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<   No. 1636   2007-07-20   >

Comic #1636

1 Dr No: Now you have no escape, Mr Stud, except to fall into the seething pool of radioactive water below!
2 [sound]: Trip!
3 {Dr No falls into the seething pool of radioactive water below.}
3 Dr No: Aaaargh!!!
3 [sound]: Splash!
4 Stud: Now see, that wouldn't have happened if you'd built this precarious elevated platform with railings.

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The nuclear reactor in the film Dr No, and by extension the one depicted here, are of a type commonly portrayed in visual media. It is a pool reactor, in which the reactor core of nuclear material and control rods is submerged in an open pool of water. This may not look particularly safe to be working around, but it is in fact safe enough to stand next to with no other radiation shielding at all. The water acts as:

The water itself is not actually radioactive, but it wouldn't be healthy to go jumping into it, since that removes part of the shielding effect of the water and potentially exposes you to radiation from the reactor core itself. So characterising it as a seething pool of radioactive water, while not literally true, is close enough to get the correct point across.

The reason film makers love pool reactors so much is because they look cool, with that characteristic blue glow in the water surrounding the visible reactor hardware. The glow is Cherenkov radiation, which is, in itself, relatively harmless.

Cherenkov radiation occurs when electrically charged particles (such as those produced by nuclear reactions) travel at high speeds (such as those produced by nuclear reactions) through an electrically insulating material (such as those commonly used to shield nuclear reactions). The basic principle is as follows:

We have to begin with the speed of light. If you recall from my discussion of Maxwell's equations, the speed of light is equal to:

where μo is a constant called the permeability of free space and εo is a constant called the permittivity of free space. These are numbers that relate the strengths of the interactions between electric and magnetic fields. When I introduced these, I sort of glossed over them a bit, but now we have to ask about that "free space" part. These constants have certain values in a vacuum - i.e. when no matter is present. That's what's meant by free space.

* Generally. There are few odd exceptions, but they're not important right now.

** For those of you who know enough relativity to be dangerous: Einstein stated that the speed of light is constant - in a vacuum. The fact that the speed of light is slower in matter is not a violation of any of the principles of relativity.

When there's matter around, the electromagnetic permeability and permittivity can have different values. In particular, they become slightly larger*. Which means the speed at which electromagnetic waves can travel through the matter gets smaller. Restating: in certain materials, the speed of light is slower than it is in a vacuum**. This is true of pretty much any transparent material you can name: glass, water, air, etc.

Okay, so the speed of light is slower inside some materials. So what? Well, special relativity says that no material object can be accelerated to the speed of light. In a vacuum.

The speed of light in a vacuum is commonly denoted by the letter c. In water, the speed of light is actually very close to only 3/4 of that: 0.75c. But high energy radiation can consist of particles travelling at speeds close to that of light (in a vacuum): 0.9c or higher. What happens when a particle travelling at 0.9c enters water?

*** The speed of light also depends on the wavelength of the light, but only when inside some form of matter. In a vacuum, it's the same for all wavelengths. But in a medium such as water, different wavelengths (i.e. different colours) travel at different speeds. One result of this is that water splits light into colours, forming, among other things, rainbows. But that's a story for another day.

The speed of water surface waves always depends on the wavelength of the wave. But this is the least of the differences between the two types of waves, and for the purposes of today's discussion is completely irrelevant.

This is not the paradoxical situation that it might seem. Let me draw an analogy, again using water. What other sorts of waves travel in water? Surface waves - the sort that spread out as ripples when you drop a stone in a pond, or that roll in from the ocean as breakers on a beach. These waves have a characteristic speed, governed by the density and viscosity of water, the strength of Earth's gravity, and the distance between successive wave crests (the wavelength)***. A typical speed for water waves is of the order of a few metres per second.

A few metres per second is not terribly fast. You can walk faster than that. You might actually be able to swim faster than that. And boats can certainly move faster than that.

What happens when a boat travels through the surface of water at a speed faster than water surface waves? The boat disrupts the water surface as it moves. The water tries to slosh back into place, but it can only move as fast as the wave speed. By the time it can have sloshed back, the boat has moved on, and moved on by a greater distance than the water was displaced. So the water piles up at the front of the boat and falls away to the sides. We call this a wake. A boat's wake has a distinctive V-shape as it fans out to the sides and behind the moving boat. (The larger photos on that Wikipedia page are good illustrations of the effect.)

The same sort of effect occurs in air. What sort of waves travel in air? Sound waves! Sound waves have a certain speed, a few hundred metres per second. That's faster than we can run; that's faster than most vehicles can travel. But not all. Some planes can fly faster than the speed of sound. And what happens when they do? They disrupt the air in front of them, which tries to slosh back into place, but can't do it fast enough because the plane has moved on too quickly. The air piles up and falls away to the sides, creating a V-shaped cone of waves trailing behind the plane. Air waves are sound. When a plane flies past faster than the speed of sound, you hear the wake: a sonic boom.

