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124-467: Mega Ampere Spherical Tokamak ( MAST ) was a nuclear fusion experiment, testing a spherical tokamak nuclear fusion reactor , and commissioned by EURATOM / UKAEA . The original MAST experiment took place at the Culham Centre for Fusion Energy , Oxfordshire , England from December 1999 to September 2013. A successor experiment called MAST Upgrade began operation in 2020. A spherical tokamak

248-399: A chain of decays that ends in some stable isotope of lead. Calculation can be employed to determine the nuclear binding energy of nuclei. The calculation involves determining the nuclear mass defect , converting it into energy, and expressing the result as energy per mole of atoms, or as energy per nucleon. Nuclear mass defect is defined as the difference between the nuclear mass , and

372-567: A nuclear weapon . When a large nucleus splits into pieces, excess energy is emitted as gamma rays and the kinetic energy of various ejected particles ( nuclear fission products). These nuclear binding energies and forces are on the order of one million times greater than the electron binding energies of light atoms like hydrogen . An absorption or release of nuclear energy occurs in nuclear reactions or radioactive decay ; those that absorb energy are called endothermic reactions and those that release energy are exothermic reactions. Energy

496-520: 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. 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

620-508: A demo spherical tokamak. Over its lifetime MAST produced 30,471 plasmas (in pulses up to 0.5 sec). In October 2013 the reactor was shut down for the upgrade to MAST Upgrade. MAST Upgrade is the successor experiment to MAST, also at Culham Centre. The upgrade, which cost £45M, started in 2013 and was expected to significantly exceed MAST’s heating power, plasma current, magnetic field and pulse length. MAST Upgrade began operation on 29 October 2020. One of MAST Upgrade's most notable features

744-451: 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. 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

868-445: A form of energy, which can remove some mass when the energy is removed, is consistent with the mass–energy equivalence formula: where and c = the speed of light in vacuum . Nuclear energy was first discovered by French physicist Henri Becquerel in 1896, when he found that photographic plates stored in the dark near uranium were blackened like X-ray plates (X-rays had recently been discovered in 1895). Nickel-62 has

992-442: A helium atom containing four nucleons has a mass about 0.8% less than the total mass of four hydrogen atoms (each containing one nucleon). The helium nucleus has four nucleons bound together, and the binding energy which holds them together is, in effect, the missing 0.8% of mass. For lighter elements, the energy that can be released by assembling them from lighter elements decreases, and energy can be released when they fuse. This

1116-402: A helium nucleus weighs less than the sum of the weights of the two heavy hydrogen nuclei which combine to make it. The same is true for carbon, nitrogen and oxygen. For example, the carbon nucleus is slightly lighter than three helium nuclei, which can combine to make a carbon nucleus. This difference is known as the mass defect. Mass defect (also called "mass deficit") is the difference between

1240-485: A high beta (ratio of plasma pressure to the pressure from the confining magnetic field). MAST performed experiments on controlling and mitigating instabilities at the edge of the plasma – so-called Edge Localised Modes or ELMs. MAST was designed to confirm the results of the earlier Small Tight Aspect Ratio Tokamak (START) experiment (1990-1998) in a larger, more purpose-built experiment. The MAST design phase occupied 1995-1997, with construction beginning in 1997, and

1364-494: 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 ≈ (0.1–1.0) × 10  K . In artificial fusion,

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1488-416: A miniature Voitenko compressor , where a plane diaphragm was driven by the implosion wave into a secondary small spherical cavity that contained pure deuterium gas at one atmosphere. 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

1612-427: A more massive star undergoes a violent supernova at the end of its life, a process known as supernova nucleosynthesis . 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,

1736-416: 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

1860-454: 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

1984-442: A nucleus, and not to free particles, a proton may become a neutron by ejecting a positron and an electron neutrino. This is permitted if enough energy is available between parent and daughter nuclides to do this (the required energy difference is equal to 1.022 MeV, which is the mass of 2 electrons). If the mass difference between parent and daughter is less than this, a proton-rich nucleus may still convert protons to neutrons by

