that the energy can be accurately measured. Unlike the tracker, where silicon has emerged as the dominant choice, there are a wide variety of technologies used in calorimetry.

The most straightforward way, conceptually speaking, is to use a material which has strong stopping power and emits light as the particles deposit their energy in the material. Then the amount of energy that the particle originally had can be measured by the amount of light emitted. Unfortunately, such materials don't grow on trees; CMS uses crystals of lead tungstate, but these are expensive to fabricate and maintain.

A compromise solution (used in CDF, D0, and ATLAS) is to alternate slabs of a material with strong stopping power (typically lead or steel) with slabs of a material which emits light (either a plastic scintillator or liquid argon). This is much cheaper than the first alternative, since all of the materials are easily available, but at the cost of some resolution. This is called a "sampling" calorimeter.

Calorimetry is, while an extremely valuable technique, inherently limited in its precision: as a particle interacts with the material of the calorimeter, it produces a large "shower" of secondary particles created by the interaction, and measuring the energy from all particles in a shower is inherently imperfect.

Typically, calorimeters are divided into two parts: the inner, or "electromagnetic", section absorbs particles which deposit their energy rapidly (electrons, photons, and pi-zeros), while the outer, or "hadronic" section absorbes heavier particles (hadrons) which lose energy less quickly.

* Muon chambers: Ideally, in the calorimeters everything is absorbed, with two exceptions: neutrinos, which can't (practically speaking) be detected by anything in an ordinary particle detector, and muons. A muon, which is a heavier relative of an electron, is extremely penetrating, and will make it through the lead or steel of the calorimeter without being terribly affected. So, typically, outside the calorimeter there's another tracker which detects the muons (and, occasionally, incoming cosmic rays). This tracker is usually another set of drift chambers, like the central tracker, but with much less demanding specifications (the central tracker has to deal with hundreds of particles in a very small area, while the muon chambers typically only have one or two muons to detect in a much larger area). Muons are very useful as triggers, since the presence of a muon almost always signals that something interesting has happened, so the muon chambers (which tend to be pretty slow) are usually supplemented with fast scintillators (which don't give you much position information, but which do tell you that a muon has passed by) to provide a trigger.

There are, of course, lots of other, smaller, systems involved in a detector, but these are the principal ones.

Friday, January 21, 2005

Musical Interlude #1
(Part of an occasional series, I hope.)

It might not surprise you to learn that the first semester of my senior year in high school (OMG THAT WAS TEN YEARS AGO [hush, you, it's barely more than nine]) was not one of the happiest periods of my life. Sure, my junior year was great, but by senior year, there was the stress of college applications, I had assumed a little more responsibility in various organizations than I was perhaps ready for, and I desperately, desperately needed a girlfriend -- for the sake of brevity, let's just say that things had not been going so well on that front by the time a dark December night rolled around. On that particular night, I had to do a paper for my AP American Government class (on Texas v. Johnson, if my memory serves me correctly). I had put it off to the last moment, as usual, and about 9, I set off for the USF library. (Since my father, at that time, was still teaching for USF, I would occasionally borrow his ID so I could use the library there. The principal advantage was the extended hours, which I was taking advantage of in this case.) Anyway, to sum everything up, I wasn't in the best of moods when I set off, and by the time I arrived, the darkness and the loneliness and the stress had combined to make me miserable. Then, just as I was pulling into a parking spot, a song came over the radio. I sat there in the car and listened to the whole thing, and it was so beautiful, it had a nearly magical effect on me. By the time I got out of the car, I still had work to do, but it felt manageable and I wasn't so unhappy about everything. It's the first time I can recall that a piece of music had anywhere near that profound an effect on me.

Needless to say, while I've tried to replicate this effect later, it's never been quite the same. It was just once of those unique confluences, the right event at the right time, and I'm sure that trying to make it happen probably makes it less likely to work, too. It's still a pretty little piece, though. That piece was the Bergamasca from Ottorino Respighi's Ancient Airs and Dances Suite No. 2. (This was back in the days when I still listened to classical music on the radio some of the time. But that's for another story.)
Comments are now fixed
Looks like the change from PHP3 to PHP4 broke the comments. I shold probably junk this old commenting system and get something more modern. Hopefully comment spam won't become a problem. If it does, that might force my hand.

Incidentally, if you did try to comment, it was never recorded, so it's lost into the void. Not that I suspect this is a big problem.
The obligatory technical issues post
It looks like comments aren't working (probably broken by the move to the new bantha), so if you're dying to leave your wisdom here, you'll just have to wait a bit. I'll try to fix them today.

Thursday, January 20, 2005

Celebrating one year of inactivity...oh, damn.

Well, it's now been one year since the last post here. I see that the Blogger interface has changed considerably.

Anyhow, if you're wondering if I'm planning to resurrect the blog, probably not. But there are still occasionally things that I want to post. For instance, the other day we were eating at Fuddrucker's in Emeryville after watching House of Flying Daggers. The sound system was playing the usual extra-schmaltzy Christmas-season music, when suddenly, I noticed an extraordinarily familiar melody: the Troika from the Lt. Kije Suite. You can color me pleasantly surprised.

There's a couple of longer posts which will appear here in the next couple of days.