Nuclear reactor physics
A reactor consists of an assembly of nuclear fuel (a reactor core), usually surrounded by a neutron moderator such as regular water, heavy water, graphite, or zirconium hydride, and fitted with mechanisms such as control rods which control the rate of the reaction.
This equation's factors are roughly in order of potential occurrence for a fission born neutron during critical operation.
is positive, then the core is supercritical and the rate of neutron production will grow exponentially until some other effect stops the growth.
At least one neutron is required to "strike" a chain reaction, and if the spontaneous fission rate is sufficiently low it may take a long time (in 235U reactors, as long as many minutes) before a chance neutron encounter starts a chain reaction even if the reactor is supercritical.
A common type of startup neutron source is a mixture of an alpha particle emitter such as 241Am (americium-241) with a lightweight isotope such as 9Be (beryllium-9).
Uranium-235 undergoes a small rate of natural spontaneous fission, so there are always some neutrons being produced even in a fully shutdown reactor.
Once the chain reaction is begun, the primary starter source may be removed from the core to prevent damage from the high neutron flux in the operating reactor core; the secondary sources usually remains in situ to provide a background reference level for control of criticality.
Even in a subcritical assembly such as a shut-down reactor core, any stray neutron that happens to be present in the core (for example from spontaneous fission of the fuel, from radioactive decay of fission products, or from a neutron source) will trigger an exponentially decaying chain reaction.
Although the chain reaction is not self-sustaining, it acts as a multiplier that increases the equilibrium number of neutrons in the core.
This process will continue and after a long enough time, the number of neutrons in the reactor will be, This series will converge because for the subcritical core,
As a measurement technique, subcritical multiplication was used during the Manhattan Project in early experiments to determine the minimum critical masses of 235U and of 239Pu.
As a power-generating technique, subcritical multiplication allows generation of nuclear power for fission where a critical assembly is undesirable for safety or other reasons.
and enable a chain reaction, natural or low enrichment uranium-fueled reactors must include a neutron moderator that interacts with newly produced fast neutrons from fission events to reduce their kinetic energy from several MeV to thermal energies of less than one eV, making them more likely to induce fission.
To be effective, moderator materials must thus contain light elements with atomic nuclei that tend to scatter neutrons on impact rather than absorb them.
In addition to hydrogen, beryllium and carbon atoms are also suited to the job of moderating or slowing down neutrons.
This has effects on how reactors are controlled: when a small amount of control rod is slid into or out of the reactor core, the power level changes at first very rapidly due to prompt subcritical multiplication and then more gradually, following the exponential growth or decay curve of the delayed critical reaction.
Furthermore, increases in reactor power can be performed at any desired rate simply by pulling out a sufficient length of control rod.
The kinetics of the reactor is described by the balance equations of neutrons and nuclei (fissile, fission products).
In practice, buildup of reactor poisons in nuclear fuel is what determines the lifetime of nuclear fuel in a reactor: long before all possible fissions have taken place, buildup of long-lived neutron absorbing fission products damps out the chain reaction.
In practice, both the difficulty of handling the highly radioactive fission products and other political concerns make fuel reprocessing a contentious subject.
The most important such element is xenon, because the isotope 135Xe, a secondary fission product with a half-life of about 9 hours, is an extremely strong neutron absorber.
In an operating reactor, each nucleus of 135Xe becomes 136Xe (which may later sustain beta decay) by neutron capture almost as soon as it is created, so that there is no buildup in the core.
Because the 135Xe absorbs neutrons strongly, starting a reactor in a high-Xe condition requires pulling the control rods out of the core much farther than normal.
135Xe played a large part in the Chernobyl accident: about eight hours after a scheduled maintenance shutdown, workers tried to bring the reactor to a zero power critical condition to test a control circuit.
Since the core was loaded with 135Xe from the previous day's power generation, it was necessary to withdraw more control rods to achieve this.
As a result, the overdriven reaction grew rapidly and uncontrollably, leading to steam explosion in the core, and violent destruction of the facility.
Nuclear reactors with heavy water or graphite moderation can operate with natural uranium, eliminating altogether the need for enrichment and preventing the fuel from being useful for nuclear weapons; the CANDU power reactors used in Canadian power plants are an example of this type.
Other candidates for future reactors include Americium but the process is even more difficult than the Uranium enrichment because the chemical properties of 235U and 238U are identical, so physical processes such as gaseous diffusion, gas centrifuge, laser, or mass spectrometry must be used for isotopic separation based on small differences in mass.
About two billion years ago, a water-saturated uranium deposit (in what is now the Oklo mine in Gabon, West Africa) underwent a naturally occurring chain reaction that was moderated by groundwater and, presumably, controlled by the negative void coefficient as the water boiled from the heat of the reaction.
Uranium from the Oklo mine is about 50% depleted compared to other locations: it is only about 0.3% to 0.7% 235U; and the ore contains traces of stable daughters of long-decayed fission products.
