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121-455: An operational license for the MAPLE I reactor was granted in 1999, and the reactor went critical for the first time in early 2000. MAPLE II followed in the fall of 2003. Problems with the reactors during the testing period, most notably an unexpected positive power co-efficient of reactivity , led to the cancellation of the project in 2008 and the shutdown of both reactors. With the completion of

242-504: A p e {\displaystyle P_{escape}} is the probability that it will "escape" by leaving the core altogether. n a v g {\displaystyle n_{avg}} is the number of neutrons produced, on average, by a fission event—it is between 2 and 3 for both U and Pu (e.g., for thermal neutrons in U, n a v g {\displaystyle n_{avg}} = 2.4355 ± 0.0023 ). If α {\displaystyle \alpha }

363-401: A neutron poison or active neutron-absorber, decreases in fission rate are limited in speed, because even if the reactor is taken deeply subcritical to stop prompt fission neutron production, delayed neutrons are produced after ordinary beta decay of fission products already in place, and this decay-production of neutrons cannot be changed. The rate of change of reactor power is determined by

484-427: A neutron reflector surrounding the fissile material. Once the mass of fuel is prompt supercritical, the power increases exponentially. However, the exponential power increase cannot continue for long since k decreases when the amount of fission material that is left decreases (i.e. it is consumed by fissions). Also, the geometry and density are expected to change during detonation since the remaining fission material

605-612: A racquets court below the bleachers of Stagg Field at the University of Chicago . Fermi's experiments at the University of Chicago were part of Arthur H. Compton 's Metallurgical Laboratory of the Manhattan Project ; the lab was renamed Argonne National Laboratory and tasked with conducting research in harnessing fission for nuclear energy. In 1956, Paul Kuroda of the University of Arkansas postulated that

726-764: A bomb. Originally planned to complete construction in 1999 and 2000, both reactors were instead completed in May 2000. An operational license was granted in August 1999 for the MAPLE I reactor, and extended to include the MAPLE II reactor in June 2000. Commissioning testing was begun immediately, with the MAPLE I achieving its first sustained reaction in February 2000, and MAPLE II following in October 2003. However, during testing, it

847-420: A chain reaction, and if the spontaneous fission rate is sufficiently low it may take a long time (in U reactors, as long as many minutes) before a chance neutron encounter starts a chain reaction even if the reactor is supercritical. Most nuclear reactors include a "starter" neutron source that ensures there are always a few free neutrons in the reactor core, so that a chain reaction will begin immediately when

968-498: A controlled rate of fission in a nuclear reactor for the production of energy. Most nuclear reactors use a chain reaction to induce a controlled rate of nuclear fission in fissile material, releasing both energy and free neutrons . 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

1089-433: A critical assembly is undesirable for safety or other reasons. A subcritical assembly together with a neutron source can serve as a steady source of heat to generate power from fission. Including the effect of an external neutron source ("external" to the fission process, not physically external to the core), one can write a modified evolution equation: where R e x t {\displaystyle R_{ext}}

1210-412: A factor of (1 + 0.01) , or about 1.1: a 10% increase. This is a controllable rate of change. Most nuclear reactors are hence operated in a prompt subcritical , delayed critical condition: the prompt neutrons alone are not sufficient to sustain a chain reaction, but the delayed neutrons make up the small difference required to keep the reaction going. This has effects on how reactors are controlled: when

1331-427: A fissile atom undergoes nuclear fission, it breaks into two or more fission fragments. Also, several free neutrons, gamma rays , and neutrinos are emitted, and a large amount of energy is released. The sum of the rest masses of the fission fragments and ejected neutrons is less than the sum of the rest masses of the original atom and incident neutron (of course the fission fragments are not at rest). The mass difference

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1452-405: A fission born neutron during critical operation. As already mentioned before, k = (Neutrons produced in one generation)/(Neutrons produced in the previous generation). In other words, when the reactor is critical, k = 1; when the reactor is subcritical, k < 1; and when the reactor is supercritical, k > 1. Reactivity is an expression of the departure from criticality. δk = (k − 1)/k. When

1573-603: A larger share of uranium on Earth in the geological past because of the different half-lives of the isotopes U and U , the former decaying almost an order of magnitude faster than the latter. Kuroda's prediction was verified with the discovery of evidence of natural self-sustaining nuclear chain reactions in the past at Oklo in Gabon in September 1972. To sustain a nuclear fission chain reaction at present isotope ratios in natural uranium on Earth would require

1694-429: A mass of fissile fuel that is prompt supercritical. For a given mass of fissile material the value of k can be increased by increasing the density. Since the probability per distance travelled for a neutron to collide with a nucleus is proportional to the material density, increasing the density of a fissile material can increase k . This concept is utilized in the implosion method for nuclear weapons. In these devices,

1815-471: A natural fission reactor may have once existed. Since nuclear chain reactions may only require natural materials (such as water and uranium, if the uranium has sufficient amounts of U ), it was possible to have these chain reactions occur in the distant past when uranium-235 concentrations were higher than today, and where there was the right combination of materials within the Earth's crust . Uranium-235 made up

