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Encyclopedia > Nuclear fusion
The deuterium-tritium (D-T) fusion reaction is considered the most promising for producing sustainable fusion power. From the top: 1. the deuterium (2 D) and tritium (3 T) nuclei are accelerated towards each other at thermonuclear speeds/temperatures; 2. they combine to create an unstable helium-5 (5 He) nucleus; 3. the 5 He nucleus decays, resulting in the ejection of a neutron and repulsion of the remaining Helium-4 (4 He) nucleus, both with high energies.

In physics and nuclear chemistry, nuclear fusion is the process by which multiple atomic particles join together to form a heavier nucleus. It is accompanied by the release or absorption of energy. Iron and nickel nuclei have the largest binding energies per nucleon of all nuclei and therefore are the most stable. The fusion of two nuclei lighter than iron or nickel generally releases energy while the fusion of nuclei heavier than iron or nickel absorbs energy; vice-versa for the reverse process, nuclear fission. Image File history File links Question_book-3. ... Image File history File links D-T_fusion. ... Image File history File links D-T_fusion. ... Deuterium, also called heavy hydrogen, is a stable isotope of hydrogen with a natural abundance in the oceans of Earth of approximately one atom in 6500 of hydrogen (~154 PPM). ... Tritium (symbol T or Â³H) is a radioactive isotope of hydrogen. ... Internal view of the JET tokamak superimposed with an image of a plasma taken with a visible spectrum video camera. ... Exotic helium isotopes are the unstable isotopes of helium. ... Exotic helium isotopes are the unstable isotopes of helium. ... This article or section does not adequately cite its references or sources. ... Helium-4 is a non-radioactive and light isotope of helium. ... Internal view of the JET tokamak superimposed with an image of a plasma taken with a visible spectrum video camera. ... The basics of the Tellerâ€“Ulam configuration: a fission bomb uses radiation to compress and heat a separate section of fusion fuel. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... Nuclear chemistry is a subfield of chemistry dealing with radioactivity, nuclear processes and nuclear properties. ... General Name, symbol, number iron, Fe, 26 Chemical series transition metals Group, period, block 8, 4, d Appearance lustrous metallic with a grayish tinge Standard atomic weight 55. ... For other uses, see Nickel (disambiguation). ... Binding energy is the energy required to disassemble a whole into separate parts. ... For the generation of electrical power by fission, see Nuclear power plant. ...

Nuclear fusion occurs naturally in stars. Artificial fusion in human enterprises has also been achieved, although not yet completely controlled. Building upon the nuclear transmutation experiments of Ernest Rutherford done a few years earlier, fusion of light nuclei (hydrogen isotopes) was first observed by Mark Oliphant in 1932, and the steps of the main cycle of nuclear fusion in stars were subsequently worked out by Hans Bethe throughout the remainder of that decade. Research into fusion for military purposes began in the early 1940s, as part of the Manhattan Project, but was not successful until 1952. Research into controlled fusion for civilian purposes began in the 1950s, and continues to this day. Nuclear transmutation is the conversion of one chemical element or isotope into another, which occurs through nuclear reactions. ... Ernest Rutherford, 1st Baron Rutherford of Nelson OM PC FRS (30 August 1871 â€“ 19 October 1937), widely referred to as Lord Rutherford, was a chemist (B.Sc. ... Sir Marcus Mark Laurence Elwin Oliphant AC KBE (October 8, 1901 â€“ July 14, 2000) was an Australian physicist and humanitarian who played a fundamental role in the development of the Atomic bomb. ... Hans Albrecht Bethe (pronounced bay-tuh; July 2, 1906 â€“ March 6, 2005), was a German-American physicist who won the Nobel Prize in Physics in 1967 for his work on the theory of stellar nucleosynthesis. ... This article is about the World War II nuclear project. ...

Nuclear physics
Nuclear fission
Nuclear fusion
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When the fusion reaction is a sustained uncontrolled chain, it can result in a thermonuclear explosion, such as that generated by a hydrogen bomb. Reactions which are not self-sustaining can still release considerable energy, as well as large numbers of neutrons. A 23 kiloton tower shot called BADGER, fired on April 18, 1953 at the Nevada Test Site, as part of the Operation Upshot-Knothole nuclear test. ... The mushroom cloud of the atomic bombing of Nagasaki, Japan, in 1945 lifted nuclear fallout some 18 km (60,000 feet) above the epicenter. ... This article or section does not adequately cite its references or sources. ...

Research into controlled fusion, with the aim of producing fusion power for the production of electricity, has been conducted for over 50 years. It has been accompanied by extreme scientific and technological difficulties, but resulted in steady progress. As of the present, break-even (self-sustaining) controlled fusion reaction have been demonstrated in a few tokamak - type reactors around the world and resulted in producing workable design of the reactor which will deliver ten times more fusion energy than the amount of energy needed to heat up its plasma to required temperatures (see ITER which is scheduled to be operational in 2016). Internal view of the JET tokamak superimposed with an image of a plasma taken with a visible spectrum video camera. ... This article is about the fusion reactor device. ... ITER is an international tokamak (magnetic confinement fusion) research/engineering project designed to prove the scientific and technological feasibility of a full-scale fusion power reactor. ...