2108-471: A relatively small mass and a relatively large binding energy per nucleon . Fusion of nuclei lighter than these releases energy (an exothermic process), while the fusion of heavier nuclei results in energy retained by the product nucleons, and the resulting reaction is endothermic . The opposite is true for the reverse process, called nuclear fission . Nuclear fusion uses lighter elements, such as hydrogen and helium , which are in general more fusible; while

2232-422: 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

2356-525: A small amount of deuterium–tritium gas to enhance the fission yield. The first thermonuclear weapon detonation, where the vast majority of the yield comes from fusion, was the 1952 Ivy Mike test of a liquid deuterium-fusing device. 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

2480-530: 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 synthesize heavier elements. The heaviest elements are synthesized by fusion that occurs when

2604-424: A static fuel-infused target, known as beam–target fusion, or by accelerating two streams of ions towards each other, beam–beam fusion. 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

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2728-455: A tiny volume and repel each other. The energy of the strong force holding the nucleus together also increases, but at a slower rate, as if inside the nucleus, only nucleons close to each other are tightly bound, not ones more widely separated. The net binding energy of a nucleus is that of the nuclear attraction, minus the disruptive energy of the electric force. As nuclei get heavier than helium, their net binding energy per nucleon (deduced from

2852-448: 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. Private companies pursuing

2976-399: A useful energy source, a fusion reaction must satisfy several criteria. It must: Nuclear binding energy Nuclear binding energy in experimental physics is the minimum energy that is required to disassemble the nucleus of an atom into its constituent protons and neutrons , known collectively as nucleons . The binding energy for stable nuclei is always a positive number, as

3100-530: A very hot gas. Hydrogen hot enough for combining to helium requires an enormous pressure to keep it confined, but suitable conditions exist in the central regions of the Sun, where such pressure is provided by the enormous weight of the layers above the core, pressed inwards by the Sun's strong gravity. The process of combining protons to form helium is an example of nuclear fusion. Producing helium from normal hydrogen would be practically impossible on earth because of

3224-406: 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 He nucleus, which immediately ejects a neutron with 14.1 MeV. The recoil energy of

3348-414: Is a close-range force (it is strongly attractive at a distance of 1.0 fm and becomes extremely small beyond a distance of 2.5 fm), and virtually no effect of this force is observed outside the nucleus. The nuclear force also pulls neutrons together, or neutrons and protons. The energy of the nucleus is negative with regard to the energy of the particles pulled apart to infinite distance (just like

3472-400: Is a graph that plots the binding energy per nucleon against atomic mass. This curve has its main peak at iron and nickel and then slowly decreases again, and also a narrow isolated peak at helium, which is more stable than other low-mass nuclides. The heaviest nuclei in more than trace quantities in nature, uranium U, are unstable, but having a half-life of 4.5 billion years, close to the age of

3596-423: Is a technique using particle accelerators to achieve particle kinetic energies sufficient to induce light-ion fusion reactions. 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. The system can be arranged to accelerate ions into

3720-415: Is consumed or released because of differences in the nuclear binding energy between the incoming and outgoing products of the nuclear transmutation. The best-known classes of exothermic nuclear transmutations are nuclear fission and nuclear fusion . Nuclear energy may be released by fission, when heavy atomic nuclei (like uranium and plutonium) are broken apart into lighter nuclei. The energy from fission

3844-433: 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

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3968-500: Is manifested as either the release or absorption of energy . This difference in mass arises due to the difference in nuclear binding energy between the atomic nuclei before and after the reaction. Nuclear fusion is the process that powers active or main-sequence stars and other high-magnitude stars, where large amounts of energy are released . A nuclear fusion process that produces atomic nuclei lighter than iron-56 or nickel-62 will generally release energy. These elements have

