Nuclear fusion

Nuclear fusion

Overview
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

. Fusion is the process that powers active star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

s, the hydrogen bomb and experimental devices examining fusion power
Fusion power
Fusion power is the power generated by nuclear fusion processes. In fusion reactions two light atomic nuclei fuse together to form a heavier nucleus . In doing so they release a comparatively large amount of energy arising from the binding energy due to the strong nuclear force which is manifested...

 for electrical generation.

The fusion of two nuclei with lower masses than iron
Iron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...

 (which, along with nickel
Nickel
Nickel is a chemical element with the chemical symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel belongs to the transition metals and is hard and ductile...

, has the largest binding energy
Binding energy
Binding energy is the mechanical energy required to disassemble a whole into separate parts. A bound system typically has a lower potential energy than its constituent parts; this is what keeps the system together—often this means that energy is released upon the creation of a bound state...

 per nucleon
Nucleon
In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...

) generally releases energy, while the fusion of nuclei heavier than iron absorbs energy.
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Encyclopedia
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

. Fusion is the process that powers active star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

s, the hydrogen bomb and experimental devices examining fusion power
Fusion power
Fusion power is the power generated by nuclear fusion processes. In fusion reactions two light atomic nuclei fuse together to form a heavier nucleus . In doing so they release a comparatively large amount of energy arising from the binding energy due to the strong nuclear force which is manifested...

 for electrical generation.

The fusion of two nuclei with lower masses than iron
Iron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...

 (which, along with nickel
Nickel
Nickel is a chemical element with the chemical symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel belongs to the transition metals and is hard and ductile...

, has the largest binding energy
Binding energy
Binding energy is the mechanical energy required to disassemble a whole into separate parts. A bound system typically has a lower potential energy than its constituent parts; this is what keeps the system together—often this means that energy is released upon the creation of a bound state...

 per nucleon
Nucleon
In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...

) generally releases energy, while the fusion of nuclei heavier than iron absorbs energy. The opposite is true for the reverse process, nuclear fission
Nuclear fission
In nuclear physics and nuclear chemistry, nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts , often producing free neutrons and photons , and releasing a tremendous amount of energy...

. This means that fusion generally occurs for lighter elements only, and likewise, that fission normally occurs only for heavier elements. There are extreme astrophysical
Astrophysics
Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...

 events that can lead to short periods of fusion with heavier nuclei. This is the process that gives rise to nucleosynthesis
Nucleosynthesis
Nucleosynthesis is the process of creating new atomic nuclei from pre-existing nucleons . It is thought that the primordial nucleons themselves were formed from the quark–gluon plasma from the Big Bang as it cooled below two trillion degrees...

, the creation of the heavy elements during events like supernova
Supernova
A supernova is a stellar explosion that is more energetic than a nova. It is pronounced with the plural supernovae or supernovas. Supernovae are extremely luminous and cause a burst of radiation that often briefly outshines an entire galaxy, before fading from view over several weeks or months...

s.

Creating the required conditions for fusion on Earth is very difficult, to the point that it has not been accomplished at any scale for protium, the common light isotope
Isotope
Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...

 of hydrogen that undergoes natural fusion in stars. In nuclear weapon
Nuclear weapon
A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission or a combination of fission and fusion. Both reactions release vast quantities of energy from relatively small amounts of matter. The first fission bomb test released the same amount...

s, some of the energy released by an atomic bomb is used to compress and heat a fusion fuel containing heavier isotopes of hydrogen, and also sometimes lithium
Lithium
Lithium is a soft, silver-white metal that belongs to the alkali metal group of chemical elements. It is represented by the symbol Li, and it has the atomic number 3. Under standard conditions it is the lightest metal and the least dense solid element. Like all alkali metals, lithium is highly...

, to the point of "ignition". At this point, the energy released in the fusion reactions is enough to briefly maintain the reaction. Fusion-based nuclear power
Nuclear power
Nuclear power is the use of sustained nuclear fission to generate heat and electricity. Nuclear power plants provide about 6% of the world's energy and 13–14% of the world's electricity, with the U.S., France, and Japan together accounting for about 50% of nuclear generated electricity...

 experiments attempt to create similar conditions using less dramatic means, although to date these experiments have failed to maintain conditions needed for ignition long enough for fusion to be a viable commercial power source.

Building upon the nuclear transmutation
Nuclear transmutation
Nuclear transmutation is the conversion of one chemical element or isotope into another. In other words, atoms of one element can be changed into atoms of other element by 'transmutation'...

 experiments by Ernest Rutherford
Ernest Rutherford
Ernest Rutherford, 1st Baron Rutherford of Nelson OM, FRS was a New Zealand-born British chemist and physicist who became known as the father of nuclear physics...

, carried out several years earlier, the laboratory fusion of heavy hydrogen isotopes was first accomplished by Mark Oliphant
Mark Oliphant
Sir Marcus 'Mark' Laurence Elwin Oliphant, AC, KBE, FRS was an Australian physicist and humanitarian who played a fundamental role in the first experimental demonstration of nuclear fusion and also the development of the atomic bomb.During his retirement, Oliphant was appointed as the Governor of...

 in 1932. During the remainder of that decade the steps of the main cycle of nuclear fusion in stars were worked out by Hans Bethe
Hans Bethe
Hans Albrecht Bethe was a German-American nuclear physicist, and Nobel laureate in physics for his work on the theory of stellar nucleosynthesis. A versatile theoretical physicist, Bethe also made important contributions to quantum electrodynamics, nuclear physics, solid-state physics and...

. Research into fusion for military purposes began in the early 1940s as part of the Manhattan Project
Manhattan Project
The Manhattan Project was a research and development program, led by the United States with participation from the United Kingdom and Canada, that produced the first atomic bomb during World War II. From 1942 to 1946, the project was under the direction of Major General Leslie Groves of the US Army...

, but this was not accomplished until 1951 (see the Greenhouse Item
Greenhouse Item
Greenhouse Item was an American nuclear test conducted on May 25, 1951, as part of Operation Greenhouse at the Pacific Proving Ground, specifically on the island of Engebi in the Eniwetok Atoll in the Central Pacific Ocean. This test explosion was the first test of a boosted fission weapon...

 nuclear test), and nuclear fusion on a large scale in an explosion was first carried out on November 1, 1952, in the Ivy Mike
Ivy Mike
Ivy Mike was the codename given to the first United States test of a thermonuclear weapon, in which a major part of the explosive yield came from nuclear fusion. It was detonated on November 1, 1952 by the United States at on Enewetak, an atoll in the Pacific Ocean, as part of Operation Ivy...

 hydrogen bomb test.