The energy released in most nuclear reactions is much larger than that in chemical reactions, because the binding energy that holds a nucleus together is far greater than the energy that holds electrons to a nucleus. For example, the ionization energy gained by adding an electron to a hydrogen nucleus is 13.6 electron volts - less than one-millionth of the 17 MeV released in the D-T (deuterium-tritium) reaction shown to the top right. Fusion reactions have an energy density many times greater than nuclear fission-that is, per unit of mass the reactions produce far greater energies, even though individual fission reactions are generally much more energetic than individual fusion reactions-which are themselves millions of times more energetic than chemical reactions. Only the direct conversion of mass into energy, such as with collision of matter and antimatter, is more energetic per unit of mass than nuclear fusion. In nuclear physics, a nuclear reaction is a process in which two nuclei or nuclear particles collide to produce products different from the initial particles. ... For other uses, see Chemical reaction (disambiguation). ... Binding energy is the energy required to disassemble a whole into separate parts. ... For other uses, see Electron (disambiguation). ... The ionization energy (IE) of an atom or of a molecule is the energy required to strip it of an electron. ... To help compare different orders of magnitude we list here energies between 10−18 joules and 10−17 joules (6. ... An electronvolt (symbol: eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. ... To help compare different orders of magnitude this page lists energies between 10−12 joules (a picojoule, symbol pJ) and 10−11 joules (6. ... Deuterium, also called heavy hydrogen, is a stable isotope of hydrogen with a natural abundance in the oceans of Earth of approximately one atom in 6500 of hydrogen (~154 PPM). ... Tritium (symbol T or Â³H) is a radioactive isotope of hydrogen. ... Energy density is the amount of energy stored in a given system or region of space per unit volume, or per unit mass, depending on the context. ... For the generation of electrical power by fission, see Nuclear power plant. ... 15ft sculpture of Einsteins 1905 E = mcÂ² formula at the 2006 Walk of Ideas, Germany In physics, mass-energy equivalence is the concept that all mass has an energy equivalence, and all energy has a mass equivalence. ... For other senses of this term, see antimatter (disambiguation). ...

## Requirements

A substantial energy barrier must be overcome before fusion can occur. At large distances two naked nuclei repel one another because of the repulsive electrostatic force between their positively charged protons. If two nuclei can be brought close enough together, however, the electrostatic repulsion can be overcome by the attractive nuclear force which is stronger at close distances. In physics, the electrostatic force is the force arising between static (that is, non-moving) electric charges. ... This box:      Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... This article is about the force sometimes called the residual strong force. ...

When a nucleon such as a proton or neutron is added to a nucleus, the nuclear force attracts it to other nucleons, but primarily to its immediate neighbors due to the short range of the force. The nucleons in the interior of a nucleus have more neighboring nucleons than those on the surface. Since smaller nuclei have a larger surface area-to-volume ratio, the binding energy per nucleon due to the strong force generally increases with the size of the nucleus but approaches a limiting value corresponding to that of a fully surrounded nucleon. In physics a nucleon is a collective name for two baryons: the neutron and the proton. ... For other uses, see Proton (disambiguation). ... This article or section does not adequately cite its references or sources. ...

The electrostatic force, on the other hand, is an inverse-square force, so a proton added to a nucleus will feel an electrostatic repulsion from all the other protons in the nucleus. The electrostatic energy per nucleon due to the electrostatic force thus increases without limit as nuclei get larger.

The electrostatic force caused by positively charged nuclei is very strong over long distances, but at short distances the nuclear force is stronger. As such, the main technical difficulty for fusion is getting the nuclei close enough to fuse. Distances not to scale.

The net result of these opposing forces is that the binding energy per nucleon generally increases with increasing size, up to the elements iron and nickel, and then decreases for heavier nuclei. Eventually, the binding energy becomes negative and very heavy nuclei are not stable. The four most tightly bound nuclei, in decreasing order of binding energy, are 62 Ni, 58 Fe, 56 Fe, and 60 Ni.[1] Even though the nickel isotope ,62 Ni, is more stable, the iron isotope 56 Fe is an order of magnitude more common. This is due to a greater disintegration rate for 62 Ni in the interior of stars driven by photon absorption. Image File history File links Nuclear_fusion_forces_diagram. ... Image File history File links Nuclear_fusion_forces_diagram. ... In physics, the electrostatic force is the force arising between static (that is, non-moving) electric charges. ... This article is about the force sometimes called the residual strong force. ... General Name, symbol, number iron, Fe, 26 Chemical series transition metals Group, period, block 8, 4, d Appearance lustrous metallic with a grayish tinge Standard atomic weight 55. ... For other uses, see Nickel (disambiguation). ... Nickel-62 is an isotope of nickel with 28 protons and 34 neutrons. ... Naturally occurring Iron (Fe) consists of four isotopes: 5. ... Iron-56 is the most common isotope of iron. ... Nickel (Ni) Standard atomic mass: 58. ... Nickel (Ni) Standard atomic mass: 58. ... Iron (Fe) Standard atomic mass: 55. ... An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. ...

A notable exception to this general trend is the helium-4 nucleus, whose binding energy is higher than that of lithium, the next heavier element. The Pauli exclusion principle provides an explanation for this exceptional behavior — it says that because protons and neutrons are fermions, they cannot exist in exactly the same state. Each proton or neutron energy state in a nucleus can accommodate both a spin up particle and a spin down particle. Helium-4 has an anomalously large binding energy because its nucleus consists of two protons and two neutrons; so all four of its nucleons can be in the ground state. Any additional nucleons would have to go into higher energy states. General Name, symbol, number helium, He, 2 Chemical series noble gases Group, period, block 18, 1, s Appearance colorless Standard atomic weight 4. ... This article is about the chemical element. ... The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925. ... In particle physics, fermions are particles with half-integer spin, such as protons and electrons. ...