4092-436: Is more stable, the iron isotope Fe is an order of magnitude more common. This is due to the fact that there is no easy way for stars to create Ni 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

4216-493: 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 13.6  eV —less than one-millionth of the 17.6  MeV 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 ;

4340-411: Is referred to as a chemical bond and is responsible for the formation of all chemical compounds . The electric force does not hold nuclei together, because all protons carry a positive charge and repel each other. If two protons were touching, their repulsion force would be almost 40 newtons. Because each of the neutrons carries total charge zero, a proton could electrically attract a neutron if

4464-455: Is shaped more like a cored apple than the conventional, doughnut-shaped toroidal design used by experiments such as ITER . Spherical tokamaks are more efficient in their use of the magnetic field. MAST included a neutral beam injector for plasma heating. It used a merging compression technique for plasma formation instead of the conventional direct induction. Merging compression saves central solenoid flux, which can then be used to increase

4588-412: Is still the combination of protons to form helium. A branch of physics, the study of controlled nuclear fusion , has tried since the 1950s to derive useful power from nuclear fusion reactions that combine small nuclei into bigger ones, typically to heat boilers, whose steam could turn turbines and produce electricity. No earthly laboratory can match one feature of the solar powerhouse: the great mass of

4712-411: 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

4836-557: Is the Super-X divertor. The divertor removes excess heat and impurities from the plasma. Conventional divertor designs, at powerplant scale, will experience high heat loads and will need to be regularly replaced. The Super-X divertor was expected to produce heat loads that are lower by around a factor of ten and has been seen as initially successful. The design of the next generation Spherical Tokamak for Energy Production (STEP) began in 2019 with £220 million in government funding. The plan

4960-402: Is the energy source of the Sun and of most stars. The sun is composed of 74 percent hydrogen (measured by mass), an element having a nucleus consisting of a single proton. Energy is released in the Sun when 4 protons combine into a helium nucleus, a process in which two of them are also converted to neutrons. The conversion of protons to neutrons is the result of another nuclear force, known as

5084-399: Is the minimum energy required to disassemble the nucleus into its constituent nucleons. This conversion is done with the mass-energy equivalence : E = ∆ mc . However it must be expressed as energy per mole of atoms or as energy per nucleon. Nuclear energy is released by the splitting (fission) or merging (fusion) of the nuclei of atom (s). The conversion of nuclear mass – energy to

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5208-422: Is to begin operations in the 2040s. The current plan does not include a tritium generation facility. Nuclear fusion Nuclear fusion is a reaction in which two or more atomic nuclei , usually deuterium and tritium (hydrogen isotopes ), combine to form one or more different atomic nuclei and subatomic particles ( neutrons or protons ). The difference in mass between the reactants and products

5332-408: Is to merge two FRC's rotating in opposite directions, 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- B that are too difficult to attempt using conventional approaches. Muon-catalyzed fusion is a fusion process that occurs at ordinary temperatures. It

5456-407: Is to use conventional high explosive material to compress a fuel to fusion conditions. The UTIAS explosive-driven-implosion facility was used to produce stable, centred and focused hemispherical implosions 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

5580-514: Is to use very strong magnetic fields, because charged particles (like those trapped in the Earth's radiation belt) are guided by magnetic field lines. In the main isotopes of light elements, such as carbon, nitrogen and oxygen, the most stable combination of neutrons and of protons occurs when the numbers are equal (this continues to element 20, calcium). However, in heavier nuclei, the disruptive energy of protons increases, since they are confined to

5704-512: Is true for nuclei lighter than iron / nickel . For heavier nuclei, more energy is needed to bind them, and that energy may be released by breaking them up into fragments (known as nuclear fission ). Nuclear power is generated at present by breaking up uranium nuclei in nuclear power reactors, and capturing the released energy as heat, which is converted to electricity. As a rule, very light elements can fuse comparatively easily, and very heavy elements can break up via fission very easily; elements in

