What Caused the High Cl-38 Radioactivity in the Fukushima Daiichi Reactor #1

http://www.japanfocus.org/-Arjun-Makhijani/3509

What Caused the High Cl-38 Radioactivity in the Fukushima Daiichi Reactor #1?[1]

What Caused the High Cl-38 Radioactivity in the Fukushima Daiichi Reactor #1?^[1]

A bilingual Japanese-English text is available here.

THIS IS A PDF. You can see the content of the Japanese PDF at the bottom of this article without the photos.

F. Dalnoki-Veress with an introduction by Arjun Makhijani

Important article update April 23, 2011 A Japanese translation by Kyoko Selden of this update is available here.

ALSO ADDED AT THE BOTTOM

In its press release of April 20, TEPCO has retracted the Cl-38 radioactivity concentration measurement (1.6 MBq/mL) for the seawater used to cool reactor #1that it had issued on March 25, saying that it was “below minimum detectable density”. Based on this original measurement, we had determined that the value was too high to be explained without invoking the possibility of inadvertent, transient criticalities. We are pleased that TEPCO has retracted this result and has set out to improve its analysis protocol as described in the same press release. But we would appreciate further explanation of why previous results were simply retracted with inadequate categorization and explanation of the errors, as in the TEPCO press release. (The Cl-38 reading was changed on April 20th from 1.6MBq to a value “below detection limit” with the following explanation: “Identification and determination of radioactivity density were conducted based on main peaks.”) For example, the main gamma lines of Cl-38 are at 1.64 MeV and 2.16 MeV. What lines did these interfere with that required a downscaling of 6 orders of magnitude? If the count rate could not be attributed to Cl-38 what isotope had a count rate equivalent to 1.6 MBq/mL?

While appreciating the steps that TEPCO has taken since the April 4th NISA reprimand, we recommend further rigor in isotopic measurement protocol and timely reporting of results. Otherwise, public trust in the important measurements that TEPCO is making will further erode. We therefore recommend that TEPCO take the following steps:

1) Release full spectra data (not just a number)

2) Release the time/date sample was taken

3) Release the time/date sample was measured including counting time and dead time

4) Repeat measurements at different times of the day

5) Please measure other isotopes of interest (such as Te-129, which was retracted by TEPCO on April 20th as well), even if they are below the detection limit

6) If retractions are necessary due to an honest mistake, please provide full explanation of the mistake

7) If third-party, independent analyses are done, please state the name of the analyst/lab that has cross-checked TEPCO’s interpretation of the results

TEPCO/NISA and the Japanese government have a monumental task ahead of them and important decisions will be based on measurement results. Therefore, it is important that rigorous protocol be followed both in analysis and in communicating the results. F. Dalnoki-Veress

This is a first for The Asia-Pacific Journal: publication of a technical scientific paper addressing critical issues pertaining to the leakage of radioactive water at the Fukushima reactors. Our goal is to make this information available to the Japanese and international scientific communities, to Japanese government authorities, and TEPCO as they address the formidable issues of cleanup and safety. But we also believe that the information is of importance to informed citizens and the press in the face of further dangers that have gone unmentioned not only in government statements, but also in the press. Arjun Makhijani’s introduction provides a lucid explanation of the problem and the issues, followed by F. Dalnoki-Veress’s paper. Asia-Pacific Journal

Introduction by Arjun Makhijani

The presence of highly radioactive water in three turbine buildings at the Fukushima Daiichi nuclear plant is widely understood to be from the damaged fuel rods in the reactors. This has rightly raised concerns because it indicates several problems including extensive fuel damage and leaks in the piping system. Less attention has been paid to the presence of a very short-lived radionuclide, chlorine-38, in the water in the turbine building of Unit 1. The following paper evaluates whether its presence provides evidence of a serious problem – one or more unintended chain reactions (technically: unintended criticalities) – in the reactor. Such chain reactions create bursts of fission products and energy, both of which could cause further damage and aggravate working conditions that are already very difficult.

Chlorine-38, which has a half-life of only 37 minutes, is created when stable chlorine-37, which is about one-fourth of the chlorine in salt, absorbs a neutron. Since seawater has been used to cool, there is now a large amount of salt – thousands of kilograms – in all three reactors. Now, if a reactor is truly shut down, there is only one significant source of neutrons, namely, the spontaneous fission of some heavy metals which are created when the reactor is working and remain present in the reactor fuel. The most important ones are two isotopes of plutonium and two of curium. But if accidental chain reactions are occurring, it means that the efforts to completely shut down the reactor by mixing boron with the seawater have not completely succeeded. Periodic criticalities, or even a single accidental one, would mean that highly radioactive fission and activation products are being (or have been) created at least in Unit 1 since it was shut down. It would also mean that one or more intense bursts of neutrons, which cause heavy radiation damage to people, have occurred and possibly could occur again, unless the mechanism is understood and measures taken to prevent it. Measures would also need to be taken to protect workers and to measure potential neutron and gamma radiation exposure.

This paper examines whether spontaneous fission alone could be responsible for the chlorine-38 found in the water of the turbine building of Unit 1. If that could be the only explanation, there would be less to be concerned about. However, the analysis indicates that it is quite unlikely that spontaneous fission is the sole or even the main explanation for the measured concentration of chlorine-38. Presuming the reported measurements are correct, this leaves only one other explanation – one or more unintended chain reactions. This paper is presented in the spirit of encouraging discussion of whether further safety measures might be needed, and whether supplementary measures to bring the reactors under control should be considered. It is also presented as a preliminary analysis for scientific discussion of a terrible and technically challenging nuclear crisis at the Fukushima Daiichi plant.

Arjun Makhijani March 30, 2011

I have been consumed over the last few weeks by the events unfolding in Japan. I keep alternating between complete disbelief and acceptance of the gravity of the situation, but mostly disbelief. And I am not the only one. Most of the nuclear physicists and engineers with whom I have spoken since the incident cannot – will not – believe that it is possible that some of the fuel that is melting could somehow produce little pockets that could go critical. I believed them for the longest time until the following appeared on the Kyodo news website (relevant text italicized below for emphasis) and I did the following analysis. FD-V March 30, 2011

“Neutron beam observed 13 times at crippled Fukushima nuke plant
TOKYO, March 23, Kyodo
Tokyo Electric Power Co. said Wednesday it has observed a neutron beam, a kind of radioactive ray, 13 times on the premises of the Fukushima Daiichi nuclear plant after it was crippled by the massive March 11 quake-tsunami disaster.
TEPCO, the operator of the nuclear plant, said the neutron beam measured about 1.5 kilometers southwest of the plant’s No. 1 and 2 reactors over three days from March 13 and is equivalent to 0.01 to 0.02 microsieverts per hour and that this is not a dangerous level.
The utility firm said it will measure uranium and plutonium, which could emit a neutron beam, as well.
In the 1999 criticality accident at a nuclear fuel processing plant run by JCO Co. in Tokaimura, Ibaraki Prefecture, uranium broke apart continually in nuclear fission, causing a massive amount of neutron beams.
In the latest case at the Fukushima Daiichi nuclear plant, such a criticality accident has yet to happen.
But the measured neutron beam may be evidence that uranium and plutonium leaked from the plant’s nuclear reactors and spent nuclear fuels have discharged a small amount of neutron beams through nuclear fission.”
==Kyodo News

Also, on March 25^th, TEPCO made public a measurement of the contributions of different isotopes to the extremely high measured radioactivity of the seawater used to cool reactor #1. The reasons why these measurements were taken so late in the crisis (or why the information was released so late) is unclear at present.

Table 1: The contribution of different isotopes to the radioactivity from a sample taken in the turbine building of reactor #1^[2]

The measured levels of Cesium and Iodine, Cs-137 and I-131, were expectedly very high. The very high concentration of one isotope however – Cl-38 – was the figure that drew my attention. Why worry? Cl-38 has a 37-min half-life beta decay; in a couple of days it will be gone. However, the fact that it was there at all, and in such high concentration, puzzled me. Could it be that the incident flux of neutrons converted the 24% Cl-37 present naturally in salt to Cl-38 through radiative neutron capture (a simple reaction: add a neutron give up a gamma, and you have Cl-38)? What flux could have produced the observed radioactivity? In what follows, I attempt to calculate the neutron flux that would have been able to produce the observed radioactivity. There is a bit of math, but you can skip to the conclusions. All calculations assume that the TEPCO measurements reported in Table 1 are correct.

