Neutron Balance in Reactors

The chain reaction in a nuclear reactor can be sustained and fuel conversion can be obtained under the conditions that, for each fission,

  a little over one neutron is available to initiate a new fission.

  a little over one neutron is available to change a fertile nucleus into a fissile nucleus so as to replace the fissile nuclei consumed.

If, moreover, additional neutrons are available, they can allow breeding, or the transmutation of radioactive waste. We will call these neutrons the available neutrons. Their number depends on the fuel cycle, the neutron spectrum, the number of neutron lost in the reactor.

Available Neutrons

The number of neutrons needed to produce the fission of a fissile nucleus is larger than one because the fissionless capture cross section, $\sigma_{{\textrm{c}}}^{}$, is never equal to zero. The number of neutrons needed per fission can be written ($\sigma_{{\textrm{f}}}^{}$ + $\sigma_{{\textrm{c}}}^{}$)/$\sigma_{{\textrm{f}}}^{}$ or (1 + $\sigma_{{\textrm{c}}}^{}$/$\sigma_{{\textrm{f}}}^{}$). Thus, there are, per fission, $\alpha$ = $\sigma_{{\textrm{c}}}^{}$/$\sigma_{{\textrm{f}}}^{}$ fissile nuclei that do not directly yield a fission so that a fission is obtained not with 1 but with (1 + $\alpha$) fissile nuclei per fission: in order to ensure conversion, the number of fertile nuclei that are changed to fissile nuclei has to be, for each fission, (1 + $\alpha$).

As a consequence, the number of neutrons needed per fission, if conversion is to be ensured, is equal to 2(1 + $\alpha$).

In addition, neutron losses occur, either through capture in the reactor structures or the moderator, or because they escape from the core. Such losses depend on the reactor geometry and the materials used, they must be as small as possible, they are one of the factors that determine the number of available neutrons. They can be kept as low as 0.1 neutrons per fission, but with difficulty.

Finally, the number of neutrons released by a fission, $\nu$, depends on the nucleus that fissions, therefore on the fuel cycle chosen.

The number of available neutrons is equal to

N_d = $\nu$ - 2(1 + $\alpha$) - losses

The values of N _d for various systems are shown below.

Figure 1 : Number of available neutrons for the U-Pu et Th-U fuel cycles, with fast and thermal neutrons.

With the U-Pu cycle, the number of available neutrons is large for fast neutrons and very small for thermal neutrons - conversion would be very difficult with thermal neutrons, it can be obtained only with fast neutrons in the U-Pu cycle.

With the Th-U cycle, the number of available neutrons is the same for fast and for thermal neutrons, it is not very large. Computer simulations show that, still, a Thorium based reactor can operate as a converter and even as a breeder. Both of these solutions are worth exploring.

Last Update: 4 April 2002