Critical mass

Critical mass is a fundamental concept in nuclear physics. It refers to the minimum amount of fissile material required to sustain a nuclear chain reaction. Fissile materials are substances capable of undergoing nuclear fission, which is the process of splitting an atomic nucleus. When a nucleus splits, it releases energy and several neutrons. If these neutrons strike other nuclei, they can cause further fission events. This creates a self-sustaining cycle known as a chain reaction.

Understanding this threshold is essential for designing nuclear reactors and nuclear weapons.

The mechanism of criticality relies on a delicate balance of neutrons. In a subcritical mass, the reaction cannot sustain itself. This occurs because the escape probability is too high. The escape probability is the chance that neutrons will leave the material without hitting another nucleus. When neutrons are released, they can disperse into space. If a mass is subcritical, any introduced population of neutrons will decrease exponentially. However, if the mass reaches a critical state, the reaction becomes steady. In this state, the neutron population, power, and temperature do not increase or decrease. If the mass becomes supercritical, the reaction proceeds at an increasing rate.

Several physical properties determine the specific critical mass of a material. One key concept is elastic scattering. This happens when particles collide and bounce off one another while retaining their kinetic energy. This scattering changes the direction of the neutrons. By bouncing neutrons around, elastic scattering increases the chance of a collision. This reduces the escape probability and allows for a smaller critical mass. Higher density also lowers the required critical mass. When a material is compressed, the atoms are closer together. This increases the likelihood of neutron collisions.

Shape and temperature also act as major variables. A perfect sphere is the most efficient shape for a critical mass. This is because a sphere has the lowest surface-area-to-volume ratio. A lower surface area means fewer neutrons can escape through the surface. As the shape becomes less like a sphere, the material becomes less reactive. Temperature also affects the reaction through thermal expansion. As fuel gets hotter, the atoms move further apart. This increase in volume lowers the density. Because of this, hot fuel is generally less reactive than cold fuel. This is known as a negative temperature coefficient of reactivity.

Scientists can manipulate these variables using a neutron reflector. A reflector is a material that surrounds the fissile mass to bounce neutrons back inside. This increases the efficiency of the reaction and lowers the required critical mass. Common reflector materials include beryllium, graphite, and heavy metals like tungsten carbide. Beryllium is effective because it has a low neutron absorption cross-section. This means it does not soak up many neutrons. Graphite is often used because it can act as both a moderator and a reflector. Heavy metals like stainless steel are used to significantly reduce neutron escape.

In specific applications like nuclear weapons, a device may use a tamper. A tamper is a dense shell that surrounds the fissile core. It serves two main purposes. First, it uses inertia to hold the expanding fissioning material together. This increases the efficiency of the explosion. Second, it acts as a neutron reflector. In a bomb, the tamper can decrease the required critical mass by a factor of four. If the tamper is made of depleted uranium, it may even undergo fission itself due to high-energy neutrons. This can greatly increase the total energy yield of the device.

Historical experiments have demonstrated the dangers of managing these states. For example, re-creations of accidents involving the "Demon core" show how improper handling can lead to criticality. In such cases, a plutonium pit might be surrounded by tungsten carbide blocks. If a block is placed incorrectly, the mass can suddenly go supercritical. This release of energy is a direct result of the sudden increase in the neutron multiplication factor. This factor represents the average number of neutrons released per fission that go on to cause another fission event. Managing these factors remains a central challenge in nuclear engineering and research.