5828-489: Is used to generate electric power in hundreds of locations worldwide. Nuclear energy is also released during fusion, when light nuclei like hydrogen are combined to form heavier nuclei such as helium. The Sun and other stars use nuclear fusion to generate thermal energy which is later radiated from the surface, a type of stellar nucleosynthesis. In any exothermic nuclear process, nuclear mass might ultimately be converted to thermal energy, emitted as heat. In order to quantify

5952-952: Is useful to perform an average over the distributions of the product of cross-section and velocity. This average is called the 'reactivity', denoted ⟨ σv ⟩ . The reaction rate (fusions per volume per time) is ⟨ σv ⟩ times the product of the reactant number densities: If a species of nuclei is reacting with a nucleus like itself, such as the DD reaction, then the product n 1 n 2 {\displaystyle n_{1}n_{2}} must be replaced by n 2 / 2 {\displaystyle n^{2}/2} . ⟨ σ v ⟩ {\displaystyle \langle \sigma v\rangle } increases from virtually zero at room temperatures up to meaningful magnitudes at temperatures of 10 – 100  keV. At these temperatures, well above typical ionization energies (13.6 eV in

6076-478: The nuclear force (or residual strong force ) holds the nucleons of nuclei together. This force is a residuum of the strong interaction , which binds quarks into nucleons at an even smaller level of distance. The fact that nuclei do not clump together (fuse) under normal conditions suggests that the nuclear force must be weaker than the electric repulsion at larger distances, but stronger at close range. Therefore, it has short-range characteristics. An analogy to

6200-542: 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

6324-535: 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,

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6448-479: The Polywell , MIX POPS and Marble concepts. 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/cm ), the energy release rate is only 276 μW/cm —about a quarter of the volumetric rate at which a resting human body generates heat. Thus, reproduction of stellar core conditions in

6572-607: 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." Prior to this breakthrough, controlled fusion reactions had been unable to produce break-even (self-sustaining) controlled fusion. The two most advanced approaches for it are magnetic confinement (toroid designs) and inertial confinement (laser designs). Workable designs for

6696-410: 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 Ni , Fe , Fe , and Ni . Even though the nickel isotope , Ni ,

6820-459: The decay chains of heavier elements. Generally, the heavier the nuclei are, the faster they spontaneously decay. Iron nuclei are the most stable nuclei (in particular iron-56 ), and the best sources of energy are therefore nuclei whose weights are as far removed from iron as possible. One can combine the lightest ones—nuclei of hydrogen (protons)—to form nuclei of helium, and that is how the Sun generates its energy. Alternatively, one can break up

6944-410: The weak (nuclear) force . The weak force, like the strong force, has a short range, but is much weaker than the strong force. The weak force tries to make the number of neutrons and protons into the most energetically stable configuration. For nuclei containing less than 40 particles, these numbers are usually about equal. Protons and neutrons are closely related and are collectively known as nucleons. As

7068-523: 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. The US National Ignition Facility , which uses laser-driven inertial confinement fusion , was designed with a goal of break-even fusion; the first large-scale laser target experiments were performed in June 2009 and ignition experiments began in early 2011. On 13 December 2022,

7192-520: 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 . Accelerator-based light-ion fusion

7316-543: The Earth, they are still relatively abundant; they (and other nuclei heavier than helium) have formed in stellar evolution events like supernova explosions preceding the formation of the Solar System . The most common isotope of thorium, Th, also undergoes alpha particle emission, and its half-life (time over which half a number of atoms decays) is even longer, by several times. In each of these, radioactive decay produces daughter isotopes that are also unstable, starting

7440-499: 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. It takes considerable energy to force nuclei to fuse, even those of

7564-428: The Sun, whose weight keeps the hot plasma compressed and confines the nuclear furnace to the Sun's core. Instead, physicists use strong magnetic fields to confine the plasma, and for fuel they use heavy forms of hydrogen, which burn more easily. Magnetic traps can be rather unstable, and any plasma hot enough and dense enough to undergo nuclear fusion tends to slip out of them after a short time. Even with ingenious tricks,