Now finally, when an electrically charged particle travels faster than the speed of light inside a material, it disrupts electrical particles as it passes them. They try to slosh back into place. Here's where the direct analogy breaks down, so I need to make a small digression.

When a charged particle travels through a material at a respectable (slow) speed, it disrupts electrons in the medium. They slosh back into place. But as we know from Maxwell's equations, when electrical charges slosh back and forth, they generate electromagnetic waves, or light. The thing is, a whole sequence of particles is sloshing back and forth, excited by the passage of the intruding particle passing through. The particles adjacent to one another are disrupted at slightly different times, and so the electromagnetic waves they generate are slightly out of synch with one another. When you combine this across a distance of roughly the wavelength of light, you find you have gotten completely out of synch and the waves that are generated interfere with one another - in effect they cancel each other out. So the slow charged particle travelling through a material ends up not producing any noticeable electromagnetic effects.

But a particle travelling faster than the local speed of light in the material doesn't give the disrupted electrons enough time to get out of synch with one another. A disrupted electron here, and a disrupted electron a wavelength further along, are still mostly synchronised, because the particle that disrupted them passed by so darn fast. So when the disrupted electrons slosh back, the electromagnetic waves they generate don't interfere with one another, they actually partially synchronise and reinforce one another.

Although the analogy with our water wakes and sonic booms is not exact, the effect is very similar. The disrupted electrons produce electromagnetic waves that fall away to the sides and produce a V-shaped cone. Of light - because that's what electromagnetic waves are. That light is Cherenkov radition. That's the blue glow you can see in water pool nuclear reactors.

And what good is Cherenkov radiation, other than making cool movie special effects?

Neutrinos are highly energetic particles produced by nuclear reactions, that barely interact with matter at all once produced. Gazillions of them are produced by our Sun and other stars, and pass straight through Earth constantly without us even noticing them. They form an important observational tool for astrophysical studies and our understanding of the universe. But how do we detect them? Despite their low interactivity, a rare few neutrinos will interact with matter as they pass through. When they do, they produce a pair of charged particles with extremely high velocities. If this happens in water, these particles will produce a characteristic flash of Cherenkov radiation, which can be measured by light detectors. The conical pattern of the radiation can be used to determine the direction the neutrino came from as well as its energy.

Such observations can be made at neutrino telescopes, such as Super-Kamiokande in Japan, which are basically huge tanks of water surrounded by light detectors. They provide us with important measurements and experimental data regarding the events in distant stars, and especially supernovae.

2017-10-28 Rerun commentary: That bit about how light only travels at "the speed of light" when in a vacuum is important in many other physical systems too. An interesting point to be aware of is that even the depths of outer space are not a complete vacuum. The interstellar medium - the space between the stars - contains matter, mostly hydrogen, with a bit of helium and some dust grains made of heavier elements. The temperature of the interstellar medium varies with the local environment: hotter near stars and other radiation sources, cooler further away. Depending on the temperature, the hydrogen can exist either as ionised particles ( a plasma of protons and electrons), hydrogen atoms, or diatomic hydrogen molecules. Typical densities vary between roughly 1 and a 1,000,000 (i.e. 106) gas atoms or molecules per cubic centimetre.

By contrast, Earth's atmosphere at sea level has a density of about 1019 molecules per cubic centimetre. It would take a cube of interstellar space roughly 1000 km long on each side to contain as much gas as a cubic centimetre of what you're breathing right now.

Despite its tenuousness, the interstellar medium has plenty of matter in it to slow down light waves by a little bit. The effect on radio waves can be even more dramatic. Ionised hydrogen slows down radio waves in a way that depends on the frequency of the radio waves. This is similar to how glass and water slow down light of different colours by different amounts, leading to the refraction (or bending) of different colours by different amounts, and so producing rainbows and other visible spectra. This effect, of light waves or radio waves travelling at different speeds depending on their colour or frequency, is called dispersion.

Anyway, if you have an astronomical source of radio waves, and it generates radio waves across a wide range of frequencies, then it turns out that the higher frequency radio waves travel through the interstellar medium a bit faster than lower frequency radio waves. For many radio sources, you can't really tell that this is happening just by receiving the radio waves. But pulsars produce radio waves in discrete pulses, separated by very precise time intervals. If you listen to the pulses of a pulsar at a single radio frequency, you might hear a pulse roughly once every second. But if you change the radio frequency you're listening to, you'll notice that the pulses are still separated by exactly the same interval, but they're shifted in time by a fraction of a second compared to the original frequency. As you go to higher radio frequencies, the pulses shift earlier and earlier, and as you go to lower radio frequencies, they shift later and later. This dispersion effect varies with the amount of ionised hydrogen encountered by the travelling radio waves: greater dispersion means the waves have passed through more ionised hydrogen since leaving the pulsar.

So by measuring the dispersion of radio pulses from pulsars, we can roughly map out the density of ionised hydrogen gas in the Galaxy around us. Cool, huh!

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