Research into developing controlled thermonuclear fusion for civil purposes also began in earnest in the 1950s, and it continues to this day. Two projects, the National Ignition Facility
National Ignition Facility
The National Ignition Facility, or NIF is a large, laser-based inertial confinement fusion research device located at the Lawrence Livermore National Laboratory in Livermore, California. NIF uses powerful lasers to heat and compress a small amount of hydrogen fuel to the point where nuclear fusion...

 and ITER
ITER
ITER is an international nuclear fusion research and engineering project, which is currently building the world's largest and most advanced experimental tokamak nuclear fusion reactor at Cadarache in the south of France...

 are in the process of reaching breakeven after 60 years of design improvements developed from previous experiments.

Overview



Fusion reactions power the star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

s and produce virtually all elements in a process called nucleosynthesis
Nucleosynthesis
Nucleosynthesis is the process of creating new atomic nuclei from pre-existing nucleons . It is thought that the primordial nucleons themselves were formed from the quark–gluon plasma from the Big Bang as it cooled below two trillion degrees...

.

Generally, when dealing with elements lighter than iron
Iron peak
The iron peak is a local maximum in the vicinity of Fe on the graph of the abundances of chemical elements, as seen below....

, the lower the ratio of atomic mass
Atomic mass
The atomic mass is the mass of a specific isotope, most often expressed in unified atomic mass units. The atomic mass is the total mass of protons, neutrons and electrons in a single atom....

 to mass number
Mass number
The mass number , also called atomic mass number or nucleon number, is the total number of protons and neutrons in an atomic nucleus. Because protons and neutrons both are baryons, the mass number A is identical with the baryon number B as of the nucleus as of the whole atom or ion...

 is, the heavier the nucleus is. This is known as mass defect. Fusion of lighter nuclei into heavier nuclei leads to loss of mass when the energy of binding is removed (this energy carries away the lost mass), even though no nucleon
Nucleon
In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...

s are lost. This lost mass is present in the released energy in accordance with E=mc2. Most of the excess binding energy
Binding energy
Binding energy is the mechanical energy required to disassemble a whole into separate parts. A bound system typically has a lower potential energy than its constituent parts; this is what keeps the system together—often this means that energy is released upon the creation of a bound state...

 is released as kinetic energy of the resulting particles. When these particles are slowed, such as in collisions with one another, this energy is available to do work or be converted to electromagnetic radiation or heat.

The fusion of lighter elements in stars releases energy (and the mass that always accompanies it). For example, in the fusion of four hydrogen nuclei to form helium, seven-tenths of 1 percent of the mass is carried away from the system in the form of kinetic energy or other forms of energy (such as electromagnetic radiation). However, the production of elements heavier than iron
Iron peak
The iron peak is a local maximum in the vicinity of Fe on the graph of the abundances of chemical elements, as seen below....

 absorbs energy.

Research into controlled fusion, with the aim of producing fusion power for the production of electricity, has been conducted for over 60 years. It has been accompanied by extreme scientific and technological difficulties, but has resulted in progress. At present, controlled fusion reactions have been unable to produce break-even (self-sustaining) controlled fusion reactions. Workable designs for a reactor that theoretically will deliver ten times more fusion energy than the amount needed to heat up plasma to required temperatures (see ITER
ITER
ITER is an international nuclear fusion research and engineering project, which is currently building the world's largest and most advanced experimental tokamak nuclear fusion reactor at Cadarache in the south of France...

) were originally scheduled to be operational in 2018, however this has been delayed and a new date has not been stated.

It takes considerable energy to force nuclei to fuse, even those of the lightest element, hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

. This is because all nuclei have a positive charge (due to their protons), and as like charges repel, nuclei strongly resist being put too close together. Accelerated to high speeds (that is, heated to thermonuclear temperatures), they can overcome this electrostatic repulsion and get close enough for the attractive nuclear force
Nuclear force
The nuclear force is the force between two or more nucleons. It is responsible for binding of protons and neutrons into atomic nuclei. The energy released causes the masses of nuclei to be less than the total mass of the protons and neutrons which form them...

 to be sufficiently strong to achieve fusion. The fusion of lighter nuclei, which creates a heavier nucleus and often a free neutron or proton, generally releases more energy than it takes to force the nuclei together; this is an exothermic process
Exothermic reaction
An exothermic reaction is a chemical reaction that releases energy in the form of light or heat. It is the opposite of an endothermic reaction. Expressed in a chemical equation:-Overview:...

 that can produce self-sustaining reactions. The National Ignition Facility
National Ignition Facility
The National Ignition Facility, or NIF is a large, laser-based inertial confinement fusion research device located at the Lawrence Livermore National Laboratory in Livermore, California. NIF uses powerful lasers to heat and compress a small amount of hydrogen fuel to the point where nuclear fusion...

, which uses laser-driven inertial confinement fusion
Inertial confinement fusion
Inertial confinement fusion is a process where nuclear fusion reactions are initiated by heating and compressing a fuel target, typically in the form of a pellet that most often contains a mixture of deuterium and tritium....

, is thought to be capable of break-even fusion.

The first large-scale laser target experiments were performed in June 2009 and ignition experiments are beginning early in 2011.

Energy released in most nuclear reactions is much larger than in chemical reaction
Chemical reaction
A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, typically following the input of some type of energy, such as heat, light or electricity...

s, because the binding energy
Binding energy
Binding energy is the mechanical energy required to disassemble a whole into separate parts. A bound system typically has a lower potential energy than its constituent parts; this is what keeps the system together—often this means that energy is released upon the creation of a bound state...

 that holds a nucleus together is far greater than the energy that holds electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s to a nucleus. For example, the ionization energy
Ionization energy
The ionization energy of a chemical species, i.e. an atom or molecule, is the energy required to remove an electron from the species to a practically infinite distance. Large atoms or molecules have a low ionization energy, while small molecules tend to have higher ionization energies.The property...

 gained by adding an electron to a hydrogen nucleus is —less than one-millionth of the released in the deuterium
Deuterium
Deuterium, also called heavy hydrogen, is one of two stable isotopes of hydrogen. It has a natural abundance in Earth's oceans of about one atom in of hydrogen . Deuterium accounts for approximately 0.0156% of all naturally occurring hydrogen in Earth's oceans, while the most common isotope ...

tritium
Tritium
Tritium is a radioactive isotope of hydrogen. The nucleus of tritium contains one proton and two neutrons, whereas the nucleus of protium contains one proton and no neutrons...