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7688-456: 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

7812-459: The binding energy means. The mass of an atomic nucleus is less than the sum of the individual masses of the free constituent protons and neutrons. The difference in mass can be calculated by the Einstein equation , E = mc , where E is the nuclear binding energy, c is the speed of light, and m is the difference in mass. This 'missing mass' is known as the mass defect, and represents

7936-462: The cage, by generating the field using a non-neutral cloud. These include a plasma oscillating device, a Penning trap and the polywell . 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. Other IEC devices include:

8060-472: 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. One of the most recent breakthroughs to date in maintaining a sustained fusion reaction occurred in France's WEST fusion reactor. It maintained

8184-584: The confinement in most cases lasts only a small fraction of a second. Small nuclei that are larger than hydrogen can combine into bigger ones and release energy, but in combining such nuclei, the amount of energy released is much smaller compared to hydrogen fusion. The reason is that while the overall process releases energy from letting the nuclear attraction do its work, energy must first be injected to force together positively charged protons, which also repel each other with their electric charge. For elements that weigh more than iron (a nucleus with 26 protons),

8308-416: The core of a star ), can such a process take place. There are around 94 naturally occurring elements on Earth. The atoms of each element have a nucleus containing a specific number of protons (always the same number for a given element), and some number of neutrons , which is often roughly a similar number. Two atoms of the same element having different numbers of neutrons are known as isotopes of

8432-449: The current advanced technical state. 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

8556-400: The difference in mass between the nucleus and the sum of masses of component nucleons) grows more and more slowly, reaching its peak at iron. As nucleons are added, the total nuclear binding energy always increases—but the total disruptive energy of electric forces (positive protons repelling other protons) also increases, and past iron, the second increase outweighs the first. Iron-56 ( Fe) is

8680-558: The difficulty in creating deuterium . Research is being undertaken on developing a process using deuterium and tritium . The Earth's oceans contain a large amount of deuterium that could be used and tritium can be made in the reactor itself from lithium , and furthermore the helium product does not harm the environment, so some consider nuclear fusion a good alternative to supply our energy needs. Experiments to carry out this form of fusion have so far only partially succeeded. Sufficiently hot deuterium and tritium must be confined. One technique

8804-448: The disruptive energy, the weak interaction allows the number of neutrons to exceed that of protons—for instance, the main isotope of iron has 26 protons and 30 neutrons. Isotopes also exist where the number of neutrons differs from the most stable number for that number of nucleons. If changing one proton into a neutron or one neutron into a proton increases the stability (lowering the mass), then this will happen through beta decay , meaning

8928-404: 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

9052-499: The element. Different isotopes may have different properties – for example one might be stable and another might be unstable, and gradually undergo radioactive decay to become another element. The hydrogen nucleus contains just one proton. Its isotope deuterium, or heavy hydrogen , contains a proton and a neutron. The most common isotope of helium contains two protons and two neutrons, and those of carbon, nitrogen and oxygen – six, seven and eight of each particle, respectively. However,

9176-415: The energy released or absorbed in any nuclear transmutation, one must know the nuclear binding energies of the nuclear components involved in the transmutation. Electrons and nuclei are kept together by electrostatic attraction (negative attracts positive). Furthermore, electrons are sometimes shared by neighboring atoms or transferred to them (by processes of quantum physics ); this link between atoms

9300-534: The energy that was released when the nucleus was formed. The term "nuclear binding energy" may also refer to the energy balance in processes in which the nucleus splits into fragments composed of more than one nucleon. If new binding energy is available when light nuclei fuse ( nuclear fusion ), or when heavy nuclei split ( nuclear fission ), either process can result in release of this binding energy. This energy may be made available as nuclear energy and can be used to produce electricity, as in nuclear power , or in