The situation is similar if two nuclei are brought together. As they approach each other, all the protons in one nucleus repel all the protons in the other. Not until the two nuclei actually come in contact can the strong nuclear force take over. Consequently, even when the final energy state is lower, there is a large energy barrier that must first be overcome. It is called the Coulomb barrier. This article is about the force sometimes called the residual strong force. ... The Coulomb barrier, named after physicist Charles-Augustin de Coulomb (1736â€”1806), is the energy barrier due to electrostatic interaction that two nuclei need to overcome so they can get close enough to undergo nuclear fusion. ...

The Coulomb barrier is smallest for isotopes of hydrogen—they contain only a single positive charge in the nucleus. A bi-proton is not stable, so neutrons must also be involved, ideally in such a way that a helium nucleus, with its extremely tight binding, is one of the products.

Using deuterium-tritium fuel, the resulting energy barrier is about 0.01 MeV.[citation needed] In comparison, the energy needed to remove an electron from hydrogen is 13.6 eV, about 750 times less energy. The (intermediate) result of the fusion is an unstable 5He nucleus, which immediately ejects a neutron with 14.1 MeV.[citation needed] The recoil energy of the remaining 4He nucleus is 3.5 MeV,[citation needed] so the total energy liberated is 17.6 MeV.[citation needed] This is many times more than what was needed to overcome the energy barrier. For other uses, see Electron (disambiguation). ... This article is about the chemistry of hydrogen. ...

If the energy to initiate the reaction comes from accelerating one of the nuclei, the process is called beam-target fusion; if both nuclei are accelerated, it is beam-beam fusion. If the nuclei are part of a plasma near thermal equilibrium, one speaks of thermonuclear fusion. Temperature is a measure of the average kinetic energy of particles, so by heating the nuclei they will gain energy and eventually have enough to overcome this 0.01 MeV. Converting the units between electronvolts and kelvins shows that the barrier would be overcome at a temperature in excess of 120 million kelvins, obviously a very high temperature. For the DC Comics Superhero also called Atom Smasher, see Albert Rothstein. ... A Plasma lamp In physics and chemistry, a plasma is an ionized gas, and is usually considered to be a distinct phase of matter. ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ...

There are two effects that lower the actual temperature needed. One is the fact that temperature is the average kinetic energy, implying that some nuclei at this temperature would actually have much higher energy than 0.01 MeV, while others would be much lower. It is the nuclei in the high-energy tail of the velocity distribution that account for most of the fusion reactions. The other effect is quantum tunneling. The nuclei do not actually have to have enough energy to overcome the Coulomb barrier completely. If they have nearly enough energy, they can tunnel through the remaining barrier. For this reason fuel at lower temperatures will still undergo fusion events, at a lower rate. For other uses, see Temperature (disambiguation). ... In physics, a particles distribution function is a function of seven variables, , which gives the number of particles per unit volume in phase space. ... Quantum tunneling is the quantum-mechanical effect of transitioning through a classically-forbidden energy state. ...

The fusion reaction rate increases rapidly with temperature until it maximizes and then gradually drops off. The DT rate peaks at a lower temperature (about 70 keV, or 800 million kelvins) and at a higher value than other reactions commonly considered for fusion energy.

The reaction cross section σ is a measure of the probability of a fusion reaction as a function of the relative velocity of the two reactant nuclei. If the reactants have a distribution of velocities, e.g. a thermal distribution with thermonuclear fusion, then it is useful to perform an average over the distributions of the product of cross section and velocity. The reaction rate (fusions per volume per time) is <σv> times the product of the reactant number densities: Image File history File links This is a lossless scalable vector image. ... Image File history File links This is a lossless scalable vector image. ... In nuclear and particle physics, the concept of a cross section is used to express the likelihood of interaction between particles. ...

$f = n_1 n_2 langle sigma v rangle.$

If a species of nuclei is reacting with itself, such as the DD reaction, then the product n1n2 must be replaced by (1 / 2)n2.

$langle sigma v rangle$ increases from virtually zero at room temperatures up to meaningful magnitudes at temperatures of 10 – 100 keV. At these temperatures, well above typical ionization energies (13.6 eV in the hydrogen case), the fusion reactants exist in a plasma state. To help compare different orders of magnitude we list here energies between 10−15 joules (a femtojoule, symbol fJ) and 10−14 joules (6,200 and 62,000 eV). ... To help compare different orders of magnitude this page lists energies between 10−14 joules and 10−13 joules (62,000 eV and 620,000 eV). ... This article is about the electrically charged particle. ... A Plasma lamp In physics and chemistry, a plasma is an ionized gas, and is usually considered to be a distinct phase of matter. ...

The significance of <σv> as a function of temperature in a device with a particular energy confinement time is found by considering the Lawson criterion. In nuclear fusion research, the Lawson criterion, first derived by John D. Lawson in 1957, is an important general measure of a system that defines the conditions needed for a fusion reactor to reach ignition, that is, that the heating of the plasma by the products of the fusion reactions... This article or section does not cite its references or sources. ...

### Fuel confinement methods

#### Gravitational

One force capable of confining the fuel well enough to satisfy the Lawson criterion is gravity. The mass needed, however, is so great that gravitational confinement is only found in stars (the smallest of which are brown dwarfs). Even if the more reactive fuel deuterium were used, a mass greater than that of the planet Jupiter would be needed. This article or section does not cite its references or sources. ... Gravity is a force of attraction that acts between bodies that have mass. ... STARS can mean: Shock Trauma Air Rescue Society Special Tactics And Rescue Service, a fictional task force that appears in Capcoms Resident Evil video game franchise. ... This brown dwarf (smaller object) orbits the star Gliese 229, which is located in the constellation Lepus about 19 light years from Earth. ... For other uses, see Jupiter (disambiguation). ...

