Nuclear fusion

Template:Short description Template:Hatnote group Template:Use dmy dates Template:Use American English Template:Multiple image Template:Nuclear physics

Nuclear fusion is a reaction in which two or more atomic nuclei combine to form a larger nuclei, nuclei/neutron by-products. The difference in mass between the reactants and products is manifested as either the release or absorption of energy. This difference in mass arises as a result of the difference in nuclear binding energy between the atomic nuclei before and after the fusion reaction. Nuclear fusion is the process that powers all active stars, via many reaction pathways.

Fusion processes require an extremely large triple product of temperature, density, and confinement time. These conditions occur only in stellar cores, advanced nuclear weapons, and are approached in fusion power experiments.

A nuclear fusion process that produces atomic nuclei lighter than nickel-62 is generally exothermic, due to the positive gradient of the nuclear binding energy curve. The most fusible nuclei are among the lightest, especially deuterium, tritium, and helium-3. The opposite process, nuclear fission, is most energetic for very heavy nuclei, especially the actinides.

Applications of fusion include fusion power, thermonuclear weapons, boosted fission weapons, neutron sources, and superheavy element production.

HistoryEdit

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TheoryEdit

File:EffetTunnel.gif

Animation of an electron's wave function as quantum tunneling allows transit through a barrier with a low probability. In the same fashion, an atomic nucleus can quantum tunnel through the Coulomb barrier to another nucleus, making a fusion reaction possible.

American chemist William Draper Harkins was the first to propose the concept of nuclear fusion in 1915.<ref name=":0"> Template:Cite journal</ref> Francis William Aston's 1919 invention of the mass spectrometer allowed the discovery that four hydrogen atoms are heavier than one helium atom. Thus in 1920, Arthur Eddington correctly predicted fusion of hydrogen into helium could be the primary source of stellar energy.<ref>Template:Cite journal

Reprinted in: Template:Cite journal
Reprinted in: Template:Cite journal</ref>

Quantum tunneling was discovered by Friedrich Hund in 1927, with relation to electron levels.<ref>Template:Cite journal</ref><ref>Tunnelling was independently observed by Soviet scientists Grigory Samuilovich Landsberg and Leonid Isaakovich Mandelstam. See:

Template:Cite journal
Template:Cite journal
Template:Cite journal</ref> In 1928, George Gamow was the first to apply tunneling to the nucleus, first to alpha decay, then to fusion as an inverse process. From this, in 1929, Robert Atkinson and Fritz Houtermans made the first estimates for stellar fusion rates.<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref>

In 1938, Hans Bethe worked with Charles Critchfield to enumerate the proton–proton chain that dominates Sun-type stars. In 1939, Bethe published the discovery of the CNO cycle common to higher-mass stars.

Early experimentsEdit

File:27-inch cyclotron.jpg

M. Stanley Livingston and Ernest Lawrence in front of UCRL's 27-inch cyclotron in 1934. These devices were used for many early experiments demonstrating deuterium fusion.

During the 1920s, Patrick Blackett made the first conclusive experiments in artificial nuclear transmutation at the Cavendish Laboratory. There, John Cockcroft and Ernest Walton built their generator on the inspiration of Gamow's paper. In April 1932, they published experiments on the reaction:

Template:Nuclide + p → Template:SimpleNuclide → 2 Template:Nuclide

where the intermediary nuclide was later confirmed to be the extremely short-lived beryllium-8.<ref name="b4852">Template:Cite journal</ref> This has a claim to the first artificial fusion reaction.Template:Citation needed

In papers from July and November 1933, Ernest Lawrence et. al. at the University of California Radiation Laboratory, in some of the earliest cyclotron experiments, accidentally produced the first deuterium–deuterium fusion reactions:

Template:Nuclide + Template:Nuclide → Template:Nuclide + p

Template:Nuclide + Template:Nuclide → Template:Nuclide + Template:SubatomicParticle

The Radiation Lab, only detecting the resulting energized protons and neutrons,<ref name="n665">Template:Cite journal</ref><ref name="m978">Template:Cite journal</ref> misinterpreted the source as an exothermic disintegration of the deuterons, now known to be impossible.<ref name="m343">Template:Cite journal</ref> In May 1934, Mark Oliphant, Paul Harteck, and Ernest Rutherford at the Cavendish Laboratory,<ref name="v423">Template:Cite journal</ref> published an intentional deuterium fusion experiment, and made the discovery of both tritium and helium-3. This is widely considered the first experimental demonstration of fusion.<ref name="m343" />

In 1938, Arthur Ruhlig at the University of Michigan made the first observation of deuterium–tritium (DT) fusion and its characteristic 14 MeV neutrons, now known as the most favourable reaction:

Template:Nuclide + Template:Nuclide → Template:Nuclide + Template:SubatomicParticle

WeaponizationEdit

Template:Main page Research into fusion for military purposes began in the early 1940s as part of the Manhattan Project. In 1941, Enrico Fermi and Edward Teller had a conversation about the possibility of a fission bomb creating conditions for thermonuclear fusion. In 1942, Emil Konopinski brought Ruhlig's work on the deuterium–tritium reaction to the projects attention. J. Robert Oppenheimer initially commissioned physicists at Chicago and Cornell to use the Harvard University cyclotron to secretly investigate its cross-section, and that of the lithium reaction (see below). Measurements were obtained at Purdue, Chicago, and Los Alamos from 1942 to 1946. Theoretical assumptions about DT fusion gave it a similar cross-section to DD. However, in 1946 Egon Bretscher discovered a resonance enhancement giving the DT reaction a cross-section ~100 times larger.<ref name="r126">Template:Cite journal</ref>

