Criticality describes the point where a system containing fissile material, like uranium or plutonium, can sustain a nuclear chain reaction. This state is achieved when each fission event releases enough neutrons to cause, on average, one more fission. This balance between neutron production and loss is fundamental to operating nuclear reactors for power generation and is a central consideration in safety protocols to prevent unintended reactions.
The Nuclear Chain Reaction
Nuclear fission begins when the nucleus of a fissile atom like uranium-235 absorbs a neutron, making it unstable. The nucleus splits into two smaller atoms, known as fission fragments, releasing significant energy and two to three additional neutrons. These neutrons can then strike other fissile nuclei, causing them to split and release even more neutrons. This sustained cascade is a nuclear chain reaction.
The state of a chain reaction is defined by the effective neutron multiplication factor, or k-effective (k). This factor is the ratio of neutrons in one generation to the number in the preceding one. The value of k determines if the reaction is dying out, stable, or accelerating.
The reaction has three possible states based on the value of k. A subcritical state (k<1) occurs when fewer than one neutron from each fission causes another, causing the reaction to stop. A critical state (k=1) is achieved when exactly one neutron from each fission induces another, creating a stable, self-sustaining reaction. A supercritical state (k>1) results when more than one neutron causes another fission, leading to an exponentially increasing rate of energy release.
Factors Influencing Criticality
Several physical factors determine if a collection of fissile material will achieve criticality. These variables dictate the probability that neutrons will cause further fission instead of being absorbed or escaping the system.
- Mass: A minimum amount of material, known as the critical mass, is required to sustain a chain reaction. Below this mass, too many neutrons escape from the surface for the system to remain critical. For example, a bare sphere of 95% pure plutonium-239 has a critical mass of 9.8 kilograms.
- Geometry: A sphere is the most efficient shape for achieving criticality because it has the lowest possible surface-area-to-volume ratio. This geometry minimizes the number of neutrons that can leak from the surface relative to the volume of fissile material.
- Density: Compressing fissile material brings the atomic nuclei closer together. This increases the probability that a traveling neutron will strike a nucleus and cause a fission event, making criticality more likely.
- Neutron Speed: Neutrons released during fission are very fast, but slower-moving (thermal) neutrons are much more likely to be captured by a fissile nucleus like uranium-235. For this reason, materials called moderators, such as water or graphite, are used to slow down the fast neutrons through collisions, increasing the efficiency of the chain reaction.
- Neutron Reflector: By surrounding the fissile material with a material that scatters neutrons without absorbing them, such as beryllium, neutrons that would otherwise escape can be bounced back into the core. This reflection increases the number of neutrons available to cause fission, effectively reducing the critical mass required.
Achieving and Controlling Criticality
Nuclear power reactors are engineered to maintain a critical state, where the k-effective factor equals one. This allows for a continuous release of heat, which is used to generate electricity. During startup, a reactor is briefly made supercritical to increase its power level before being stabilized at criticality for normal operation.
The primary mechanism for managing this reaction is the use of control rods. These rods are made from materials that are strong neutron absorbers, such as boron or cadmium. When inserted into the reactor core, they absorb neutrons that would otherwise contribute to the chain reaction, reducing the reactor’s power level or shutting it down.
To increase power, operators slowly withdraw the control rods from the core. This reduces neutron absorption, allowing more fissions to occur and the power level to grow. The precise positioning of these rods allows operators to tune the chain reaction and ensure a constant power output.
Consequences of Uncontrolled Criticality
An uncontrolled nuclear chain reaction, known as a criticality accident or an excursion, occurs when a system with fissile material unintentionally becomes supercritical. Instead of the steady energy release in a reactor, an accident results in a sudden burst of neutron and gamma radiation, which is hazardous to anyone in the immediate vicinity.
The heat generated by the excursion can cause the materials to expand or change state, which can sometimes alter the system’s geometry enough to stop the reaction. In other scenarios, the reaction can oscillate as these changes temporarily make the system subcritical before it returns to a critical state. These accidents often result from procedural violations or unforeseen conditions in handling fissile materials.
A criticality accident should be distinguished from the detonation of a nuclear weapon. A weapon is designed to achieve a rapid and massive supercritical state, often by using explosives to compress a subcritical mass. This creates an explosive release of energy. A criticality accident, while dangerous, does not create the conditions for a nuclear explosion because the necessary design features do not arise by chance.