Friday, November 11, 2011

Nuclear Chain Reactions and Forms of Criticality

Last night I began reading Tom Zoellner's excellent book: Uranium: War, Energy, and the Rock that Shaped the World.

The book helped me better understand the events at Fukushima. What follows is my effort to understand how Fukushima continues to actively produce radiation in the absence of a nuclear explosion. I am drawing upon Zoellner's book and also Wikipedia's account of a Nuclear Chain Reaction found here (

Direct quotes are in quotation marks. 

Uranium is naturally unstable and Uranium-235 is the most unstable isotope.

Uranium-235 must be distilled and “enriched” to create nuclear fuel.

U-235 is uniquely equipped to release energy when its nucleus is torn apart because it is the “heaviest element that occurs in nature, with ninety-two protons jammed into its nucleus” (p. ix)

A sphere of enriched U-235 the size of a grapefruit can destroy an entire city.
Uranium naturally loses protons because it is unstable and decays into radium, then radon, and then polonium. It eventually rests as lead.

In order for the Uranium-235 to sustain a nuclear chain reaction it must be enriched to more than 20%

How is Uranium-235 split? That is, how does fission occur?

The answer is that Uranium is split by aiming neutrons at the atom’s nucleus. Protons and electrons are charged and therefore do not penetrate the nucleus but neutrons have no charge and therefore can penetrate the atom.

When an atom of enriched Uranium-235 is split by one neutron, it emits two neutrons. The process of this occurring in an uninterrupted chain form is a nuclear chain reaction.

Thus, enriched U-235 can sustain a nuclear chain reaction.

Wikipedia describes a nuclear chain reaction:
“A nuclear chain reaction occurs when one nuclear reaction causes an average of one or more nuclear reactions, thus leading to a self-propagating number of these reactions. The specific nuclear reaction may be the fission of heavy isotopes (e.g. 235U) or the fusion of light isotopes (e.g. 2H and 3H). The nuclear chain reaction releases several million times more energy per reaction than any chemical reaction. (

First Sustained Nuclear Chain Reaction from Wikipedia:
Enrico Fermi created the first artificial self-sustaining nuclear chain reaction, called Chicago Pile-1 (CP-1), in a racquets court below the bleachers of Stagg Field at the University of Chicago on December 2, 1942. Fermi's experiments at the University of Chicago were part of Arthur H. Compton's Metallurgical Laboratory facility, which was part of the Manhattan Project(

Wikipedia also has some propaganda about the impossibility of a nuclear reactor having an explosion:
Nuclear power plants operate by precisely controlling the rate at which nuclear reactions occur, and that control is maintained through the use of several redundant layers of safety measures. Moreover, the materials in a nuclear reactor core and the uranium enrichment level make a nuclear explosion impossible, even if all safety measures failed…” (

Nuclear fission of U-235 doesn’t just free neutrons, it also releases gamma rays and neutrinos, thereby releasing energy that had been “stored” in the atom

So, I conclude from this discussion that fission is most definitely occurring at Fukushima. 

The question is what is “the effective neutron multiplication factor” and are the chain reactions occurring at Fukushima criticalities or supercriticalities.

According to Wikipedia, the effective neutron multiplication factor or “k” “is the average number of neutrons from one fission that cause another fission.” The value of k determines whether (I'm paraphrasing here):

k < 1: the system cannot sustain a chain reaction (subcriticality)

k = 1: the system sustains a constant level of fission so that every fission causes an average of one more fission, creating a constant level of fission (criticality)

k > 1: the system achieves “supercriticality” which means “for every fission in the material, it is likely that there will be ‘k’ fissions after the next mean generating time. The result is that the number of fission reactions increases exponentially” (

Wikipedia explains that there are 2 variants of supercriticality, prompt and delayed
  “The region of supercriticality between k = 1 and k = 1/(1-β) is known as delayed supercriticality (or delayed criticality). It is in this region that all nuclear power reactors operate. The region of supercriticality for k > 1/(1-β) is known as prompt supercriticality (or prompt criticality), which is the region in which nuclear weapons operate…

MAJIA HERE: the question is, what is k at Fukushima?

It seems that the debate about fission that occurred over the last week was really a debate about the level of criticality.

It seems to me that there is considerable evidence of k=1 and perhaps delayed supercriticality.

I think that currently the scientists weighing in think that a prompt supercriticality situation has not yet been achieved, although it may be feasible. 

Potrblog has been discussing this possibility but states that they don't have enough data to determine the likelihood of a  nuclear explosion (i.e., prompt supercriticality).

Enenews ran this headline Nov 9: Co-chair of Russia’s Ecodefence and others “still fear criticality” at Fukushima — “I don’t think there is a reason to say situation has improved much actually 

This article has some confusing quotes that might make more sense if we decode them using the vocabulary I’ve outlined above

For example, the article states: “Spontaneous fission should not be confused with nuclear criticality, said Aoki, especially since both the temperature and the pressure levels have remained stable in the reactor. But he did say that “the chances of criticality taking place is not zero.

MAJIA HERE: The article doesn’t make a lot of sense to anyone who has been following the radiation releases and knows that radiation is continuing to be released in large quantities and that some of the radionuclides such as Iodine-131 indicate recent fission.

However, if we interpret Aoki’s comment in relation to the levels of criticality above we might conclude that what he really was saying is that k=1 (criticality) or perhaps even delayed supercriticality has been achieved where The region of supercriticality between k = 1 and k = 1/(1-β) is known as delayed supercriticality (or delayed criticality)

Given this interpretation of what is going on, the real debate that is occurring in a veiled way among and between the world’s nuclear physicists is about whether or not PROMPT SUPERCRITICALITY is likely to occur.

Prompt supercriticality could result in a nuclear explosion.

However, even in the absence of prompt supercriticality, short-to-medium duration criticalities that fail to reach supercriticality (fail to reach k > 1) are still producing radiation and that radiation is still contaminating Japan and the rest of the northern hemisphere.


1 comment:

  1. "MAJIA HERE: the question is, what is k at Fukushima?"

    All the talk of criticality is just a smokescreen. Even a k of less than one, which means an infinite chain reaction is not possible, can still release plenty of nuclear trash. A chain reaction can still be long even if it isn't infinite (a k value of slightly less than one). If the fuel does reach a k of one, the fuel will get very hot very quickly, and this will stop the chain reaction as the fuel vaporizes or otherwise spreads itself out. :-(

    Good luck on educating yourself, as the media is not going to help you much, if at all. Yay, internets!