 (D–T) reaction shown in the diagram to the right. Fusion reactions have an energy density
Energy density
Energy density is a term used for the amount of energy stored in a given system or region of space per unit volume. Often only the useful or extractable energy is quantified, which is to say that chemically inaccessible energy such as rest mass energy is ignored...

 many times greater than nuclear fission
Nuclear fission
In nuclear physics and nuclear chemistry, nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts , often producing free neutrons and photons , and releasing a tremendous amount of energy...

; the reactions produce far greater energies per unit of mass even though individual fission reactions are generally much more energetic than individual fusion ones, which are themselves millions of times more energetic than chemical reactions. Only direct conversion of mass into energy
Mass-energy equivalence
In physics, mass–energy equivalence is the concept that the mass of a body is a measure of its energy content. In this concept, mass is a property of all energy, and energy is a property of all mass, and the two properties are connected by a constant...

, such as that caused by the annihilatory
Annihilation
Annihilation is defined as "total destruction" or "complete obliteration" of an object; having its root in the Latin nihil . A literal translation is "to make into nothing"....

 collision of matter
Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...

 and antimatter
Antimatter
In particle physics, antimatter is the extension of the concept of the antiparticle to matter, where antimatter is composed of antiparticles in the same way that normal matter is composed of particles...

, is more energetic per unit of mass than nuclear fusion.

Requirements


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
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

 protons. If two nuclei can be brought close enough together, however, the electrostatic repulsion can be overcome by the attractive nuclear force
Nuclear force
The nuclear force is the force between two or more nucleons. It is responsible for binding of protons and neutrons into atomic nuclei. The energy released causes the masses of nuclei to be less than the total mass of the protons and neutrons which form them...

, which is stronger at close distances.

When a nucleon
Nucleon
In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...

 such as a proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

 or neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

 is added to a nucleus, the nuclear force attracts it to other nucleons, but primarily to its immediate neighbours due to the short range of the force. The nucleons in the interior of a nucleus have more neighboring nucleons than those on the surface. Since smaller nuclei have a larger surface area-to-volume ratio, the binding energy per nucleon due to the nuclear force
Nuclear force
The nuclear force is the force between two or more nucleons. It is responsible for binding of protons and neutrons into atomic nuclei. The energy released causes the masses of nuclei to be less than the total mass of the protons and neutrons which form them...

 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 the above picture is a toy model
Toy model
In physics, a toy model is a simplified set of objects and equations relating them that can nevertheless be used to understand a mechanism that is also useful in the full, non-simplified theory....

 because nucleons are quantum objects, and so, for example, since two neutrons in a nucleus are identical to each other, 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 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 get larger.

The net result of these opposing forces is that the binding energy per nucleon generally increases with increasing size, up to the elements iron
Iron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...

 and nickel
Nickel
Nickel is a chemical element with the chemical symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel belongs to the transition metals and is hard and ductile...

, and then decreases for heavier nuclei. Eventually, the binding energy
Binding energy
Binding energy is the mechanical energy required to disassemble a whole into separate parts. A bound system typically has a lower potential energy than its constituent parts; this is what keeps the system together—often this means that energy is released upon the creation of a bound state...

 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
Binding energy
Binding energy is the mechanical energy required to disassemble a whole into separate parts. A bound system typically has a lower potential energy than its constituent parts; this is what keeps the system together—often this means that energy is released upon the creation of a bound state...

 per nucleon, are , , , and . Even though the nickel isotope
Isotopes of nickel
Naturally occurring nickel is composed of five stable isotopes; , , , and with being the most abundant . 58Ni may decay by double beta-plus decay to 58Fe. 26 radioisotopes have been characterised with the most stable being with a half-life of 76,000 years, with a half-life of 100.1 years,...

, , is more stable, the iron isotope
Isotopes of iron
Naturally occurring iron consists of four isotopes: 5.845% of 54Fe , 91.754% of 56Fe, 2.119% of 57Fe and 0.282% of 58Fe. There are 24 known radioactive isotopes and their half-lives are shown below...

  is an order of magnitude
Order of magnitude
An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the exponent being applied to this amount...

 more common. This is due to a greater disintegration rate for in the interior of stars driven by photon absorption.

A notable exception to this general trend is the helium-4
Helium-4
Helium-4 is a non-radioactive isotope of helium. It is by far the most abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on earth. Its nucleus is the same as an alpha particle, consisting of two protons and two neutrons. Alpha decay of heavy...

 nucleus, whose binding energy is higher than that of lithium
Lithium
Lithium is a soft, silver-white metal that belongs to the alkali metal group of chemical elements. It is represented by the symbol Li, and it has the atomic number 3. Under standard conditions it is the lightest metal and the least dense solid element. Like all alkali metals, lithium is highly...

, the next heaviest element. The Pauli exclusion principle
Pauli exclusion principle
The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement is that the total wave function for two identical fermions is anti-symmetric with respect to exchange of the particles...

 provides an explanation for this exceptional behavior—it says that because protons and neutrons are fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....

s, they cannot exist in exactly the same state. Each proton or neutron energy state in a nucleus can accommodate both a spin up particle and a spin down particle. Helium-4 has an anomalously large binding energy because its nucleus consists of two protons and two neutrons; so all four of its nucleons can be in the ground state. Any additional nucleons would have to go into higher energy states.

The situation is similar if two nuclei are brought together. As they approach each other, all the protons in one nucleus repel all the protons in the other. Not until the two nuclei actually come in contact can the strong nuclear force
Nuclear force
The nuclear force is the force between two or more nucleons. It is responsible for binding of protons and neutrons into atomic nuclei. The energy released causes the masses of nuclei to be less than the total mass of the protons and neutrons which form them...

 take over. Consequently, even when the final energy state is lower, there is a large energy barrier that must first be overcome. It is called the Coulomb barrier
Coulomb barrier
The Coulomb barrier, named after Coulomb's law, which is named after physicist Charles-Augustin de Coulomb , is the energy barrier due to electrostatic interaction that two nuclei need to overcome so they can get close enough to undergo a nuclear reaction...

.

The Coulomb barrier is smallest for isotopes of hydrogen, as their nuclei contain only a single positive charge. A diproton
Diproton
A diproton is a hypothetical isotope of helium nucleus consisting of two protons and no neutrons, and is predicted to be less stable than 5He...

 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
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

 from hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

 is 13.6 eV, about 7500 times less energy. 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.

