nuclear+fusion

   Fusion of deuterium with tritium creating helium-4, freeing a neutron, and releasing 17.59 MeV of energy, as an appropriate amount of mass converting to the kinetic energy of the products, in agreement with //E = Δm c2//.[1] In nuclear physics and nuclear chemistry, **nuclear fusion** is the process by which multiple like-charged atomic nuclei join together to form a heavier nucleus. It is accompanied by the release or absorption of energy, which allows matter to enter a plasma state. The fusion of two nuclei with lower mass than iron (which, along with nickel, has the largest binding energy per nucleon) generally releases energy while the fusion of nuclei heavier than iron absorbs energy; vice-versa for the reverse process, nuclear fission. In the simplest case of hydrogen fusion, two protons have to be brought close enough for their mutual electric repulsion to be overcome by the nuclear force and the subsequent release of energy. Nuclear fusion occurs naturally in stars. Artificial fusion in human enterprises has also been achieved, although has not yet been 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; 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 physics ** || Radioactive decay Nuclear fission  ||  || Becquerel · Bethe · Curie · Fermi · Rutherford || || || Fusion reactions power the stars and produce all but the lightest elements in a process called nucleosynthesis. Although the fusion of lighter elements in stars releases energy, production of the heavier elements absorbs energy. 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. 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 has resulted in progress. At present, break-even (self-sustaining) controlled fusion reactions have not been demonstrated in the few tokamak-type reactors around the world.[2] Workable designs for a reactor which will theoretically deliver ten times more fusion energy than the amount needed to heat up plasma to required temperatures (see ITER) is scheduled to be operational in 2018. It takes considerable energy to force nuclei to fuse, even those of the lightest element, hydrogen. This is because all nuclei have a positive charge (due to their protons), and as like charges repel, nuclei strongly resist being put too close together. Accelerated to high speeds (that is, heated to thermonuclear temperatures), they can overcome this electromagnetic repulsion and get close enough for the attractive nuclear force to be sufficiently strong to achieve fusion. The fusion of lighter nuclei, which creates a heavier nucleus and a free neutron, generally releases more energy than it takes to force the nuclei together; this is an exothermic process that can produce self-sustaining reactions. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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 in the diagram to the right. Fusion reactions have an energy density many times greater than nuclear fission; i.e., the reactions produce far greater energies per unit of mass even though //individual// fission reactions are generally much more energetic than //individual// fusion ones, which are themselves millions of times more energetic than chemical reactions. Only direct conversion of mass into energy, such as that caused by the collision of matter and antimatter, is more energetic per unit of mass than nuclear fusion. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">A substantial energy barrier of electrostatic forces 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. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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 neighbours 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 nuclear force generally increases with the size of the nucleus but approaches a limiting value corresponding to that of a nucleus with a diameter of about four nucleons. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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. <span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12pt; text-decoration: none;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">At short distances the attractive nuclear force is stronger than the repulsive electrostatic force. As such, the main technical difficulty for fusion is getting the nuclei close enough to fuse. <span style="font-family: "Times New Roman","serif"; font-size: 10pt;">Distances not to scale. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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 (all with more than 208 nucleons, corresponding to a diameter of about 6 nucleons) are not stable. The four most tightly bound nuclei, in decreasing order of binding energy, are 62Ni, 58Fe, 56Fe, and 60Ni.[3] Even though the nickel isotope ,62Ni, is more stable, the iron isotope 56Fe is an order of magnitude more common. This is due to a greater disintegration rate for 62Ni in the interior of stars driven by photon absorption. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">A notable exception to this general trend is the helium-4 nucleus, whose binding energy is higher than that of lithium, the next heaviest 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. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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. <span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12pt; text-decoration: none;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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: <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">If a species of nuclei is reacting with itself, such as the DD reaction, then the product //n//1//n//2 must be replaced by (1 / 2)//n//2. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">The significance of as a function of temperature in a device with a particular energy confinement time is found by considering the Lawson criterion. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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. In stars heavy enough, after the supply of hydrogen is exhausted in their cores, their cores (or a shell around the core) start fusing helium to carbon. In the most massive stars (at least 8-11 solar masses), the process is continued until some of their energy is produced by fusing lighter elements to iron. As iron has one of the highest binding energies, reactions producing heavier elements are generally endothermic. Therefore significant amounts of heavier elements are not formed during stable periods of massive star evolution, but are formed in supernova explosions and some lighter stars. Some of these heavier elements can in turn produce energy in nuclear fission. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Electrically charged particles (such as fuel ions) will follow magnetic field lines (see Guiding center). The fusion fuel can therefore be trapped using a strong magnetic field. A variety of magnetic configurations exist, including the toroidal geometries of tokamaks and stellarators and open-ended mirror confinement systems. //<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">. //<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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. Another method is to use conventional high explosive material to compress a fuel to fusion conditions.[4][5] The UTIAS explosive-driven-implosion facility was used to produce stable, centered and focused hemispherical implosions[6] to generate neutrons from D-D reactions. The simplest and most direct method proved to be in a predetonated stoichiometric mixture of deuterium-oxygen. The other successful method was using a miniature Voitenko compressor,[7] where a plane diaphragm was driven by the implosion wave into a secondary small spherical cavity that contained pure deuterium gas at one atmosphere.[8] <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Some confinement principles have been investigated, such as muon-catalyzed fusion, the Farnsworth-Hirsch fusor and Polywell (inertial electrostatic confinement), and bubble fusion. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">A variety of methods are known to effect 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. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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[//citation needed//] 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. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">In sonofusion (sometimes called "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. As of 2005, experiments to determine whether fusion is occurring gave conflicting results. If fusion is occurring, it is because the local temperature and pressure are sufficiently high to produce hot fusion.[9] In an episode of Horizon, on BBC television, results were presented showing 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.[//citation needed//] <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">The Polywell is a concept for a tabletop device in which fusion occurs. The device is a non-thermodynamic equilibrium machine which uses electrostatic confinement to accelerate ions into a center where they fuse together. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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.[10] 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.[11][12][13][14] <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">In "standard" "hot" fusion, the fuel reaches tremendous temperature and pressure inside a fusion reactor or nuclear weapon. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">The methods in the second group are examples of non-equilibrium systems, in which very high temperatures and pressures are produced in a relatively small region adjacent to material of much lower temperature. In his doctoral thesis for MIT, Todd Rider did a theoretical study of all quasineutral, isotropic, non-equilibrium fusion systems. He demonstrated that all such systems will leak energy at a rapid rate due to bremsstrahlung produced when electrons in the plasma hit other electrons or ions at a cooler temperature and suddenly decelerate. The problem is not as pronounced in a hot plasma because the range of temperatures, and thus the magnitude of the deceleration, is much lower. Note that Rider's work does not apply to non-neutral and/or anisotropic non-equilibrium plasmas. <span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12pt; text-decoration: none;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">The proton-proton chain dominates in stars the size of the Sun or smaller. <span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12pt; text-decoration: none;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">The CNO cycle dominates in stars heavier than the Sun. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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.[15] 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. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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//. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">In order to be useful as a source of energy, a fusion reaction must satisfy several criteria. It must <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Few reactions meet these criteria. The following are those with the largest cross sections[//citation needed//]: <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">(1) || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">→ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">42 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">( || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">3.5 MeV  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">)  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">n0 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">( || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">14.1 MeV  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">) || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">(2i) || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">→ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">( || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1.01 MeV  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">)  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">p+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">( || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">3.02 MeV  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">)  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">50% || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">(2ii) || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">→ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">( || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">0.82 MeV  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">)  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">n0 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">( || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2.45 MeV  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">)  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">50% || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">(3) || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">→ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">42 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">( || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">3.6 MeV  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">)  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">p+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">( || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">14.7 MeV  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">) ||   ||   ||   ||   ||   ||   || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">(4) || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">→ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">42 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2 n0 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">11.3 MeV ||  ||   || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">(5) || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">→ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">42 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2 p+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">12.9 MeV ||  ||   || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">(6i) || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">→ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">42 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">p+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">n0 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">12.1 MeV || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">51% || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">(6ii) || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">→ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">42 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">( || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">4.8 MeV  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">)  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">( || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">9.5 MeV  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">)  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">43% || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">(6iii) || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">→ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">42 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">( || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">0.5 MeV  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">)  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">n0 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">( || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1.9 MeV  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">)  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">p+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">( || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">11.9 MeV  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">)  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">6% || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">(7i) || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">63 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Li || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">→ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2 <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">42 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">22.4 MeV ||  ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">(7ii) || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">→ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">42 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">n0 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2.56 MeV ||  ||   || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">(7iii) || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">→ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">73 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Li || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">p+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">5.0 MeV ||  ||   || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">(7iv) || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">→ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">74 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Be || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">n0 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">3.4 MeV ||  ||   || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">(8) || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">p+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">63 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Li || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">→ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">42 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">( || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1.7 MeV  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">)  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">( || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2.3 MeV  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">) ||   ||   ||   ||   ||   ||   || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">(9) || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">63 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Li || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">→ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2 <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">42 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">p+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">16.9 MeV ||  ||   || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">(10) || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">p+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">115 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">B || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">→ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">3 <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">42 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">8.7 MeV ||  ||   ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 24pt;">Nuclear fusion **
 * <span style="font-family: "Times New Roman","serif"; font-size: 18pt;">Overview **
 * <span style="font-family: "Times New Roman","serif"; font-size: 18pt;">Overview **
 * <span style="color: windowtext; font-family: "Times New Roman","serif"; text-decoration: none;"> <span style="font-family: "Times New Roman","serif";"> ||
 * Nuclear fusion**
 * <span style="font-family: "Times New Roman","serif"; font-size: 7.5pt;">
 * <span style="font-family: "Times New Roman","serif"; font-size: 18pt;">Requirements **
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Gravitational confinement **
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Magnetic confinement **
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Inertial confinement **
 * <span style="font-family: "Times New Roman","serif"; font-size: 13.5pt;">Production methods **
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Locally cold fusion **
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Generally cold, locally hot fusion **
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Hot fusion **
 * <span style="font-family: "Times New Roman","serif"; font-size: 18pt;">Important reactions **
 * <span style="font-family: "Times New Roman","serif"; font-size: 13.5pt;">Astrophysical reaction chains **
 * <span style="font-family: "Times New Roman","serif"; font-size: 13.5pt;">Criteria and candidates for terrestrial reactions **
 * **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">be exothermic **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">: 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 4He the most common product because of its extraordinarily tight binding, although 3He and 3H also show up;
 * **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">involve low //Z// nuclei **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">: This is because the electrostatic repulsion must be overcome before the nuclei are close enough to fuse;
 * **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">have two reactants **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">: 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;
 * **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">have two or more products **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">: This allows simultaneous conservation of energy and momentum without relying on the electromagnetic force;
 * **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">conserve both protons and neutrons **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">: The cross sections for the weak interaction are too small.

**<span style="font-family: "Times New Roman","serif";">Nucleosynthesis **<span style="font-family: "Times New Roman","serif";"> || **<span style="font-family: "Times New Roman","serif";">Related topics **<span style="font-family: "Times New Roman","serif";"> || <span style="font-family: "Times New Roman","serif"; font-size: 7.5pt;">edit <span style="font-family: "Times New Roman","serif";"> || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Some reaction candidates can be eliminated at once.[16] The D-6Li reaction has no advantage compared to p+- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">115 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">B because it is roughly as difficult to burn but produces substantially more neutrons through <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D side reactions. There is also a p+- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">73 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Li reaction, but the cross section is far too low, except possibly when //T//i > 1 MeV, but at such high temperatures an endothermic, direct neutron-producing reaction also becomes very significant. Finally there is also a p+- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">94 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Be reaction, which is not only difficult to burn, but <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">94 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Be can be easily induced to split into two alpha particles and a neutron. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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: <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">n0 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">63 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Li || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">→ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">42 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">n0 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">73 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Li || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">→ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">42 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">n0 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">To evaluate the usefulness of these reactions, in addition to the reactants, the products, and the energy released, one needs to know something about the cross section. Any given fusion device will have a maximum plasma pressure that it can sustain, and an economical device will always operate near this maximum. Given this pressure, the largest fusion output is obtained when the temperature is chosen so that <σv>/T² is a maximum. This is also the temperature at which the value of the triple product //nT//τ required for ignition is a minimum, since that required value is inversely proportional to <σv>/T² (see Lawson criterion). (A plasma is "ignited" if the fusion reactions produce enough power to maintain the