1936-517: A new facility would be needed to continue the production of medical isotopes. In the late 1980s, AECL began to acknowledge that continued isotope production would require the construction of a new reactor to replace capacity lost by the planned closing of the NRX in 1992, and the planned closing of the NRU early in the new millennium. Design work on a replacement, originally under the name "Maple-X10", began in

2057-403: A nuclear chain reaction proceeds: When describing kinetics and dynamics of nuclear reactors, and also in the practice of reactor operation, the concept of reactivity is used, which characterizes the deflection of reactor from the critical state: ρ =  ⁠ k eff  − 1 / k eff ⁠ . InHour (from inverse of an hour , sometimes abbreviated ih or inhr) is a unit of reactivity of

2178-412: A nuclear reactor with a neutron moderator . A nuclear weapon primary stage using uranium uses HEU enriched to ~90% U, though the secondary stage often uses lower enrichments. Nuclear reactors with water moderator require at least some enrichment of U. Nuclear reactors with heavy water or graphite moderation can operate with natural uranium, eliminating altogether the need for enrichment and preventing

2299-474: A nuclear reactor. In a nuclear reactor, k eff will actually oscillate from slightly less than 1 to slightly more than 1, due primarily to thermal effects (as more power is produced, the fuel rods warm and thus expand, lowering their capture ratio, and thus driving k eff lower). This leaves the average value of k eff at exactly 1 during a constant power run. Both delayed neutrons and the transient fission product " burnable poisons " play an important role in

2420-401: A preliminary chain reaction that destroys the fissile material before it is ready to produce a large explosion, which is known as predetonation . To keep the probability of predetonation low, the duration of the non-optimal assembly period is minimized, and fissile and other materials are used that have low spontaneous fission rates. In fact, the combination of materials has to be such that it

2541-504: A result of neutron capture , uranium-239 is produced, which undergoes two beta decays to become plutonium-239. Plutonium once occurred as a primordial element in Earth's crust, but only trace amounts remain so it is predominantly synthetic. Another proposed fuel for nuclear reactors, which however plays no commercial role as of 2021, is uranium-233 , which is "bred" by neutron capture and subsequent beta decays from natural thorium , which

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2662-411: A slow enough time scale to permit intervention by additional effects (e.g., mechanical control rods or thermal expansion). Consequently, all nuclear power reactors (even fast-neutron reactors ) rely on delayed neutrons for their criticality. An operating nuclear power reactor fluctuates between being slightly subcritical and slightly delayed-supercritical, but must always remain below prompt-critical. It

2783-432: 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. However, without addition of

2904-482: A typical core is on the order of a millisecond , so if the exponential factor α {\displaystyle \alpha } is as small as 0.01, then in one second the reactor power will vary by a factor of (1 + 0.01) , or more than ten thousand . Nuclear weapons are engineered to maximize the power growth rate, with lifetimes well under a millisecond and exponential factors close to 2; but such rapid variation would render it practically impossible to control

3025-429: A way to generate fission power without the risks associated with a critical mass. If k {\displaystyle k} is the neutron multiplication factor of a subcritical core and S 0 {\displaystyle S_{0}} is the number of neutrons coming per generation in the reactor from an external source, then at the instant when the neutron source is switched on, number of neutrons in

3146-463: Is xenon , because the isotope Xe , 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 Xe becomes Xe (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. However, when a reactor shuts down, the level of Xe builds up in the core for about 9 hours before beginning to decay. The result

3267-400: Is a function of the incident neutron speed. Also, note that these equations exclude energy from neutrinos since these subatomic particles are extremely non-reactive and therefore rarely deposit their energy in the system. The prompt neutron lifetime , l {\displaystyle l} , is the average time between the emission of a neutron and either its absorption or escape from

3388-426: Is accounted for in the release of energy according to the equation E=Δmc : Due to the extremely large value of the speed of light , c , a small decrease in mass is associated with a tremendous release of active energy (for example, the kinetic energy of the fission fragments). This energy (in the form of radiation and heat) carries the missing mass when it leaves the reaction system (total mass, like total energy,

3509-553: Is almost 100% composed of the isotope thorium-232 . This is called the thorium fuel cycle . The fissile isotope uranium-235 in its natural concentration is unfit for the vast majority of nuclear reactors. In order to be prepared for use as fuel in energy production, it must be enriched. The enrichment process does not apply to plutonium. Reactor-grade plutonium is created as a byproduct of neutron interaction between two different isotopes of uranium. The first step to enriching uranium begins by converting uranium oxide (created through

3630-535: Is always conserved ). While typical chemical reactions release energies on the order of a few eVs (e.g. the binding energy of the electron to hydrogen is 13.6 eV), nuclear fission reactions typically release energies on the order of hundreds of millions of eVs. Two typical fission reactions are shown below with average values of energy released and number of neutrons ejected: Note that these equations are for fissions caused by slow-moving (thermal) neutrons. The average energy released and number of neutrons ejected

3751-585: Is because U has a larger cross section for slow neutrons, and also because U is much less likely to absorb a thermal neutron than a freshly produced neutron from fission. Neutron moderators are thus materials that slow down neutrons. Neutrons are most effectively slowed by colliding with the nucleus of a light atom, hydrogen being the lightest of all. 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