If the energy to initiate the reaction comes from accelerating
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...

 one of the nuclei, the process is called beam-target fusion; if both nuclei are accelerated, it is beam-beam fusion. If the nuclei are part of a plasma near thermal equilibrium, the process is called thermonuclear fusion. Temperature is a measure of the average kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

 of particles, so by heating the nuclei they will gain energy and eventually have enough to overcome this 0.1 MeV. Converting the units between electronvolts and kelvin shows that the barrier would be overcome at a temperature in excess of 120 million kelvins.

There are two effects that lower the actual temperature needed. One is the fact that temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

 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
Distribution function
In molecular kinetic theory in physics, a particle's distribution function is a function of seven variables, f, which gives the number of particles per unit volume in phase space. It is the number of particles per unit volume having approximately the velocity near the place and time...

 that account for most of the fusion reactions. The other effect is quantum tunneling. The nuclei do not actually have to have enough energy to overcome the Coulomb barrier completely. If they have nearly enough energy, they can tunnel through the remaining barrier. For these reasons fuel at lower temperatures will still undergo fusion events, at a lower rate.

The reaction cross section
Cross section (physics)
A cross section is the effective area which governs the probability of some scattering or absorption event. Together with particle density and path length, it can be used to predict the total scattering probability via the Beer-Lambert law....

σ is a measure of the probability of a fusion reaction as a function of the relative velocity of the two reactant nuclei. If the reactants have a distribution of velocities, e.g. a thermal distribution with thermonuclear fusion, then it is useful to perform an average over the distributions of the product of cross section and velocity. The reaction rate (fusions per volume per time) is <σv> times the product of the reactant number densities:


If a species of nuclei is reacting with itself, such as the DD reaction, then the product must be replaced by .

increases from virtually zero at room temperatures up to meaningful magnitudes at temperatures of 10–100 keV. At these temperatures, well above typical ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...

ization energies (13.6 eV in the hydrogen case), the fusion reactants exist in a plasma state.

The significance of as a function of temperature in a device with a particular energy confinement time is found by considering the Lawson criterion
Lawson criterion
In nuclear fusion research, the Lawson criterion, first derived on fusion reactors by John D. Lawson in 1955 and published in 1957, is an important general measure of a system that defines the conditions needed for a fusion reactor to reach ignition, that is, that the heating of the plasma by the...

.

Gravitational confinement


One force capable of confining the fuel well enough to satisfy the Lawson criterion
Lawson criterion
In nuclear fusion research, the Lawson criterion, first derived on fusion reactors by John D. Lawson in 1955 and published in 1957, is an important general measure of a system that defines the conditions needed for a fusion reactor to reach ignition, that is, that the heating of the plasma by the...

 is gravity. The mass needed, however, is so great that gravitational confinement is only found in star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

s–the least massive stars capable of sustained fusion are red dwarf
Red dwarf
According to the Hertzsprung-Russell diagram, a red dwarf star is a small and relatively cool star, of the main sequence, either late K or M spectral type....

s, while brown dwarf
Brown dwarf
Brown dwarfs are sub-stellar objects which are too low in mass to sustain hydrogen-1 fusion reactions in their cores, which is characteristic of stars on the main sequence. Brown dwarfs have fully convective surfaces and interiors, with no chemical differentiation by depth...

s are able to fuse deuterium
Deuterium
Deuterium, also called heavy hydrogen, is one of two stable isotopes of hydrogen. It has a natural abundance in Earth's oceans of about one atom in of hydrogen . Deuterium accounts for approximately 0.0156% of all naturally occurring hydrogen in Earth's oceans, while the most common isotope ...

 and lithium
Lithium
Lithium is a soft, silver-white metal that belongs to the alkali metal group of chemical elements. It is represented by the symbol Li, and it has the atomic number 3. Under standard conditions it is the lightest metal and the least dense solid element. Like all alkali metals, lithium is highly...

 if they are of sufficient mass. In stars heavy enough
Asymptotic Giant Branch
The asymptotic giant branch is the region of the Hertzsprung-Russell diagram populated by evolving low to medium-mass stars. This is a period of stellar evolution undertaken by all low to intermediate mass stars late in their lives....

, after the supply of hydrogen is exhausted in their cores, their cores (or a shell around the core) start fusing helium to carbon
Triple-alpha process
The triple alpha process is a set of nuclear fusion reactions by which three helium-4 nuclei are transformed into carbon.Older stars start to accumulate helium produced by the proton–proton chain reaction and the carbon–nitrogen–oxygen cycle in their cores...

. 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
Silicon burning process
In astrophysics, silicon burning is a very brief sequence of nuclear fusion reactions that occur in massive stars with a minimum of about 8–11 solar masses. Silicon burning is the final stage of fusion for massive stars that have run out of the fuels that power them for their long lives in the main...

. As iron has one of the highest binding energies, reactions producing heavier elements are generally endothermic
Endothermic
In thermodynamics, the word endothermic describes a process or reaction in which the system absorbs energy from the surroundings in the form of heat. Its etymology stems from the prefix endo- and the Greek word thermasi,...

. Therefore significant amounts of heavier elements are not formed during stable periods of massive star evolution, but are formed in supernova explosions
R-process
The r-process is a nucleosynthesis process, likely occurring in core-collapse supernovae responsible for the creation of approximately half of the neutron-rich atomic nuclei that are heavier than iron. The process entails a succession of rapid neutron captures on seed nuclei, typically Ni-56,...

. Some lighter stars
S-process
The S-process or slow-neutron-capture-process is a nucleosynthesis process that occurs at relatively low neutron density and intermediate temperature conditions in stars. Under these conditions the rate of neutron capture by atomic nuclei is slow relative to the rate of radioactive beta-minus decay...

 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
Exothermic
In thermodynamics, the term exothermic describes a process or reaction that releases energy from the system, usually in the form of heat, but also in the form of light , electricity , or sound...

 in the process of being split again back toward the size of iron, in the process of nuclear fission
Nuclear fission
In nuclear physics and nuclear chemistry, nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts , often producing free neutrons and photons , and releasing a tremendous amount of energy...

. Nuclear fission thus releases energy which has been stored, sometimes billions of years before, during stellar nucleosynthesis
Nucleosynthesis
Nucleosynthesis is the process of creating new atomic nuclei from pre-existing nucleons . It is thought that the primordial nucleons themselves were formed from the quark–gluon plasma from the Big Bang as it cooled below two trillion degrees...

.