From 1945, John von Neumann, Teller, and other Los Alamos scientists used ENIAC, one of the first electronic computers, to simulate thermonuclear weapon detonations.<ref name="c888">Template:Cite journal</ref>

The first artificial thermonuclear fusion reaction occurred during the 1951 US Greenhouse George nuclear test, using a small amount of deuterium–tritium gas. This produced the largest yield to date, at 225 kt, 15 times that of Little Boy. The first "true" thermonuclear weapon detonation i.e. a two-stage device, was the 1952 Ivy Mike test of a liquid deuterium-fusing device, yielding over 10 Mt. The key to this jump was the full utilization of the fission blast by the Teller–Ulam design.

The Soviet Union had begun their focus on a hydrogen bomb program earlier, and in 1953 carried out the RDS-6s test. This had international impacts as the first air-deliverable bomb using fusion, but yielded 400 kt and was limited by its single-stage design. The first Soviet two-stage test was RDS-37 in 1955 yielding 1.5 Mt, using an independently reached version of the Teller–Ulam design.

Modern devices benefit from the usage of solid lithium deuteride with an enrichment of lithium-6. This is due to the Jetter cycle involving the exothermic reaction:

Template:Nuclide + Template:SubatomicParticle → Template:Nuclide + Template:Nuclide

During thermonuclear detonations, this provides tritium for the highly energetic DT reaction, and benefits from its neutron production, creating a closed neutron cycle.<ref name="m027">Template:Cite arXiv</ref>

Fusion energyEdit

While fusion bomb detonations were loosely considered for energy production, the possibility of controlled and sustained reactions remained the scientific focus for peaceful fusion power. Research into developing controlled fusion inside fusion reactors has been ongoing since the 1930s, with Los Alamos National Laboratory's Scylla I device producing the first laboratory thermonuclear fusion in 1958, but the technology is still in its developmental phase.<ref>Template:Cite news</ref>

The first experiments producing large amounts of controlled fusion power were the experiments with mixes of deuterium and tritium in Tokamaks. Experiments in the TFTR at the PPPL in Princeton University Princeton NJ, USA during 1993–1996 produced created 1.6 GJ fusion energy. The peak fusion power was 10.3 MW from Template:Val reactions per second, and peak fusion energy created in one discharge was 7.6 MJ. Subsequent experiments in the JET in 1997 achieved a peak fusion power of 16 MW (Template:Val). The central Q, defined as the local fusion power produced to the local applied heating power, is computed to be 1.3.<ref>"Core fusion power gain and alpha heating in JET, TFTR, and ITER", R.V. Budny, J.G. Cordey and TFTR Team and JET Contributors, Nuclear Fus. (2016) <56> 056002 #5 (May) https://iopscience.iop.org/article/10.1088/0029-5515/56/5/056002 //home/budny/papers/NF/core_q_dt/nf_56_5_056002.pdf</ref> A JET experiment in 2024 produced 69 MJ of fusion power, consuming 0.2 mgm of D and T.

The US National Ignition Facility, which uses laser-driven inertial confinement fusion, was designed with a goal of achieving a fusion energy gain factor (Q) of larger than one; the first large-scale laser target experiments were performed in June 2009 and ignition experiments began in early 2011.<ref name="programsNIF">Template:Cite journal</ref><ref>Template:Cite journal</ref> On 13 December 2022, the United States Department of Energy announced that on 5 December 2022, they had successfully accomplished break-even fusion, "delivering 2.05 megajoules (MJ) of energy to the target, resulting in 3.15 MJ of fusion energy output."<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> The rate of supplying power to the experimental test cell is hundreds of times larger than the power delivered to the target.

Prior to this breakthrough, controlled fusion reactions had been unable to produce break-even (self-sustaining) controlled fusion.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> The two most advanced approaches for it are magnetic confinement (toroid designs) and inertial confinement (laser designs). Workable designs for a toroidal reactor that theoretically will deliver ten times more fusion energy than the amount needed to heat plasma to the required temperatures are in development (see ITER). The ITER facility is expected to finish its construction phase in 2025. It will start commissioning the reactor that same year and initiate plasma experiments in 2025, but is not expected to begin full deuterium–tritium fusion until 2035.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

Private companies pursuing the commercialization of nuclear fusion received $2.6 billion in private funding in 2021 alone, going to many notable startups including but not limited to Commonwealth Fusion Systems, Helion Energy Inc., General Fusion, TAE Technologies Inc. and Zap Energy Inc.<ref>Template:Cite news</ref>

One of the most recent breakthroughs to date in maintaining a sustained fusion reaction occurred in France's WEST fusion reactor. It maintained a 90 million degree plasma for a record time of six minutes. This is a tokamak style reactor which is the same style as the upcoming ITER reactor.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

ProcessEdit

File:Deuterium-tritium fusion.svg

Fusion of deuterium with tritium creating helium-4, freeing a neutron, and releasing 17.59 MeV as kinetic energy of the products while a corresponding amount of mass disappears, in agreement with kinetic E = ∆mc², where Δm is the decrease in the total rest mass of particles<ref name=Shultis> Template:Cite book</ref>

The release of energy with the fusion of light elements is due to the interplay of two opposing forces: the nuclear force, a manifestation of the strong interaction, which holds protons and neutrons tightly together in the atomic nucleus; and the Coulomb force, which causes positively charged protons in the nucleus to repel each other.<ref>Physics Flexbook Template:Webarchive. Ck12.org. Retrieved 19 December 2012.</ref> Lighter nuclei (nuclei smaller than iron and nickel) are sufficiently small and proton-poor to allow the nuclear force to overcome the Coulomb force. This is because the nucleus is sufficiently small that all nucleons feel the short-range attractive force at least as strongly as they feel the infinite-range Coulomb repulsion. Building up nuclei from lighter nuclei by fusion releases the extra energy from the net attraction of particles. For larger nuclei, however, no energy is released, because the nuclear force is short-range and cannot act across larger nuclei.