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3872-712: Is considered "subcritical" and exhibits decreasing power. The " Six-factor formula " is the neutron life-cycle balance equation, which includes six separate factors, the product of which is equal to the ratio of the number of neutrons in any generation to that of the previous one; this parameter is called the effective multiplication factor k, also denoted by K eff , where k = Є L f ρ L th f η, where Є = "fast-fission factor", L f = "fast non-leakage factor", ρ = " resonance escape probability ", L th = "thermal non-leakage factor", f = "thermal fuel utilization factor", and η = "reproduction factor". This equation's factors are roughly in order of potential occurrence for

3993-470: Is destroyed rapidly—this has the same effect as very rapidly removing a great length of control rod from the core, and can cause the reaction to grow too rapidly or even become prompt critical . Xe 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

4114-454: Is exactly zero, then the reactor is critical and its output does not vary in time ( d N / d t = 0 {\displaystyle dN/dt=0} , from above). Nuclear reactors are engineered to reduce P e s c a p e {\displaystyle P_{escape}} and P a b s o r b {\displaystyle P_{absorb}} . Small, compact structures reduce

4235-402: Is impossible for a nuclear power plant to undergo a nuclear chain reaction that results in an explosion of power comparable with a nuclear weapon, but even low-powered explosions from uncontrolled chain reactions (that would be considered "fizzles" in a bomb) may still cause considerable damage and meltdown in a reactor . For example, the Chernobyl disaster involved a runaway chain reaction, but

4356-427: Is known as delayed supercriticality (or delayed criticality ). It is in this region that all nuclear power reactors operate. The region of supercriticality for k > 1/(1 − β) is known as prompt supercriticality (or prompt criticality ), which is the region in which nuclear weapons operate. The change in k needed to go from critical to prompt critical is defined as a dollar . Nuclear fission weapons require

4477-525: Is made necessary by the nature of medical isotopes; many have short half-lives , and must be used within a few days of production. With treatments being constantly carried out around the globe, an uninterruptible supply was essential. There had been some local opposition to the use of highly enriched uranium ( HEU ) in the reactor, as well as from activists in the United States who fear that the uranium could be stolen by terrorists and used to fabricate

4598-471: Is positive, then the core is supercritical and the rate of neutron production will grow exponentially until some other effect stops the growth. If α {\displaystyle \alpha } is negative, then the core is "subcritical" and the number of free neutrons in the core will shrink exponentially until it reaches an equilibrium at zero (or the background level from spontaneous fission). If α {\displaystyle \alpha }

4719-513: Is separating the uranium hexafluoride from the depleted U-235 left over. This is typically done with centrifuges that spin fast enough to allow for the 1% mass difference in uranium isotopes to separate themselves. A laser is then used to enrich the hexafluoride compound. The final step involves reconverting the enriched compound back into uranium oxide, leaving the final product: enriched uranium oxide. This form of UO 2 can now be used in fission reactors inside power plants to produce energy. When

4840-449: Is that, about 6–8 hours after a reactor is shut down, it can become physically impossible to restart the chain reaction until the Xe has had a chance to decay over the next several hours. This temporary state, which may last several days and prevent restart, is called the iodine pit or xenon-poisoning. It is one reason why nuclear power reactors are usually operated at an even power level around

4961-433: Is the fact that spent uranium nuclear fuel contains significant quantities of Pu, a prime ingredient in nuclear weapons (see breeder reactor ). Short-lived reactor poisons in fission products strongly affect how nuclear reactors can operate. Unstable fission product nuclei transmute into many different elements ( secondary fission products ) as they undergo a decay chain to a stable isotope. The most important such element

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5082-424: Is the fissile isotope of uranium and it makes up approximately 0.7% of all naturally occurring uranium . Because of the small amount of U that exists, it is considered a non-renewable energy source despite being found in rock formations around the world. Uranium-235 cannot be used as fuel in its base form for energy production; it must undergo a process known as refinement to produce the compound UO 2 . The UO 2

5203-416: Is the main technical hurdle to production of nuclear fuel and simple nuclear weapons, enrichment technology is politically sensitive. Modern deposits of uranium contain only up to ~0.7% U (and ~99.3% U), which is not enough to sustain a chain reaction moderated by ordinary water. But U has a much shorter half-life (700 million years) than U (4.5 billion years), so in the distant past the percentage of U

5324-479: Is the probability that a particular neutron will strike a fuel nucleus, P f i s s i o n {\displaystyle P_{fission}} is the probability that the neutron, having struck the fuel, will cause that nucleus to undergo fission, P a b s o r b {\displaystyle P_{absorb}} is the probability that it will be absorbed by something other than fuel, and P e s c

5445-464: Is the rate at which the external source injects neutrons into the core in neutrons/Δt. In equilibrium , the core is not changing and dN/dt is zero, so the equilibrium number of neutrons is given by: If the core is subcritical, then α {\displaystyle \alpha } is negative so there is an equilibrium with a positive number of neutrons. If the core is close to criticality, then α {\displaystyle \alpha }

