Friday, June 21, 2013

Fermi Problem Friday: X-Ray Assassins

A few days ago, a KKK member and his accomplice were arrested for their roles in a plot to build a portable x-ray machine that they hoped to use to murder Muslims. Their plan, which is detailed in the 67 page FBI warrant (see full text of the warrant at the bottom of this post), was to expose their victims to doses of radiation that would lead to their death in a matter of days.

Over the course of a year, Glendon Crawford and Eric Feight worked to acquire x-ray tubes, develop software, and build a remote triggering device to allow them to operate an truck- mounted x-ray source from nearly a half mile away. But is it possible, and feasible, to build such a device? That is the subject of today's Fermi Problem.

Crawford wanted a machine that would deliver a dose of up to 10 Grays to a victim. One Gray is enough radiation to deposit one joule of energy per kilogram. Assuming he was after adult men, who typically weigh about 80 kilograms in North America, that requires a total of 800 joules of x-ray energy.

It's a fairly modest amount of energy. A reasonably healthy person could produce that much energy pedaling a stationary bike in a few minutes

X-ray tubes, however, aren't very efficient. Typically, only about one percent of the energy to run one turns into x-rays. The rest of the energy goes to heat the tube, which has to be cooled to keep it from overheating or melting. Producing 800 joules of x-rays, therefore, takes about 80,000 joules of energy. That's still not an unreasonably large number. A typical gasoline generator from a hardware store could provide enough energy to do that in 10 to 20 seconds.

But not all the x-rays coming from a source would make it to a target. X-ray tubes produce a point source radiation that spreads out like light from a bulb - only a fraction of the radiation would travel in the direction of one of Crawford's intended victims unless he had lenses to focus the x-rays. But unlike visible light, focusing x-rays is very difficult, typically requiring optical elements made of lead or other dense materials. In fact, as you can read in the FBI warrant below, transcripts of Crawford's cell calls make it clear that he had no intention of focusing the x-rays because he cites the "inverse squared law" that results from radiation spreading out in a sphere, and decreasing in intensity the farther you are from a point source.

If you assume that the surface area of a person is about 1 square meter, and that the source of radiation is 2 meters away, only about a fiftieth of the x-rays coming from the source would actually hit the person. Considering that Crawford had planned to park the truck containing his machine outside the home of a victim, two meters is probably the very closest he could get to someone who was, say, asleep in a bedroom with one exterior wall.

To expose a person to 800 joules of x-rays would require fifty times 80,000 joules from the source, or about 4,000,000 joules.

Of course, with the exception of our bones, the human body is mostly transparent to x-rays. If you estimate that only 10 % of x-rays that pass through our bodies hits a bone (a pretty reasonable estimate, considering that bones are a fairly thin framework surrounded by lots of flesh), the total x-ray output has to be increased by another factor of 10, to 40,000,000 joules, which is just about as much energy there is in a kilogram of gasoline.

The wall of the truck and the building would also absorb x-rays and reduce the energy that would have made it to one of the terrorists intended victims, perhaps requiring another factor of 2 in energy, but that's still only 100,000,000 joules or so. A generator powering an x-ray source for a few hours could do that easily.

There would have been plenty of other complications. As far as I can tell, no single, commercially available, x-ray tube could produce the intensity of x-rays long enough to do what Crawford had in mind. But it appears that he had hoped to build a system with multiple tubes to boost the output.

Getting rid of the 90,000,000 joules of waste heat would have required a significant, and probably noisy, cooling system. Considering the amount of energy pumped into the room in the form of x-rays, I'm guessing the room would get uncomfortably hot as well, perhaps prompting a person inside to leave or investigate the source of the heat and the noisy truck parked next to their bedroom wall. Finally, while x-rays are technically invisible, very intense x-rays great a blue glow that is not completely understood, but could give someone an idea that something odd was underway. Still, it's possible that a deeply sleeping person (or someone to old or too young to escape) could be exposed to a lethal x-ray dose, despite the various potential danger signs.

Was it possible to do what these domestic terrorist had in mind. Absolutely - it would have been feasible to assassinate people with a portable, homemade x-ray machine. It wouldn't have been easy to build, or to get away with, but there's no fundamental reason I can find to rule it out.

Thank goodness the FBI was on the job.




   Crawford Complaint - Searchable

2 comments:

  1. The news story I saw about this said they planned to run it off a 2kW battery, in which case depositing 100,000,000 J of energy would require 50,000 seconds, or just about 14 hours. That seems an improbably long time for someone to stay still in the field and not notice any problems.

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  2. A 2 KW battery would certainly take way too long, especially since it would have to run the cooling equipment too. In the warrant, Crawford says he'd like to use a battery, but admits he'd probably have to go with a generator. I'm not sure where the 2kw battery info comes from, but there doesn't seem to be any mention of that specifically in the warrant.

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