Fusion powers stars and produces most elements lighter than cobalt in a process called nucleosynthesis. The Sun is a main-sequence star, and, as such, generates its energy by nuclear fusion of hydrogen nuclei into helium. In its core, the Sun fuses 620 million metric tons of hydrogen and makes 616 million metric tons of helium each second. The fusion of lighter elements in stars releases energy and the mass that always accompanies it. For example, in the fusion of two hydrogen nuclei to form helium, 0.645% of the mass is carried away in the form of kinetic energy of an alpha particle or other forms of energy, such as electromagnetic radiation.<ref name="bulletin1950">Template:Cite journal</ref>

It takes considerable energy to force nuclei to fuse, even those of the lightest element, hydrogen. When accelerated to high enough speeds, nuclei can overcome this electrostatic repulsion and be brought close enough such that the attractive nuclear force is greater than the repulsive Coulomb force. The strong force grows rapidly once the nuclei are close enough, and the fusing nucleons can essentially "fall" into each other and the result is fusion; this is an exothermic process.<ref>Template:Cite book</ref>

Energy released in most nuclear reactions is much larger than in chemical reactions, because the binding energy that holds a nucleus together is 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 Template:Val—less than one-millionth of the Template:Val released in the deuterium–tritium (D–T) reaction shown in the adjacent diagram. Fusion reactions have an energy density many times greater than nuclear fission; the reactions produce far greater energy 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. Via the mass–energy equivalence, fusion yields a 0.7% efficiency of reactant mass into energy. This can be only be exceeded by the extreme cases of the accretion process involving neutron stars or black holes, approaching 40% efficiency, and antimatter annihilation at 100% efficiency. (The complete conversion of one gram of matter would expel Template:Val of energy.)

In astrophysicsEdit

Fusion is responsible for the astrophysical production of the majority of elements lighter than iron. This includes most types of Big Bang nucleosynthesis and stellar nucleosynthesis. Non-fusion processes that contribute include the s-process and r-process in neutron merger and supernova nucleosynthesis, responsible for elements heavier than iron.

StarsEdit

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File:Fusion in the Sun.svg

The proton–proton chain reaction, branch I, dominates in stars the size of the Sun or smaller.

File:CNO Cycle.svg

The CNO cycle dominates in stars heavier than the Sun.

An important fusion process is the stellar nucleosynthesis that powers stars, including the Sun. In the 20th century, it was recognized that the energy released from nuclear fusion reactions accounts for the longevity of stellar heat and light. The fusion of nuclei in a star, starting from its initial hydrogen and helium abundance, provides that energy and synthesizes new nuclei. Different reaction chains are involved, depending on the mass of the star (and therefore the pressure and temperature in its core).

Around 1920, Arthur Eddington anticipated the discovery and mechanism of nuclear fusion processes in stars, in his paper The Internal Constitution of the Stars.<ref name=eddington>Template:Cite journal</ref><ref name=eddington2>Template:Cite journal</ref> At that time, the source of stellar energy was unknown; Eddington correctly speculated that the source was fusion of hydrogen into helium, liberating enormous energy according to Einstein's equation Template:Math. This was a particularly remarkable development since at that time fusion and thermonuclear energy had not yet been discovered, nor even that stars are largely composed of hydrogen (see metallicity). Eddington's paper reasoned that:

The leading theory of stellar energy, the contraction hypothesis, should cause the rotation of a star to visibly speed up due to conservation of angular momentum. But observations of Cepheid variable stars showed this was not happening.
The only other known plausible source of energy was conversion of matter to energy; Einstein had shown some years earlier that a small amount of matter was equivalent to a large amount of energy.
Francis Aston had also recently shown that the mass of a helium atom was about 0.8% less than the mass of the four hydrogen atoms which would, combined, form a helium atom (according to the then-prevailing theory of atomic structure which held atomic weight to be the distinguishing property between elements; work by Henry Moseley and Antonius van den Broek would later show that nucleic charge was the distinguishing property and that a helium nucleus, therefore, consisted of two hydrogen nuclei plus additional mass). This suggested that if such a combination could happen, it would release considerable energy as a byproduct.
If a star contained just 5% of fusible hydrogen, it would suffice to explain how stars got their energy. (It is now known that most 'ordinary' stars are usually made of around 70% to 75% hydrogen)
Further elements might also be fused, and other scientists had speculated that stars were the "crucible" in which light elements combined to create heavy elements, but without more accurate measurements of their atomic masses nothing more could be said at the time.

All of these speculations were proven correct in the following decades.