First we calculate the number of Cl-38 nuclei that are present that would explain the observed radioactivity. The half-life of Cl-38 = 37.24 min which corresponds to a decay constant of λ₃₈ = 0.00031021 s^-1. So that: dN₃₈/dt = –λ₃₈N₃₈where, dN₃₈/dt = 1.6e6 s^-1 and N₃₈ = 5.16e9 Cl-38 nuclei. This means that the activity measured is consistent with the production of 5.16e9 Cl-38 nuclei. The next question is how much Cl-37 was present in the seawater in the first place? The mass of chlorine in seawater is 19345 mg/kg = 19.345g Cl/kg^[3]. Also, the fraction of Cl-37 in natural Cl is = 24.23% (see Table 2 below).

Table 2: The isotopic abundance and molar mass of chlorine

The mass of Cl-37 can then be found to be 25% (we must account for the difference in molar mass of the two isotopes: it is a very small difference but it adjusts the fraction Cl-38 by mass to be 25%) of 19.345 g Cl/kg = 4.89g Cl-37/kg. Using Avogadro’s number we can calculate the total number of Cl-37 nuclei/g of seawater to be N₃₇ = 7.96e19.

We now know that N₃₇ = 7.96e19 Cl-37 nuclei/g of seawater, and we observed that 5.16e9 of these have been converted to Cl-38. The question then becomes what flux could have produced this many Cl-38 nuclei?

We now assume Cl-38 was produced as the seawater was being circulated through the fuel. What is the flux of neutrons we need to produce the observed N₃₈?

Since Cl-38 is radioactive with a decay constant given by λ₃₈ the rate of change of the number of Cl-38 nuclei is given by:

This is the familiar equation of series decay where one isotope is being produced and at the same time is decaying. This equation can be easily solved (see for example I. Kaplan, Nuclear Physics, 1958, p 463.):

Where, ϕ is the flux in n/cm².s, and σ_(γ,n) = 383.7mb is the radiative capture cross-section which would result in the production of Cl-38 at the Maxwellian distribution average temperature. Note that the thermal neutron cross-section is not very different at 432 mb so similar results would be obtained if we assumed that all the neutrons are thermalized.

Now, we know that after activation we produced N₃₈(t) = 5.16e9 Cl-38/cm3, so we let t = T, the time when activation stopped so that N₃₈(T)=5.16e9 nuclei/cm³. We also know the value of the factor σ_(γ,n)N₃₇/λ₃₈= 0.098445192.

So that the flux can be expressed very simply as a function of irradiation time T:

We assume that the production of Cl-38 started with the deliberate introduction of seawater on March 23^rd (according to the TEPCO press briefing^[4]) into reactor #1. Therefore, since the measurement appears to have been done on March 25^thit means that we have a maximum activation time of 2 days. In fact, we really have two regions of flux that are significant. The first region is where the denominator is < 1 (corresponding to activation time T0.4 days.

A lower limit in the flux is set when T is long (i.e. > 0.5 d) so that the denominator approaches unity. We call this flux (ϕ = 5.241e10 n/cm².s) and it is the lower limit of the flux that could have produced the Cl-38 nuclei radioactivity observed.

What might have caused the concentration of Cl-38?

The first possible explanation to consider is that the seawater was circulated among the core intercepting neutrons from natural spontaneous fission of the used nuclear fuel. The second possible explanation to consider is localized criticalities.

Recall that nuclear fuel changes its isotopic composition upon irradiation in a reactor. This is the reason why we are concerned about plutonium production in nuclear reactors from a nonproliferation point of view. We investigated this by calculating the number of spontaneous fissions from a typical BWR with 4% enriched fuel after 45 MWdth/kg burnup (see IAEA-TECDOC-1535, pg. 74). The inventory we get for 1 metric ton fuel for the primary neutron producing isotopes are shown in Table 2.

Table 2: The isotopic inventory, nuclei/g, branching ratio for spontaneous fission, half-life, and decay constant for different neutron producing isotopes present in spent nuclear fuel. The largest flux comes from even Pu isotopes and Cm. Note: MTHM= metric ton heavy metal and refers to the active component of the fuel SF= spontaneous fission. Isotopic inventory obtained from IAEA-TECDOC-1535, pg 74.

The neutron production rate from spontaneous fission can be calculated for each isotope by summing the contribution of spontaneous fission by each isotope.

(dN_n)/dt=∑_i=1:iso[λ_iM_iρ_i(Br_i_,SF)/100)ν_i]; where ν is the average number of neutrons. We will assume that all neutrons will be thermalized and about 3 neutrons are produced per fission. The total neutron production rate found is 6.56e8 neutrons/sec for 1 metric ton. However, the full mass of fuel in the core is 69 metric tons. Therefore, the source strength of the core due to spontaneous fission is 4.53e10 neutrons/sec.

At this rate we can use the formula for simultaneous production and decay to calculate the number of Cl-38 produced as a function of time.

However, knowing the source strength does not tell us the flux. To determine the flux we have to know the configuration of the fuel with respect to the seawater. This is difficult to determine given the little information that is known about the status of reactor #1. To get an estimate we will consider several hypothetical scenarios:

1) Scenario 1: The fuel has melted, and has assembled in the bottom of the inpedestal and expedestal regions of the reactor vessel (the “bulb”) as shown in Figure 1. The seawater is assumed to come into contact and cover the melting fuel as shown in Figure 2. This scenario was predicted in C. R.Hyman’s report (“Contain calculation of debris conditions adjacent to the BWR Mark I drywell shell during the later phases of a severe accident”, Nucl. Engin. and Design., 121, 1990, p 379-393.).

Figure 1: Figure showing the pressure vessel and Mark I containment and the inpedestal and expedestal regions which are the regions where it is assumed that the melted fuel would assemble (Figure adapted from C. R. Hyman, Nucl. Eng. and Des., 121, 1990, Fig 2).

The flux is calculated by assuming a simple slab geometry as is shown in Figure 2 where the neutron source is assumed to rest underneath the layer of water and half of the neutrons are expected to go on average up and half down. The flux is defined by the number of neutrons that intersect a 1 cm² area which is half the source strength divided by the area of the slab. We assume that the slab area is the sum of the inpedestal and expedestal areas (according to C. R. Hyman op cit).

Figure 2: Figure showing how the neutron flux is calculated. We assume a simple slab geometry where the seawater covers the fuel and ½ of the neutrons source travels up and half travels down. The flux intersecting the neutrons is the ratio of the area of 1 cm³ to the area of the slab which is assumed to be the sum of the inpedestal and expedestal areas (illustration of Mark-I adapted from Wikipedia).

We use the familiar equation from before and find that:

Now, the maximum number of Cl-38 nuclei are produced when T is long and is maximum at 1.71e4Cl-38 nuclei. As time increases as many Cl-38 nuclei are produced as decay and an equilibrium is established. So assuming that the seawater covers the fuel in the floor of the “bulb” it is clear that in this proposed scenario not enough neutrons are produced to account for a 1.6 MBq Cl-38 radioactivity.

2) Scenario 2: The second scenario is if the fuel partially melts but the core leaves crevices through which the seawater can flow. In this case the 1 cm³ water is assumed to be surrounded by a homogeneous neutron emitting fuel.

The flux is calculated by calculating the ratio of the 1 cm³ as compared to the complete volume of the fuel. We know that the total mass of the fuel is 69 metric tons and the density of the fuel changes considerably at high temperatures (see Figure 3).

Figure 3: Figure showing how the UO2 fuel density changes as a function of temperature (Figure taken from W.D. Drotning, Thermal Expansion of Molten Uranium Dioxide, CONF-81069601).

We assume that the density is approximately 8.86 g/cm³ at temperatures exceeding 3120 K so that the volume occupied by the fuel is 6.77e6 cm³. Therefore the fraction of the flux that is intercepted by the 1 cm³ volume is 1.48e-7. We assume that the flux through the 1 cm3 volume is also proportional to this fraction. Therefore, the flux is assumed to be = 4.53e10*1.48e-7 = 6703 n/cm².s. and the number of Cl-38 nuclei can be calculated as before:

In this scenario we find that the number of Cl-38 nuclei reaches a maximum at 7×10² which again is certainly not enough to explain the observed Cl-38 radioactivity of 1.6 MBq.So this scenariois just as implausible as scenario 1 above, making it obvious that spontaneous fission cannot account for the reported concentration of Cl-38.

