Nuclear fusion

In physics, nuclear fusion is the process by which two nuclei join together to form a heavier nucleus. It is accompanied by the release or absorbtion of energy depending on the masses of the nuclei involved. The iron nucleus has the largest binding energy of all nuclei and so is the most stable. The fusion of two nuclei to produce a nucleus lighter than iron generally gives off energy while the fusion of nuclei heavier than iron absorbs energy. Nuclear fusion of light elements is the energy source which causes stars to shine and hydrogen bombs to explode. Nuclear fusion of heavy elements occurs in the extreme conditions of a supernova explosion. Nuclear fusion in stars and supernovae is the primary process by which new natural elements are created.

Requirements for fusion

A substantial energy barrier opposes the fusion reaction. The positive electrical charges of the nuclei repel each other via the electrostatic force, attempting to break any nuclei apart. Opposing this is the slightly more powerful strong nuclear force, which tries to hold them together. It is the tension between these two powerful forces that makes nuclear reactions so powerful.

Related Topics:
Electrostatic - Strong nuclear force - Tension

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The strong force only operates over short distances. When a nucleon (proton or neutron) is added to a nucleus, it is attracted by the strong force to other nucleons, but only to those in direct contact. The nucleons in the interior have neighbors on all sides, but those on the surface only have neighbors on one side. Since smaller nuclei have a larger surface to volume ratio, the binding energy per nucleon due to the strong force increases with size up to a limit.

Related Topics:
Nucleon - Proton - Neutron

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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 the nuclei get larger.

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The net result of these opposing forces is that the binding energy per nucleon generally increases with increasing size, namely up to the element iron, and then starts decreasing again. Eventually, the binding energy becomes negative and the nuclei are no longer stable.

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A notable exception to this trend is the element helium, whose nucleus consists of two protons and two neutrons. In a sense, protons and neutrons are two states of a single particle, and each of these states can have spin up or spin down. Consequently, all the nucleons in a helium nucleus can be in the ground state, making it extremely tightly bound. If any nucleons are added, they have to go into a higher energy state due to the Pauli exclusion principle.

Related Topics:
Helium - Pauli exclusion principle

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The situation is similar if two nuclei are brought together. As they approach each other, all the protons in one nucleus repel all the protons in the other. Not until the two nuclei actually come in contact can the strong nuclear force take over. Consequently, even when the final energy state is lower, there is a large energy barrier that must first be overcome. In chemistry, one would speak of the activation energy. In nuclear physics it is called the Coulomb barrier.

Related Topics:
Activation energy - Coulomb barrier

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

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Using D-T fuel, the resulting energy barrier is about 0.1 MeV. In comparison, the energy needed to remove an electron from hydrogen is 13 eV, about 7,500 times less energy. Once the fusion reaction is complete, the new nucleus drops to a lower-energy configuration and gives up additional energy by ejecting a neutron with 17.59 MeV, considerably more than what was needed to fuse them in the first place. This means that the D-T fusion reaction is very highly exothermic, making it a powerful energy source.

Related Topics:
Electron - Exothermic

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If the energy to initiate the reaction comes from accelerating one of the nuclei, the process is called beam-target fusion; if both nuclei are accelerated, it is beam-beam fusion. If the nuclei are part of a plasma near thermal equilibrium, one speaks of thermonuclear fusion. Temperature is a measure of the average kinetic energy of particles, so by heating the nuclei they will gain energy and eventually have enough to overcome this 0.1 MeV barrier. Converting the units between eV and kelvins shows that the barrier would be overcome at a temperature in excess of 1 GK, obviously a very high temperature.

Related Topics:
Accelerating - Plasma - Kinetic energy - GK

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There are two effects that lower the actual temperature needed. One is the fact that temperature is the average kinetic energy, implying that some nuclei at this temperature would actually have much higher energy than 0.1 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 tunneling. The nuclei do not actually have to have enough energy to overcome the Coulomb barrier completely. If they have nearly enough energy, they can tunnel through the remaining barrier. For this reason fuel at lower temperatures will still undergo fusion events, at a lower rate.

Related Topics:
Temperature - Velocity distribution - Quantum tunneling

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The reaction cross section ? 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 of over the distributions of the product of cross section and velocity. The reaction rate (fusions per volume per time) is

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:f = n_1 n_2 langle sigma v angle

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If a species of nuclei is reacting with itself, such as the DD reaction, then the product n_1n_2 must be replaced by (1/2)n^2.

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langle sigma v angle 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 eV in the hydrogen case), the fusion reactants exist in a plasma state.

Related Topics:
10 - 100 - Ionization - Plasma

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The significance of

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Methods of fuel confinement

The fusion reaction can sustain itself if enough of the energy produced goes into keeping the fuel hot.

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Gravitational confinement

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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. Even if the more reactive fuel deuterium were used, a mass about the size of the Moon would be needed.

Related Topics:
Lawson criterion - Stars - Moon

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Magnetic confinement

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Since plasmas are very good electrical conductors, magnetic fields can also be used to confine fusion fuel. A variety of magnetic configurations can be used, the most basic distinction being between mirror confinement and toroidal confinement, especially tokamaks and stellarators.

Related Topics:
Plasma - Magnetic field - Mirror confinement - Tokamak - Stellarator

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Inertial confinement

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A third confinement principle is to apply a rapid pulse of energy to a measure 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, but is also attempted in "controlled" nuclear fusion, where the driver is a laser, ion, or electron beam.

Related Topics:
Hydrogen bomb - X-rays - Laser - Ion - Electron

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Some other confinement principles have been investigated, such as muon-catalyzed fusion, the Farnsworth-Hirsch fusor (inertial electrostatic confinement), and bubble fusion.

Related Topics:
Muon-catalyzed fusion - Farnsworth-Hirsch fusor - Inertial electrostatic confinement - Bubble fusion

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