#### Magnetic

The charged ions of fusion fuel follow spiral orbits around magnetic field lines (see Guiding center#Gyration), and the fuel is therefore trapped along the field lines. A variety of magnetic configurations exist, including the toroidal geometries of tokamaks and stellarators and open ended mirror confinement systems. Magnetic Fusion Energy (MFE) is a sustained nuclear fusion reaction in a plasma that is contained by magnetic fields. ... For the indie-pop band, see The Magnetic Fields. ... Charged particle drifts in a homegenous magnetic field. ... This article is about the fusion reactor device. ... Stellarator magnetic field and magnets A stellarator is a device used to confine a hot plasma with magnetic fields in order to sustain a controlled nuclear fusion reaction. ... A magnetic mirror is a magnetic field configuration where the field strength changes when moving along a field line. ...

#### Inertial

A third confinement principle is to apply a rapid pulse of energy to a large part of the surface of a pellet of fusion fuel, causing it to simultaneously "implode" and heat to very high pressure and temperature. If the fuel is dense enough and hot enough, the fusion reaction rate will be high enough to burn a significant fraction of the fuel before it has dissipated. To achieve these extreme conditions, the initially cold fuel must be explosively compressed. Inertial confinement is used in the hydrogen bomb, where the driver is x-rays created by a fission bomb. Inertial confinement is also attempted in "controlled" nuclear fusion, where the driver is a laser, ion, or electron beam, or a Z-pinch. In inertial confinement fusion (ICF), nuclear fusion reactions are initiated by heating and compressing a target – a pellet that most often contains deuterium and tritium – by the use of intense laser or ion beams. ... The mushroom cloud of the atomic bombing of Nagasaki, Japan, in 1945 lifted nuclear fallout some 18 km (60,000 feet) above the epicenter. ... An X-ray picture (radiograph), taken by Wilhelm RÃ¶ntgen in 1896, of his wife, Anna Bertha Ludwigs[1] hand X-rays (or RÃ¶ntgen rays) are a form of electromagnetic radiation with a wavelength in the range of 10 to 0. ... For other uses, see Laser (disambiguation). ... This article is about the electrically charged particle. ... For other uses, see Electron (disambiguation). ... It has been suggested that this article or section be merged into Pinch (plasma physics). ...

Some other confinement principles have been investigated, such as muon-catalyzed fusion, the Farnsworth-Hirsch fusor and Polywell (inertial electrostatic confinement), and bubble fusion. Muon-catalyzed fusion is a process allowing nuclear fusion to take place at room temperature. ... US3386883 - fusor -- June 4, 1968 The Farnsworth-Hirsch Fusor, or simply fusor, is an apparatus designed by Philo T. Farnsworth to create nuclear fusion. ... WB-6, the latest experiment, assembled The Polywell is a gridless inertial electrostatic confinement fusion concept utilizing multiple magnetic mirrors. ... Inertial electrostatic confinement (often abbreviated as IEC) is a concept for retaining a plasma using an electrostatic field. ... Bubble fusion or sonofusion is the common name for a nuclear fusion reaction hypothesized to occur during sonoluminescence, an extreme form of acoustic cavitation; officially, this reaction is termed acoustic inertial confinement fusion (AICF) since the inertia of the collapsing bubble wall confines the energy causing a rise in temperature. ...

### Production methods

A variety of methods are known to affect nuclear fusion. Some are "cold" in the strict sense that no part of the material is hot (except for the reaction products), some are "cold" in the limited sense that the bulk of the material is at a relatively low temperature and pressure but the reactants are not, and some are "hot" fusion methods that create macroscopic regions of very high temperature and pressure.

#### Locally cold fusion

• Muon-catalyzed fusion is a well-established and reproducible fusion process that occurs at ordinary temperatures. It was studied in detail by Steven Jones in the early 1980s. It has not been reported to produce net energy. Net energy production from this reaction is not believed to be possible because of the energy required to create muons, their 2.2 µs half-life, and the chance that a muon will bind to the new alpha particle and thus stop catalyzing fusion.
• "Cold fusion" also refers to a simple method using electrodes (generally palladium) in heavy water, which has not been verified to be possible.

Muon-catalyzed fusion is a process allowing nuclear fusion to take place at room temperature. ... Steven E. Jones For other uses, see Stephen Jones. ... The muon (from the letter mu (Î¼)--used to represent it) is an elementary particle with negative electric charge and a spin of 1/2. ... Half-Life For a quantity subject to exponential decay, the half-life is the time required for the quantity to fall to half of its initial value. ... An alpha particle is deflected by a magnetic field Alpha radiation consists of helium-4 nuclei and is readily stopped by a sheet of paper. ... This article is about the nuclear reaction. ... For other uses, see Palladium (disambiguation). ... Heavy water is dideuterium oxide, or D2O or 2H2O. It is chemically the same as normal water, H2O, but the hydrogen atoms are of the heavy isotope deuterium, in which the nucleus contains a neutron in addition to the proton found in the nucleus of any hydrogen atom. ...