To summarize: We can compare the calculated number of Cl-38 nuclei determined from the measured Cl-38 radioactivity, to the upper limit of the number of Cl-38 nuclei assuming the two scenarios and express this as a percentage. We find that the scenario where the molten fuel pours into the inpedestal and expedestal areas suggests a Cl-38 number that is 3.3e-4% of what is needed to explain the observed Cl-38 radioactivity. Also, the second scenario in whicha small 1 cm3 sample is embedded in a uniform neutron flux suggests a Cl-38 number which is even smaller at 1.3e-5%. Barring significant information that we do not possess, neither spontaneous fission and seawater option explains the observed radioactivity.

Conclusions

So we are left with the uncomfortable realization that the cause of the Cl-38 concentrations is not seawater intercepting neutrons fromnatural spontaneous fission of the used nuclear fuel. There has to be another reason.

Assuming that the TEPCO measurements are correct,this analysis seems to indicate that we cannot discount the possibility that there was another strong neutron source during the time that the workers were sending seawater into the core of reactor #1. However, without knowing the details of the configuration of the core and how the seawater came in contact with the fuel, it is difficult to be certain. Given these uncertainties it is nonetheless important for TEPCO to be aware of the possibility of transient criticalities when work is being done; otherwise workers would be in considerably greater danger than they already are when trying to working to contain the situation. A transient criticality could explain the observed 13“neutron beams” reported by Kyodo news agency (see above). This analysis is not a definitive proof, but it does mean that we cannot rule out localized criticality and TEPCO should assure that the workers take the necessary precautions.

For a discussion of the article at Nature see Jeff Brumfiel, Japan faces more than a decade of nuclear clean-up.

For further discussion of related issues see Fukushima Physicists Forum.

Ferenc Dalnoki-Veress Response to Comments (Update)

Thanks everyone for all your excellent comments. I wrote this paper because I wanted to rule out criticality in reactor #1 and with the scenarios that I invoked came to the uncomfortable conclusion that I could not. A colleague of mine (Patricia Lewis) had been wondering about the temperatures of the molten core and whether we could any longer think of the integrity of the fuel. We had investigated already the melting point of reactor grade steel, the effect of heating on volumes and the possible viscosities of the molten fuel and the reported 13 “beams” of neutrons also added into our concerns; so we were aware that transient critical masses could not be ruled out. In addition, we were concerned about the basing the entire analysis on one reported measurement of Cl-38 but that amount of Cl-38 activity would have been a red flag to any physicist and I did not have a reason at the time to dispute it. A healthy type of skepticism in all of the measurement numbers coming from Fukushima is absolutely necessary, but, I share Peter Raffaele’s statement “What can go wrong will. And if you are not paranoid you are naïve”. What is the probability that the reactor will not go critical again, if only for an instant? If your answer to that question is well it’s not zero, then you are where I am. In emergency preparedness we have to stretch our mind a bit further than we might want to. We have to imagine the impossible even if it goes against every instinct until it is ruled out absolutely.

Can We Believe the Cl-38 Number?

TEPCO has made many measurement errors, from mixing up I-131 and I-134 to adjusting the numbers for Tc-99m etc. So it is absolutely reasonable to question whether TEPCO correctly measured the Cl-38. Red_Blue is correct that the start time of seawater injection was March 12^th, not March 23^rd as I surmised. However, this does not change the analysis much because of the equilibrium that is established due to production and decay. I whole-heartedly agree with Red_Blue and many others that conclusions could be drawn when TEPCO re-samples and measures the water. Although, that would only be true if there have been further high neutron flux incidents. If these had been transient criticalities over a given period of time, the short half-life of Cl-38 would mean that resampling would not necessarily help us.

I also agree that a valid criticism of my analysis is the assumption that the seawater is pumped through the system in a continuous flow with a salt concentration identical to that of seawater. However, we can relax this assumption and take the maximum salt concentration (40 g/mL) which is a factor of 20 more salt/mL than my assumption. However, this is not large enough to account for the large Cl-38 concentration of 1.6 MBq/cm3. We are talking six orders of magnitude difference. That is quite a significant difference.

I agree with Eve that TEPCO should have also monitored the Na-24 1.368 MeV and 2.754 MeV gammas. I don’t presume to know why they didn’t or why they didn’t redo the Cl-38 measurements considering that these should have triggered an alarm. I agree with JamesLthat it would have been nice to be able to time-correlate the reported observation of the “neutron bursts” with other measurements and I would urge TEPCO to publish them. I would also recommend TEPCO to publish the time when all samples are taken as well as when they are measured so the time difference can be accounted for. However, I disagree with Red_Blue and Old Jim Hardy that there are many fission product gammas that the Cl-38 could have been confused with. The spectra for the two isotopes are very distinct: Cl-38 has two gammas a 1.64 MeV and 2.17 MeV whereas I-134 has prominent emissions at 0.847 MeV and 0.884 MeV and no significant gammas at higher energies (see INL Spectra Catalog at http://www.inl.gov/gammaray/catalogs/ge/catalog_ge.shtml) . Beta spectroscopy is a little bit more complicated but Cl-38 has a 56% probability high 4.92 Q-value whereas I-134 has a complicated scheme with the highest beta endpoint at 2.2 MeV and most betas < 1.2 MeV. However, I come back to where I started: if you are absolutely certain that the reactor won’t go critical then by all means dismiss the Cl-38 number. However, if you think the probability is non-zero then it is prudent to consider all possibilities since the consequences could be serious.

With respect to my esteemed colleague, I have to disagree with Dr. Jim Rushton of Oak Ridge National Laboratory’s assertion “Even if they [inadvertent criticalities] did occur briefly, they would not add much radioactivity or heat beyond what workers are already dealing with from the radioactive material that accumulated when the reactors were running at full power (see New Scientist at http://www.newscientist.com/article/dn20322-are-nuclear-reactions-restarting-at-fukushima.html) . ” Neutrons affect human tissue so very differently than gammas. We know from other transient (and non-explosive) criticality accidents that people have died very quickly from large neutron bursts – even recently in Japan, there have been fatal consequences of criticality accidents.

Consequences of Possible “Inadvertent Criticalities”

So now let’s assume that “inadvertent criticalities” do occur in reactor #1. What could the consequences be and how might they manifest themselves? Many of you brain-stormed on this topic and I will reserve comments and summarize what you have all said across different blogs and fora. Damfuzzy reminds us of the fact that new BWR fuel assemblies are located on the refueling floor which at least in one Fukushima reactor is exposed to the atmosphere and may have been disrupted from explosions. He suggests the possibility that the “spontaneous fires” that have been reported may be due to criticality excursions. Roger T Crouch postulates that rod-collapse could lead to loose material where vibrations, water flow and structural collapse of the assembly grid and control rod systems could result in a self-sustaining chain reaction. Many of you have worried about the possibility of starting a chain reaction that becomes super-critical rather than turning itself off due to negative feedback effects. The main explanation for not going super critical is that – if transient criticalities have taken place – they are probably due to small globules of fissile material that is expanding and moving in a viscous soup of molten metals and oxides, thus continually changing their mean free path.

What Must be Done Right Now?

The purpose of the Cl-38 calculation was to exclude the possibility that an “inadvertent criticality” can occur at the Fukushima reactor #1 which I was unable to do. Therefore, it is prudent that TEPCO takes seriously the possibility of criticality excursions and monitors the neutron flux with independent neutron detectors close to the core. A sudden increase in the neutron flux would be immediately measurable above the background due to the spontaneous fission of the different actinides in the fuel. TEPCO must continue to mix Boric acid with the fresh cooling water to ensure that no criticality excursions can occur especially in reactor #1. All efforts must be made to protect the workers when the probability for “inadvertent criticalities” are non-zero. I suggest that TEPCO takes the following actions:

– Install a neutron detector to monitor the core of Fukushima Daiichi reactor #1

– Keep mixing neutron absorbers with the cooling water for cooling reactor cores and spent nuclear fuel ponds

– Give complete gamma spectra rather than just the summaries of the results

– Include not only sampling times but also measurement times for all measurements and repeat measurements to increase confidence in the results

Let’s keep the conversation going. We owe it to all those heroic Fukushima Daiichi workers.