5566-431: Is the rate of change of the neutron count in the core. This type of differential equation describes exponential growth or exponential decay , depending on the sign of the constant α {\displaystyle \alpha } , which is just the expected number of neutrons after one average neutron lifetime has elapsed: Here, P i m p a c t {\displaystyle P_{impact}}

5687-413: Is then pressed and formed into ceramic pellets, which can subsequently be placed into fuel rods. This is when UO 2 can be used for nuclear power production. The second most common isotope used in nuclear fission is plutonium-239 , because it is able to become fissile with slow neutron interaction. This isotope is formed inside nuclear reactors by exposing U to the neutrons released during fission. As

5808-412: Is torn apart from the explosion. Detonation of a nuclear weapon involves bringing fissile material into its optimal supercritical state very rapidly (about one microsecond , or one-millionth of a second). During part of this process, the assembly is supercritical, but not yet in an optimal state for a chain reaction. Free neutrons, in particular from spontaneous fissions , can cause the device to undergo

5929-423: Is unlikely that there is even a single spontaneous fission during the period of supercritical assembly. In particular, the gun method cannot be used with plutonium. Chain reactions naturally give rise to reaction rates that grow (or shrink) exponentially , whereas a nuclear power reactor needs to be able to hold the reaction rate reasonably constant. To maintain this control, the chain reaction criticality must have

6050-520: Is very small and thus the final number of neutrons can be made arbitrarily large. To improve P f i s s i o n {\displaystyle P_{fission}} 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. This

6171-441: The P f i s s i o n {\displaystyle P_{fission}} term in the evolution equation, and more moderation reduces the effectiveness by increasing the P e s c a p e {\displaystyle P_{escape}} term. Most moderators become less effective with increasing temperature, so under-moderated reactors are stable against changes in temperature in

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6292-554: The NRX reactor in 1947, AECL 's Chalk River Laboratories possessed the world's most powerful research reactor. While the large neutron fluxes available in the reactor led to advances in such fields as condensed matter physics and neutron spectroscopy, many experiments were carried out involving the production of new isotopes . The field of nuclear medicine developed when it was realized that some of these artificially created isotopes could be used to diagnose and treat many diseases, especially cancers. Pioneering medical work done in

6413-494: The four factor formula , which is the same as described above with P F N L {\displaystyle P_{\mathrm {FNL} }} and P T N L {\displaystyle P_{\mathrm {TNL} }} both equal to 1. Not all neutrons are emitted as a direct product of fission; some are instead due to the radioactive decay of some of the fission fragments. The neutrons that occur directly from fission are called "prompt neutrons", and

6534-528: The reactor core ; the effective prompt neutron lifetime (referred to as the adjoint weighted over space, energy, and angle) refers to a neutron with average importance. The mean generation time , λ, is the average time from a neutron emission to a capture that results in fission. The mean generation time is different from the prompt neutron lifetime because the mean generation time only includes neutron absorptions that lead to fission reactions (not other absorption reactions). The two times are related by

6655-448: The United States require a negative void coefficient of reactivity (this means that if coolant is removed from the reactor core, the nuclear reaction will tend to shut down, not increase). This eliminates the possibility of the type of accident that occurred at Chernobyl (which was caused by a positive void coefficient). However, nuclear reactors are still capable of causing smaller chemical explosions even after complete shutdown, such as

6776-432: The atmosphere from this process. However, such explosions do not happen during a chain reaction, but rather as a result of energy from radioactive beta decay, after the fission chain reaction has been stopped. Nuclear reactor physics#Moderators and reactor design Nuclear reactor physics is the field of physics that studies and deals with the applied study and engineering applications of chain reaction to induce

6897-406: The chain reaction becomes self-sustaining. Note that while a neutron source is provided in the reactor, this is not essential to start the chain reaction, its main purpose is to give a shutdown neutron population which is detectable by instruments and so make the approach to critical more observable. The reactor will go critical at the same control rod position whether a source is loaded or not. Once

7018-441: 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

7139-422: The chain reaction, reducing α {\displaystyle \alpha } . P a b s o r b {\displaystyle P_{absorb}} is also controlled by the recent history of the reactor core itself ( see below ). The mere fact that an assembly is supercritical does not guarantee that it contains any free neutrons at all. At least one neutron is required to "strike"

7260-417: The chain reaction. This is the reason that nuclear reprocessing is a useful activity: spent nuclear fuel contains about 96% of the original fissionable material present in newly manufactured nuclear fuel. Chemical separation of the fission products restores the nuclear fuel so that it can be used again. Nuclear reprocessing is useful economically because chemical separation is much simpler to accomplish than

7381-401: The clock. Xe buildup in a reactor core makes it extremely dangerous to operate the reactor a few hours after it has been shut down. Because the Xe absorbs neutrons strongly, starting a reactor in a high-Xe condition requires pulling the control rods out of the core much farther than normal. However, if the reactor does achieve criticality, then the neutron flux in the core becomes high and Xe