The primary source of solar energy, and that of similar size stars, is the fusion of hydrogen to form helium (the proton–proton chain reaction), which occurs at a solar-core temperature of 14 million kelvin. The net result is the fusion of four protons into one alpha particle, with the release of two positrons and two neutrinos (which changes two of the protons into neutrons), and energy. In heavier stars, the CNO cycle and other processes are more important. As a star uses up a substantial fraction of its hydrogen, it begins to fuse heavier elements. In massive cores, silicon-burning is the final fusion cycle, leading to a build-up of iron and nickel nuclei.

Nuclear binding energy makes the production of elements heavier than nickel via fusion energetically unfavorable. These elements are produced in non-fusion processes: the s-process, r-process, and the variety of processes that can produce p-nuclei. Such processes occur in giant star shells, or supernovae, or neutron star mergers.

Brown dwarfsEdit

Brown dwarfs fuse deuterium and in very high mass cases also fuse lithium.

White dwarfsEdit

Carbon–oxygen white dwarfs, which accrete matter either from an active stellar companion or white dwarf merger, approach the Chandrasekhar limit of 1.44 solar masses. Immediately prior, carbon burning fusion begins, destroying the Earth-sized dwarf within one second, in a Type Ia supernova.

Much more rarely, helium white dwarfs may merge, which does not cause an explosion but begins helium burning in an extreme type of helium star.

Neutron starsEdit

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Some neutron stars accrete hydrogen and helium from an active stellar companion. Periodically, the helium accretion reaches a critical level, and a thermonuclear burn wave propagates across the surface, on the timescale of one second.<ref name="y734">Template:Cite journal</ref>

Black hole accretion disksEdit

Similar to stellar fusion, extreme conditions within black hole accretion disks can allow fusion reactions. Calculations show the most energetic reactions occur around lower stellar mass black holes, below 10 solar masses, compared to those above 100. Beyond five Schwarzschild radii, carbon-burning and fusion of helium-3 dominates the reactions. Within this distance, around lower mass black holes, fusion of nitrogen, oxygen, neon, and magnesium can occur. In the extreme limit, the silicon-burning process can begin with the fusion of silicon and selenium nuclei.<ref name="b407">Template:Cite journal</ref>

Big BangEdit

Template:Main article From the period approximately 10 seconds to 20 minutes after the Big Bang, the universe cooled from over 100 keV to 1 keV. This allowed the combination of protons and neutrons in deuterium nuclei, and beginning a rapid fusion chain into tritium and helium-3 and ending in predominantly helium-4, with a minimal fraction of lithium, beryllium, and boron nuclei.

RequirementsEdit

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File:Binding energy curve - common isotopes.svg

The nuclear binding energy curve. The formation of nuclei with masses up to iron-56 releases energy, as illustrated above.

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 quantum effect in which nuclei can tunnel through coulomb forces.

When a nucleon such as a proton or neutron is added to a nucleus, the nuclear force attracts it to all the other nucleons of the nucleus (if the atom is small enough), but primarily to its immediate neighbors due to the short range of the force. The nucleons in the interior of a nucleus have more neighboring nucleons than those on the surface. Since smaller nuclei have a larger surface-area-to-volume ratio, the binding energy per nucleon due to the 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. It is important to keep in mind that nucleons are quantum objects. So, for example, since two neutrons in a nucleus are identical to each other, the goal of distinguishing one from the other, such as which one is in the interior and which is on the surface, is in fact meaningless, and the inclusion of quantum mechanics is therefore necessary for proper calculations.

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 atomic number grows.

File:Nuclear fusion forces diagram.svg

The electrostatic force between the positively charged nuclei is repulsive, but when the separation is small enough, the quantum effect will tunnel through the wall. Therefore, the prerequisite for fusion is that the two nuclei be brought close enough together for a long enough time for quantum tunneling to act.

The net result of the opposing electrostatic and strong nuclear 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 per nucleon, are Template:SimpleNuclide, Template:SimpleNuclide, Template:SimpleNuclide, and Template:SimpleNuclide.<ref>The Most Tightly Bound Nuclei Template:Webarchive. Hyperphysics.phy-astr.gsu.edu. Retrieved 17 August 2011.</ref> Even though the nickel isotope, Template:SimpleNuclide, is more stable, the iron isotope Template:SimpleNuclide is an order of magnitude more common. This is due to the fact that there is no easy way for stars to create Template:SimpleNuclide through the alpha process.

An exception to this general trend is the helium-4 nucleus, whose binding energy is higher than that of lithium, the next heavier element. This is because protons and neutrons are fermions, which according to the Pauli exclusion principle cannot exist in the same nucleus in exactly the same state. Each proton or neutron's 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 (it is a doubly magic nucleus), so all four of its nucleons can be in the ground state. Any additional nucleons would have to go into higher energy states. Indeed, the helium-4 nucleus is so tightly bound that it is commonly treated as a single quantum mechanical particle in nuclear physics, namely, the alpha particle.

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 close enough for long enough so the strong attractive nuclear force can take over and overcome the repulsive electrostatic force. This can also be described as the nuclei overcoming the so-called Coulomb barrier. The kinetic energy to achieve this can be lower than the barrier itself because of quantum tunneling.

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

Using deuterium–tritium fuel, the resulting energy barrier is about 0.1 MeV. In comparison, the energy needed to remove an electron from hydrogen is 13.6 eV. The (intermediate) result of the fusion is an unstable ⁵He nucleus, which immediately ejects a neutron with 14.1 MeV. The recoil energy of the remaining ⁴He nucleus is 3.5 MeV, so the total energy liberated is 17.6 MeV. This is many times more than what was needed to overcome the energy barrier.

