While the size of critical reactors may be arbitrary, the presence of a localized primary neutron source constrains the size and total power of hybrid reac­tors. In this chapter we shall examine this issue, first using a simple, intuitive spherical reactor model, and then taking the example of the optimization of the size of a possible demonstration set-up.

10.1 The homogeneous spherical reactor

Because the neutron source is localized in character, one expects the size of hybrid reactors to be limited. Optimization of the reactor has to be done with respect to several key quantities:

1. The value of the source multiplication factor ks, which relates the beam power to the total power of the reactor, and thus to the energy gain. The possibility of innovative designs, in this respect, is discussed in section 6.4.

2. The value of the effective multiplication factor keff which determines the safety of the reactor. Because of the general positive correlation between keff and ks, the highest values of keff, compatible with safety, are sought. In section 3.6 we have seen that for fast systems a limit of keff = 0.98 seems reasonable.

3. A specific power maximum value is set by the heat removal system. Prac­tically, maximum specific powers of the order of 500 W/cm3 are possible with standard liquid metal cooling.

4. It is important to minimize the fuel volume, and at the same time to minimize the range of specific powers within the system.

In order to give the reader a feeling for the size of hybrid reactors we study a simple spherical reactor model. The reactor is made of three concentric zones:

• The central zone (1), where the spallation reaction takes place and where we neglect neutron absorptions. This spherical zone has radius R1.

• The fuel zone (2) between radius R1 and radius R2.

• A reflector zone (3) between R2 and infinity.

Our treatment is based on the solution of the one-group diffusion equa­tion, which appears to be a reasonable approximation for fast reactors.