9424-415: 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 virtually all elements 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,

9548-488: The first plasma obtained in 1999. The first results of the MAST demonstrate that mode-H is reached with more ease and less energy than expected with a considerable improvement in confinement, a fundamental point for any energy production scenario. Finally, different scenarios have been successfully tested to decrease the energy flow in the central solenoid vs plasma current, which represents another fundamental point for designing

9672-455: The fusion process no longer releases energy. In even heavier nuclei energy is consumed, not released, by combining similarly sized nuclei. With such large nuclei, overcoming the electric repulsion (which affects all protons in the nucleus) requires more energy than is released by the nuclear attraction (which is effective mainly between close neighbors). Conversely, energy could actually be released by breaking apart nuclei heavier than iron. With

9796-516: The fusion reaction may occur before the plasma starts to expand, so the plasma's inertia is keeping the material together. 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

9920-478: The gravitational energy of planets of the Solar System), because energy must be utilized to split a nucleus into its individual protons and neutrons. Mass spectrometers have measured the masses of nuclei, which are always less than the sum of the masses of protons and neutrons that form them, and the difference—by the formula E = mc —gives the binding energy of the nucleus. The binding energy of helium

10044-402: The heavier elements, such as uranium , thorium and plutonium , are more fissionable. The extreme astrophysical event of a supernova can produce enough energy to fuse nuclei into elements heavier than iron. American chemist William Draper Harkins was the first to propose the concept of nuclear fusion in 1915. Then in 1921, Arthur Eddington suggested hydrogen–helium fusion could be

10168-403: The heaviest ones—nuclei of uranium or plutonium—into smaller fragments, and that is what nuclear reactors do. An example that illustrates nuclear binding energy is the nucleus of C (carbon-12), which contains 6 protons and 6 neutrons. The protons are all positively charged and repel each other, but the nuclear force overcomes the repulsion and causes them to stick together. The nuclear force

10292-453: 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

10416-446: The high temperature of the Sun's core, and the heat also keeps the gas pressure high, keeping the Sun at its present size, and stopping gravity from compressing it any more. There is now a stable balance between gravity and pressure. Different nuclear reactions may predominate at different stages of the Sun's existence, including the proton–proton reaction and the carbon–nitrogen cycle—which involves heavier nuclei, but whose final product

10540-501: The highest binding energy per nucleon of any isotope . If an atom of lower average binding energy per nucleon is changed into two atoms of higher average binding energy per nucleon, energy is emitted. (The average here is the weighted average.) Also, if two atoms of lower average binding energy fuse into an atom of higher average binding energy, energy is emitted. The chart shows that fusion, or combining, of hydrogen nuclei to form heavier atoms releases energy, as does fission of uranium,

10664-458: The hydrogen case), the fusion reactants exist in a plasma state. The significance of ⟨ σ v ⟩ {\displaystyle \langle \sigma v\rangle } 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

10788-403: 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

10912-471: 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 . Energy released in most nuclear reactions

11036-474: The mass of an object and the sum of the masses of its constituent particles. Discovered by Albert Einstein in 1905, it can be explained using his formula E  =  mc , which describes the equivalence of energy and mass . The decrease in mass is equal to the energy emitted in the reaction of an atom's creation divided by c . By this formula, adding energy also increases mass (both weight and inertia), whereas removing energy decreases mass. For example,

11160-520: 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 . 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 E = mc . This

11284-413: The middle are more stable and it is difficult to make them undergo either fusion or fission in an environment such as a laboratory. The reason the trend reverses after iron is the growing positive charge of the nuclei, which tends to force nuclei to break up. It is resisted by the strong nuclear interaction , which holds nucleons together. The electric force may be weaker than the strong nuclear force, but