#### Generally cold, locally hot fusion

• Accelerator based light-ion fusion. Using particle accelerators it is possible to achieve particle kinetic energies sufficient to induce many light ion fusion reactions. Accelerating light ions is relatively easy, cheap, and can be done in an efficient manner - all it takes is a vacuum tube, a pair of electrodes, and a high-voltage transformer; fusion can be observed with as little as 10 kilovolt between electrodes. The key problem with accelerator-based fusion (and with cold targets in general) is that fusion cross sections are many orders of magnitude lower than Coulomb interaction cross sections. Therefore vast majority of ions ends up expending their energy on bremsstrahlung and ionization of atoms of the target. Devices referred to as sealed-tube neutron generators are particularly relevant to this discussion. These small devices are miniature particle accelerators filled with deuterium and tritium gas in an arrangement which allows ions of these nuclei to be accelerated against hydride targets, also containing deuterium and tritium, where fusion takes place. Hundreds of neutron generators are produced annually for use in the petroleum industry where they are used in measurement equipment for locating and mapping oil reserves. Despite periodic reports in the popular press by scientists claiming to have invented "table-top" fusion machines, neutron generators have been around for half a century. The sizes of these devices vary but the smallest instruments are often packaged in sizes smaller than a loaf of bread. These devices do not produce a net power output.
• In sonoluminescence, acoustic shock waves create temporary bubbles that collapse shortly after creation, producing very high temperatures and pressures. In 2002, Rusi P. Taleyarkhan reported the possibility that bubble fusion occurs in those collapsing bubbles (aka sonofusion). As of 2005, experiments to determine whether fusion is occurring give conflicting results. If fusion is occurring, it is because the local temperature and pressure are sufficiently high to produce hot fusion.[2] In an episode of Horizon, on BBC television, it was conclusively shown that, although temperatures were reached which could initiate fusion on a large scale, no fusion was occurring, and inaccuracies in the measuring system were the cause of anomalous results.
• The Farnsworth-Hirsch Fusor is a tabletop device in which fusion occurs. This fusion comes from high effective temperatures produced by electrostatic acceleration of ions. The device can be built inexpensively, but it too is unable to produce a net power output.
• Antimatter-initialized fusion uses small amounts of antimatter to trigger a tiny fusion explosion. This has been studied primarily in the context of making nuclear pulse propulsion feasible. This is not near becoming a practical power source, due to the cost of manufacturing antimatter alone.
• Pyroelectric fusion was reported in April 2005 by a team at UCLA. The scientists used a pyroelectric crystal heated from −34 to 7°C (−30 to 45°F), combined with a tungsten needle to produce an electric field of about 25 gigavolts per meter to ionize and accelerate deuterium nuclei into an erbium deuteride target. Though the energy of the deuterium ions generated by the crystal has not been directly measured, the authors used 100 keV (a temperature of about 109 K) as an estimate in their modeling.[3] At these energy levels, two deuterium nuclei can fuse together to produce a helium-3 nucleus, a 2.45 MeV neutron and bremsstrahlung. Although it makes a useful neutron generator, the apparatus is not intended for power generation since it requires far more energy than it produces.[4][5][6][7]

#### Hot fusion

In "standard" "hot" fusion, the fuel reaches tremendous temperature and pressure inside a fusion reactor or nuclear weapon. Internal view of the JET tokamak superimposed with an image of a plasma taken with a visible spectrum video camera. ... Also try: fusion power This article is about a fictional warship in the game Halo. ... The mushroom cloud of the atomic bombing of Nagasaki, Japan, 1945, rose some 18 kilometers (11 mi) above the hypocenter A nuclear weapon derives its destructive force from nuclear reactions of fusion or fission. ...

## Important reactions

### Astrophysical reaction chains

The proton-proton chain dominates in stars the size of the Sun or smaller.
The CNO cycle dominates in stars heavier than the Sun.

The most important fusion process in nature is that which powers the stars. The net result is the fusion of four protons into one alpha particle, with the release of two positrons, two neutrinos (which changes two of the protons into neutrons), and energy, but several individual reactions are involved, depending on the mass of the star. For stars the size of the sun or smaller, the proton-proton chain dominates. In heavier stars, the CNO cycle is more important. Both types of processes are responsible for the creation of new elements as part of stellar nucleosynthesis. Image File history File links FusionintheSun. ... Image File history File links FusionintheSun. ... The proton-proton chain reaction is one of two fusion reactions by which stars convert hydrogen to helium, the other being the CNO cycle. ... Image File history File links CNO_Cycle. ... Image File history File links CNO_Cycle. ... This article does not cite its references or sources. ... For other uses, see Proton (disambiguation). ... An alpha particle is deflected by a magnetic field Alpha radiation consists of helium-4 nuclei and is readily stopped by a sheet of paper. ... A positron is the antiparticle of the electron. ... For other uses, see Neutrino (disambiguation). ... The proton-proton chain reaction is one of two fusion reactions by which stars convert hydrogen to helium, the other being the CNO cycle. ... This article does not cite its references or sources. ... Cross section of a red giant showing nucleosynthesis and elements formed Stellar nucleosynthesis is the collective term for the nuclear reactions taking place in stars to build the nuclei of the heavier elements. ...

At the temperatures and densities in stellar cores the rates of fusion reactions are notoriously slow. For example, at solar core temperature (T ≈ 15 MK) and density (160 g/cm³), the energy release rate is only 276 μW/cm³—about a quarter of the volumetric rate at which a resting human body generates heat. [8] Thus, reproduction of stellar core conditions in a lab for nuclear fusion power production is completely impractical. Because nuclear reaction rates strongly depend on temperature (exp(−E/kT)), then in order to achieve reasonable rates of energy production in terrestrial fusion reactors 10–100 times higher temperatures (compared to stellar interiors) are required T ≈ 0.1–1.0 GK.