temperature without external heating.) This optimum temperature and the value of <σv>/T² at that temperature is given for a few of these reactions in the following table. **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">fuel ** || **//<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T //****<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> [keV] ** || **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"><σv>/T² [m³/s/keV²] ** || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">13.6 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1.24×10−24 || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">15 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1.28×10−26 || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">58 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2.24×10−26 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">p+- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">63 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Li || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">66 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1.46×10−27 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">p+- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">115 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">B || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">123 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">3.01×10−27 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Note that many of the reactions form chains. For instance, a reactor fueled with <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T and <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He will create some <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D, which is then possible to use in the <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He reaction if the energies are "right". An elegant idea is to combine the reactions (8) and (9). The <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He from reaction (8) can react with <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">63 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Li 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. <span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12pt; text-decoration: none;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> <span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12pt; text-decoration: none;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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 //E//fus, the energy of the charged fusion products //E//ch, and the atomic number //Z// of the non-hydrogenic reactant. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Specification of the <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D 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 <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T and <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He products. <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T burns so well in a deuterium plasma that it is almost impossible to extract from the plasma. The <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He reaction is optimized at a much higher temperature, so the burnup at the optimum <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D temperature may be low, so it seems reasonable to assume the <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T but not the <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He gets burned up and adds its energy to the net reaction. Thus we will count the <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D fusion energy as //E//fus = (4.03+17.6+3.27)/2 = 12.5 MeV and the energy in charged particles as //E//ch = (4.03+3.5+0.82)/2 = 4.2 MeV. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Another unique aspect of the <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D reaction is that there is only one reactant, which must be taken into account when calculating the reaction rate. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">With this choice, we tabulate parameters for four of the most important reactions **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">fuel ** || **//<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Z //**<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> || **//<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">E //****<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">fus ****<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> [MeV] ** || **//<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">E //****<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">ch ****<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> [MeV] ** || **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">neutronicity ** || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">17.6 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">3.5 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">0.80 || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">12.5 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">4.2 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">0.66 || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">18.3 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">18.3 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">~0.05 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">p+- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">115 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">B || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">5 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">8.7 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">8.7 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">~0.001 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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 (//E//fus-//E//ch)///E//fus. 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. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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 <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D reaction has only one reactant, the rate is twice as high as if the fuel were divided between two hydrogenic species. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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 <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D because each ion can react with any of the other ions, not just a fraction of them. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">We can now compare these reactions in the following table. **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">fuel ** || **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"><σv>/T² ** || **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">penalty/bonus ** || **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">reactivity ** || **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Lawson criterion ** || **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">power density (W/m3/kPa2) ** || **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">relation of power density ** || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1.24×10−24 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">34 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1 || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1.28×10−26 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">48 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">30 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">0.5 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">68 || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2.24×10−26 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2/3 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">83 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">16 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">0.43 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">80 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">p+- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">63 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Li || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1.46×10−27 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1/2 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1700 ||  || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">0.005 