Recriticaility in the Fukushima nuclear reactor

Dear Reader,

Those of you who are following the story in the press may have heard of claims that one of the reactors had gone critical again. Now I would like to state that at this point after the melt downs I think that criticality is less likely than it was before the reactors were damaged by overheating. The uranium dioxide is now in the form of a big water free lump at the bottom of the pressure vessels. As the geometry is such that water can not be mixed between the uranium dioxide pellets it will be harder to moderate the fuel thus the fuel is more likely to stay subcritical compared with a core of intact fuel elements plus water.

One of the things which had made people think that the reactor had gone critical again is the observation of xenon-135, this is a shortlived (half life 9.14 hours) fission product, the thing which is important to understand that a short lived fission is not perfect evidence of criticality. This might seem odd but I will explain.

The reason is spontaneous fission, if we assume that the fuel in unit two has the same isotope signature as the stricken chernobyl reactor had back in 1987 and that both reactors contain the same amount of fuel then I can estimate how much xenon-135 will be formed by the fuel.

The chernobyl reactor was thought to contain 26 PBq of Cm-242, according to the chart of the nuclides 0.00062 % of curium-242 decays occur via spontaneous fission.

So as 1 PBq = 1000 TBq then every second we have 161.2 x 10^9 fission events per second due to the random spontaneous fission of the curium.

As the fission yields of the different products change as the energy of the state which undergoes fission increases, then we have to choose which fission yield to use with case. The data which I have does not have a listing for spontaneous fission of curium, but I will make an educated guess and use the data for Pu-239 with fast neutrons for the curium case.

The fission the xenon isotopes are

Xe-133, 6.9 %

Xe-135, 7.4 %

So we will have 11.9 x 10 ^9 atoms of Xe-135 formed per second in the fuel, if we make a dire assumption that all the xenon will be mobile then as the decay constant of Xe-135 is

(Decay constant = ln 2 / half life = 0.69 / 32904 seconds = 2.097 x 10^-5 s-1)

As activity is = number of atoms x decay constant

Then the activity of this xenon isotope released per second by the curium decay will be 0.25 MBq of activity, now if we ignore the decay of the xenon and a charcoal filter absorbs one hour’s worth of xenon then the filter will have about 900 MBq of activity on it. The activity of the filter will be higher as I have ignored the other actinide isotopes, many of these all also undergo spontanious fission.

Cesium maps for Japanese farmland

Dear Reader,

The Japanese government have issued maps of cesium contamination on farmland in the areas near to the Fukushima reactor accident. The main map of that area of Japan is here. Based on a google translate examination of the text with the map the soil has been taken from paddy fields at up to 15 cm depth while for upland soils it is the top 30 cm of soil. If any of my readers can read Japanese then I would be very grateful if they could give me a translation of the text from the Japanese Agriculture, Forestry and Fisheries Research Information Technology Center.

The bad news is that the cesium level in some areas is high, but the good news is that there are things which normal farmers can do which will lower the transfer of cesium to the food crops. I think that farms are going to need to learn a few new skills to allow them to farm in a safe and healthy way using their contaminated land.

The nuclear powered car part II

Now I recently commented on one aspect of the folly of the ”nuclear powered car”, one of my worries was that some unqualified and reckless person might attempt to service a reactor thus causing a radiological accident.

Now I will consider some of the other aspects of the nuclear powered car. We need to consider what type of reactor fuel should be used.

We could opt for a light water reactor; we could create a very small light water reactor using solid fuel. This reactor could generate steam or very hot water which could drive the engine. The problem with this is the fuel. I think that to make the reactor very small we would need to use a fuel with a high level of enrichment. We would need to use a burnable poison in the fuel to keep the reactivity level roughly constant during the life of the core.

I imagine that the fuel and the core would be very like that which is used in a nuclear submarine, in a nuclear submarine the core is used for a very long time. Also the core of both the car and the submarine needs to be able to respond rapidly to changes in power output. In contrast a typical nuclear power plant will run the fuel at a roughly constant power output for about one year rather than yo-yoing the power output.

For example about 300 grams of ²³⁹Pu in a breakfast mug with some water will go critical and thus form a primitive nuclear reactor. The fuel would be a security problem I will go through the possible fuels which I can think of right now.

A high plutonium MOX containing ²³⁹Pu in a ²³⁸U matrix. This fuel would breed some more plutonium during use which would prolong the lifetime of the core. The great problem I see is that such a fuel would have a high potential for misuse. While a 50 : 50 mixture of ²³⁹Pu and ²³⁸U might not be suitable for direct use in a bomb, it would be possible by a simple chemical separation to obtain bomb quality plutonium so this fuel is a non starter.

If a plutonium containing a large amount of ²⁴⁰Pu was to be used then this fuel would be bad in quality for building a bomb, even after the chemical separation. 

