Understanding Radiation: Scientific Basis of Nuclear Explosions - Critical Mass for a Fission Chain
Although two to three neutrons are produced in the fission reaction for every nucleus that undergoes fission, not all of these neutrons are available for causing further fissions. Some of the fission neutrons are lost by escape, whereas others are lost in various nonfission reactions.
In order to sustain a fission chain reaction, with continuous release of energy, at least one fission neutron must be available to cause further fission for each neutron previously absorbed in fission. If the conditions arc such that the neutrons are lost at a faster rate than they are formed by fission, the chain reaction would not be self-sustaining.
Some energy would be produced, but the amount would not be large enough, and the rate of liberation would not be sufficiently fast, to cause an effective explosion. It is necessary, therefore, in order to achieve a nuclear explosion, to establish conditions under which the loss of neutrons is minimized. in this connection, it is especially important to consider the neutrons which escape from the substance undergoing fission.
The escape of neutrons occurs at the exterior of the uranium (or plutonium) material. The rate of loss by escape will thus be determined by the surface area. On the other hand, the fission process, which results in the formation of more neutrons, takes place throughout the whole of the material and its rate is, therefore, dependent upon the mass.
By increasing the mass of the fissionable material, at constant density, the ratio of the surface area to the mass is decreased; consequently, the loss of neutrons by escape relative to their formation by fission is decreased. The same result can also be achieved by having a constant mass but compressing it to a smaller volume (higher density), so that the surface area is decreased.
The situation may be understood by reference to Fig. 1.48 showing two spherical masses, one larger than the other, of fissionable material of the same density. Fission is initiated by a neutron represented by a dot within a small circle.
It is supposed that in each act of fission three neutrons are emitted; in other words, one neutron is captured and three are expelled. The removal of a neutron from the system is indicated by the head of an arrow. Thus, an arrowhead within the sphere means that fission has occurred and extra neutrons are produced, whereas an arrowhead outside the sphere implies the loss of a neutron. It is evident from Fig. 1.48 that a much greater fraction of the neutrons is lost from the smaller than from the larger mass.
Figure 1.48. Effect of increased mass of fissionable material in reducing the proportion of neutrons lost by escape.
If the quantity of a fissionable isotope of uranium (or plutonium) is such that the ratio of the surface area to the mass is large, the proportion of neutrons lost by escape will be so great that the propagation of a nuclear fission chain, and hence the production of an explosion, will not be possible. Such a quantity of material is said to be “subcritical.”
But as the mass of the piece of uranium (or plutonium) is increased (or the volume is decreased by compression) and the relative loss of neutrons is thereby decreased, a point is reached at which the chain reaction can become self-sustaining. This is referred to as the “critical mass” of the fissionable material under the existing conditions.
For a nuclear explosion to take place, the weapon must thus contain a sufficient amount of a fissionable uranium (or plutonium) isotope for the critical mass to be exceeded. Actually, the critical mass depends, among other things, on the shape of the material, its composition and density (or compression), and the presence of impurities which can remove neutrons in nonfission reactions.
By surrounding the fissionable material with a suitable neutron “reflector,” the loss of neutrons by escape can be reduced, and the critical mass can thus be decreased. Moreover, elements of high density, which make good reflectors for neutrons of high energy, provide inertia, thereby delaying expansion of the exploding material. The action of the reflector is then like the familiar tamping in blasting operations. As a consequence of its neutron reflecting and inertial properties, the “tamper” permits the fissionable material in a nuclear weapon to be used more efficiently.