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2011 年 4 月 20 日付重要更新

4月20日のプレスリリースで東京電力は、3月25日発表の、第一号機原子炉冷却に使用された海水の Cl-38 放射能濃度測定値 (1.6 MBq/mL) を撤回し、「検出限界未満」とした。この当初の測定値を元に、そのような高濃度は、不慮の過渡臨界の可能性を想起せずには説明できないと私たちは判断していた。東京電力がこの測定結果を撤回し、同プレスリリースに示されるように、分析プロトコル改善に着手したのは、喜ばしいことである。しかし、なぜ、不充分な類別記述のまま(同プレスリリーにおいて、Cl-38 の読みは 1.6MBq から「検出限界未満」と変更され、変更理由は「主要ピークによる核種の同定及び放射能濃度の決定」とされる)誤りを撤回したのかについて、説明が願わしいところである。たとえば、Cl-38 の主要ガンマ線は 1.64 MeV および 2.16 MeV にある。これらがいかなる線と干渉して6桁下げることが必要とされたのだろうか。もしカウント値が Cl-38 の為でなかったのなら、いかなる同位元素が 1.6 MBq/mL に匹敵するカウント値を持っていたのか。

4月4日の原子力安全・保安院による批判以来、東京電力が取ってきた処置は歓迎されるが、私たちは更に厳しい同位元素測定プロトコルと適時の結果報告を促したい。さもなければ、東京電力の重要な測定について一般人の信頼が更に損なわれるのではないか。よって、以下の処置を東京電力が取ることを勧めたい。

1)(単一の数字だけでなく)全スペルトルデータを公表する。 2)試料採取日時を公表する。 3)試料測定の日時を、計数時間とデッドタイムを含めて公表する。 4)測定を同じ日の違う時刻に何度か測定を繰り返す。 5)関心の対象となる他の同位元素(たとえば東京電力が4月20日に撤回した Te-129 など)も、検出限界未満であっても測定していただきたい。 6)もし純粋な誤りから撤回が必要になったのなら、どういう誤りであったのか、充分な説明を加えていただきたい。 7)もし第三者の独自の分析が為されているのであれば、東京電力の測定結果判断を検証したその分析者/研究所の名前を明示していただきたい。

東京電力/原子力安全・保安院及び日本政府は前途に多大な仕事を抱えており、測定結果に基づいて重要な諸決断がなされていくことと思われる。それゆえ、分析においても結果の報告においても、厳格なプロトコルに従うことが重要である。 F. ダルノキ=ヴェレスhttp://www.japanfocus.org/-Arjun-Makhijani/3509

Important article update April 22, 2011 Japanese translation of the update is available

1) Release full spectra data (not just a number) 2) Release the time/date sample was taken

3) Release the time/date sample was measured including counting time and dead time

4) Repeat measurements at different times of the day

5) Please measure other isotopes of interest (such as Te-129, which was retracted by TEPCO on April 20th as well), even if they are below the detection limit

6) If retractions are necessary due to an honest mistake, please provide full explanation of the mistake

7) If third-party, independent analyses are done, please state the name of the analyst/lab that has cross-checked TEPCO’s interpretation of the results

福島第一原発 1 号機(タービン建屋)で見つかった高濃度放射性塩素-38 の原因は何か?[1]

F. Dalnoki-Veress with an introduction by Arjun Makhijani F. ダルノキ–べレスアージュン・マキジャーニによる紹介文付

アジア太平洋ジャーナルは、今回初めての試みをした。福島第一原発の原子炉において、高い濃度の放射性物質を含む水が漏れたことに関連する重要な事柄を議論する科学技術論文の掲載である。この論文が、汚染水の除去と作業員の安全確保という大変な課題を扱うものであり、私たちは、日本の、そして世界の科学技術学界、日本政府当局、東京電力にこの論文を提供したいという目的をもって掲載に至った。また、この論文の内容は、政府関係の書類や報道ではまだ触れられていない危険性について論じており、一般市民やメディアにとっても重要であると信ずる。まずアージュン・マキジャーニ博士の解説文によりこの論文の扱う問題を明らかにした後、F・ダルノキ―ベレス博士の論文を紹介する。

アジア太平洋ジャーナル

1Introduction by Arjun Makhijani

解説文アージュン・マキジャーニ

福島第一原発の3つのタービン建屋(訳者注:1号機から3号機のタービン建屋)の溜まり水の高放射線の原因は、原子炉の炉心が損傷を受けていることであると広く理解されている。これは炉心の損傷が進んでいることと、配管システムに漏れが生じていることをはじめとする数々の問題を示唆しており、懸念が高まるのは当然である。しかし1号機のタービン建屋の溜まり水に、塩素38という短命の放射性核種があることにはあまり関心が注がれていない。この論文は、この物質の存在が深刻な

問題、つまり、意図しない連鎖反応が1回か複数回起こっている(技術的には、「意図しない再臨界」といえる)ことの証拠になっているかどうかを検証する。このような連鎖反応は、核分裂生成物とエネルギーの急速な放出をもたらし、その両方が損傷を悪化させ、すでに非常に困難な作業環境をさらに悪化させる可能性がある。

塩素38は半減期が37分と短く、天然の塩素に4分の1ほど含まれる塩素37が中性子を吸収するときに作られる。海水が冷却に使われたために、3つの原子炉すべてに何千(何万)キロもの大量の塩がある。原子炉が本当に停止しているのなら、中性子の出所は1つしかないはずだ。それはすなわち、原子炉が稼働しているときにつくられ、炉心の中に存在し続けるいくつかの重金属(訳者注:超ウラン)の自発的な分裂のことである。一番重要なものとして、プルトニウム2つ、キュリウム2つの同位体がある。しかし、もし予想外の連鎖反応が起きているとしたら、ホウ素を混ぜた海水で原子炉を完全に停止しようとする努力は、完全には成功していないということになる。断続的な臨界が起きているとしたら、いや、1回だけ偶発的に起きたにせよ、高い放射能を持つ放射性核分裂生成物と放射化生成物が、原子炉停止後も(少なくとも1号機では)生成され続けている(もしくは生成された)ということを意味している。それはまた、人に多大な放射線被害をもたらす中性子の集中的な発生が、1度かそれ以上起きていたという意味であり、その仕組みがわかり、もう起こらないような予防策が取られない限り、さらに起こる可能性があるということである。作業員の安全を確保し、発生している可能性がある中性子とガンマ線被ばくを測定するための対策を取るべきである。

indicates that it is quite unlikely that spontaneous fission is the sole or even the main explanation for the measured concentration of chlorine-38. Presuming the reported measurements are correct, this leaves only one other explanation – one or more unintended chain reactions. This paper is presented in the spirit of encouraging discussion of whether further safety measures might be needed, and whether supplementary measures to bring the reactors under control should be

considered. It is also presented as a preliminary analysis for scientific discussion of a terrible and technically challenging nuclear crisis at the Fukushima Daiichi plant.

