Even if fast reactors are used to consume radioactive waste in due course their main function is likely to be to breed fissile material because in this way they can have a transforming effect on the world’s energy resources.

Consider a uranium-fuelled reactor in which N atoms of 235U are fissioned. While this is happening CN new fissile atoms of 239Pu can be produced. If these in turn are fissioned in the same reactor and the conversion or breeding ratio C is unchanged (this is unlikely to be quite true because the fissile material has been changed, but the effect on the argument is not important), a further C2N fissile atoms are produced. If these are fissioned, C3N are produced, and so on indefinitely. The total number of atoms fissioned is therefore N(1 + C + C2 + …). If C < 1, the series converges and its sum is N/(l — C).

Conversion ratios for 235U-fuelled thermal reactors are in the range 0.6 (for light-water reactors) to 0.8 (for heavy-water reactors and gas — cooled reactors). L is particularly large in light-water reactors because neutrons are readily absorbed by hydrogen.

If the fuel is natural uranium N cannot exceed 0.7% of the total number of uranium atoms supplied. If the reactor is a thermal reactor with a conversion ratio of 0.7 and the plutonium bred is recycled indefinitely the total number of atoms fissioned cannot exceed 0.7/(1 — 0.7) и 2.3% of the number of uranium atoms supplied.

In a real system not even this number can be fissioned. When the fuel is reprocessed to remove the fission products and the excess 238U some 235U is inevitably lost. In addition some 239Pu is lost by conversion to higher isotopes of plutonium. As a result thermal converter reactors can make use of at most about 2% of natural uranium.

For a breeder reactor, however, with C > 1, the series diverges and in principle all the fertile atoms supplied can be fissioned. In practice, however, some are lost for the reasons mentioned earlier and the limit is around 60% of the fertile feed. Thus from a given quantity of natural uranium fast breeder reactors can fission about 30 times as many atoms as thermal converters and as a result can extract about 30 times as much energy.

To determine the importance of this difference we have to know how much uranium and thorium are available. The amount depends on the price, and a 2010 estimate by the World Energy Council suggests that, worldwide, about 230000 tonnes of uranium are recoverable at a price up to $40/kg, but that if the price were to rise to $260/kg ten times as much would be accessible. The extent of reserves of thorium is much less certain but seems to be comparable with those of uranium. Thorium can be made available as an energy resource only by means of breeder reactors.

Complete fission of a tonne of uranium, were that possible, would generate about 1 TWd, or 0.09 EJ, of energy in the form of heat. (An exajoule, EJ, is 1018 joules.) Thus if all the $40/kg uranium in the world were used as fuel for thermal reactors that, with recycling, fissioned 2% of the feed, some 400 EJ thermal would be produced. If the same uranium were to be recycled to exhaustion in fast breeder reactors it would produce about 12000 EJ. But if the higher utilisation would allow the higher price of $260/kg to be paid so that the greater resource became available the production would rise to 1.2 x 105 EJ. These quantities can be compared with about 9.0 x 1011 tonnes of “proved recoverable” coal reserves that could yield some 3000 EJ, or 1.6 x 1011 tonnes of “proved recoverable” oil that could yield about 800 EJ. In 2007 some 71 EJ of electricity was generated throughout the world.

There is considerable uncertainty about the true extent of mineral reserves in the earth’s crust because new discoveries continue to be made. However, in spite of this the overall conclusion is that uranium used in thermal reactors has the potential to make a contribution to the world’s energy consumption that is comparable with, but smal­ler than, that of oil, whereas uranium used in fast breeder reactors could contribute considerably more than, possibly 40 times as much as, all the world’s fossil fuel. Thorium used in breeder reactors could probably make a similar contribution. Together they could provide the world with all the energy it needs for centuries to come. And they would do this without adding to the amount of carbon dioxide in the atmosphere.