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">6800 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">p+- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">115 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">B || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">3.01×10−27 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1/3 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1240 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">500 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">0.014 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2500 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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 <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T reaction under comparable conditions. The column "Lawson criterion" weights these results with //E//ch and gives an indication of how much more difficult it is to achieve ignition with these reactions, relative to the difficulty for the <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T reaction. The last column is labeled "power density" and weights the practical reactivity with //E//fus. It indicates how much lower the fusion power density of the other reactions is compared to the <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T reaction and can be considered a measure of the economic potential. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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.[17] **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">fuel ** || **//<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T //****<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">i ****<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> (keV) ** || **//<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">P //****<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">fusion ****<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">///P//Bremsstrahlung ** || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">50 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">140 || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">500 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2.9 || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">100 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">5.3 || <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1000 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">0.72 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">p+- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">63 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Li || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">800 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">0.21 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">p+- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">115 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">B || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">300 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">0.57 || <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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 <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T very much because the Bremsstrahlung fraction is low, but it will push the other fuels into regimes where the power density relative to <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">31 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">T is even lower and the required confinement even more difficult to achieve. For <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D and <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">21 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">D- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He, Bremsstrahlung losses will be a serious, possibly prohibitive problem. For <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">32 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">He, p+- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">63 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Li and p+- <span style="font-family: "Times New Roman","serif"; font-size: 9.5pt;">115 <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">B 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.[18] This limitation does not apply to non-neutral and anisotropic plasmas; however, these have their own challenges to contend with. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">
 * <span style="color: windowtext; font-family: "Times New Roman","serif"; text-decoration: none;">[[image:file:///C:/DOCUME%7E1/PERSONAL/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image016.gif width="85" height="99" caption="Wpdms physics proton proton chain 1.svg" link="http://en.wikipedia.org/wiki/File:Wpdms_physics_proton_proton_chain_1.svg"]] <span style="font-family: "Times New Roman","serif";"> * <span style="font-family: "Times New Roman","serif";">Stellar nucleosynthesis
 * <span style="font-family: "Times New Roman","serif";">Big Bang nucleosynthesis
 * <span style="font-family: "Times New Roman","serif";">Supernova nucleosynthesis
 * <span style="font-family: "Times New Roman","serif";">Cosmic ray spallation ||
 * * <span style="font-family: "Times New Roman","serif";">Astrophysics
 * **<span style="font-family: "Times New Roman","serif";">Nuclear fusion **<span style="font-family: "Times New Roman","serif";">
 * <span style="font-family: "Times New Roman","serif";">R-process
 * <span style="font-family: "Times New Roman","serif";">S-process
 * <span style="font-family: "Times New Roman","serif";">Nuclear fission ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 13.5pt;">Neutronicity, confinement requirement, and power density **
 * <span style="font-family: "Times New Roman","serif"; font-size: 13.5pt;">Bremsstrahlung losses in quasineutral, isotropic plasmas **
 * <span style="font-family: "Times New Roman","serif"; font-size: 18pt;">References **
 * 1) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> J. Kenneth Shultis, Richard E. Faw (2002). //Fundamentals of nuclear science and engineering//. CRC Press. p. 151. ISBN 0824708342. http://books.google.com/books?id=SO4Lmw8XoEMC&pg=PA151.
 * 2) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> [1]
 * 3) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> The Most Tightly Bound Nuclei
 * 4) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> F. Winterberg"Conjectured Metastable Super-Explosives formed under High Pressure for Thermonuclear Ignition"
 * 5) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Zhang, Fan (Medicine Hat, CA)Murray, Stephen Burke (Medicine Hat, CA)Higgins, Andrew (Montreal, CA)(2005)"Super compressed detonation method and device to effect such detonation"
 * 6) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> I.I. Glass and J.C. Poinssot"IMPLOSION DRIVEN SHOCK TUBE"
 * 7) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> D.Sagie and I.I Glass(1982)"Explosive-driven hemispherical implosions for generating fusion plasmas"
 * 8) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> T. Saito, A. K. Kudian and I. I. Glass"Temperature Measurements Of An Implosion Focus"
 * 9) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Access : Desktop fusion is back on the table : Nature News
 * 10) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Supplementary methods for “Observation of nuclear fusion driven by a pyroelectric crystal”
 * 11) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> UCLA Crystal Fusion
 * 12) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Physics News Update 729
 * 13) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Coming in out of the cold: nuclear fusion, for real | csmonitor.com
 * 14) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Nuclear fusion on the desktop ... really! - Science – MSNBC.com
 * 15) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> FusEdWeb | Fusion Education
 * 16) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> http://theses.mit.edu/Dienst/UI/2.0/Page/0018.mit.theses/1995-130/30?npages=306
 * 17) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> http://theses.mit.edu/Dienst/UI/2.0/Page/0018.mit.theses/1995-130/26?npages=306
 * 18) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">^ **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> http://fusion.ps.uci.edu/artan/Posters/aps_poster_2.pdf Portable Document Format (PDF)