# Will Japan exist until 2084

Will Japan exist until 2084

This article is provoked by the famous publication by Andrew Amalrik, "Will the Soviet Union Survive Until 1984?" [1], by the book by Sakyo Komatsu Japan Sinks (日本沈没, "Nihon Chinbotsu") [2] and the events of explosions of the nuclear reactors causing the Chernobyl disaster and the Fukushima disaster.

Very simple, primitive model is considered below.

## Model

Assume, that in some Country, there exist $$N$$ nuclear reactors. Assume, they are safe enough, and each of then is expected to explode with small probability of order of $$q$$ per year. Then one may expect of order of $$qN$$ explosions per year; and this quantity is also expected to be small. Each of presidents of each nuclear company may expect that no serious accident will not happen during his presidentship.

Now, consider the damage at the explosions. Assume, the only serious explosions are counted; explosions that destroy the system of cooling in such a way, that the relaxation heat blows up the most of the nuclear fuel into the atmosphere, as it took place at the Chernobyl disaster. Similar scenario was expected for the Fukushima disaster, and, according to the publications, the only heroic efforts of the suicide workers and good luck allowed to avoid this; so, the blowing of the nuclear fuel into the atmosphere should be considered as a typical case. Assume, at such a blowing up, the $$k$$th part of the territory of the Country becomes unusable for habitation and agriculture, although, perhaps, still can be used for the storage of the nuclear waste. The decay times of such contaminants as Uranium-235, Uranium-233 and Plutonium count thousands years; so, the reduction of the radioactivity due to the decay has no need to be taken into account for the analysis at the scale of centuries.

The rate of contamination of the Country can be estimated as $$qN/k$$ per year. After time $$T=k/(qN)$$, the most of territory of the Country becomes the nuclear waste storage; the citizen have to concentrate at the rest (that is not yet contaminated) or emigrate to other countries (or other planets, if the other countries follow the similar policy with respect to the use of the nuclear energy).

The question is to estimate the time scale $$T$$ for each of countries.

## Japan

By year 2007, Japan had 54 of the world's 442 nuclear reactors and plans to build even more. [3]. During a half-century, only three of them (at Fukushima Daichi) had serious explosions; this gives an estimate $$q=3/(50 \mathrm{year})=0.06/\mathrm{year}$$. Within few tens of years, Japan may have of order of hundred reactors, that gives order of magnitude of $$N=100$$.

The estimate of the area of contamination is pretty subjective: one may arguably consider the addition of 0.1 microSv/hour to the natural background as serious contamination, or to allow 1microSv/hour. Perhaps, even in the last case, the population living at such a territory still keeps the ability to the self-reproduction. The detailed analysis should consider the statistics of earthquakes and tsunamis, the resistance of the nuclear reactors and so on. For the rough estimate, assume, that k=100, id set, at the serious eruption of a single reactor, 1/100 part of the territory converts to the storage for the nuclear waste and unusable for the habitation.

For the estimates above, the lifetime of Japan can be estimated as follows: $$T=k/(qN)\approx 100/(0.06 \times 100) ~\mathrm{year}=100/6~ \mathrm{year}\approx 16~ \mathrm{year}$$

This is pretty pessimistic estimate; one may indicate, that the realistic probability of the serious disaster is an order of magnitude smaller; and the resulting estimate will give the lifetime of Japan of order of a century.

The claims for the future reduction of the estimate of the probability of a serious disaster seem to be non supported; at least, for the reactors that are completely dependent on the pumps of the cooling system.

## Ways of survival

The conventional ground based nuclear reactors are dangerous. They are completely dependent on the forced cooling systems. Even at the shut-down of the chain reaction, the decay heat greatly exceeds the energy of vaporization of the nuclear fuel, together with the reactor and the containment vessel.

The laureate of the Nobel Prix Andrew Sakharov had indicated that the only deep underground placement of the reactor may provide the required level of security. At the failure of the cooling systems, the active zone should be asthmatically filled with water, providing the passive convection and preventing the vaporization of the nuclear fuel into the atmosphere. The filling of the active zone with water should be default, so unavoidable, as a big aircraft heavier than air unavoidably reaches the ground at the failure of the engine.

Unfortunately, the current (economically efficient) design of the commercial nuclear plants have opposite default, at the failure of the cooling system, the reactor tends to become a nuclear chimney; and the only heroic efforts may in some cases prevent its total blowing into the atmosphere.

The problem is aggravated with the customs of delivery of information; the people gets the contamination map with delay of months, when the harvest and the cattle are already contaminated and almost unusable. At the in-time information, one could cover at least some part of land with a plastic film with drain of the radioactive rain water and snow. This would greatly reduce the contamination of the soil.

The survival of the Country could be provided by the law, that orders the operators of the ground-based nuclear plant to arrange the protecting roofs for all the agricultural fields, say, within a hundred kilometer zone around the plant. Id est, to provide the automatically enfolding roofs for thousands of square kilometers around each ground-based nuclear plant. This is very expense, and such expenses should make the safe reactors economically - computable.

## Ignorance

The estimates above could be adjusted and improved, but they should not be ignored in the way the Soviet government ignored the estimate by Andrei Amalrik. Amalrik missed only for 8 years in his estimate; he had estimated and indicated the correct order of magnitude of the lifetime of the Soviet Union. However, the Soviet veterans ruling the USSR were too stupid, corrupted and selfish; they did not even consider the Amalrik's warning.

I would not like Japan to repeat the errors of the USSR.

## Conclusions

The lifetime of a small industrial country with nuclear reactors as main source of power is estimated to be of order of a century. This life can be extended by the special law, that forces the operators of the ground-based reactors to provide the anti‚Äìcontamination devices to all the people in vicinity, and, in particular, the covering of all the fields around with the automatically-unfolding roofs. This should be done before the nuclear disaster, because in the case of the disaster, the funds of the company are not sufficient for this.

The operators of the nuclear plants should have choice: either they provide the Geiger counters and the automatic roofs for each farm and agricultural field in vicinity, or they use only reactors that cannot become an "nuclear chimney" even at the failure of the cooling systems. Perhaps, the electric companies will choose the last option.

The law mentioned above seem to be essential condition for the survival of the Country.

## References

1. http://www.vehi.net/politika/amalrik.html Андрей Амальрик. ПРОСУЩЕСТВУЕТ ЛИ СОВЕТСКИЙ СОЮЗ ДО 1984 ГОДА? Апрель-май-июнь 1969.
2. http://en.wikipedia.org/wiki/Japan_Sinks
3. http://search.japantimes.co.jp/cgi-bin/nn20110716f1.html ERIC JOHNSTON. Key players got nuclear ball rolling. Saturday, July 16, 2011. In 1960, the Japan Atomic Industrial Forum, consisting mostly of companies in the nuclear power business, was ordered by the Science and Technology Agency to prepare a cost estimate. They concluded that in the worst-case scenario, the government could face ¥3.7 trillion in liability claims. At the time, the national budget was about ¥1.7 trillion. .. by 2007, Japan had 54 of the world's 442 nuclear reactors and plans to build even more. (For information: one trillion means some number between 1012 and 1018; so the estimates are pretty qualitative and fussy.)