この論文での分析結果は、1号機の溜まり水から検出された塩素38の原因として考えられるのは自発的な核分裂だけなのかということである。それしか説明として考えられいのであれば、それほど心配することではない。しかし、この論文の分析では、計測された塩素38の濃度は、自発的な核分裂が唯一の原因であるどころか、主要な原因でさえない可能性が高いということを示唆する。報告されている計測値が正確であると仮定すると、残された可能性は一つしかないことになる。それは、1回かそれ以上の連鎖反応である。この論文は、安全策のさらなる強化が必要なのか、また、原子炉を安定させるための追加策が必要なのかという問題意識のもとで提示している。また、福島第一原発における、悲惨で、技術的にも困難な核の危機の、科学的議論の予備的分析を提供するものである。

Arjun Makhijani March 30, 2011

アージュン・マキジャーニ 2011年3月30日 (ここから本論文)

この数週間私は日本で次第に明らかになってくる事ごとに気を奪われるばかりであった。とても信じられないという思いと事態の重大性を認めざるを得ないという思いの間を行きつ戻りつしていたが、殆どは不信であった。そして私だけではない。この事故以来私が話し合った核物理学者や原子力エンジニアは殆どが、溶融している燃料の幾らかが何らかの理由で臨界に至る可能性のある小さなポケットを形成することがありうる、そんな可能性を信ずることはできないし、信じようとしない。共同通信のニュースウェブサイトに次のようなニュー

ス(関連する部分を強調のため下ではイタリック体にした)が出される迄、私が以下の分析

をし終えるまでは、この間ずっと彼らと思いを共にしてきた。FD-V(F. ダルノキ-べレス) 2011 年 3 月 30 日

“Neutron beam observed 13 times at crippled Fukushima nuke plant

「中性子ビームを損傷した福島原子力発電所で 13 回観測 TOKYO, March 23, Kyodo 東京、3 月 23 日、共同

Tokyo Electric Power Co. said Wednesday it has observed a neutron beam, a kind of radioactive ray, 13 times the Fukushima Daiichi nuclear plant after it was crippled by the massive March 11 quake-tsunami disaster.

東京電力株式会社は水曜日、3 月 11 日の地震–津波大災害で福島第一原子力発電所が損傷を受けて以降、敷地内で放射線の一種である中性子ビームを 13 回観測した、と述べた。

TEPCO, the operator of the nuclear plant, said the neutron beam measured about 1.5 kilometers southwest of the plant’s No. 1 and 2 reactors over three days from March 13 and is equivalent to 0.01 to 0.02 microsieverts per hour and that this is not a dangerous level.

この原発を操業している東京電力は、1 号機と 2 号機の西南約 1.5km のところで 3 月 13 日から 3 日間にわたって測定された中性子ビームは 0.01 から 0.02 マイクロシーベルト毎時相当であり、これは危険なレベルではない、と述べた。

The utility firm said it will measure uranium and plutonium, which could emit a neutron beam, as well.

電力会社は、中性子ビームを放射する可能性のあるウランとプルトニウムも測定するつもりであると述べた。

In the 1999 criticality accident at a nuclear fuel processing plant run by JCO Co. in Tokaimura, Ibaraki Prefecture, uranium broke apart continually in nuclear fission, causing a massive amount of neutron beams.

茨城県東海村の株式会社ジェー・シー・オーが運転する核燃料加工プラントで 1999 年に起こった臨界事故では、ウランが核分裂で連続的に分裂し、大量の中性子ビームの原因となった。

In the latest case at the Fukushima Daiichi nuclear plant, such a criticality accident has yet to happen.

今回の福島第一原子力発電所の場合、そのような臨界事故はまだ起こっていない。

But the measured neutron beam may be evidence that uranium and plutonium leaked from the plant’s nuclear reactors and spent nuclear fuels have discharged a small amount of neutron beams through nuclear fission.”

しかし、測定された中性子ビームは発電所の原子炉や使用済核燃料から漏出したウランとプルトニウムが核分裂によって少量の中性子ビームを放出した証拠かもしれない。」

==Kyodo News ==共同ニュース[訳者注:日本語の共同ニュースのサイトにはこの記事は見当たらな

い。読売の記事を参照。]

Also, on March 25th, TEPCO made public a measurement of the contributions of different isotopes to the extremely high measured radioactivity of the seawater used to cool reactor #1. The reasons why these measurements were taken so late in the crisis (or why the information was released so late) is unclear at present.

また、3 月 25 日、東京電力は、1 号機の冷却に使われた海水で測定された極めて高い放射能への種々の同位体からの寄与を測定した結果を公表した。このような危機の時に何故これほど遅れてこの測定を行ったのか(或いは何故情報開示がこんなに遅れたのか) は今のところはっきりしてない。

放射性核種

Cl-38 As-74 Y-91 I-131 Cs-134 Cs-136 Cs-137 La-140

濃度(Bq/cm3) 1.6×106 3.9×102 5.2×104 2.1×105 1.6×105 1.7×104 1.8×106 3.4×102

Table 1: The contribution of different isotopes to the radioactivity from a sample taken in the turbine building of reactor #1[2]

表1 1号機タービン建屋で採取された放射能に対する種々の同位体の寄与[2] [訳者注:表及び文中で「e6」などは「106」などを意味するが、訳文中では後者に置き換えた。]

Cl-38)? What flux could have produced the observed radioactivity? In what follows, I attempt to calculate the neutron flux that would have been able to produce the observed radioactivity. There is a bit of math, but you can skip to the conclusions. All calculations assume that the TEPCO measurements reported in Table 1 are correct.

セシウムとヨウ素、Cs-137 と I-131、の測定値は予想通り大変高かった。しかし同位体の一つ、Cl-38、の濃度の値が大変高いことが私の注意を惹いた。何故気になるのか。Cl-38 のベータ崩壊の半減期は 37 分であり、数日のうちに消滅してしまうだろう。しかし、この同位体がそこに存在したことそのこと自体、そしてそんなに高濃度で存在していたことが私を当

惑させた。中性子入射フラックスが天然の塩素中に 24%存在する Cl-37 を放射中性子捕獲 (単純な反応:中性子を取り込みガンマ線を放出すれば Cl-38 を得る)で Cl-38 に変換した、ということが起こり得るのだろうか。どのくらいのフラックスなら観測された放射能を生成できるだろうか。以下に、観測された放射能を生成することが可能である中性子フラックスの算出を試みる。数学が尐しあるが、飛ばして結論に行くことができる。すべての計算で表 1 に報じられている東電の測定値が正しいものと仮定している。

First we calculate the number of Cl-38 nuclei that are present that would explain the observed radioactivity. The half-life of Cl-38 = 37.24 min which corresponds to a decay constant of λ38 = 0.00031021 s-1. So that: dN38/dt = –λ38N38 where, dN38/dt = 1.6e6 s-1 and N38 = 5.16e9 Cl-38 nuclei. This means that the activity measured is consistent with the production of 5.16e9 Cl-38 nuclei. The next question is how much Cl-37 was present in the seawater in the first place? The mass of chlorine in seawater is 19345 mg/kg = 19.345g Cl/kg[3]. Also, the fraction of Cl-37 in natural Cl is = 24.23% (see Table 2 below).

最初に、観測された放射能を説明できる Cl-38 核の存在数を計算する。Cl-38 の半減期 =37.24min は崩壊定数 λ38 = 0.00031021 s-1 に対応する。それ故:dN38/dt = -λ38N38 ここで dN38/dt = – 1.6×106 s-1 なので N38 = 5.16×109 Cl-38 核である。これは測定された放射能強度は 5,16×109 個の核生成に相当することを意味する。次の問題は最初に海水中にどれだけの Cl-37 が存在したかである。海水中の塩素の質量は 19345 mg/kg = 19.345g Cl/kg[3].である。また、天然の Cl 中の Cl-37 の割合は=24.23%(下の表 2 を見よ)。[訳者注: 原文の dN38/dt = 1.6e6 s-1 の右辺にはマイナス記号「-」が必要である。なお、著者から許可を得たので、原文中の明白な誤りは訳文中では訂正を施した。]

同位体

Cl-35 Cl-37

モル質量

34.9688527 36.9659026

75.77 24.23

Table 2: The isotopic abundance and molar mass of chlorine 表 2 塩素の同位体存在比とモル質量

Avogadro’s number we can calculate the total number of Cl-37 nuclei/g of seawater to be N37 = 7.96e19.

Cl-37 の質量はしたがって 19.345 g Cl/kg の 25.26%(二つの同位体のモル質量の差を考慮に入れなければならない:差は極めて小さいが、Cl38 の質量割合の修正値は 25.26%になる) = 4.89g Cl-37/kg となることがわかる。アボガドロ数を用いて海水中の Cl-37 の合計数、核数/g は N37 = 7.96×1019.と算出できる。[訳者注:質量割合の修正値は厳密には 25.26%。この値、或いは四捨五入した 25.3%を用いた結果が本文の 4.89g Cl-37/kg。上記括弧内

の 25%を使うと 4.84 g Cl-37/kg となる。上記本文中の 25%は、25.26%或いは 25.3%とすべきだろう。]

We now know that N37 = 7.96e19 Cl-37 nuclei/g of seawater, and we observed that 5.16e9 of these have been converted to Cl-38. The question then becomes what flux could have produced this many Cl-38 nuclei?