Magnetic confinement



Electrically charged particles (such as fuel ions) will follow magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

 lines (see Guiding center). The fusion fuel can therefore be trapped using a strong magnetic field. A variety of magnetic configurations exist, including the toroidal geometries of tokamak
Tokamak
A tokamak is a device using a magnetic field to confine a plasma in the shape of a torus . Achieving a stable plasma equilibrium requires magnetic field lines that move around the torus in a helical shape...

s and stellarator
Stellarator
A stellarator is a device used to confine a hot plasma with magnetic fields in order to sustain a controlled nuclear fusion reaction. It is one of the earliest controlled fusion devices, first invented by Lyman Spitzer in 1950 and built the next year at what later became the Princeton Plasma...

s and open-ended mirror confinement
Magnetic mirror
A magnetic mirror is a magnetic field configuration where the field strength changes when moving along a field line. The mirror effect results in a tendency for charged particles to bounce back from the high field region....

 systems.

Inertial confinement



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
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...

, ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...

, or electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

 beam, or a Z-pinch
Z-pinch
In fusion power research, the Z-pinch, also known as zeta pinch or Bennett pinch , is a type of plasma confinement system that uses an electrical current in the plasma to generate a magnetic field that compresses it...

. Another method is to use conventional high explosive material
Explosive material
An explosive material, also called an explosive, is a reactive substance that contains a great amount of potential energy that can produce an explosion if released suddenly, usually accompanied by the production of light, heat, sound, and pressure...

 to compress a fuel to fusion conditions. The UTIAS explosive-driven-implosion facility was used to produce stable, centered and focused hemispherical implosions to generate neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

s from D-D reactions. The simplest and most direct method proved to be in a predetonated stoichiometric mixture of deuterium
Deuterium
Deuterium, also called heavy hydrogen, is one of two stable isotopes of hydrogen. It has a natural abundance in Earth's oceans of about one atom in of hydrogen . Deuterium accounts for approximately 0.0156% of all naturally occurring hydrogen in Earth's oceans, while the most common isotope ...

-oxygen
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...

. The other successful method was using a miniature Voitenko compressor
Voitenko compressor
The Voitenko compressor is a shaped charge adapted from its original purpose of piercing thick steel armour to the task of accelerating shock waves. It was proposed by a Russian scientist in 1965. It slightly resembles a wind tunnel....

, where a plane diaphragm was driven by the implosion wave into a secondary small spherical cavity that contained pure deuterium
Deuterium
Deuterium, also called heavy hydrogen, is one of two stable isotopes of hydrogen. It has a natural abundance in Earth's oceans of about one atom in of hydrogen . Deuterium accounts for approximately 0.0156% of all naturally occurring hydrogen in Earth's oceans, while the most common isotope ...

 gas at one atmosphere.

Some other confinement principles have been investigated, such as muon-catalyzed fusion
Muon-catalyzed fusion
Muon-catalyzed fusion is a process allowing nuclear fusion to take place at temperatures significantly lower than the temperatures required for thermonuclear fusion, even at room temperature or lower...

, the Farnsworth–Hirsch fusor and Polywell
Polywell
A polywell device is a type of fusion reactor that was originated by Robert Bussard under a U.S. Navy research contract. It traps electrons in a magnetic confinement inside its hollow center. The negatively charged electrons then accelerate positively charged ions for the purpose of achieving...

 (inertial electrostatic confinement
Inertial electrostatic confinement
Inertial electrostatic confinement is a concept for retaining a plasma using an electrostatic field. The field accelerates charged particles radially inward, usually in a spherical but sometimes in a cylindrical geometry. Ions can be confined with IEC in order to achieve controlled nuclear fusion...

), and bubble fusion
Bubble fusion
Bubble fusion, also known as sonofusion, is the non-technical name for a nuclear fusion reaction hypothesized to occur during a high-pressure version of sonoluminescence, an extreme form of acoustic cavitation...

.

Production methods


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

Muon-catalyzed fusion


Muon-catalyzed fusion
Muon-catalyzed fusion
Muon-catalyzed fusion is a process allowing nuclear fusion to take place at temperatures significantly lower than the temperatures required for thermonuclear fusion, even at room temperature or lower...

 is a well-established and reproducible fusion process that occurs at ordinary temperatures. It was studied in detail by Steven Jones
Steven E. Jones
Steven Earl Jones is an American physicist. For most of his career, Jones was known mainly for his work on muon-catalyzed fusion. In the fall of 2006, amid controversy surrounding his work on the collapse of the World Trade Center , he was relieved of his teaching duties...

 in the early 1980s. It has not been reported to produce net energy. Net energy production from this reaction cannot occur because of the energy required to create muon
Muon
The muon |mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...

s, their 2.2 µs half-life
Half-life
Half-life, abbreviated t½, is the period of time it takes for the amount of a substance undergoing decay to decrease by half. The name was originally used to describe a characteristic of unstable atoms , but it may apply to any quantity which follows a set-rate decay.The original term, dating to...

, and the chance that a muon will bind to the new alpha particle
Alpha particle
Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus, which is classically produced in the process of alpha decay, but may be produced also in other ways and given the same name...

 and thus stop catalyzing fusion.

Generally cold, locally hot fusion


Accelerator-based light-ion fusion 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—all it takes is a vacuum tube, a pair of electrodes, and a high-voltage transformer; fusion can be observed with as little as 10 kV between electrodes. The key problem with accelerator-based fusion (and with cold targets in general) is that fusion cross sections are many orders of magnitude lower than Coulomb interaction cross sections. Therefore the vast majority of ions end up expending their energy on bremsstrahlung
Bremsstrahlung
Bremsstrahlung is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into a photon because energy is conserved. The term is...

 and ionization of atoms of the target. Devices referred to as sealed-tube neutron generator
Neutron generator
Neutron generators are neutron source devices which contain compact linear accelerators and that produce neutrons by fusing isotopes of hydrogen together. The fusion reactions take place in these devices by accelerating either deuterium, tritium, or a mixture of these two isotopes into a metal...

s 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 these nuclei to be accelerated against hydride targets, also containing deuterium and tritium, where fusion takes place. Hundreds of neutron generators are produced annually for use in the petroleum industry where they are used in measurement equipment for locating and mapping oil reserves. Despite periodic reports in the popular press by scientists claiming to have invented "table-top" fusion machines, neutron generators have been around for half a century. The sizes of these devices vary but the smallest instruments are often packaged in sizes smaller than a loaf of bread. These devices do not produce a net power output.

Sonofusion or bubble fusion
Bubble fusion
Bubble fusion, also known as sonofusion, is the non-technical name for a nuclear fusion reaction hypothesized to occur during a high-pressure version of sonoluminescence, an extreme form of acoustic cavitation...