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7502-530: The commissioning and start-up of the reactors". In this statement, AECL indicated that they would move to further extend the licence of the operating NRU reactor to continue the production of medical isotopes. The statement left unclear what long-term direction AECL would take for its medical isotope production business. Nuclear chain reaction In nuclear physics , a nuclear chain reaction occurs when one single nuclear reaction causes an average of one or more subsequent nuclear reactions, thus leading to

7623-421: The core is made critical. A common type of startup neutron source is a mixture of an alpha particle emitter such as Am ( americium-241 ) with a lightweight isotope such as Be ( beryllium-9 ). The primary sources described above have to be used with fresh reactor cores. For operational reactors, secondary sources are used; most often a combination of antimony with beryllium . Antimony becomes activated in

7744-417: The core was loaded with Xe 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. While many fissionable isotopes exist in nature, one useful fissile isotope found in viable quantities is U . About 0.7% of

7865-415: The core will be S 0 {\displaystyle S_{0}} . After 1 generation, this neutrons will produce k × S 0 {\displaystyle k\times S_{0}} neutrons in the reactor and reactor will have a totality of k × S 0 + S 0 {\displaystyle k\times S_{0}+S_{0}} neutrons considering

7986-486: The cost of the entire unit used to perform the first cobalt-60 treatment was about $ 50,000. By way of contrast, it would cost $ 50,000,000 just to produce enough radium (which had been previously used as a therapy source) to perform the same procedure. With this promising start, AECL came to be a major world supplier of medical isotopes, using both the NRX reactor, and the NRU reactor, which came on-line in 1957. However, as these reactors began to age, it became clear that

8107-418: The critical size and geometry ( critical mass ) necessary in order to obtain an explosive chain reaction. The fuel for energy purposes, such as in a nuclear fission reactor, is very different, usually consisting of a low-enriched oxide material (e.g. uranium dioxide , UO 2 ). There are two primary isotopes used for fission reactions inside of nuclear reactors. The first and most common is uranium-235 . This

8228-425: The difficult isotope separation required to prepare nuclear fuel from natural uranium ore, so that in principle chemical separation yields more generated energy for less effort than mining, purifying, and isotopically separating new uranium ore. In practice, both the difficulty of handling the highly radioactive fission products and other political concerns make fuel reprocessing a contentious subject. One such concern

8349-414: The fact that much greater amounts of energy were produced by the reaction than the proton supplied. Ernest Rutherford commented in the article that inefficiencies in the process precluded use of it for power generation. However, the neutron had been discovered by James Chadwick in 1932, shortly before, as the product of a nuclear reaction . Szilárd, who had been trained as an engineer and physicist, put

8470-484: The fast fission factor ε {\displaystyle \varepsilon } , the resonance escape probability p {\displaystyle p} , the probability of thermal non-leakage P T N L {\displaystyle P_{\mathrm {TNL} }} , the thermal utilization factor f {\displaystyle f} , and the neutron reproduction factor η {\displaystyle \eta } (also called

8591-481: The fission products (almost always negative beta decay ), is followed by immediate neutron emission from the excited daughter product, with an average life time of the beta decay (and thus the neutron emission) of about 15 seconds. These so-called delayed neutrons increase the effective average lifetime of neutrons in the core, to nearly 0.1 seconds, so that a core with α {\displaystyle \alpha } of 0.01 would increase in one second by only

8712-753: The fission reaction was not yet discovered, or even suspected. Instead, Szilárd proposed using mixtures of lighter known isotopes which produced neutrons in copious amounts. He filed a patent for his idea of a simple nuclear reactor the following year. In 1936, Szilárd attempted to create a chain reaction using beryllium and indium but was unsuccessful. Nuclear fission was discovered by Otto Hahn and Fritz Strassmann in December 1938 and explained theoretically in January 1939 by Lise Meitner and her nephew Otto Robert Frisch . In their second publication on nuclear fission in February 1939, Hahn and Strassmann used

8833-424: The following formula: In this formula k eff is the effective neutron multiplication factor, described below. The six factor formula effective neutron multiplication factor, k eff , is the average number of neutrons from one fission that cause another fission. The remaining neutrons either are absorbed in non-fission reactions or leave the system without being absorbed. The value of k eff determines how

8954-677: 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 U and U 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. Because enrichment

9075-401: 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 subcritical multiplication effect can be used in two ways: as a probe of how close a core is to criticality, and as

9196-487: The impacting neutron. Water or heavy water have the advantage of being transparent liquids , so that, in addition to shielding and moderating a reactor core, they permit direct viewing of the core in operation and can also serve as a working fluid for heat transfer. Carbon in the form of graphite has been widely used as a moderator. It was used in Chicago Pile-1 , the world's first man-made critical assembly, and

9317-498: The job of moderating or slowing down neutrons. Hydrogen moderators include water (H 2 O), heavy water ( D 2 O), and zirconium hydride (ZrH 2 ), all of which work because a hydrogen nucleus has nearly the same mass as a free neutron: neutron-H 2 O or neutron-ZrH 2 impacts excite rotational modes of the molecules (spinning them around). Deuterium nuclei (in heavy water) absorb kinetic energy less well than do light hydrogen nuclei, but they are much less likely to absorb