If we consider low energy neutrons (0.0253 eV) then for ²³⁹Pu we have the following data

 

Total cross section 1026 barns

Elastic scattering cross section 8 barns

Fission cross section 747 barns

Radiative capture cross section 270 barns

 

While for ²⁴⁰Pu we have the following data

 

Total cross section 291 barns

Elastic scattering cross section 1.6 barns

Fission cross section 0.059 barns

Radiative capture cross section 289 barns

It is clear to me that the ²⁴⁰Pu will capture neutrons and form ²⁴¹Pu, this might sounds like a harmless effect but it is far from nice. The problem is that ²⁴¹Pu decays by beta decay to form ²⁴¹Am which is an intense emitter of alpha emitters. This americium would increase the amount of radiotoxic (alpha emitting) medium lived waste. If the used cores from the cars were reprocessed than the lanthanide rich fraction would be very alpha active. In conventional PUREX reprocessing the lanthanides and the post-plutonium actinides end up in a mixture with all the other fission products.

I know that if you were to run a light water reactor on pure ²³⁹Pu some ²⁴¹Pu would be generated but with a power reactor grade plutonium which is ²⁴⁰Pu rich this problem would far greater.

To avoid the generation of plutonium, americium, curium and the other transuranium elements we could opt for a highly enriched ²³⁵U, this would be a bad choice for security reasons. Such a fuel (when fresh) would have even greater misuse potential than the bomb grade ²³⁹Pu. So as a result I think that this fuel is totally out of the question.

Another alternative fuel would be a blend of natural thorium with some fissile matter. While pure ²³³U or ²³⁵U in ²³²ThO₂ (thorium dioxide) would be a security problem, because after a simple chemical separation you could obtain bomb grade uranium, we might be able to imagine a fuel where a ²³⁹Pu / ²⁴⁰Pu is in the thorium dioxide matrix. This fuel would become more and more plutonium lean with use, while the level of uranium-233 would grow during the lifetime of the core. The ²³³U level would grow and would hopefully become steady thus allowing the reactor to function for a long time.

The great disadvantage I see of this fuel is that the used fuel would have considerable misuse potential. If the uranium was separated form the fuel then the isotope signature would be very favourable for bomb making and very unfavourable for world peace / goodwill to all men. So for these reasons I think that I can not think of a perfect fuel to run a small reactor on for a long time.

I hope to get onto some of the other problems which I can imagine would plague a nuclear reactor powered car in another post. While you might think that the “nuclear powered car” is a stupid idea which should not be considered, it is not a totally stupid idea even when it might be a stupid product. The idea allows us to consider some of the issues associated with a small mobile power reactor.

More isotope data from Japan

Dear Reader,

As promised I am going to share with you some of the isotope data which I have obtained from the NISA and the JAIF in Japan. I have looked at the data and I have come to some conclusions.

1. The uranium level in the soil close to the reactor is about the right range for a normal soil, and the isotope signature matches natural uranium. I think that if the majority of the uranium in the soil was from the nuclear fuel at the plant then the isotope signature would be different.

2. The transuranium actinides (Plutonium and curium) need to be considered. The level of the actinides (when the activities are normalised to make the Cs-137 levels the same) is much lower, this suggests to me that the level of damage to the nuclear fuel is much less in the Japanese accident than it was at Chernobyl. At the Chernobyl accident a nasty big steam explosion smashed the fuel into small fragments which were flung out of the reactor building. The Nb-95 : Cs-137 ratio at Fukuashima also suggests that the level of damage to the fuel is lower. The Zr-95 and Nb-95 isotopes are very important, this is because ZrO2 has very similar solid state chemistry to plutonium.

3. The lack of Mo-99, Tc-99m and Ru-106 in the release from Japan suggest to me that the fuel has been subject to less mechanical violence and heating in an oxygen rich environment. The Mo could form volatile MoO3 if it is heated in air, while the Ru can form RuO4 when it is heated in air.

4. The Sr : Cs ratios also suggest that at Fukuashima that the fuel has been damaged less, I think that the steam explosion at Chernobyl would have flung a lot of solid and less water soluble forms of strontium out of the reactor. This would have included the SrZrO3 phase which is present in used nuclear fuel. This SrZrO3 phase is the perovskite phase which is found in used uranium dioxide (and MOX) fuel.

Part of the isotope signatures of the Chernboyl and Fukuashima accidents

One of the things which I think should be done in Japan is that a sample of the soil with the radioactive contamination should be subjected to a series of chemical leaching.

Firstly the soil should be extracted with water, to extract the water soluble fission products which do not bind to soil minerals. Then the soil should be subject to a series of extractions, each extraction should be more harsh than the last. The idea of such an experiment is to get some idea of the chemical forms of the radioactive isotopes which are present in the fallout.

Rather than being a “waste of time experiment” the results of this experiment would help by giving clues on how the radioactvity will behave in the wide wide world. We need to know how easy it will be for the radioactivity to enter the food chain and thus endanger humans. The leaching rate of the solid particles of the fallout is very important, for example plutonium which is formed by neutron activation of uranium in an atom bomb is more soluble (and able to enter living things) than the plutonium in bomb fallout which was part of the plutonium used to build an atom bomb.