, a controversial variation on the sonoluminescence
Sonoluminescence
Sonoluminescence is the emission of short bursts of light from imploding bubbles in a liquid when excited by sound.-History:The effect was first discovered at the University of Cologne in 1934 as a result of work on sonar. H. Frenzel and H. Schultes put an ultrasound transducer in a tank of...

 theme, suggests that acoustic shock waves, creating temporary bubbles (cavitation) that expand and collapse shortly after creation, can produce temperatures and pressures sufficient for nuclear fusion.

The Farnsworth–Hirsch fusor is a tabletop device in which fusion occurs. This fusion comes from high effective temperatures produced by electrostatic acceleration of ions. The device can be built inexpensively, but it too is unable to produce a net power output.

The Polywell
Polywell
A polywell device is a type of fusion reactor that was originated by Robert Bussard under a U.S. Navy research contract. It traps electrons in a magnetic confinement inside its hollow center. The negatively charged electrons then accelerate positively charged ions for the purpose of achieving...

 is a non-thermodynamic equilibrium machine that uses electrostatic confinement to accelerate ions into a center where they fuse together.

Antimatter-initialized fusion
Antimatter catalyzed nuclear pulse propulsion
Antimatter catalyzed nuclear pulse propulsion is a variation of nuclear pulse propulsion based upon the injection of antimatter into a mass of nuclear fuel which normally would not be useful in propulsion...

 uses small amounts of antimatter
Antimatter
In particle physics, antimatter is the extension of the concept of the antiparticle to matter, where antimatter is composed of antiparticles in the same way that normal matter is composed of particles...

 to trigger a tiny fusion explosion. This has been studied primarily in the context of making nuclear pulse propulsion
Nuclear pulse propulsion
Nuclear pulse propulsion is a proposed method of spacecraft propulsion that uses nuclear explosions for thrust. It was first developed as Project Orion by DARPA, after a suggestion by Stanislaw Ulam in 1947...

, and pure fusion bombs feasible. This is not near becoming a practical power source, due to the cost of manufacturing antimatter alone.

Pyroelectric fusion
Pyroelectric fusion
Pyroelectric fusion refers to the technique of using pyroelectric crystals to generate high strength electrostatic fields to accelerate deuterium ions into a metal hydride target also containing deuterium with sufficient kinetic energy to cause these ions to undergo nuclear fusion. It was...

 was reported in April 2005 by a team at UCLA
University of California, Los Angeles
The University of California, Los Angeles is a public research university located in the Westwood neighborhood of Los Angeles, California, USA. It was founded in 1919 as the "Southern Branch" of the University of California and is the second oldest of the ten campuses...

. The scientists used a pyroelectric
Pyroelectricity
Pyroelectricity is the ability of certain materials to generate a temporary voltage when they are heated or cooled. The change in temperature modifies the positions of the atoms slightly within the crystal structure, such that the polarization of the material changes. This polarization change...

 crystal heated from −34 to 7 °C (−29 to 45 °F), combined with a tungsten
Tungsten
Tungsten , also known as wolfram , is a chemical element with the chemical symbol W and atomic number 74.A hard, rare metal under standard conditions when uncombined, tungsten is found naturally on Earth only in chemical compounds. It was identified as a new element in 1781, and first isolated as...

 needle to produce an electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...

 of about 25 gigavolts per meter to ionize and accelerate deuterium
Deuterium
Deuterium, also called heavy hydrogen, is one of two stable isotopes of hydrogen. It has a natural abundance in Earth's oceans of about one atom in of hydrogen . Deuterium accounts for approximately 0.0156% of all naturally occurring hydrogen in Earth's oceans, while the most common isotope ...

 nuclei into an erbium
Erbium
Erbium is a chemical element in the lanthanide series, with the symbol Er and atomic number 68. A silvery-white solid metal when artificially isolated, natural erbium is always found in chemical combination with other elements on Earth...

 deuteride target. Though the energy of the deuterium ions generated by the crystal has not been directly measured, the authors used 100 keV (a temperature of about 109 K
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...

) as an estimate in their modeling. At these energy levels, two deuterium nuclei can fuse together to produce a helium-3
Helium-3
Helium-3 is a light, non-radioactive isotope of helium with two protons and one neutron. It is rare on Earth, and is sought for use in nuclear fusion research...

 nucleus, a 2.45 MeV neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

 and bremsstrahlung
Bremsstrahlung
Bremsstrahlung is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into a photon because energy is conserved. The term is...

. Although it makes a useful neutron generator, the apparatus is not intended for power generation since it requires far more energy than it produces.

Hot fusion


In hot fusion
Fusion power
Fusion power is the power generated by nuclear fusion processes. In fusion reactions two light atomic nuclei fuse together to form a heavier nucleus . In doing so they release a comparatively large amount of energy arising from the binding energy due to the strong nuclear force which is manifested...

, the fuel reaches tremendous temperature and pressure inside a fusion reactor or star.

The methods in the second group are examples of non-equilibrium systems, in which very high temperatures and pressures are produced in a relatively small region adjacent to material of much lower temperature. In his doctoral thesis for MIT
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...

, Todd Rider did a theoretical study of all quasineutral, isotropic, non-equilibrium fusion systems. He demonstrated that all such systems will leak energy at a rapid rate due to bremsstrahlung
Bremsstrahlung
Bremsstrahlung is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into a photon because energy is conserved. The term is...

 produced when electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s in the plasma
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...

 hit other electrons or ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...

s at a cooler temperature and suddenly decelerate. The problem is not as pronounced in a hot plasma because the range of temperatures, and thus the magnitude of the deceleration, is much lower. Note that Rider's work does not apply to non-neutral and/or anisotropic non-equilibrium plasmas.

Astrophysical reaction chains


The most important fusion process in nature is the one that powers stars. The net result is the fusion of four proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

s into one alpha particle
Alpha particle
Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus, which is classically produced in the process of alpha decay, but may be produced also in other ways and given the same name...

, with the release of two positron
Positron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...

s, two neutrino
Neutrino
A neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...

s (which changes two of the protons into neutrons), and energy, but several individual reactions are involved, depending on the mass of the star. For stars the size of the sun or smaller, the proton-proton chain dominates. In heavier stars, the CNO cycle
CNO cycle
The CNO cycle is one of two sets of fusion reactions by which stars convert hydrogen to helium, the other being the proton–proton chain. Unlike the proton–proton chain reaction, the CNO cycle is a catalytic cycle. Theoretical models show that the CNO cycle is the dominant source of energy in stars...

 is more important. Both types of processes are responsible for the creation of new elements as part of stellar nucleosynthesis
Stellar nucleosynthesis
Stellar nucleosynthesis is the collective term for the nuclear reactions taking place in stars to build the nuclei of the elements heavier than hydrogen. Some small quantity of these reactions also occur on the stellar surface under various circumstances...