11408-459: The most efficiently bound nucleus meaning that it has the least average mass per nucleon. However, nickel-62 is the most tightly bound nucleus in terms of binding energy per nucleon. (Nickel-62's higher binding energy does not translate to a larger mean mass loss than Fe, because Ni has a slightly higher ratio of neutrons/protons than does iron-56, and the presence of the heavier neutrons increases nickel-62's average mass per nucleon). To reduce

11532-417: 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. Designs have been proposed to avoid the problems associated with

11656-437: The new Sun formed when gravity pulled together a vast cloud of hydrogen and dust, from which the Earth and other planets also arose. The gravitational pull released energy and heated the early Sun, much in the way Helmholtz proposed. Thermal energy appears as the motion of atoms and molecules: the higher the temperature of a collection of particles, the greater is their velocity and the more violent are their collisions. When

11780-469: The nuclear force is the force between two small magnets: magnets are very difficult to separate when stuck together, but once pulled a short distance apart, the force between them drops almost to zero. Unlike gravity or electrical forces, the nuclear force is effective only at very short distances. At greater distances, the electrostatic force dominates: the protons repel each other because they are positively charged, and like charges repel. For that reason,

11904-511: The nuclei of elements heavier than lead , the electric repulsion is so strong that some of them spontaneously eject positive fragments, usually nuclei of helium that form stable alpha particles . This spontaneous break-up is one of the forms of radioactivity exhibited by some nuclei. Nuclei heavier than lead (except for bismuth , thorium , and uranium ) spontaneously break up too quickly to appear in nature as primordial elements , though they can be produced artificially or as intermediates in

12028-480: The nucleus must gain energy for the nucleons to move apart from each other. Nucleons are attracted to each other by the strong nuclear force . In theoretical nuclear physics, the nuclear binding energy is considered a negative number. In this context it represents the energy of the nucleus relative to the energy of the constituent nucleons when they are infinitely far apart. Both the experimental and theoretical views are equivalent, with slightly different emphasis on what

12152-419: The nucleus to repel each other. 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

12276-433: The nuclide will be radioactive. The two methods for this conversion are mediated by the weak force, and involve types of beta decay . In the simplest beta decay, neutrons are converted to protons by emitting a negative electron and an antineutrino. This is always possible outside a nucleus because neutrons are more massive than protons by an equivalent of about 2.5 electrons. In the opposite process, which only happens within

12400-443: The number of particles increases toward a maximum of about 209, the number of neutrons to maintain stability begins to outstrip the number of protons, until the ratio of neutrons to protons is about three to two. The protons of hydrogen combine to helium only if they have enough velocity to overcome each other's mutual repulsion sufficiently to get within range of the strong nuclear attraction. This means that fusion only occurs within

12524-406: 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. 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,

12648-410: 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

12772-437: The plasma current and/or maintain the required current flat-top. MAST's plasma volume was about 8 cubic meters. It confined plasmas with densities on the order of 10/m. MAST's plasma had an almost circular outer profile. The extensions off the top and bottom are plasma flowing to the ring divertors , a key feature of modern tokamak designs. MAST confirmed the increased operating efficiency of spherical tokamaks, demonstrating

12896-424: 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

13020-435: The primary source of stellar energy. Quantum tunneling was discovered by Friedrich Hund in 1927, and shortly afterwards Robert Atkinson and Fritz Houtermans used the measured masses of light elements to demonstrate that large amounts of energy could be released by fusing small nuclei. Building on the early experiments in artificial nuclear transmutation by Patrick Blackett , laboratory fusion of hydrogen isotopes

13144-666: The process of electron capture , in which a proton simply electron captures one of the atom's K orbital electrons, emits a neutrino, and becomes a neutron. Among the heaviest nuclei, starting with tellurium nuclei (element 52) containing 104 or more nucleons, electric forces may be so destabilizing that entire chunks of the nucleus may be ejected, usually as alpha particles , which consist of two protons and two neutrons (alpha particles are fast helium nuclei). ( Beryllium-8 also decays, very quickly, into two alpha particles.) This type of decay becomes more and more probable as elements rise in atomic weight past 104. The curve of binding energy

