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Synchronization

July 12, 2013

People who are not scientists, and this category includes most politicians, have very little idea of the considerable number of technologies that were involved in the successful detonation of the first "atom bomb" in the Trinity test. In their minds, you just get a bunch of radioactive stuff and blow it up. Getting the isotopically-enriched material was the most difficult part of the venture, and that involved a lot of physics, chemistry and engineering. However, the "blowing it up" part was difficult as well.

A critical mass is the quantity of material needed for a chain reaction, and this depends on the shape of the mass, and the nuclear properties of surrounding material. The critical mass of plutonium-239 explosive for the Trinity test was a sphere less than ten centimeters in diameter. The trick was creating such a sphere at the desired time.

Several years ago, I watched a made-for-television movie in which the heroine government agent needed to defuse a nuclear device seconds before detonation. Her solution wasn't to pull out some exposed wire, the common solution in most such movies, but to pry off a single piece of the bomb casing. This simple action was a very scientific solution. By removing that piece, a properly symmetrical implosion could not happen, and a nuclear explosion was rendered impossible.

The Trinity test method for achieving critical mass was to shape the plutonium as a hollow sphere. A surrounding sphere of explosives compressed this into a smaller sphere. Since the forces are directed inwards, and not outwards, this is called an implosion, not an explosion. In the Trinity test, the plutonium was surrounded by 32 hexagonal and pentagonal patches of explosive, as shown in the figure.

Inner sphere of Fat Man nuclear deviceThe first nuclear devices looked somewhat like this, with the inner plutonium sphere (called a "pit") surrounded by explosives and their detonators. The arrangement of hexagons and pentagons is like that of a soccer ball.

(Source image via Wikimedia Commons.)

When all the pieces of the explosive sphere are fabricated and assembled correctly, you still need to detonate them all simultaneously. Today, you could use a high intensity pulse from a single laser directed through some optical waveguides, but in 1945, you needed to use electronics. You needed fast detonators, and you also needed a way to trigger these simultaneously. In some cases, but not here, the lengths of wire connecting to the electronics box might need to be the same length, to eliminate speed of light errors.

Nobel Physics Laureate, Luis Alvarez, and Lawrence Johnston invented the exploding-bridgewire detonator for this purpose. To achieve rapid detonation, the device vaporized a wire in just a few microseconds by application of a large electrical current. The heat and acoustic shock wave resulting from this vaporization initiated the explosive reaction.

Fig. 1 of US Patent No. 3,040,660, 'Electric Initiator With Exploding Bridge Wire,' by Lawrence H. Johnston, June 26, 1962.Fig. 1 of US Patent No. 3,040,660, "Electric Initiator With Exploding Bridge Wire," by Lawrence H. Johnston, June 26, 1962.
(Reformatted to fit page, via Google Patents.[1])

As can be seen in the above figure, the power source for vaporizing the wire is a capacitor (10), first charged by a battery (12). The capacitor is important, since its discharge fixes the current profile through the wire. The vaporizing wire is at (3), topped by explosive at (2). Alvarez went on to use his experience in electronics and nuclear physics to do the work for which his Nobel Prize was awarded.[2]

The controlled implosion at Trinity was effected by a controller sending synchronized signals to the detonators. Some physical systems will synchronize in the absence of a controller when the action of one part changes the excitation forces of another. An early example of this is when pendulums will synchronize when placed on the same table. The swaying action of one pendulum is transmitted as a small swaying action of the table, and this influences the sway of the second pendulum.

As I wrote in a previous article (Coupled Oscillators, November 15, 2011), this coupling can be an out of phase coupling; that is, the pendulums will swing at the same rate, but in opposite directions. Christiaan Huygens, who was the inventor of the pendulum clock, noticed this effect, which he called odd sympathy, in pendulums that shared a traverse arm.[3-6] Research on this effect at Georgia Tech showed that Huygens' discovery was a fortunate accident, since there are a lot of variables that enter into the coupling between such pendulums.[5-6]

The mathematical analysis of synchronization such as found by Huygens is quite involved, but the problem has been tackled by mathematicians at the University of Pittsburgh (Pittsburgh, PA), who have applied it to cases for which the coupling is through a slowly evolving dynamic medium. Such is the case for neurons coupled through extracellular potassium, and they were able to reproduce the spike-to-spike asynchrony found in such a system. In this model, the neurons are weakly coupled oscillators similar to Huygens' pendulums.

A pendulum is an analog device, but neurons function digitally, through on-off signals. They get their message across by firing at different rates. The Pitt approach was to first describe the average properties of their system to obtain a periodic solution, and then exploit the small fluctuations around this average performance to analyze the coupling between units.[7]

This research may have application to the study of epilepsy. During epileptic seizure, neurons are overly active and fail to turn off.[8] Says G. Bard Ermentrout of the University of Pittsburgh Department of Mathematics,
"For neurons, we have shown that the slow nature of these interactions encouraged 'asynchrony,' or firing at different parts of the cycle... In these seizure-like states, the slow dynamics that couple the neurons together are such that they encourage the neurons to fire all out of phase with each other."[8]
The mathematical model may also explain complex oscillations involved in predator-prey systems. When foxes prey on rabbits, and wolves prey on sheep, there will be oscillatory behavior in the fox-rabbit and wolf-sheep populations. When another variable is added, such as availability of the common food supply for the rabbits and sheep, these oscillating populations will couple with each other.[8] This work was supported by the National Science Foundation.[8]

References:

  1. Lawrence H. Johnston, "Electric Initiator With Exploding Bridge Wire," US Patent No. 3,040,660, June 26, 1962.
  2. Alvarez was cited by the Nobel Committee "for his decisive contributions to elementary particle physics, in particular the discovery of a large number of resonance states, made possible through his development of the technique of using hydrogen bubble chamber and data analysis."
  3. M. Nijhoff, Ed., "Ouevres Completes de Christian Huygens," (Societe Hollandaise des Sciences, The Hague, The Netherlands, 1893), vol. 5, p. 247 (in French).
  4. Erica Klarreich, "Huygens's Clocks Revisited," American Scientist, vol. 90, no. 4 (July-August 2002).
  5. Matthew Bennett, Michael F. Schatz, Heidi Rockwood and Kurt Wiesenfeld, "Huygens's clocks," Proc. R. Soc. Lond. A, vol. 458, (March 8, 2002), pp. 563-579.
  6. Erica Klarreich, "Discovery of Coupled Oscillation Put 17th-Century Scientist Ahead of his Time," SIAM News, vol. 35, no. 8, October, 2002.
  7. Jonathan J. Rubin, Jonathan E. Rubin and G. Bard Ermentrout, "Analysis of Synchronization in a Slowly Changing Environment: How Slow Coupling Becomes Fast Weak Coupling," Physical Review Letters, vol. 110, no. 20 (May 17, 2013), Document No. 204101 (5 pages).
  8. B. Rose Huber, "Pendulum Swings Back on 350-Year-Old Mathematical Mystery, University of Pittsburgh Press Release, June 10, 2013.

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