9438-532: The late 1940s and early 1950s established cobalt-60 as a useful isotope, as the relatively high-energy gamma rays produced when it undergoes beta decay are able to penetrate the skin of the patient, and deliver a greater portion of the dose directly to the tumor. The high neutron efficiency of the NRX's heavy water -moderated design, coupled with the high neutron flux of the reactor, made it relatively inexpensive for AECL to produce medical-grade cobalt-60. For example,

9559-463: The late 1980s. As part of a restructuring taking place around the same time, the medical isotopes side of AECL was reorganized as Nordion in 1988. Work on the X10 project essentially ended at this point. Nordion company was purchased by MDS in 1991, and an agreement was reached between AECL and MDS Nordion that a new facility dedicated to the production of medical isotopes would be needed. A formal agreement

9680-408: The neutron efficiency factor). The six-factor formula is traditionally written as follows: k e f f = P F N L ε p P T N L f η {\displaystyle k_{eff}=P_{\mathrm {FNL} }\varepsilon pP_{\mathrm {TNL} }f\eta } Where: In an infinite medium, the multiplication factor may be described by

9801-402: The newly entered neutrons in the reactor. Similarly after 2 generation, number of neutrons produced in the reactor will be k × ( k × S 0 + S 0 ) + S 0 {\displaystyle k\times (k\times S_{0}+S_{0})+S_{0}} and so on. This process will continue and after a long enough time, the number of neutrons in

9922-446: The nuclear chain reaction begins after increasing the density of the fissile material with a conventional explosive. In a gun-type fission weapon , two subcritical masses of fuel are rapidly brought together. The value of k for a combination of two masses is always greater than that of its components. The magnitude of the difference depends on distance, as well as the physical orientation. The value of k can also be increased by using

10043-402: The nuclear physics of the fuel, and is often expressed as a cross section . Reactors are usually controlled by adjusting P a b s o r b {\displaystyle P_{absorb}} . Control rods made of a strongly neutron-absorbent material such as cadmium or boron can be inserted into the core: any neutron that happens to impact the control rod is lost from

10164-471: The number of free neutrons in a reactor core and τ {\displaystyle \tau } for the average lifetime of each neutron (before it either escapes from the core or is absorbed by a nucleus), then the reactor will follow the differential equation ( evolution equation ). where α {\displaystyle \alpha } is a constant of proportionality, and d N / d t {\displaystyle dN/dt}

10285-584: The ones that are a result of radioactive decay of fission fragments are called "delayed neutrons". The fraction of neutrons that are delayed is called β, and this fraction is typically less than 1% of all the neutrons in the chain reaction. The delayed neutrons allow a nuclear reactor to respond several orders of magnitude more slowly than just prompt neutrons would alone. Without delayed neutrons, changes in reaction rates in nuclear reactors would occur at speeds that are too fast for humans to control. The region of supercriticality between k = 1 and k = 1/(1 − β)

10406-459: The periphery of the core. Fission reactions and subsequent neutron escape happen very quickly; this is important for nuclear weapons , where the objective is to make a nuclear pit release as much energy as possible before it physically explodes . Most neutrons emitted by fission events are prompt : they are emitted effectively instantaneously. Once emitted, the average neutron lifetime ( τ {\displaystyle \tau } ) in

10527-482: The possibility of a self-propagating series or "positive feedback loop" of these reactions. The specific nuclear reaction may be the fission of heavy isotopes (e.g., uranium-235 , U). A nuclear chain reaction releases several million times more energy per reaction than any chemical reaction . Chemical chain reactions were first proposed by German chemist Max Bodenstein in 1913, and were reasonably well understood before nuclear chain reactions were proposed. It

10648-478: The possibility of a fuel meltdown . Over-moderated reactors are unstable against changes in temperature (there is a "positive temperature coefficient" in the reactivity of the core), and so are less inherently safe than under-moderated cores. Some reactors use a combination of moderator materials. For example, TRIGA type research reactors use ZrH 2 moderator mixed with the U fuel, an H 2 O-filled core, and C (graphite) moderator and reflector blocks around

10769-399: The presence of a neutron moderator like heavy water or high purity carbon (e.g. graphite) in the absence of neutron poisons , which is even more unlikely to arise by natural geological processes than the conditions at Oklo some two billion years ago. Fission chain reactions occur because of interactions between neutrons and fissile isotopes (such as U). The chain reaction requires both

10890-418: The probability of direct escape by minimizing the surface area of the core, and some materials (such as graphite ) can reflect some neutrons back into the core, further reducing P e s c a p e {\displaystyle P_{escape}} . The probability of fission, P f i s s i o n {\displaystyle P_{fission}} , depends on

11011-461: The rate of the reaction. The physics of nuclear fission has several quirks that affect the design and behavior of nuclear reactors. This article presents a general overview of the physics of nuclear reactors and their behavior. In a nuclear reactor, the neutron population at any instant is a function of the rate of neutron production (due to fission processes) and the rate of neutron losses (due to non-fission absorption mechanisms and leakage from

11132-429: The reaction rates in a nuclear reactor. Fortunately, the effective neutron lifetime is much longer than the average lifetime of a single neutron in the core. About 0.65% of the neutrons produced by U fission, and about 0.20% of the neutrons produced by Pu fission, are not produced immediately, but rather are emitted from an excited nucleus after a further decay step. In this step, further radioactive decay of some of