File:Fusion rxnrate.svg

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 kelvin) and at a higher value than other reactions commonly considered for fusion energy.

The reaction cross section (σ) is a measure of the probability of a fusion reaction as a function of the relative velocity of the two reactant nuclei. If the reactants have a distribution of velocities, e.g. a thermal distribution, then it is useful to perform an average over the distributions of the product of cross-section and velocity. This average is called the 'reactivity', denoted Template:Math. The reaction rate (fusions per volume per time) is Template:Math times the product of the reactant number densities:

<math>f = n_1 n_2 \langle \sigma v \rangle.</math>

If a species of nuclei is reacting with a nucleus like itself, such as the DD reaction, then the product <math>n_1n_2</math> must be replaced by <math>n^2/2</math>.

<math>\langle \sigma v \rangle</math> increases from virtually zero at room temperatures up to meaningful magnitudes at temperatures of Template:Val. At these temperatures, well above typical ionization energies (13.6 eV in the hydrogen case), the fusion reactants exist in a plasma state.

The significance of <math>\langle \sigma v \rangle</math> as a function of temperature in a device with a particular energy confinement time is found by considering the Lawson criterion. This is an extremely challenging barrier to overcome on Earth, which explains why fusion research has taken many years to reach the current advanced technical state.<ref name=lawson>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref><ref>Template:Cite journal</ref>

Artificial fusionEdit

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Thermonuclear fusionEdit

{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= {{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= Template:Ambox }} }} Thermonuclear fusion is the process of atomic nuclei combining or "fusing" using high temperatures to drive them close enough together for this to become possible. Such temperatures cause the matter to become a plasma and, if confined, fusion reactions may occur due to collisions with extreme thermal kinetic energies of the particles. There are two forms of thermonuclear fusion: uncontrolled, in which the resulting energy is released in an uncontrolled manner, as it is in thermonuclear weapons ("hydrogen bombs") and in most stars; and controlled, where the fusion reactions take place in an environment allowing some or all of the energy released to be harnessed.

Temperature is a measure of the average kinetic energy of particles, so by heating the material it will gain energy. After reaching sufficient temperature, given by the Lawson criterion, the energy of accidental collisions within the plasma is high enough to overcome the Coulomb barrier and the particles may fuse together.

In a deuterium–tritium fusion reaction, for example, the energy necessary to overcome the Coulomb barrier is 0.1 MeV. Converting between energy and temperature shows that the 0.1 MeV barrier would be overcome at a temperature in excess of 1.2 billion kelvin.

There are two effects that are needed to lower the actual temperature. 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 0.1 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 tunnelling. 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 these reasons fuel at lower temperatures will still undergo fusion events, at a lower rate.

Thermonuclear fusion is one of the methods being researched in the attempts to produce fusion power. If thermonuclear fusion becomes favorable to use, it would significantly reduce the world's carbon footprint.

Beam–beam or beam–target fusionEdit

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Accelerator-based light-ion fusion is a technique using particle accelerators to achieve particle kinetic energies sufficient to induce light-ion fusion reactions.<ref>Template:Cite book</ref>

Accelerating light ions is relatively easy, and can be done in an efficient manner—requiring only a vacuum tube, a pair of electrodes, and a high-voltage transformer; fusion can be observed with as little as 10 kV between the electrodes.Template:Citation needed The system can be arranged to accelerate ions into a static fuel-infused target, known as beam–target fusion, or by accelerating two streams of ions towards each other, beam–beam fusion.Template:Citation needed 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, the vast majority of ions expend their energy emitting bremsstrahlung radiation and the 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 that allows ions of those nuclei to be accelerated against hydride targets, also containing deuterium and tritium, where fusion takes place, releasing a flux of neutrons. 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.Template:Citation needed

A number of attempts to recirculate the ions that "miss" collisions have been made over the years. One of the better-known attempts in the 1970s was Migma, which used a unique particle storage ring to capture ions into circular orbits and return them to the reaction area. Theoretical calculations made during funding reviews pointed out that the system would have significant difficulty scaling up to contain enough fusion fuel to be relevant as a power source. In the 1990s, a new arrangement using a field-reversed configuration (FRC) as the storage system was proposed by Norman Rostoker and continues to be studied by TAE Technologies Template:As of. A closely related approach is to merge two FRC's rotating in opposite directions,<ref>J. Slough, G. Votroubek, and C. Pihl, "Creation of a high-temperature plasma through merging and compression of supersonic field reversed configuration plasmoids" Nucl. Fusion 51,053008 (2011).</ref> which is being actively studied by Helion Energy. Because these approaches all have ion energies well beyond the Coulomb barrier, they often suggest the use of alternative fuel cycles like p-¹¹B that are too difficult to attempt using conventional approaches.<ref>A. Asle Zaeem et al "Aneutronic Fusion in Collision of Oppositely Directed Plasmoids" Plasma Physics Reports, Vol. 44, No. 3, pp. 378–386 (2018).</ref>

Element synthesisEdit

Template:See also Fusion of very heavy target nuclei with accelerated ion beams is the primary method of element synthesis. In early 1930s nuclear experiments, deuteron beams were used, to discover the first synthetic elements, such as technetium, neptunium, and plutonium:

<math chem="">\begin{align} \ce{ {^{238}_{92}U} + {^{2}_{1}H} ->} &\ce{ {^{238}_{93}Np} + 2^{1}_{0}n} \end{align}</math>