### Criteria and candidates for terrestrial reactions

In man-made fusion, the primary fuel is not constrained to be protons and higher temperatures can be used, so reactions with larger cross-sections are chosen. This implies a lower Lawson criterion, and therefore less startup effort. Another concern is the production of neutrons, which activate the reactor structure radiologically, but also have the advantages of allowing volumetric extraction of the fusion energy and tritium breeding. Reactions that release no neutrons are referred to as aneutronic. This article or section does not cite its references or sources. ... Tritium (symbol T or Â³H) is a radioactive isotope of hydrogen. ... Aneutronic fusion is any form of fusion power where no more than 1% of the total energy released is carried by neutrons. ...

In order to be useful as a source of energy, a fusion reaction must satisfy several criteria. It must

• be exothermic: This may be obvious, but it limits the reactants to the low Z (number of protons) side of the curve of binding energy. It also makes helium He-4 the most common product because of its extraordinarily tight binding, although He-3 and H-3 also show up;
• involve low Z nuclei: This is because the electrostatic repulsion must be overcome before the nuclei are close enough to fuse;
• have two reactants: At anything less than stellar densities, three body collisions are too improbable. It should be noted that in inertial confinement, both stellar densities and temperatures are exceeded to compensate for the shortcomings of the third parameter of the Lawson criterion, ICF's very short confinement time;
• have two or more products: This allows simultaneous conservation of energy and momentum without relying on the electromagnetic force;
• conserve both protons and neutrons: The cross sections for the weak interaction are too small.

Few reactions meet these criteria. The following are those with the largest cross sections:

 (1) 21D + 31T → 42He ( 3.5 MeV ) + n0 ( 14.1 MeV ) (2i) 21D + 21D → 31T ( 1.01 MeV ) + p+ ( 3.02 MeV ) 50% (2ii) → 32He ( 0.82 MeV ) + n0 ( 2.45 MeV ) 50% (3) 21D + 32He → 42He ( 3.6 MeV ) + p+ ( 14.7 MeV ) (4) 31T + 31T → 42He + 2 n0 + 11.3 MeV (5) 32He + 32He → 42He + 2 p+ + 12.9 MeV (6i) 32He + 31T → 42He + p+ + n0 + 12.1 MeV 51% (6ii) → 42He ( 4.8 MeV ) + 21D ( 9.5 MeV ) 43% (6iii) → 42He ( 0.5 MeV ) + n0 ( 1.9 MeV ) + p+ ( 11.9 MeV ) 6% (7i) 21D + 63Li → 2 42He + 22.4 MeV (7ii) → 32He + 42He + n0 + 2.56 MeV (7iii) → 73Li + p+ + 5.0 MeV (7iv) → 74Be + n0 + 3.4 MeV (8) p+ + 63Li → 42He ( 1.7 MeV ) + 32He ( 2.3 MeV ) (9) 32He + 63Li → 2 42He + p+ + 16.9 MeV (10) p+ + 115B → 3 42He + 8.7 MeV

For reactions with two products, the energy is divided between them in inverse proportion to their masses, as shown. In most reactions with three products, the distribution of energy varies. For reactions that can result in more than one set of products, the branching ratios are given.

Some reaction candidates can be eliminated at once.[9] The D-6Li reaction has no advantage compared to p+-115B because it is roughly as difficult to burn but produces substantially more neutrons through 21D-21D side reactions. There is also a p+-73Li reaction, but the cross section is far too low, except possibly when Ti > 1 MeV, but at such high temperatures an endothermic, direct neutron-producing reaction also becomes very significant. Finally there is also a p+-94Be reaction, which is not only difficult to burn, but 94Be can be easily induced to split into two alpha particles and a neutron. For other uses, see Proton (disambiguation). ... Boron (B) Standard atomic mass: 10. ... For other uses, see Proton (disambiguation). ... General Name, Symbol, Number Lithium, Li, 3 Series Alkali metal Group, Period, Block 1(IA), 2, s Density, Hardness 535 kg/m3, 0. ... For other uses, see Proton (disambiguation). ... Although beryllium (Be) has multiple isotopes, only one of these isotopes is stable; as such, it is considered a monoisotopic element. ... Although beryllium (Be) has multiple isotopes, only one of these isotopes is stable; as such, it is considered a monoisotopic element. ...

In addition to the fusion reactions, the following reactions with neutrons are important in order to "breed" tritium in "dry" fusion bombs and some proposed fusion reactors:

 n0 + 63Li → 31T + 42He n0 + 73Li → 31T + 42He + n0

fuel T [keV] <σv>/T² [m³/s/keV²]
21D-31T 13.6 1.24×10-24
21D-21D 15 1.28×10-26
21D-32He 58 2.24×10-26
p+-63Li 66 1.46×10-27
p+-115B 123 3.01×10-27

Note that many of the reactions form chains. For instance, a reactor fueled with 31T and 32He will create some 21D, which is then possible to use in the 21D-32He reaction if the energies are "right". An elegant idea is to combine the reactions (8) and (9). The 32He from reaction (8) can react with 63Li in reaction (9) before completely thermalizing. This produces an energetic proton which in turn undergoes reaction (8) before thermalizing. A detailed analysis shows that this idea will not really work well, but it is a good example of a case where the usual assumption of a Maxwellian plasma is not appropriate. The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ...

### Neutronicity, confinement requirement, and power density

The only fusion reactions thus far produced by humans to achieve ignition are those which have been created in hydrogen bombs; the first of which, Ivy Mike, is shown here.