11253-500: The reaction; boron or cadmium control rods are the best example. Many reactor poisons are produced by the fission process itself, and buildup of neutron-absorbing fission products affects both the fuel economics and the controllability of nuclear reactors. 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

11374-430: The reactor and produces high-energy gamma photons , which produce photoneutrons from beryllium. Uranium-235 undergoes a small rate of natural spontaneous fission, so there are always some neutrons being produced even in a fully shutdown reactor. When the control rods are withdrawn and criticality is approached the number increases because the absorption of neutrons is being progressively reduced, until at criticality

11495-407: The reactor core: if the core overheats, then the quality of the moderator is reduced and the reaction tends to slow down (there is a "negative temperature coefficient" in the reactivity of the core). Water is an extreme case: in extreme heat, it can boil, producing effective voids in the reactor core without destroying the physical structure of the core; this tends to shut down the reaction and reduce

11616-415: The reactor in a settlement. The MAPLE facility was granted an extension on its operating license on 25 October 2007, which would permit operations until 31 October 2011. This (final) submission envisioned that the MAPLE I reactor would be operational in late 2008. On 16 May 2008, AECL released a statement announcing that the MAPLE program had been terminated, as it had become "no longer feasible to complete

11737-418: The reactor is critical, δk = 0. When the reactor is subcritical, δk < 0. When the reactor is supercritical, δk > 0. Reactivity is also represented by the lowercase Greek letter rho ( ρ ). Reactivity is commonly expressed in decimals or percentages or pcm (per cent mille) of Δk/k. When reactivity ρ is expressed in units of delayed neutron fraction β, the unit is called the dollar . If we write 'N' for

11858-597: The reactor period T {\displaystyle T} , which is related to the reactivity ρ {\displaystyle \rho } through the Inhour equation . The kinetics of the reactor is described by the balance equations of neutrons and nuclei (fissile, fission products). Any nuclide that strongly absorbs neutrons is called a reactor poison , because it tends to shut down (poison) an ongoing fission chain reaction. Some reactor poisons are deliberately inserted into fission reactor cores to control

11979-439: The reactor will be, This series will converge because for the subcritical core, 0 < k < 1 {\displaystyle 0<k<1} . So the number of neutrons in the reactor will be simply, The fraction 1 1 − k {\displaystyle {\frac {1}{1-k}}} is called subcritical multiplication factor (α). As a measurement technique, subcritical multiplication

12100-451: The reactors was markedly slowed. During the subsequent eight-year-long delay in the start of commercial production, the project significantly overran its budgeted cost. The original budget was $ 140 million, but by 2005 it had already cost $ 300 million. Disputes over responsibility for the overruns between AECL and MDS Nordion added a further layer of complexity to the process. After considerable negotiation, AECL assumed full responsibility for

12221-426: The release of neutrons from fissile isotopes undergoing nuclear fission and the subsequent absorption of some of these neutrons in fissile isotopes. When an atom undergoes nuclear fission, a few neutrons (the exact number depends on uncontrollable and unmeasurable factors; the expected number depends on several factors, usually between 2.5 and 3.0) are ejected from the reaction. These free neutrons will then interact with

12342-458: The result was a low-powered steam explosion from the relatively small release of heat, as compared with a bomb. However, the reactor complex was destroyed by the heat, as well as by ordinary burning of the graphite exposed to air. Such steam explosions would be typical of the very diffuse assembly of materials in a nuclear reactor, even under the worst conditions. In addition, other steps can be taken for safety. For example, power plants licensed in

12463-418: The same analysis. This discovery prompted the letter from Szilárd and signed by Albert Einstein to President Franklin D. Roosevelt , warning of the possibility that Nazi Germany might be attempting to build an atomic bomb. On December 2, 1942, a team led by Fermi (and including Szilárd) produced the first artificial self-sustaining nuclear chain reaction with the Chicago Pile-1 experimental reactor in

12584-601: The surrounding medium, and if more fissile fuel is present, some may be absorbed and cause more fissions. Thus, the cycle repeats to produce a reaction that is self-sustaining. Nuclear power plants operate by precisely controlling the rate at which nuclear reactions occur. Nuclear weapons, on the other hand, are specifically engineered to produce a reaction that is so fast and intense it cannot be controlled after it has started. When properly designed, this uncontrolled reaction will lead to an explosive energy release. Nuclear weapons employ high quality, highly enriched fuel exceeding

12705-402: The system). When a reactor's neutron population remains steady from one generation to the next (creating as many new neutrons as are lost), the fission chain reaction is self-sustaining and the reactor's condition is referred to as "critical". When the reactor's neutron production exceeds losses, characterized by increasing power level, it is considered "supercritical", and when losses dominate, it

12826-421: The system. The neutrons that occur directly from fission are called prompt neutrons, and the ones that are a result of radioactive decay of fission fragments are called delayed neutrons. The term lifetime is used because the emission of a neutron is often considered its birth , and its subsequent absorption or escape from the core is considered its death . For "thermal" (slow-neutron) fission reactors,