Fusion of very heavy target nuclei with heavy ion beams has been used to discover superheavy elements:

<math chem="">\begin{align} \ce{ {^{208}_{82}Pb} + {^{62}_{28}Ni} ->} &\ce{ {^{269}_{110}Ds} + ^{1}_{0}n} \end{align}</math>

<math chem="">\begin{align} \ce{ {^{249}_{98}Cf} + {^{48}_{20}Ca} ->} &\ce{ {^{294}_{118}Og} + 3^{1}_{0}n} \end{align}</math>

Muon-catalyzed fusionEdit

Muon-catalyzed fusion is a fusion process that occurs at ordinary temperatures. It was studied in detail by Steven Jones in the early 1980s. Net energy production from this reaction has been unsuccessful because of the high energy required to create muons, their short 2.2 μs half-life, and the high chance that a muon will bind to the new alpha particle and thus stop catalyzing fusion.<ref>Template:Cite journal</ref>

Other principlesEdit

File:TCV vue gen.jpg

The Tokamak à configuration variable, research fusion reactor, at the École Polytechnique Fédérale de Lausanne (Switzerland)

Some other confinement principles have been investigated.

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, and pure fusion bombs feasible. This is not near becoming a practical power source, due to the cost of manufacturing antimatter alone.
Pyroelectric fusion was reported in April 2005 by a team at UCLA. The scientists used a pyroelectric crystal heated from Template:Convert, 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. At the estimated energy levels,<ref>Supplementary methods for "Observation of nuclear fusion driven by a pyroelectric crystal" Template:Webarchive. Main article Template:Cite journal</ref> the D–D fusion reaction may occur, producing helium-3 and a 2.45 MeV neutron. Although it makes a useful neutron generator, the apparatus is not intended for power generation since it requires far more energy than it produces.<ref>UCLA Crystal Fusion. Rodan.physics.ucla.edu. Retrieved 17 August 2011. Template:Webarchive</ref><ref>Template:Cite journal</ref><ref>Coming in out of the cold: nuclear fusion, for real Template:Webarchive. The Christian Science Monitor. (6 June 2005). Retrieved 17 August 2011.</ref><ref>Nuclear fusion on the desktop ... really! Template:Webarchive. MSNBC (27 April 2005). Retrieved 17 August 2011.</ref> D–T fusion reactions have been observed with a tritiated erbium target.<ref>Template:Cite journal</ref>
Nuclear fusion–fission hybrid (hybrid nuclear power) is a proposed means of generating power by use of a combination of nuclear fusion and fission processes. The concept dates to the 1950s, and was briefly advocated by Hans Bethe during the 1970s, but largely remained unexplored until a revival of interest in 2009, due to the delays in the realization of pure fusion.<ref name="hybrid">Template:Cite journal</ref>
Project PACER, carried out at Los Alamos National Laboratory (LANL) in the mid-1970s, explored the possibility of a fusion power system that would involve exploding small hydrogen bombs (fusion bombs) inside an underground cavity. As an energy source, the system is the only fusion power system that could be demonstrated to work using existing technology. However, it would also require a large, continuous supply of nuclear bombs, making the economics of such a system rather questionable.
Bubble fusion also called sonofusion was a proposed mechanism for achieving fusion via sonic cavitation which rose to prominence in the early 2000s. Subsequent attempts at replication failed and the principal investigator, Rusi Taleyarkhan, was judged guilty of research misconduct in 2008.<ref>Template:Cite news</ref>

Confinement in thermonuclear fusionEdit

The key problem in achieving thermonuclear fusion is how to confine the hot plasma. Due to the high temperature, the plasma cannot be in direct contact with any solid material, so it has to be located in a vacuum. Also, high temperatures imply high pressures. The plasma tends to expand immediately and some force is necessary to act against it. This force can take one of three forms: gravitation in stars, magnetic forces in magnetic confinement fusion reactors, or inertial as the fusion reaction may occur before the plasma starts to expand, so the plasma's inertia is keeping the material together.

Gravitational confinementEdit

{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}}{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= {{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= Template:Ambox }} }} 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 least massive stars capable of sustained fusion are red dwarfs, while brown dwarfs are able to fuse deuterium and lithium if they are of sufficient mass. 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. Some lighter stars also form these elements in the outer parts of the stars over long periods of time, by absorbing energy from fusion in the inside of the star, by absorbing neutrons that are emitted from the fusion process.

All of the elements heavier than iron have some potential energy to release, in theory. At the extremely heavy end of element production, these heavier elements can produce energy in the process of being split again back toward the size of iron, in the process of nuclear fission. Nuclear fission thus releases energy that has been stored, sometimes billions of years before, during stellar nucleosynthesis.

Magnetic confinementEdit

{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} Electrically charged particles (such as fuel ions) will follow magnetic field lines (see Guiding centre). 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.