こうして海水中の N37 = 7.96×1019 Cl-37 核数/g であることがわかり、そしてこれらのうち 5.16×109 が Cl-38 に変換されていることを観測した。すると問題は、これだけ多くの Cl-38 核を生成したフラックスは幾らかということになる。

We now assume Cl-38 was produced as the seawater was being circulated through the fuel. What is the flux of neutrons we need to produce the observed N38?

今度は、Cl-38 は海水が核燃料の間を循環させられていた間に生成された、と仮定する。観測された N38 を生成するにはどれだけの中性子フラックスが必要か。

Since Cl-38 is radioactive with a decay constant given by λ38 the rate of change of the number of Cl-38 nuclei is given by:

Cl-38 は λ38 で与えられる崩壊定数の放射能なので、Cl-38 の核数の変化の速度は

で与えられる。

これは一つの同位体が生成されると同時に崩壊する系列崩壊の身近な式である。この式は容易に解くことができる(例えばカプラン、核物理学、1958 年、p463 参照)。

Where, φ is the flux in n/cm2.s, and σ(γ,n) = 383.7mb is the radiative capture cross-section which would result in the production of Cl-38 at the Maxwellian distribution average temperature. Note that the thermal neutron cross-section is not very different at 432 mb so similar results would be obtained if we assumed that all the neutrons are thermalized.

ここで φ は n/cm2.s で表したフラックスであり、σ(γ,n) = 383.7mb はマクスウェル分布平均温度での Cl-38 を生成する放射捕獲断面積である。熱中性子断面積はそれほど違いは無い 432mb であることに注意すると、すべての中性子は熱中性子化されていると仮定すれば同じような結果が得られるはずである。

Now, we know that after activation we produced N38(t) = 5.16e9 Cl-38/cm3, so we let t = T, the time when activation stopped so that N38(T)=5.16e9 nuclei/cm3. We also know the value of the factor σ(γ,n)N37/λ38 = 0.098445192.

ところで、励起後 N38(t) = 5.16×109Cl-38/cm3 を生成したことがわかっているので、t = T、励起が止まった時間と置くと、N38(T) = 5.16×109Cl-38/cm3 である。我われはまた係数の値 σ(γ,n)N37/λ38 = 0.098445192 もわかっている。

So that the flux can be expressed very simply as a function of irradiation time T:

したがって、フラックスは照射時間 T の関数として大変簡単に以下のように表すことができ

る。

φ =5.2415×10 10 /{1-exp(-λ38T)}

We assume that the production of Cl-38 started with the deliberate introduction of seawater on March 23rd (according to the TEPCO press briefing[4]) into reactor #1. Therefore, since the measurement appears to have been done on March 25th it means that we have a maximum activation time of 2 days. In fact, we really have two regions of flux that are significant. The first region is where the denominator is < 1 (corresponding to activation time T0.4 days).

我われは Cl-38 の生成は 1 号機の原子炉に意図的に海水を導入した 3 月 23 日(東電の記者会見[4]に従って)に始まったと仮定する。従って、測定は 3 月 25 日に行われたようなので、最長活性化時間は 2 日間であることを意味する。実際には二つの領域でのフラックスが重要である。第一の領域は上式の分母が< 1 の領域である(活性化時間 T0.4 日に対応する)。

A lower limit in the flux is set when T is long (i.e. > 0.5 d) so that the denominator approaches unity. We call this flux (φ = 5.241e10 n/cm2.s) and it is the lower limit of the flux that could have produced the Cl-38 nuclei radioactivity observed.

フラックスが下限になるのはTが長く(すなわち >0.5d)分母が1に近づくときである。これをフラックス(φ = 5.241×1010n/cm2.s)と呼ぶと、それは Cl-38 核の観測された放射線量を生成することのできるフラックスの下限である。

What might have caused the concentration of Cl-38?

この Cl-38 濃度をもたらしたのは何か?

可能性のある説明として第一に考えるべきことは、海水が、使用されていた核燃料の自然の自発核分裂から発生した中性子を捕獲しながら炉心を循環させられていたことである。可能性のある説明として第二に考慮すべきことは、局所的な臨界である。

number of spontaneous fissions from a typical BWR with 4% enriched fuel after 45 MWdth/kg burnup (see IAEA-TECDOC-1535, pg. 74). The inventory we get for 1 metric ton fuel for the primary neutron producing isotopes are shown in Table 2.

原子炉中で照射されるにつれて核燃料はその同位体組成を変えることを思い起こそう。我われが原子炉内でのプルトニウム生成に核不拡散の観点から関心を持つ理由がここにある。我われは 4%濃縮燃料を装填した典型的な BWR の燃焼度 45 MWdth/kg (IAEA-TECDOC-1535、p74 を見よ)の燃料からの自発核分裂の数を計算することでこれを調べた。一次中性子を発生する同位体について、燃料 1 トンに対する核種の存在量を表 2 に示す。[訳者注:MWdth/kg =megawatt days thermal/kg]

同位体

Pu-238 Pu-240 Pu-242

Cm-242 Cm-244

同位体

存在量

同位体の BrSF=SF 個数同位体核/g 分岐比

半減期

= T1/2

単位:年

8.77×101 6.56×103 3.73×105

1.63×102 1.81×101

同位体の崩壊定数

=λiso 単位:s-1

2.51×10-10 3.35×10-12 5.89×10-14

1.35×10-10 1.21×10-9

中性子生成数/sec

9.35×105 3.72×106 1.65×106

1.29×106 6.49×108

Miso =# g/MTHM =ρiso (%)

2.66×102 2.57×103 6.79×102

2.02×101 5.26×101

2.53×1021 1.85×10-7 2.51×1021 5.75×10-7 2.49×1021 5,54×10-4

2.49×1021 6.37×10-6 2.47×1021 1.37×10-4

表 2 使用済核燃料中に存在する種々の中性子生成同位体の、同位体存在量、核数/g、自発核分裂に対する分岐比、半減期、及び崩壊定数。最大のフラックスが実に Pu および Cm 同位体から生じている。注:MTHM=metric ton heavy metal(重金属 1 ト

ン)で燃料の活性成分を表す。SF=spontaneous fission(自発核分裂)。同位体存在量は IAEA-TECDOC-1535、p74 から引用した値。

The neutron production rate from spontaneous fission can be calculated for each isotope by summing the contribution of spontaneous fission by each isotope.

それぞれの同位体について、自発核分裂からの中性子生成速度は各同位体の自発核分裂からの寄与を合計して算出することができる。

(dN_n)/dt=∑i=1:iso[λiMiρi(Bri,SF)/100)νi]; where ν is the average number of neutrons. We will assume that all neutrons will be thermalized and about 3 neutrons are produced per fission. The total neutron production rate found is 6.56e8 neutrons/sec for 1 metric ton. However, the full mass of fuel in the core is 69 metric tons. Therefore, the source strength of the core due to spontaneous fission is 4.53e10 neutrons/sec.

(dN_n)/dt=∑i=1:iso[λiMiρi(Bri,SF/100)νi]、ここで ν は中性子の平均数である。中性子はすべて熱中性子であり、1 核分裂あたり 3 個の中性子が生成されると仮定しよう。見出された全中性子生成速度は 1 トン当たり 6.55×108 中性子数/sec である。しかし、炉心の全質量は 69 トンである。したがって、自発核分裂による炉心の線源強度は 4.53×1010 中性子数 /sec である。[訳者注:原文文頭の式中、(Bri,SF)/100)は真ん中の閉じ括弧「)」を削除した (Bri,SF/100)が正しいと思われる。]

At this rate we can use the formula for simultaneous production and decay to calculate the number of Cl-38 produced as a function of time.

この速度で、生成される Cl-38 の数を時間の関数として算出するために、同時生成崩壊に対する公式を用いることができる。

しかし、線源強度を知ってもフラックスはわからない。フラックスを決定するには海水から見た核燃料の配置を知らなければならない。1 号機の状態について知られている情報はほとんどないことから、これを決定することは困難である。推定値を得るために幾つか仮定したシナリオを考える:

1) Scenario 1: The fuel has melted, and has assembled in the bottom of the inpedestal and expedestal regions of the reactor vessel (the “bulb”) as shown in Figure 1. The seawater is assumed to come into contact and cover the melting fuel as shown in Figure 2. This scenario was predicted in C. R.Hyman’s report (“Contain calculation of debris conditions adjacent to the BWR Mark I drywell shell during the later phases of a severe accident”, Nucl. Engin. and Design., 121, 1990, p 379-393.).

