Monthly Archives: November 2010

Finding hidden nuclear reactors with neutrinos

French physicists from the École Polytechnique and the Commissariat à l’Energie Atomique et aux Energies Alternatives have published a paper that looks at the possibility of finding clandestine or rogue nuclear reactors by using mobile neutrino detectors transported by supertankers.

The fission of uranium and plutonium produces fission fragments that have too many neutrons. In order for these radioactive isotopes to become stable they must lose their excess neutrons and they do this by the process of beta decay in which a neutron becomes a proton, with the emission of an electron and an electron antineutrino.

Nuclear reactors are therefore prodigious producers of neutrinos; for every gigawatt of thermal energy generated by a reactor about a thousand million million million electron antineutrinos are produced.

For example: the fission of uranium-235 can produce xenon-140 and strontium-94 fission fragments (along with two neutrons that go on to cause further fissions, thereby continuing the chain reaction):

Both xenon-140 and strontium-94 are neutron rich and must undergo a number of beta decays before they become stable and each of these beta decays results in the emission of an electron antineutrino.

Neutrinos are tiny, almost massless particles that pass through matter without interacting with it (about fifty million solar neutrinos pass through your body every second). Because they don’t interact it is impossible to prevent them from being leaving the reactor and this is what makes their detection an interesting possibility for identifying hidden reactors: burying your reactor a mile underground in a mountain won’t work, a mile of rock is nothing to a neutrino.

Neutrinos’ weakly interacting nature is a curse as well as a blessing. Neutrino detectors have to be very large so that they have a reasonable chance of capturing a neutrino “event” in a reasonable timeframe. SuperKamiokande, a neutrino detector in Japan containing fifty million kilograms of ultra-pure water in a cylinder 39m across and 41m tall, detects only about fifteen events per day.

Part of the SuperKamiokande detector, with Japanese physicists and rubber dingy for scale.

The French physicists’ paper suggest a cylindrical detector 46m across and 95m long which would be transported to its location and submerged two kilometres underwater. The detector would be filled with a hydrocarbon called linear alkylbenzene doped with gadolinium (to increase the detection rate) and surrounded by thousands of photomultiplier tubes that pick up the flashes of UV light caused when a proton in the detector “absorbs” the electron antineutrino. They suggest that they could easily locate a three hundred megawatt research reactor producing fuel for a nuclear weapon to within “a few tens of kilometres” from three hundred kilometres away after only sixth months’ observation.

via The Physics arXiv Blog

Making money from gravity

The gravitational field strength of a planet depends on size and mass, and the Earth is not uniform in either respect. Because of its rotation Earth’s radius is 21km greater at the equator than at the poles and water (which covers 71.1% of Earth’s surface) is much less dense than the rock that covers the remaining 28.9%.

These two factors, combined with the centripetal force effect of Earth’s rotation itself mean that the strength of Earth’s gravitational field varies across its surface.

This gravity map from the GRACE satellite shows the variation of the gravitational field across Earth’s surface; red indicates higher gravitational field strength and blue lower.

The place with the lowest gravitational field strength is Mexico City (9.779 N/kg, 0.28% below average) helped by it’s elevation, more than two thousand metres above sea level. The highest gravitational field strength is found in Helsinki (9.819 N/kg, 0.13% above average) at a latitude of 60°N.

Because people confuse mass and weight and because Earth’s gravitational field changes the same bar of gold will be measured to have a different mass in different locations. One kilogram of gold will be measured to have a mass of 997.18 grams in Mexico City and 1001.3 grams in Helsinki.

This lends itself to a money-making scam: if I buy gold in Mexico City and sell it in Helsinki I can make a profit of £111 per kilogram (at the current price of £27230 per kilogram). In order to pay for my plane ticket (about £1500) I only need to carry thirteen and a half kilograms of gold (a cube with 9cm sides) with me, though this will cost me about £367000.

You can download the Excel spreadsheet I used to do the calculations for this post: gravity-gold-calculator (31kB, .xls).

How far away is the horizon?

It’s relatively easy to calculate how far away the horizon is if you know two things: the height of your eye above the ground, and how big the Earth is.

Because we know r, the radius of the Earth, and we can measure h, the height of the eye above the ground, we can use Pythagorus’s theorem to calculate d, the distance to the horizon.

Which gives an equation for the distance to the horizon d as a function of r and h:

For the average person’s height of 1.62 m and the average radius of the Earth of 6367.5 km that gives a distance to the horizon of 4542 metres or 2.8 miles.

From the world’s highest public observation deck, on the 100th floor of the Shanghai World Financial Centre at a height of 474 metres the distance to the horizon is 77.8 kilometres, giving a viewable area of nineteen billion square metres, over seven thousand square miles.