13268-500: The process of alpha radioactivity—the emission of helium nuclei, each containing two protons and two neutrons. (Helium nuclei are an especially stable combination.) Because of this process, nuclei with more than 94 protons are not found naturally on Earth (see periodic table ). The isotopes beyond uranium (atomic number 92) with the longest half-lives are plutonium-244 (80 million years) and curium-247 (16 million years). The nuclear fusion process works as follows: five billion years ago,

13392-441: The proton could induce the neutron to become electrically polarized . However, having the neutron between two protons (so their mutual repulsion decreases to 10 N) would attract the neutron only for an electric quadrupole (− + + −) arrangement. Higher multipoles, needed to satisfy more protons, cause weaker attraction, and quickly become implausible. After the proton and neutron magnetic moments were measured and verified , it

13516-422: The protons forming the nuclei of ordinary hydrogen —for instance, in a balloon filled with hydrogen—do not combine to form helium (a process that also would require some protons to combine with electrons and become neutrons ). They cannot get close enough for the nuclear force, which attracts them to each other, to become important. Only under conditions of extreme pressure and temperature (for example, within

13640-431: 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 as of 2021 . A closely related approach

13764-553: 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. Only direct conversion of mass into energy , such as that caused by the annihilatory collision of matter and antimatter , is more energetic per unit of mass than nuclear fusion. (The complete conversion of one gram of matter would release 9 × 10  joules of energy.) An important fusion process

13888-411: The remaining He 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. 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

14012-417: 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

14136-465: 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 for constructive purposes. 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

14260-421: 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 . 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

14384-519: The strong force has a much more limited range: in an iron nucleus, each proton repels the other 25 protons, while the nuclear force only binds close neighbors. So for larger nuclei, the electrostatic forces tend to dominate and the nucleus will tend over time to break up. As nuclei grow bigger still, this disruptive effect becomes steadily more significant. By the time polonium is reached (84 protons), nuclei can no longer accommodate their large positive charge, but emit their excess protons quite rapidly in

14508-433: The sum of the masses of the constituent nucleons. It is given by Δ m = Z m p + ( A − Z ) m n − M = Z m p + N m n − M {\displaystyle \Delta m=Zm_{p}+(A-Z)m_{n}-M=Zm_{p}+Nm_{n}-M} where: The nuclear mass defect is usually converted into nuclear binding energy, which

14632-608: 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

14756-531: The temperature at the center of the newly formed Sun became great enough for collisions between hydrogen nuclei to overcome their electric repulsion, and bring them into the short range of the attractive nuclear force , nuclei began to stick together. When this began to happen, protons combined into deuterium and then helium, with some protons changing in the process to neutrons (plus positrons, positive electrons, which combine with electrons and annihilate into gamma-ray photons). This released nuclear energy now keeps up

14880-410: The toroidal geometries of tokamaks and stellarators and open-ended mirror confinement systems. 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

15004-469: 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: 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

15128-491: Was accomplished by Mark Oliphant in 1932. In the remainder of that decade, the theory of the main cycle of nuclear fusion in stars was worked out by Hans Bethe . Research into fusion for military purposes began in the early 1940s as part of the Manhattan Project . The first artificial thermonuclear fusion reaction occurred during the 1951 Greenhouse Item test of the first boosted fission weapon , which uses

15252-479: Was apparent that their magnetic forces might be 20 or 30 newtons, attractive if properly oriented. A pair of protons would do 10 joules of work to each other as they approach – that is, they would need to release energy of 0.5 MeV in order to stick together. On the other hand, once a pair of nucleons magnetically stick, their external fields are greatly reduced, so it is difficult for many nucleons to accumulate much magnetic energy. Therefore, another force, called

15376-430: 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. Some other confinement principles have been investigated. The key problem in achieving thermonuclear fusion

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