Nuclear fission is the process where the nucleus of a heavy atom, like Uranium-235 or Plutonium-239, is split into two or more smaller nuclei. This splitting releases a large amount of energy and produces free neutrons. For this process to be harnessed effectively, a self-sustaining chain reaction must occur. Critical mass is the minimum amount of fissile material required to maintain this continuous chain reaction.
Defining the Critical State
Critical mass is defined by whether the production rate of new neutrons equals or exceeds the rate at which neutrons are lost. This balance is quantified by the neutron multiplication factor, known as \(k\), which represents the average number of neutrons from one fission event that cause another fission event. If \(k=1\), the mass is critical, meaning the fission rate is stable and self-sustaining, which is the goal for a nuclear power reactor. If \(k<1[/latex], the mass is subcritical and the chain reaction quickly dies out; if [latex]k>1\), the mass is supercritical, causing the number of fissions to increase exponentially, leading to an instantaneous energy release.
Sustaining the Nuclear Chain Reaction
Maintaining a chain reaction requires that neutrons remain within the material long enough to strike another nucleus. The main challenge is neutron loss through leakage (escaping the surface) and non-fission absorption. Critical mass overcomes leakage by ensuring a sufficiently large volume of material, as the probability of a neutron causing new fission increases with volume relative to surface area. Because a perfect sphere offers the lowest surface-area-to-volume ratio, the critical mass value is smallest when the material is arranged in a spherical geometry.
Physical Variables That Influence Critical Mass
Material and Density
The specific mass required to achieve the critical state is highly dependent on several physical factors. The type of fissile material is the most significant; Plutonium-239 requires a much smaller critical mass than Uranium-235 (e.g., 10 kg vs. 52 kg for bare spheres). Density also plays a substantial role, as critical mass is inversely proportional to the square of the density. Compressing the material increases its density, shortening the distance a neutron must travel to strike another nucleus, thereby reducing the required mass. This compression method is central to the design of modern nuclear weapons.
Neutron Reflectors
Surrounding the fissile core with a neutron reflector, sometimes called a tamper, significantly reduces the needed critical mass. A reflector is a layer of material, such as beryllium or tungsten carbide, that scatters escaping neutrons back into the core. This external layer improves the neutron economy, meaning fewer neutrons are lost, and thus less fissile material is needed to maintain the chain reaction.
Critical Mass in Power Generation and Weaponry
Power Generation
Nuclear reactors are designed to operate precisely at the critical state (\(k=1\)), generating heat at a steady, controlled rate. Control is achieved through the use of control rods, typically made of neutron-absorbing materials like cadmium or boron. These rods are inserted into the core to absorb excess neutrons, preventing the reaction from becoming supercritical. Operators adjust the position of these rods to maintain the necessary balance between neutron production and loss for sustained power output.
Weaponry
Nuclear weapons are designed to achieve a state of high supercriticality (\(k>>1\)) as rapidly as possible to maximize the explosive energy yield. This is accomplished by storing the fissile material in a subcritical configuration and then rapidly assembling it into a supercritical mass. The gun-type assembly fires one subcritical piece of material into another to form a single supercritical mass. The more advanced implosion method uses chemical explosives to symmetrically compress a subcritical sphere, drastically increasing its density and instantaneously forcing it into a highly supercritical state.