.

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. Thus, reproduction of stellar core conditions in a lab for nuclear fusion power production is completely impractical. Because nuclear reaction rates strongly depend on temperature (exp(−E/kT)), achieving reasonable energy production rates in terrestrial fusion reactors requires 10–100 times higher temperatures (compared to stellar interiors): T ≈ 0.1–1.0 GK.

Criteria and candidates for terrestrial reactions


In man-made fusion, the primary fuel is not constrained to be protons and higher temperatures can be used, so reactions with larger cross-sections are chosen. This implies a lower Lawson criterion
Lawson criterion
In nuclear fusion research, the Lawson criterion, first derived on fusion reactors by John D. Lawson in 1955 and published in 1957, is an important general measure of a system that defines the conditions needed for a fusion reactor to reach ignition, that is, that the heating of the plasma by the...

, and therefore less startup effort. Another concern is the production of neutrons, which activate the reactor structure radiologically, but also have the advantages of allowing volumetric extraction of the fusion energy and tritium
Tritium
Tritium is a radioactive isotope of hydrogen. The nucleus of tritium contains one proton and two neutrons, whereas the nucleus of protium contains one proton and no neutrons...

 breeding. Reactions that release no neutrons are referred to as aneutronic
Aneutronic fusion
Aneutronic fusion is any form of fusion power where neutrons carry no more than 1% of the total released energy. The most-studied fusion reactions release up to 80% of their energy in neutrons...

.

To be a useful energy source, a fusion reaction must satisfy several criteria. It must
  • Be exothermic
    Exothermic
    In thermodynamics, the term exothermic describes a process or reaction that releases energy from the system, usually in the form of heat, but also in the form of light , electricity , or sound...

    : This may be obvious, but it limits the reactants to the low Z (number of protons) side of the curve of binding energy. It also makes helium the most common product because of its extraordinarily tight binding, although and also show up.
  • Involve low Z nuclei: This is because the electrostatic repulsion must be overcome before the nuclei are close enough to fuse.
  • Have two reactants: At anything less than stellar densities, three body collisions are too improbable. 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:
{| border="0"

|- style="height:2em;"
|(1) || ||+ || ||→ || ||( ||3.5 MeV ||) ||+ ||n0
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

 ||( ||14.1 MeV ||)
|- style="height:2em;"
|(2i) || ||+ || ||→ || ||( ||1.01 MeV ||) ||+ ||p+
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

 ||( ||3.02 MeV ||) || || || || || || 50%
|- style="height:2em;"
|(2ii) || || || ||→ || ||( ||0.82 MeV ||) ||+ ||n0
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

 ||( ||2.45 MeV ||) || || || || || || 50%
|- style="height:2em;"
|(3) || ||+ || ||→ || ||( ||3.6 MeV ||) ||+ ||p+
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

 ||( ||14.7 MeV ||)
|- style="height:2em;"
|(4) || ||+ || ||→ || || || || ||+ ||2 n0
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

 || || || || || ||+ ||11.3 MeV
|- style="height:2em;"
|(5) || ||+ || ||→ || || || || ||+ ||2 p+
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

 || || || || || ||+ ||12.9 MeV
|- style="height:2em;"
|(6i) || ||+ || ||→ || || || || ||+ ||p+
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

 ||+ ||n0
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

 || || || ||+ ||12.1 MeV || || 51%
|- style="height:2em;"
|(6ii) || || || ||→ || ||( ||4.8 MeV ||) ||+ || ||( ||9.5 MeV ||) || || || || || || 43%
|- style="height:2em;"
|(6iii) || || || ||→ || ||( ||0.5 MeV ||) ||+ ||n0
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

 ||( ||1.9 MeV ||) ||+ ||p+
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

 ||( ||11.9 MeV ||) || 6%
|- style="height:2em;"
|(7i) || ||+ || ||→ ||2  ||+ ||22.4 MeV
|- style="height:2em;"
|(7ii) || || || ||→ || ||+ || || ||+ ||n0
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

 || || || || || ||+ ||2.56 MeV
|- style="height:2em;"
|(7iii) || || || ||→ || ||+ ||p+
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

 || || || || || || || || ||+ ||5.0 MeV
|- style="height:2em;"
|(7iv) || || || ||→ || ||+ ||n0
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

 || || || || || || || || ||+ ||3.4 MeV
|- style="height:2em;"
|(8) ||p+
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

 ||+ || ||→ || ||( ||1.7 MeV ||) ||+ || ||( ||2.3 MeV ||)
|- style="height:2em;"
|(9) || ||+ || ||→ ||2  ||+ ||p+
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

 || || || || || || || || ||+ ||16.9 MeV
|- style="height:2em;"
|(10) ||p+
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

 ||+ || ||→ ||3  || || || || || || || || || || ||+ ||8.7 MeV
|}
For reactions with two products, the energy is divided between them in inverse proportion to their masses, as shown. In most reactions with three products, the distribution of energy varies. For reactions that can result in more than one set of products, the branching ratios are given.

Some reaction candidates can be eliminated at once. The D-6Li reaction has no advantage compared to p+
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

- because it is roughly as difficult to burn but produces substantially more neutrons through - side reactions. There is also a p+
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

- reaction, but the cross section is far too low, except possibly when Ti > 1 MeV, but at such high temperatures an endothermic, direct neutron-producing reaction also becomes very significant. Finally there is also a p+
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

- reaction, which is not only difficult to burn, but can be easily induced to split into two alpha particles and a neutron.

In addition to the fusion reactions, the following reactions with neutrons are important in order to "breed" tritium in "dry" fusion bombs and some proposed fusion reactors:
{| border="0"

|- style="height:2em;"
|n0
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

 ||+ || ||→ || ||+ ||
|- style="height:2em;"
|n0
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

 ||+ || ||→ || ||+ || ||+ ||n0
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...


|}

To evaluate the usefulness of these reactions, in addition to the reactants, the products, and the energy released, one needs to know something about the cross section. Any given fusion device has a maximum plasma pressure it can sustain, and an economical device would always operate near this maximum. Given this pressure, the largest fusion output is obtained when the temperature is chosen so that <σv>/T2 is a maximum. This is also the temperature at which the value of the triple product nTτ required for ignition is a minimum, since that required value is inversely proportional to <σv>/T2 (see Lawson criterion
Lawson criterion
In nuclear fusion research, the Lawson criterion, first derived on fusion reactors by John D. Lawson in 1955 and published in 1957, is an important general measure of a system that defines the conditions needed for a fusion reactor to reach ignition, that is, that the heating of the plasma by the...