Any of the reactions above can in principle be the basis of fusion power production. In addition to the temperature and cross section discussed above, we must consider the total energy of the fusion products Efus, the energy of the charged fusion products Ech, and the atomic number Z of the non-hydrogenic reactant. Image File history File links Download high resolution version (800x637, 55 KB) XX-11 IVY MIKE, was fired on Enewetak by the United States on October 31, 1952. ... Image File history File links Download high resolution version (800x637, 55 KB) XX-11 IVY MIKE, was fired on Enewetak by the United States on October 31, 1952. ... This article or section is in need of attention from an expert on the subject. ... The mushroom cloud of the atomic bombing of Nagasaki, Japan, in 1945 lifted nuclear fallout some 18 km (60,000 feet) above the epicenter. ... The mushroom cloud from the Mike shot. ... Internal view of the JET tokamak superimposed with an image of a plasma taken with a visible spectrum video camera. ...

Specification of the 21D-21D reaction entails some difficulties, though. To begin with, one must average over the two branches (2) and (3). More difficult is to decide how to treat the 31T and 32He products. 31T burns so well in a deuterium plasma that it is almost impossible to extract from the plasma. The 21D-32He reaction is optimized at a much higher temperature, so the burnup at the optimum 21D-21D temperature may be low, so it seems reasonable to assume the 31T but not the 32He gets burned up and adds its energy to the net reaction. Thus we will count the 21D-21D fusion energy as Efus = (4.03+17.6+3.27)/2 = 12.5 MeV and the energy in charged particles as Ech = (4.03+3.5+0.82)/2 = 4.2 MeV.

Another unique aspect of the 21D-21D reaction is that there is only one reactant, which must be taken into account when calculating the reaction rate.

With this choice, we tabulate parameters for four of the most important reactions.

fuel Z Efus [MeV] Ech [MeV] neutronicity
21D-31T 1 17.6 3.5 0.80
21D-21D 1 12.5 4.2 0.66
21D-32He 2 18.3 18.3 ~0.05
p+-115B 5 8.7 8.7 ~0.001

The last column is the neutronicity of the reaction, the fraction of the fusion energy released as neutrons. This is an important indicator of the magnitude of the problems associated with neutrons like radiation damage, biological shielding, remote handling, and safety. For the first two reactions it is calculated as (Efus-Ech)/Efus. For the last two reactions, where this calculation would give zero, the values quoted are rough estimates based on side reactions that produce neutrons in a plasma in thermal equilibrium. Aneutronic fusion is any form of fusion power where no more than 1% of the total energy released is carried by neutrons. ...

Of course, the reactants should also be mixed in the optimal proportions. This is the case when each reactant ion plus its associated electrons accounts for half the pressure. Assuming that the total pressure is fixed, this means that density of the non-hydrogenic ion is smaller than that of the hydrogenic ion by a factor 2/(Z+1). Therefore the rate for these reactions is reduced by the same factor, on top of any differences in the values of <σv>/T². On the other hand, because the 21D-21D reaction has only one reactant, the rate is twice as high as if the fuel were divided between two hydrogenic species.

Thus there is a "penalty" of (2/(Z+1)) for non-hydrogenic fuels arising from the fact that they require more electrons, which take up pressure without participating in the fusion reaction. (It is usually a good assumption that the electron temperature will be nearly equal to the ion temperature. Some authors, however discuss the possibility that the electrons could be maintained substantially colder than the ions. In such a case, known as a "hot ion mode", the "penalty" would not apply.) There is at the same time a "bonus" of a factor 2 for 21D-21D due to the fact that each ion can react with any of the other ions, not just a fraction of them.

We can now compare these reactions in the following table.

fuel <σv>/T² penalty/bonus reactivity Lawson criterion power density
21D-31T 1.24×10-24 1 1 1 1
21D-21D 1.28×10-26 2 48 30 68
21D-32He 2.24×10-26 2/3 83 16 80
p+-115B 3.01×10-27 1/3 1240 500 2500

The maximum value of <σv>/T² is taken from a previous table. The "penalty/bonus" factor is that related to a non-hydrogenic reactant or a single-species reaction. The values in the column "reactivity" are found by dividing 1.24×10-24 by the product of the second and third columns. It indicates the factor by which the other reactions occur more slowly than the 21D-31T reaction under comparable conditions. The column "Lawson criterion" weights these results with Ech and gives an indication of how much more difficult it is to achieve ignition with these reactions, relative to the difficulty for the 21D-31T reaction. The last column is labeled "power density" and weights the practical reactivity with Efus. It indicates how much lower the fusion power density of the other reactions is compared to the 21D-31T reaction and can be considered a measure of the economic potential. This article or section does not cite its references or sources. ...

### Bremsstrahlung losses in quasineutral, isotropic plasmas

The ions undergoing fusion in many systems will essentially never occur alone but will be mixed with electrons that in aggregate neutralize the ions' bulk electrical charge and form a plasma. The electrons will generally have a temperature comparable to or greater than that of the ions, so they will collide with the ions and emit x-ray radiation of 10-30 keV energy (Bremsstrahlung). The Sun and stars are opaque to x-rays, but essentially any terrestrial fusion reactor will be optically thin for x-rays of this energy range. X-rays are difficult to reflect but they are effectively absorbed (and converted into heat) in less than mm thickness of stainless steel (which is part of a reactor's shield). The ratio of fusion power produced to x-ray radiation lost to walls is an important figure of merit. This ratio is generally maximized at a much higher temperature than that which maximizes the power density (see the previous subsection). The following table shows the rough optimum temperature and the power ratio at that temperature for several reactions.[10] For other uses, see Electron (disambiguation). ... Electric charge is a fundamental property of some subatomic particles, which determines their electromagnetic interactions. ... For other uses, see Plasma. ... In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz... (helpÂ· info), (from the German bremsen, to brake and Strahlung, radiation, thus, braking radiation), is electromagnetic radiation produced by the acceleration of a charged particle, such as an electron, when deflected by another charged particle, such as an atomic nucleus. ... A substance or object that is opaque is neither transparent nor translucent. ... This article does not cite any references or sources. ...

