Critical mass
In nuclear engineering, critical mass is the minimum mass of the fissile material needed for a sustained nuclear chain reaction in a particular setup. The critical mass of a fissionable material depends upon its nuclear properties, density, shape, enrichment, purity, temperature, and surroundings. It is an important parameter of a nuclear reactor core or nuclear weapon. The concept is important in nuclear weapon design.
Critical size is the minimum size of the fissile material needed for a sustained nuclear chain reaction in a particular setup. If the size of the reactor core is less than a certain minimum, too many fission neutrons escape through its surface and the chain reaction is not sustained. A perfect sphere, which has the lowest surface-area-to-volume ratio, gives the minimal critical size.
Criticality
When a nuclear chain reaction in a mass of fissile material is self-sustaining but not growing, the mass is said to be in a critical state, in which there is no increase or decrease in power, temperature, or neutron population.A numerical measure of a critical mass depends on the effective neutron multiplication factor, the average number of neutrons released per fission event that go on to cause another fission event rather than being absorbed or leaving the material.
A subcritical mass is a mass that does not have the ability to sustain a fission chain reaction. A population of neutrons introduced to a subcritical assembly will exponentially decrease. In this case, known as,.
A critical mass is a mass of fissile material that self-sustains a fission chain reaction. In this case, known as,. A steady rate of spontaneous fission causes a proportionally steady level of neutron activity.
A supercritical mass is a mass which, once fission has started, will proceed at an increasing rate. In this case, known as,. The constant of proportionality increases as increases. The material may settle into equilibrium at an elevated temperature/power level or destroy itself.
Due to spontaneous fission a supercritical mass will undergo a chain reaction. For example, a spherical critical mass of pure uranium-235 with a mass of about would experience around 15 spontaneous fission events per second. The probability that one such event will cause a chain reaction depends on how much the mass exceeds the critical mass. Fission can also be initiated by neutrons produced by cosmic rays.
It is possible for a fuel assembly to be critical at near zero power. If the perfect quantity of fuel were added to a slightly subcritical mass to create an "exactly critical mass", fission would be self-sustaining for only one neutron generation.
Physical properties
Escape probability
During a nuclear episode, isolated neutrons are produced because of the division of particles. As those neutrons break away from their nucleus, they have free rein to disperse throughout space. The probability that a subatomic particle and a target nucleus will not collide in an environment that contains those released neutrons is known as the escape probability. Active neutrons are less likely to escape without interfering with other subatomic particles in environments with a higher critical mass. This is because more room stimulates greater particle movement and, therefore, more collisions.Elastic scattering
Elastic scattering explains that when particles collide with other particles, they respond entirely elastically and bounce off while retaining the same kinetic energy as before the collision. The duration and length of a neutron’s path are exponentially larger due to elastic scattering; this is because the rebounding of the particle is in a different direction.Elastic scattering directly relates to escape probability because the bouncing of the particles drastically drops the probability of escaping the mass without collision. In an atomic environment with a large critical mass, there are inherently more opportunities for neutron collision as the retention of energy allows for continuous scattering.
Additionally, materials that have a high elasticity potential and therefore higher elastic scattering allow the use of less fissile material because a reduced critical mass is required. This conservation of fissile material is essential to the future of nuclear science because the cheaper and more convenient it is to retain criticality, the more investment into developing nuclear innovation there will be.
Factors
The mass where criticality occurs may be changed by modifying certain attributes such as fuel, shape, temperature, density and the installation of a neutron-reflective substance. These attributes have complex interactions and interdependencies. The factors listed are for the simplest/ideal cases.Shape
A mass may be exactly critical without being a perfect homogeneous sphere. More closely refining the shape toward a perfect sphere will make the mass supercritical. Conversely changing the shape to a less perfect sphere will decrease its reactivity and make it subcritical.Temperature
A mass may be exactly critical at a particular temperature. Fission and absorption cross-sections increase as the relative neutron velocity decreases. As fuel temperature increases, neutrons of a given energy appear faster and thus fission/absorption is less likely. This is not unrelated to Doppler broadening of the 238U resonances but is common to all fuels/absorbers/configurations. Neglecting the very important resonances, the total neutron cross-section of every material exhibits an inverse relationship with relative neutron velocity. Hot fuel is always less reactive than cold fuel. Thermal expansion associated with temperature increase also contributes a negative coefficient of reactivity since fuel atoms are moving farther apart. A mass that is exactly critical at room temperature would be sub-critical in an environment anywhere above room temperature due to thermal expansion alone.If the perfect quantity of fuel were added to a slightly subcritical mass, to create a barely supercritical mass, the temperature of the assembly would increase to an initial maximum and then decrease back to the ambient temperature after a period of time, because fuel consumed during fission brings the assembly back to subcriticality once again.
Density
The higher the density, the lower the critical mass. The density of a material at a constant temperature can be changed by varying the pressure or tension or by changing crystal structure. An ideal mass will become subcritical if allowed to expand or conversely the same mass will become supercritical if compressed. Changing the temperature may also change the density; however, the effect on critical mass is then complicated by temperature effects and by whether the material expands or contracts with increased temperature. Assuming the material expands with temperature, at an exactly critical state, it will become subcritical if warmed to lower density or become supercritical if cooled to higher density. Such a material is said to have a negative temperature coefficient of reactivity to indicate that its reactivity decreases when its temperature increases. Using such a material as fuel means fission decreases as the fuel temperature increases.Quantum chromodynamics
Quantum chromodynamics is the theory that explains the formation of atomic nuclei through the analysis of subatomic and atomic particle interactions. Similar to critical mass, quantum chromodynamics theory has a critical point that defines both the minimum temperature and potential necessary for the transition of the first-order phase to take place.Dynamic chiral symmetry breaking
Dynamic chiral symmetry breaking is the spontaneous formation of a mass through the accumulation of fermions, which are a category of subatomic particles. Its theory describes critical mass as the minimum quark mass required to separate subatomic particles. When a division of particles takes place, it leaves gaps in the fermion mass that allow for increased particle movement. As particles move, they stimulate energy gain, which ultimately increases the chances of jump-starting a nuclear reaction.Presence of a neutron reflector
Surrounding a spherical critical mass with a neutron reflector further reduces the mass needed for criticality. By using a neutron reflector to increase the likelihood of a fission event, it simultaneously increases the fuel efficiency of the entire reaction. As fuel becomes more efficient, the reaction requires a lower critical mass.Common reflector materials include beryllium, graphite, and heavy metals like tungsten carbide, with the choice of material depending on the specific reactor design and the type of neutrons being managed. When looking at the specific materials commonly used, beryllium has been identified as an effective material due to its low neutron absorption cross-section. Graphite is used because of its diverse abilities, such as being a moderator and a reflector. Heavy metals such as tungsten carbide and stainless steel are common as they reduce the amount of neutrons that escape during the reaction by a considerable amount. By reflecting neutrons, reflectors can make a subcritical mass of fissile material critical; they can also increase the rate of fission in an already critical mass.
Neutron reflectors are commonly applied in various nuclear technologies, including nuclear reactors, nuclear weapons, and even neutron supermirrors. Nuclear reactors commonly rely on neutron reflectors due to their ability to exponentially speed up and increase the likelihood of fission and fusion reactions occurring. Nuclear weapons have historically utilized neutron reflectors to increase the rate of reaching the critical mass in the use of the weapons. Lastly, neutron reflectors are vital to nuclear physics research regarding the reflection of neutron beams, otherwise known as nuclear supermirrors.