Inertial confinementEdit

{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} 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.<ref>F. Winterberg "Conjectured Metastable Super-Explosives formed under High Pressure for Thermonuclear Ignition Template:Webarchive"</ref><ref>Zhang, Fan; Murray, Stephen Burke; Higgins, Andrew (2005) "Super compressed detonation method and device to effect such detonation Template:Dead link"</ref> The UTIAS explosive-driven-implosion facility was used to produce stable, centred and focused hemispherical implosions<ref>I.I. Glass and J.C. Poinssot "IMPLOSION DRIVEN SHOCK TUBE Template:Webarchive". NASA</ref> 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,<ref>D.Sagie and I.I. Glass (1982) "Explosive-driven hemispherical implosions for generating fusion plasmas"</ref> where a plane diaphragm was driven by the implosion wave into a secondary small spherical cavity that contained pure deuterium gas at one atmosphere.<ref>T. Saito, A. K. Kudian and I. I. Glass "Temperature Measurements Of An Implosion Focus Template:Webarchive"</ref>

Electrostatic confinementEdit

{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} There are also electrostatic confinement fusion devices. These devices confine ions using electrostatic fields. The best known is the fusor. This device has a cathode inside an anode wire cage. Positive ions fly towards the negative inner cage, and are heated by the electric field in the process. If they miss the inner cage they can collide and fuse. Ions typically hit the cathode, however, creating prohibitory high conduction losses. Also, fusion rates in fusors are very low due to competing physical effects, such as energy loss in the form of light radiation.<ref>Ion Flow and Fusion Reactivity, Characterization of a Spherically convergent ion Focus. PhD Thesis, Dr. Timothy A Thorson, Wisconsin-Madison 1996.</ref> Designs have been proposed to avoid the problems associated with the cage, by generating the field using a non-neutral cloud. These include a plasma oscillating device,<ref>"Stable, thermal equilibrium, large-amplitude, spherical plasma oscillations in electrostatic confinement devices", DC Barnes and Rick Nebel, PHYSICS OF PLASMAS VOLUME 5, NUMBER 7 JULY 1998</ref> a Penning trap and the polywell.<ref>Carr, M.; Khachan, J. (2013). "A biased probe analysis of potential well formation in an electron only, low beta Polywell magnetic field". Physics of Plasmas 20 (5): 052504. Template:Bibcode. {{#invoke:doi|main}}</ref> The technology is relatively immature, however, and many scientific and engineering questions remain.

The most well known Inertial electrostatic confinement approach is the fusor. Starting in 1999, a number of amateurs have been able to do amateur fusion using these homemade devices.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref><ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref><ref>Template:Cite news</ref><ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> Other IEC devices include: the Polywell, MIX POPS<ref>Template:Cite journal</ref> and Marble concepts.<ref>"The Multiple Ambipolar Recirculating Beam Line Experiment" Poster presentation, 2011 US–Japan IEC conference, Dr. Alex Klein</ref>

Important reactionsEdit

{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= {{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= Template:Ambox }} }}

Stellar reaction chainsEdit

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.<ref>FusEdWeb | Fusion Education. Fusedweb.pppl.gov (9 November 1998). Retrieved 17 August 2011. Template:Webarchive</ref> Thus, reproduction of stellar core conditions in a lab for nuclear fusion power production is completely impractical. Because nuclear reaction rates depend on density as well as temperature, and most fusion schemes operate at relatively low densities, those methods are strongly dependent on higher temperatures. The fusion rate as a function of temperature (exp(−E/kT)), leads to the need to achieve temperatures in terrestrial reactors 10–100 times higher than in stellar interiors: T ≈ Template:Val.

Criteria and candidates for terrestrial reactionsEdit

Template:Main article In artificial fusion, the primary fuel is not constrained to be protons and higher temperatures can be used, so reactions with larger cross-sections are chosen. 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.

To be a useful energy source, a fusion reaction must satisfy several criteria. It must:

Be exothermic: This limits the reactants to the low Z (number of protons) side of the curve of binding energy. It also makes helium Template:SimpleNuclide the most common product because of its extraordinarily tight binding, although Template:SimpleNuclide and Template:SimpleNuclide also show up.
Involve low atomic number (Z) nuclei: This is because the electrostatic repulsion that must be overcome before the nuclei are close enough to fuse (Coulomb barrier) is directly related to the number of protons it contains – its atomic number.
Have two reactants: At anything less than stellar densities, three-body collisions are too improbable. In inertial confinement, both stellar densities and temperatures are exceeded to compensate for the shortcomings of the third parameter of the Lawson criterion, ICF's very short confinement time.
Have two or more products: This allows simultaneous conservation of energy and momentum without relying on the electromagnetic force.
Conserve both protons and neutrons: The cross sections for the weak interaction are too small.

Few reactions meet these criteria. The following are those with the largest cross sections:<ref> Template:Cite book</ref><ref> Template:Cite book</ref>

(1)

n⁰	+	Template:Nuclide	→	Template:Nuclide	+	Template:Nuclide + 4.784 MeV
n⁰	+	Template:Nuclide	→	Template:Nuclide	+	Template:Nuclide + n⁰ − 2.467 MeV

fuel	T [keV]	Template:Math [m³/s/keV²]
Template:Nuclide–Template:Nuclide	13.6	Template:Val
Template:Nuclide–Template:Nuclide	15	Template:Val
Template:Nuclide–Template:Nuclide	58	Template:Val
p⁺–Template:Nuclide	66	Template:Val
p⁺–Template:Nuclide	123	Template:Val