fuel Ti (keV) Pfusion/PBremsstrahlung
21D-31T 50 140
21D-21D 500 2.9
21D-32He 100 5.3
32He-32He 1000 0.72
p+-63Li 800 0.21
p+-115B 300 0.57

The actual ratios of fusion to Bremsstrahlung power will likely be significantly lower for several reasons. For one, the calculation assumes that the energy of the fusion products is transmitted completely to the fuel ions, which then lose energy to the electrons by collisions, which in turn lose energy by Bremsstrahlung. However because the fusion products move much faster than the fuel ions, they will give up a significant fraction of their energy directly to the electrons. Secondly, the plasma is assumed to be composed purely of fuel ions. In practice, there will be a significant proportion of impurity ions, which will lower the ratio. In particular, the fusion products themselves must remain in the plasma until they have given up their energy, and will remain some time after that in any proposed confinement scheme. Finally, all channels of energy loss other than Bremsstrahlung have been neglected. The last two factors are related. On theoretical and experimental grounds, particle and energy confinement seem to be closely related. In a confinement scheme that does a good job of retaining energy, fusion products will build up. If the fusion products are efficiently ejected, then energy confinement will be poor, too.

The temperatures maximizing the fusion power compared to the Bremsstrahlung are in every case higher than the temperature that maximizes the power density and minimizes the required value of the fusion triple product. This will not change the optimum operating point for 21D-31T very much because the Bremsstrahlung fraction is low, but it will push the other fuels into regimes where the power density relative to 21D-31T is even lower and the required confinement even more difficult to achieve. For 21D-21D and 21D-32He, Bremsstrahlung losses will be a serious, possibly prohibitive problem. For 32He-32He, p+-63Li and p+-115B the Bremsstrahlung losses appear to make a fusion reactor using these fuels with a quasineutral, anisotropic plasma impossible. Some ways out of this dilemma are considered — and rejected — in Fundamental limitations on plasma fusion systems not in thermodynamic equilibrium by Todd Rider.[11] This limitation does not apply to non-neutral and anisotropic plasmas; however, these have their own challenges to contend with. This article or section does not cite its references or sources. ... Helium-3 is a non-radioactive and light isotope of helium. ... Helium-3 is a non-radioactive and light isotope of helium. ... Helium-3 is a non-radioactive and light isotope of helium. ... For other uses, see Proton (disambiguation). ... General Name, Symbol, Number lithium, Li, 3 Chemical series alkali metals Group, Period, Block 1, 2, s Appearance silvery white/gray Atomic mass 6. ... For other uses, see Proton (disambiguation). ... Boron (B) Standard atomic mass: 10. ...

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Image File history File links Portal. ... Image File history File links Crystal_128_energy. ... Internal view of the JET tokamak superimposed with an image of a plasma taken with a visible spectrum video camera. ... Nuclear physics is the branch of physics concerned with the nucleus of the atom. ... For the generation of electrical power by fission, see Nuclear power plant. ... Core of a small nuclear reactor used for research. ... Nucleosynthesis is the process of creating new atomic nuclei from preexisting nucleons (protons and neutrons). ... Helium fusion is a kind of nuclear fusion, with the nuclei involved being helium. ... Helium-3 is a non-radioactive and light isotope of helium. ... A neutron source is a device, used in solid state physics (see neutron diffraction), particle physics and to start nuclear chain reactions, that emits neutrons. ... Neutron generators are devices which contain compact linear accelerators and that produce neutrons by fusing isotopes of hydrogen together. ... Timeline of significant events in the study and use of nuclear fusion: 1929 - Atkinson and Houtermans used the measured masses of light elements and applied Einsteins discovery that E=mcÂ² to predict that large amounts of energy could be released by fusing small nuclei together. ... The Periodic Table redirects here. ...

## References

1. ^ The Most Tightly Bound Nuclei
2. ^ Access : Desktop fusion is back on the table : Nature News
3. ^ http://www.nature.com/nature/journal/v434/n7037/extref/nature03575-s1.pdf
4. ^ UCLA Crystal Fusion
5. ^ Physics News Update 729
6. ^ Coming in out of the cold: nuclear fusion, for real | csmonitor.com
7. ^ Nuclear fusion on the desktop ... really! - Science - MSNBC.com
8. ^ FusEdWeb | Fusion Education
9. ^ http://theses.mit.edu/Dienst/UI/2.0/Page/0018.mit.theses/1995-130/30?npages=306
10. ^ http://theses.mit.edu/Dienst/UI/2.0/Page/0018.mit.theses/1995-130/26?npages=306
11. ^ http://fusion.ps.uci.edu/artan/Posters/aps_poster_2.pdf Portable Document Format (PDF)

Results from FactBites:

 Nuclear Fusion | Nuclear Fusion | Science | atomicarchive.com (99 words) Nuclear energy can also be released by fusion of two light elements (elements with low atomic numbers). In a hydrogen bomb, two isotopes of hydrogen, deuterium and tritium are fused to form a nucleus of helium and a neutron. Unlike nuclear fission, there is no limit on the amount of the fusion that can occur.
 Nuclear fusion - Wikipedia, the free encyclopedia (4132 words) Nuclear fusion of light elements releases the energy that causes stars to shine and hydrogen bombs to explode. Nuclear fusion of heavy elements (absorbing energy) occurs in the extremely high-energy conditions of supernova explosions. Nuclear fusion in stars and supernovae is the primary process by which new natural elements are created.
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