1) シナリオ 1:核燃料は溶融し、図 1 に示されるように原子炉容器(「バルブ」)の脚柱内および脚柱外領域の底に堆積した。海水は図 2 で示されるように溶融燃料と接触して覆うと仮定する。このシナリオは C. R. ハイマンの報告(「重大事故後期段階での BWR Mark I ドライウェル本体に接する残骸の含有物の計算」、Nucl. Engin. and Design.、121、 1990、p 379-393)の中で予想されたものである。

脚柱外領域

脚柱内領域

=29.9m2

図 1:圧力容器と Mark I 原子炉格納容器、および、溶融した燃料が集積すると仮定する領域である脚柱内および脚柱内領域を示す図(C. R. ハイマン、Nucl. Eng. and Des.、 121、 1990、図 2)。

The flux is calculated by assuming a simple slab geometry as is shown in Figure 2 where the neutron source is assumed to rest underneath the layer of water and half of the neutrons are expected to go on average up and half down. The flux is defined by the number of neutrons that intersect a 1 cm2 area which is half the source strength divided by the area of the slab. We assume that the slab area is the sum of the inpedestal and expedestal areas (according to C. R. Hyman op cit).

フラックスは図 2 で示される単純なスラブ状配置を仮定して計算し、中性子源は水の層より下部に収まり、平均して中性子の半数が上方に半数が下方に行くものと仮定する。フラックスは面積1cm2 を通過する中性子数と定義され、線源強度の 1/2 をスラブの面積で割ったものである。スラブ面積は脚柱内および脚柱外領域の面積の和と仮定する(C. R. ハイマン、既出、による)。

=102.2m2

φ=n/cm2.s で表したフラックス =(1/A[cm2])

×(線源強度[n/s]/2)

面 1cm 1cm2 体積

MARK-1 の見取り図

海水燃料

中性子は平均して上下同数放射すると仮定する

1cm3 cm2 で表した

面積

RPV SFP

原子炉圧力容器使用済燃料プール

DW SCSW

ドライウェル二次コンクリート遮蔽壁

ウェットウェル脚柱内領域の床上の溶融燃料脚柱外領域の床

面積=29.9 cm2 面積=102.2 cm2

Figure 2: Figure showing how the neutron flux is calculated. We assume a simple slab geometry where the seawater covers the fuel and 1⁄2 of the neutrons source travels up and half travels down. The flux intersecting the neutrons is the ratio of the area of 1 cm3 to the area of the slab which is assumed to be the

sum of the inpedestal and expedestal areas (illustration of Mark-I adapted from Wikipedia).

図2 中性子フラックスの計算法を示す図。単純な層形状で、海水が燃料を覆い放射中性子の 1/2 が上方に半分が下方に向うと仮定する。遮られる中性子のフラックスは 1 cm3 の立方体の面積の、脚柱内と脚柱外の面積の和と仮定しているスラブ面積に対する比である(Mark- I の模式図は Wikipedia から採った)。

We use the familiar equation from before and find that:

前にあげた使い慣れた式を用いると次のよういなる: N38(t) = φ [σ(γ,n)N37/λ38 ] {1-exp(-λ38t)}

N38(T) = 1.71×104{1-exp(-λ38T)} [訳者注:φ= (1/A[cm2])×(Source Strength[n/s]/2)

= (1/132.1×[(100cm)2])×(4.53×1010/2)=1.71×104n/cm2.s したがって N38(T) = 1.71×104×0.098445192{1-exp(-λ38T)}

= 1.69×103{1-exp(-λ38T)} 以下、訳文の中では 1.71×104 の代わりにこの値 1.69×103 を採用した。]

ここで、T が長い時に最大数の Cl-38 核が生成され、最大値は 1.69×103Cl-38 核となる。時間が長くなるにつれ崩壊と平衡が成立し、多くの Cl-38 核が生成する。従って、海水が「バブル」の底面にある燃料を覆うと仮定して、ここに提示したシナリオでは 1.6 MBq Cl-38 の放射能を説明するに十分な中性子は生成しないことは明らかである。

2) Scenario 2: The second scenario is if the fuel partially melts but the core leaves crevices through which the seawater can flow. In this case the 1 cm3 water is assumed to be surrounded by a homogeneous neutron emitting fuel.

2) シナリオ 2: 第 2 のシナリオは、燃料は部分的に溶融しているが炉心は隙間を残しそこを海水が流れることができる、というものである。この場合 1 cm3 の水が中性子を放出する一様な燃料に囲まれていると仮定する。

The flux is calculated by calculating the ratio of the 1 cm3 as compared to the complete volume of the fuel. We know that the total mass of the fuel is 69 metric tons and the density of the fuel changes considerably at high temperatures (see Figure 3).

フラックスは燃料の全体積に対する 1cm3 の比を計算して算出する。燃料の全質量は 69 トンであることと、燃料の密度が高温ではかなり変化する(図 3 を見よ)ことはわかっている。

密度(g/cm3)

10.0

9.5

9.0

個体

液体

ANL

UO2

融解に伴う密度変化 -8.8%

ANL 8.5 融点

3100

本研究

CHRISTENSEN

3200 3300 温度(K)

Figure 3: Figure showing how the UO2 fuel density changes as a function of temperature (Figure taken from W.D. Drotning, Thermal Expansion of Molten Uranium Dioxide, CONF-81069601).

図3 温度の関数としてのUO2燃料密度の変化を示す図(図はW.D. ドロトニング、溶融二酸化ウランの熱膨張、CONF-81069601、から引用)

We assume that the density is approximately 8.86 g/cm3 at temperatures exceeding 3120 K so that the volume occupied by the fuel is 6.77e6 cm3. Therefore the fraction of the flux that is intercepted by the 1 cm3 volume is 1.48e-7. We assume that the flux through the 1 cm3 volume is also proportional to this fraction. Therefore, the flux is assumed to be = 4.53e10*1.48e-7 = 6703 n/cm2.s. and the number of Cl-38 nuclei can be calculated as before:

密度は 3120K を越える温度ではほぼ 8.86g/cm3 であるので燃料が占める体積は 7.79× 106cm3 であると仮定する。したがって体積 1cm3 によって遮られるフラックスの割合は 1.28 ×10-7 である。我われは体積 1cm3 を通過するフラックスもこの割合に比例すると仮定する。よってフラックスは=4.53×1010×1.28×10-7=5798n/cm2s、そして Cl-38 核の数は前のように計算できる:

N38(t) = φ [σ(γ,n)N37/λ38 ] {1-exp(-λ38t)} N38(T) = 570.8{1-exp(-λ38T)}

[訳者注:燃料が占める体積は質量 69 トン÷密度 8.86g/cm3=7.7878104×106cm3=7.79× 106cm3 となる。したがって体積 1cm3 によって遮られるフラックスの割合も 1.28×10-7 である。

よってフラックスは=4.53×1010×1.28×10-7=5798 n/cm2s となる。著者は核燃料の全質量 69 トンを 60 トンと誤認して計算している。しかし、本分析の結論には全く影響しない。訳文の中では、全質量を 69 トンとした時の訳者の計算値を採用した。]

In this scenario we find that the number of Cl-38 nuclei reaches a maximum at 7×102 which again is certainly not enough to explain the observed Cl-38 radioactivity of 1.6 MBq. So this scenariois just as implausible as scenario 1 above, making it obvious that spontaneous fission cannot account for the reported concentration of Cl-38.