Nuclear Fusion Fuel Isotope	Half-Life	Abundance
Template:Nuclide<ref>CNO cycle#</ref><ref name=":5">CNO cycle#CNO-I</ref><ref name=":6">CNO cycle#CNO-II</ref><ref name=":7">CNO cycle#CNO-III</ref><ref name=":8">CNO cycle#CNO-IV</ref><ref name=":9">CNO cycle#HCNO-I</ref><ref name=":10">CNO cycle#HCNO-II</ref><ref name=":11">CNO cycle#HCNO-III</ref>Template:Excessive citations inline	Stable	99.98%
Template:Nuclide<ref name=":2">Nuclear fusion#Criteria and candidates for terrestrial reactions</ref><ref name=":3">Aneutronic fusion#Coulomb barrier</ref><ref name=":4">Aneutronic fusion#Candidate reactions</ref><ref name=":1">Cold fusion#Lack of expected reaction products</ref>	Stable	0.02%
Template:Nuclide<ref name=":2" /><ref name=":3" />	12.32(2) y	trace
Template:Nuclide<ref name=":2" /><ref name=":3" /><ref name=":4" />	stable	0.0002%
Template:Nuclide<ref name=":1" />	stable	99.9998%
Template:Nuclide<ref name=":2" /><ref name=":3" /><ref name=":4" />	stable	7.59%
Template:Nuclide<ref name=":2" /><ref name=":4" />	stable	92.41%
Template:Nuclide<ref name=":2" /><ref name=":3" /><ref name=":4" /><ref>Aneutronic fusion#Residual radiation</ref>	stable	80%
Template:Nuclide<ref name=":5" /><ref name=":9" />	stable	98.9%
Template:Nuclide<ref name=":5" />	stable	1.1%
Template:Nuclide<ref name=":5" /><ref name=":9" />	9.965(4) min	syn
Template:Nuclide<ref name=":5" /><ref name=":6" /><ref name=":9" />	stable	99.6%
Template:Nuclide<ref name=":5" /><ref name=":6" /><ref name=":7" /><ref name=":9" /><ref name=":10" /><ref name=":4" />Template:Excessive citations inline	stable	0.4%
Template:Nuclide<ref name=":9" />	70.621(11) s	syn
Template:Nuclide<ref name=":5" /><ref name=":6" /><ref name=":9" /><ref name=":10" />	122.266(43) s	syn
Template:Nuclide<ref name=":6" /><ref name=":7" /><ref name=":8" /><ref name=":10" /><ref name=":11" />Template:Excessive citations inline	stable	99.76%
Template:Nuclide<ref name=":6" /><ref name=":7" /><ref name=":8" />	stable	0.04%
Template:Nuclide<ref name=":7" /><ref name=":8" />	stable	0.20%
Template:Nuclide<ref name=":6" /><ref name=":7" /><ref name=":8" /><ref name=":10" /><ref name=":11" />	64.370(27) s	syn
Template:Nuclide<ref name=":7" /><ref name=":8" /><ref name=":10" /><ref name=":11" />	109.734(8) min	trace
Template:Nuclide<ref name=":8" /><ref name=":11" />	stable	100%
Template:Nuclide<ref name=":10" /><ref name=":11" />	1664.20(47) ms	trace
Template:Nuclide<ref name=":11" />	17.2569(19) s	trace

fuel	Z	E_fus [MeV]	E_ch [MeV]	neutronicity
Template:Nuclide–Template:Nuclide	1	17.6	3.5	0.80
Template:Nuclide–Template:Nuclide	1	12.5	4.2	0.66
Template:Nuclide–Template:Nuclide	2	18.3	18.3	≈0.05
p⁺–Template:Nuclide	5	8.7	8.7	≈0.001

	DT(1)	DD(2i)	DD(2ii)	DHe³(3)	TT(4)	The³(6)
A1	45.95	46.097	47.88	89.27	38.39	123.1
A2	50200	372	482	25900	448	11250
A3	Template:Val	Template:Val	Template:Val	Template:Val	Template:Val	0
A4	1.076	1.22	1.177	1.297	2.09	0
A5	409	0	0	647	0	0

	DT(1)	DD(2ii)	DHe³(3)	The⁴
<math>\epsilon_G</math>	31.3970	68.7508	31.3970	34.3827
A1	Template:Val	Template:Val	Template:Val	Template:Val
A2	Template:Val	Template:Val	Template:Val	Template:Val
A3	Template:Val	Template:Val	Template:Val	Template:Val
A4	Template:Val	0	Template:Val	Template:Val
A5	Template:Val	0	Template:Val	0
B1	0	Template:Val	0	Template:Val
B2	0	Template:Val	0	Template:Val
B3	0	Template:Val	0	Template:Val
B4	0	0	0	Template:Val
Applicable Energy Range [keV]	0.5–5000	0.3–900	0.5–4900	0.5–550
<math>(\Delta S)_{\text{max}}\%</math>	2.0	2.2	2.5	1.9

fuel	Template:Math	penalty/bonus	inverse reactivity	Lawson criterion	power density [W/m³/kPa²]	inverse ratio of power density
Template:Nuclide–Template:Nuclide	Template:Val	1	1	1	34	1
Template:Nuclide–Template:Nuclide	Template:Val	2	48	30	0.5	68
Template:Nuclide–Template:Nuclide	Template:Val	2/3	83	16	0.43	80
p⁺–Template:Nuclide	Template:Val	1/2	1700		0.005	6800
p⁺–Template:Nuclide	Template:Val	1/3	1240	500	0.014	2500

fuel	T_i [keV]	P_fusion/P_{Bremsstrahlung}
Template:Nuclide–Template:Nuclide	50	140
Template:Nuclide–Template:Nuclide	500	2.9
Template:Nuclide–Template:Nuclide	100	5.3
Template:Nuclide–Template:Nuclide	1000	0.72
p⁺–Template:Nuclide	800	0.21
p⁺–Template:Nuclide	300	0.57