). (A plasma is "ignited" if the fusion reactions produce enough power to maintain the temperature without external heating.) This optimum temperature and the value of <σv>/T2 at that temperature is given for a few of these reactions in the following table.
fuel T [keV] <σv>/T2 [m3/s/keV2]
- 13.6 1.24×10−24
- 15 1.28×10−26
- 58 2.24×10−26
p+- 66 1.46×10−27
p+- 123 3.01×10−27


Note that many of the reactions form chains. For instance, a reactor fueled with and creates some , which is then possible to use in the - reaction if the energies are "right". An elegant idea is to combine the reactions (8) and (9). The from reaction (8) can react with in reaction (9) before completely thermalizing. This produces an energetic proton, which in turn undergoes reaction (8) before thermalizing. Detailed analysis shows that this idea would not work well, but it is a good example of a case where the usual assumption of a Maxwellian plasma is not appropriate.

Neutronicity, confinement requirement, and power density



Any of the reactions above can in principle be the basis of fusion power
Fusion power
Fusion power is the power generated by nuclear fusion processes. In fusion reactions two light atomic nuclei fuse together to form a heavier nucleus . In doing so they release a comparatively large amount of energy arising from the binding energy due to the strong nuclear force which is manifested...

 production. In addition to the temperature and cross section discussed above, we must consider the total energy of the fusion products Efus, the energy of the charged fusion products Ech, and the atomic number Z of the non-hydrogenic reactant.

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

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

With this choice, we tabulate parameters for four of the most important reactions
fuel ZEfus [MeV]Ech [MeV]neutronicity
- 1 17.6 3.5 0.80
- 1 12.5 4.2 0.66
- 2 18.3 18.3 ~0.05
p+- 5 8.7 8.7 ~0.001


The last column is the neutronicity
Aneutronic fusion
Aneutronic fusion is any form of fusion power where neutrons carry no more than 1% of the total released energy. The most-studied fusion reactions release up to 80% of their energy in neutrons...

of the reaction, the fraction of the fusion energy released as neutrons. This is an important indicator of the magnitude of the problems associated with neutrons like radiation damage, biological shielding, remote handling, and safety. For the first two reactions it is calculated as (Efus-Ech)/Efus. For the last two reactions, where this calculation would give zero, the values quoted are rough estimates based on side reactions that produce neutrons in a plasma in thermal equilibrium.

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

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

We can now compare these reactions in the following table.
fuel <σv>/T2penalty/bonus reactivityLawson criterionpower density (W/m3/kPa2)relation of power density
- 1.24×10−24 1 1 1 34 1
- 1.28×10−26 2 48 30 0.5 68
- 2.24×10−26 2/3 83 16 0.43 80
p+- 1.46×10−27 1/2 1700 0.005 6800
p+- 3.01×10−27 1/3 1240 500 0.014 2500


The maximum value of <σv>/T2 is taken from a previous table. The "penalty/bonus" factor is that related to a non-hydrogenic reactant or a single-species reaction. The values in the column "reactivity" are found by dividing 1.24 by the product of the second and third columns. It indicates the factor by which the other reactions occur more slowly than the - reaction under comparable conditions. The column "Lawson criterion
Lawson criterion
In nuclear fusion research, the Lawson criterion, first derived on fusion reactors by John D. Lawson in 1955 and published in 1957, is an important general measure of a system that defines the conditions needed for a fusion reactor to reach ignition, that is, that the heating of the plasma by the...

" weights these results with Ech and gives an indication of how much more difficult it is to achieve ignition with these reactions, relative to the difficulty for the - reaction. The last column is labeled "power density" and weights the practical reactivity with Efus. It indicates how much lower the fusion power density of the other reactions is compared to the - reaction and can be considered a measure of the economic potential.

Bremsstrahlung losses in quasineutral, isotropic plasmas


The ions undergoing fusion in many systems will essentially never occur alone but will be mixed with electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s that in aggregate neutralize the ions' bulk electrical charge and form a plasma
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...

. The electrons will generally have a temperature comparable to or greater than that of the ions, so they will collide with the ions and emit x-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

 radiation of 10–30 keV energy (Bremsstrahlung
Bremsstrahlung
Bremsstrahlung is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into a photon because energy is conserved. The term is...

). The Sun and stars are opaque
Opacity (optics)
Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shielding material, glass, etc...

 to x-rays, but essentially any terrestrial fusion reactor will be optically thin
Optical depth
Optical depth, or optical thickness, is a measure of transparency. Optical depth is defined by the negative logarithm of the fraction of radiation that is not scattered or absorbed on a path...

 for x-rays of this energy range. X-rays are difficult to reflect but they are effectively absorbed (and converted into heat) in less than mm thickness of stainless steel (which is part of a reactor's shield). The ratio of fusion power produced to x-ray radiation lost to walls is an important figure of merit. This ratio is generally maximized at a much higher temperature than that which maximizes the power density (see the previous subsection). The following table shows the rough optimum temperature and the power ratio at that temperature for several reactions.
fuel Ti (keV)Pfusion/PBremsstrahlung
- 50 140
- 500 2.9
- 100 5.3
- 1000 0.72
p+- 800 0.21
p+- 300 0.57


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

The temperatures maximizing the fusion power compared to the Bremsstrahlung are in every case higher than the temperature that maximizes the power density and minimizes the required value of the fusion triple product
Lawson criterion
In nuclear fusion research, the Lawson criterion, first derived on fusion reactors by John D. Lawson in 1955 and published in 1957, is an important general measure of a system that defines the conditions needed for a fusion reactor to reach ignition, that is, that the heating of the plasma by the...

. This will not change the optimum operating point for - very much because the Bremsstrahlung fraction is low, but it will push the other fuels into regimes where the power density relative to - is even lower and the required confinement even more difficult to achieve. For - and -, Bremsstrahlung losses will be a serious, possibly prohibitive problem. For -, p+
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

- and p+
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

- the Bremsstrahlung losses appear to make a fusion reactor using these fuels with a quasineutral, isotropic plasma impossible. Some ways out of this dilemma are considered—and rejected—in Fundamental limitations on plasma fusion systems not in thermodynamic equilibrium by Todd Rider. This limitation does not apply to non-neutral and anisotropic plasmas; however, these have their own challenges to contend with.

See also


External links




Organizations