このシナリオでは Cl-38 核の数は最大値 6×102 に達するが、これもまた Cl-38 の放射能の観測値 1.6MBq を説明するには明らかに十分でない。したがってこのシナリオも上のシナリオ 1 と同様、ありそうになく、自発核分裂は報告されている Cl-38 の濃度を説明することはできないことがあきらかになる。

To summarize: We can compare the calculated number of Cl-38 nuclei determined from the measured Cl-38 radioactivity, to the upper limit of the number of Cl-38 nuclei assuming the two scenarios and express this as a percentage. We find that the scenario where the molten fuel pours into the inpedestal and expedestal areas suggests a Cl-38 number that is 3.3e-4% of what is needed to explain the observed Cl-38 radioactivity. Also, the second scenario in which a small 1 cm3 sample is embedded in a uniform neutron flux suggests a Cl-38 number which is even smaller at 1.3e-5%. Barring significant information that we do not possess, neither spontaneous fission and seawater option explains the observed radioactivity.

まとめると:我われは測定された Cl-38 の放射能から決められる Cl-38 核の数の計算値を、二つのシナリオを仮定した Cl-38 核数の上限値と比較してパーセンテージで表すことができる。脚柱内と脚柱外の部分に溶融燃料が流入するというシナリオは、Cl-38 の放射能の観測値を説明するに必要な Cl-38 核数の 3.3×10-5%であることを示唆する。同様に、1cm3 の小検体が一様な中性子フラックス中に入っているという第二のシナリオは、Cl-38 核数としてさらに小さい 1.1×10-5%という値を示唆する。我われが持っていない重要な情報がなければ、自発核分裂と海水、どちらの選択肢も放射能の観測値を説明するものではない。 [訳者注:原文の 3.3×10-4%、1.3×10-5%を訳文の中ではそれぞれ 3.3×10-5%、1.1× 10-5%とした。]

Conclusions

結論

So we are left with the uncomfortable realization that the cause of the Cl-38 concentrations is not seawater intercepting neutrons from natural spontaneous fission of the used nuclear fuel. There has to be another reason.

したがって我われは、Cl-38 濃度の原因は使用されていた核燃料の自然に起こる自発核分裂からの中性子線を海水が捕獲したためではない、という居心地の悪い認識を持ち続けている。他に理由がなければならない。

Assuming that the TEPCO measurements are correct, this analysis seems to indicate that we cannot discount the possibility that there was another strong neutron source during the time that the workers were sending seawater into the core of reactor #1. However, without knowing the details of the configuration of the core and how the seawater came in contact with the fuel, it is difficult to be certain. Given these uncertainties it is nonetheless important for TEPCO to be aware of the possibility of transient criticalities when work is being done; otherwise workers would be in considerably greater danger than they already are when trying to working to contain the situation. A transient criticality could explain the observed 13“neutron beams” reported by Kyodo news agency (see above). This analysis is not a definitive proof, but it does mean that we cannot rule out localized criticality and TEPCO should assure that the workers take the necessary precautions.

東電の測定が正確であると仮定すると、作業員たちが第 1 号機の炉心に海水を送り込んでいるときに別の強い中性子線源が存在した可能性を捨て去ることができない、と今回の分析は示しているように思われる。しかし、炉心の位置関係および海水が炉心とどのように接触したのか、詳細がわからなくては、確信を持つことは困難である。このような不確かさはあるにしろ、作業が行われているときに過渡的な臨界の可能性があることを東電が認識していることは重要である。そうでないと作業員が事態を抑え込むために懸命に働いている時に、これまでさらされていた危険よりもかなり大きな危険にさらされることになろう。過渡臨界は、共同通信社が報じた「中性子ビーム」が 13 回観測されたこと(上を見よ)を説明することができるかも知れない。本分析は決定的証拠ではないが、局所的臨界を除外することはできないことを意味するものであり、東電は作業員が必要な予防策をとることを保証すべきである。

Arjun Makhijani is president of the Institute for Energy and Environmental Research (www.ieer.org). He holds a Ph.D. in engineering (specialization: nuclear fusion) from the University of California at Berkeley and has produced many studies and articles on nuclear fuel cycle related issues, including weapons production, testing, and nuclear waste, over the past twenty years. He is the author of Carbon-Free and Nuclear-Free: A Roadmap for U.S. Energy Policy the first analysis of a transition to a

U.S. economy based completely on renewable energy, without any use of fossil fuels or nuclear power. He is the principal editor of Nuclear Wastelands and the principal author of Mending the Ozone Hole. He can be contacted here: arjun@ieer.org.

アージュン・マキジャーニはエネルギー環境研究所( www.iwwr.org )の所長である。カリフォルニア大学バークレー校からの工学(専攻:核融合)での Ph.D を持っており、兵器生産、試験、核廃棄物を含む核燃料サイクル関連事項で過去二十年以上にわたる多くの研究と論文がある。Nuclear Wastelands 誌の編集長であり、「Mending the Ozone Hole(オゾンホール修復)」の主要著者である。連絡先: arjun@ieer.org 。

Ferenc Dalnoki-Veress is a Research Scientist at the James Martin Center for Non-Proliferation Studies of the Monterey Institute of International Studies. He is a specialist on nuclear disarmament and on aspects of global proliferation of fissile materials. He holds a PhD in high energy physics from Carleton University, Canada, specializing in ultra-low radioactivity background detectors. He can be contacted here: ferenc.dalnoki@ miis.edu and 831- 647-4638.

フェレンク・ダルノキ–べレスはモンテレイ国際関係研究所のジェームス・マーチン非拡散研究センター研究員である。核軍縮及び核分裂性物質の世界的拡散の諸問題の専門家である。カナダ、カールトン大学からの高エネルギー物理分野での PhD を持ち、極低放射能バックグラウンド検出器を専門とする。連絡先: ferenc.dalnoki@miis.edu および、Phone 831-647-4638。

Recommended citation: Ferenc Dalnoki-Veress and Arjun Makhijani, What Caused the High Cl-38 Radioactivity in the Fukushima Daiichi Reactor #1?, The Asia-Pacific Journal Vol 9, Issue 14 No 3, April 4, 2011.

推奨する引用:Ferenc Dalnoki-Veress and Arjun Makhijani, What Caused the High Cl-38 Radioactivity in the Fukushima Daiichi Reactor #1?, The Asia-Pacific Journal Vol 9, Issue 14 No 3, April 4, 2011.

Notes

注

1 Thanks go to Dr. Patricia Lewis (CNS, MIIS) and Arjun Makhijani (IEER) for carefully reviewing this memo, and for thoughtful and stimulating discussions. Dr. Lewis may be contacted at patricia.lewis@miis.edu.

1 このメモを注意深く精査し示唆に富み刺激的な討論をしてくれたことに対してパトリシア・ルイス博士(CNS、MIIS)およびアージュン・マキジャーニ(IEER)に感謝する。ルイス博士の連絡先は patricia.lewis@miis.edu 。

2 Nuclear and Industrial Safety Agency, Ministry of Economy, Trade and Industry, News Release, March 26, 2011.

2 核及び工業安全局、経済産業省、News Release、3 月 26 日、2011 年。 3 Dr. J. Floor Anthoni, The Chemical Composition of Seawater (2000, 2006). 3 J. フローア・アントニ博士、海水の化学組成(2000 年、2006 年)。

4 Press Release (Mar 26, 2011) TEPCO News, Plant Status of Fukushima Daiichi Nuclear Power Station (as of 8:00 PM Mar 26th): “At approximately 2:30 am on March 23rd, seawater was started to be injected to the nuclear reactor through the feed water system.”

4 プレスリリース (2011 年 3 月 26 日)TEPCO ニュース、福島第一原子力発電所のプラント状況(3 月 26 日 8:00PM 現在):「3 月 23 日 2:30am 頃、原子炉に注水システムを通して海水注入を開始した。」[訳者注:第 1 号機についてである。相当することが日本語の TEPCO ニュース: http://www.tepco.co.jp/cc/press/11032601-j.html に出ている。]

Dalnoki-Veress’ article was translated by Terao Terumi, TUP (Translators United for Peace) ダルノキ-ベレス論文翻訳寺尾光身(TUP)

Arjun Makhijani’s introduction was translated by Norimatsu Satoko, an Asia-Pacific Journal coordinator アージュン・マキジャーニ解説文翻訳乗松聡子(アジア太平洋ジャーナル・コーディネーター)

What Caused the High Cl-38 Radioactivity in the Fukushima Daiichi Reactor #1?[1]

“Neutron beam observed 13 times at crippled Fukushima nuke plant

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What Caused the High Cl-38 Radioactivity in the Fukushima Daiichi Reactor #1?^[1]