12947-477: The term uranspaltung ( uranium fission) for the first time and predicted the existence and liberation of additional neutrons during the fission process, opening up the possibility of a nuclear chain reaction. A few months later, Frédéric Joliot-Curie , H. Von Halban and L. Kowarski in Paris searched for, and discovered, neutron multiplication in uranium, proving that a nuclear chain reaction by this mechanism

13068-499: The timing of these oscillations. The effective neutron multiplication factor k e f f {\displaystyle k_{eff}} can be described using the product of six probability factors that describe a nuclear system. These factors, traditionally arranged chronologically with regards to the life of a neutron in a thermal reactor , include the probability of fast non-leakage P F N L {\displaystyle P_{\mathrm {FNL} }} ,

13189-421: The two nuclear experimental results together in his mind and realized that if a nuclear reaction produced neutrons, which then caused further similar nuclear reactions, the process might be a self-perpetuating nuclear chain reaction, spontaneously producing new isotopes and power without the need for protons or an accelerator. Szilárd, however, did not propose fission as the mechanism for his chain reaction since

13310-421: The typical prompt neutron lifetime is on the order of 10 seconds, and for fast fission reactors, the prompt neutron lifetime is on the order of 10 seconds. These extremely short lifetimes mean that in 1 second, 10,000 to 10,000,000 neutron lifetimes can pass. The average (also referred to as the adjoint unweighted ) prompt neutron lifetime takes into account all prompt neutrons regardless of their importance in

13431-462: The uranium in most ores is the 235 isotope, and about 99.3% is the non-fissile 238 isotope. For most uses as a nuclear fuel, uranium must be enriched - purified so that it contains a higher percentage of U. Because U absorbs fast neutrons, the critical mass needed to sustain a chain reaction increases as the U content increases, reaching infinity at 94% U (6% U). Concentrations lower than 6% U cannot go fast critical, though they are usable in

13552-403: The uranium milling process) into a gaseous form. This gas is known as uranium hexafluoride , which is created by combining hydrogen fluoride , fluorine , and uranium oxide. Uranium dioxide is also present in this process and is sent off to be used in reactors not requiring enriched fuel. The remaining uranium hexafluoride compound is drained into metal cylinders where it solidifies. The next step

13673-471: Was commonplace in early reactor designs including the Soviet RBMK nuclear power plants such as the Chernobyl plant . The amount and nature of neutron moderation affects reactor controllability and hence safety. Because moderators both slow and absorb neutrons, there is an optimum amount of moderator to include in a given geometry of reactor core. Less moderation reduces the effectiveness by reducing

13794-420: Was in disagreement with the prediction of the modelling, and was a significant barrier to commissioning. A positive power co-efficient means that the reactor becomes more reactive when it heats up; in the case of an unplanned power spike, such a design can "run away" and potentially cause a meltdown . Consequently, significant efforts were made to resolve the outstanding issues, but progress towards commissioning

13915-522: Was indeed possible. On May 4, 1939, Joliot-Curie, Halban, and Kowarski filed three patents. The first two described power production from a nuclear chain reaction, the last one called Perfectionnement aux charges explosives was the first patent for the atomic bomb and is filed as patent No. 445686 by the Caisse nationale de Recherche Scientifique . In parallel, Szilárd and Enrico Fermi in New York made

14036-515: Was much higher. 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

14157-424: Was noted that some of the emergency shut-off rods in the MAPLE I reactor could fail to deploy in certain demanding situations. This failure was ascribed to workmanship and design issues, and related to fine metal particles accumulating in the control rods' housing and interfering with their free movement. In addition, later testing found that the reactors have a positive power co-efficient of reactivity (PCR), which

14278-442: Was signed to begin the project in August 1996. Following a year-long environmental assessment, construction began in December 1997. The design that resulted involved a facility with two identical reactors, each capable of supplying 100% of the world's medical isotope demand. The second reactor would function primarily as a backup, to ensure that the supply of isotopes would not be interrupted by maintenance or unplanned shutdowns. This

14399-522: Was the case of the Fukushima Daiichi nuclear disaster . In such cases, residual decay heat from the core may cause high temperatures if there is loss of coolant flow, even a day after the chain reaction has been shut down (see SCRAM ). This may cause a chemical reaction between water and fuel that produces hydrogen gas, which can explode after mixing with air, with severe contamination consequences, since fuel rod material may still be exposed to

14520-465: Was understood that chemical chain reactions were responsible for exponentially increasing rates in reactions, such as produced in chemical explosions. The concept of a nuclear chain reaction was reportedly first hypothesized by Hungarian scientist Leó Szilárd on September 12, 1933. Szilárd that morning had been reading in a London paper of an experiment in which protons from an accelerator had been used to split lithium-7 into alpha particles , and

14641-450: Was used during the Manhattan Project in early experiments to determine the minimum critical masses of U and of Pu. It is still used today to calibrate the controls for nuclear reactors during startup, as many effects (discussed in the following sections) can change the required control settings to achieve criticality in a reactor. As a power-generating technique, subcritical multiplication allows generation of nuclear power for fission where

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