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Overview Nuclear fusion of light elements releases the energy that causes stars to shine and hydrogen bombs to explode. Nuclear fusion of heavy elements (absorbing energy) occurs in the extremely high-energy conditions of supernova explosions. Nuclear fusion in stars and supernovae is the primary process by which new natural elements are created. It is this reaction that is harnessed in fusion power. It takes considerable energy to force nuclei to fuse, even those of the lightest element, hydrogen. But the fusion of lighter nuclei, which creates a heavier nucleus and a free neutron, will generally release more energy than it took to force them together—an exothermic process that can produce self-sustaining reactions. The energy released in most nuclear reactions is much larger than that for chemical reactions, because the binding energy that holds a nucleus together is far greater than the energy that holds electrons to a nucleus. For example, the ionization energy gained by adding an electron to a hydrogen nucleus is 13.6 electron volts—less than one-millionth of the 17 MeV released in the D-T (deuterium-tritium) reaction shown to the top right. Building upon the nuclear transmutation experiments of Ernest Rutherford done a few years earlier, fusion of light nuclei (hydrogen isotopes) was first observed by Mark Oliphant in 1932, and the steps of the main cycle of nuclear fusion in stars were subsequently worked out by Hans Bethe throughout the remainder of that decade. Requirements for fusion A substantial energy barrier must be overcome before fusion can occur. At large distances two naked nuclei repel one another because of the repulsive electrostatic force between their positively charged protons. If two nuclei can be brought close enough together, however, the electrostatic barrier can be overcome by the strong nuclear force which is stronger at close distances than the electrostatic repulsion. When a nucleon such as a proton or neutron is added to a nucleus, the strong force attracts it to other nucleons, but primarily to its immediate neighbors due to the short range of the force. The nucleons in the interior of a nucleus have more neighboring nucleons than those on the surface. Since smaller nuclei have a larger surface-to-volume ratio, the binding energy per nucleon due to the strong force generally increases with the size of the nucleus but approaches a limiting value corresponding to that of a fully surrounded nucleon. 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 and nickel, and then decreases for heavier nuclei. Eventually, the binding energy becomes negative and very heavy nuclei are not stable. The four most tightly bound nuclei, in decreasing order of binding energy, are 62Ni, 58Fe, 56Fe, and 60Ni *. Even though the nickel isotope 62Ni is more stable, the iron isotope 56Fe is an order of magnitude more common. This is due to a greater disintegration rate for 62Ni in the interior of stars driven by photon absorption. A notable exception to this general trend is the helium-4 nucleus, whose binding energy is higher than that of lithium, the next heavier element. The Pauli exclusion principle provides an explanation for this exceptional behavior - it says that because protons and neutrons are fermions, they cannot exist in exactly the same state. Each proton or neutron energy state in a nucleus can accommodate both a spin up particle and a spin down particle. Helium-4 has an anomalously large binding energy because its nucleus consists of two protons and two neutrons; so all four of its nucleons can be in the ground state. Any additional nucleons would have to go into higher energy states. 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, this would be known as activation energy. In nuclear physics it is called the Coulomb barrier. The Coulomb barrier is smallest for isotopes of hydrogen - they contain only a single positive charge in the nucleus. A bi-proton is not stable, so neutrons must also be involved, ideally in such a way that a helium nucleus, with its extremely tight binding, is one of the products. Using deuterium-tritium fuel, the resulting energy barrier is about 0.1 MeV. In comparison, the energy needed to remove an electron from hydrogen is 13.6 eV, about 7,500 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 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 electronvolts and kelvins shows that the barrier would be overcome at a temperature in excess of 1& 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. The reaction cross section σ is a measure of the probability of a fusion reaction as a function of the relative velocity of the two reactant nuclei. If the reactants have a distribution of velocities, e.g. a thermal distribution with thermonuclear fusion, then it is useful to perform an average of 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: angle 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 ionization energies (13.6 eV in the hydrogen case), the fusion reactants exist in a plasma state. The significance of <σv> as a function of temperature in a device with a particular energy confinement time is found by considering the Lawson criterion. Methods of fuel confinement The fusion reaction can sustain itself if enough of the energy produced goes into keeping the fuel hot. Gravitational confinement - 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 greater than that of the planet Jupiter would be needed. Magnetic confinement - Since plasmas are very good electrical conductors, magnetic fields can also 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. 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, ion, or electron beam, or a Z-pinch. Some other confinement principles have been investigated, such as muon-catalyzed fusion, the Farnsworth-Hirsch fusor (inertial electrostatic confinement), and bubble fusion. Methods to produce fusion A variety of methods are known to affect 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. Locally cold fusion Generally cold, locally hot fusion Hot fusion The methods in the second group are examples of non-equilibrium systems, in which very high temperatures and pressures are produced in a relatively small region adjacent to material of much lower temperature. In his doctoral thesis for MIT, Todd Rider did a theoretical study of all non-equilibrium fusion systems. He demonstrated that all such systems will leak energy at a rapid rate due to bremsstrahlung, radiation produced when electrons in the plasma hit other electrons or ions at a cooler temperature and suddenly decelerate. The problem is not as pronounced in a hot plasma because the range of temperatures, and thus the magnitude of the deceleration, is much lower. Astrophysical reaction chains The most important fusion process in nature is that which powers the stars. The net result is the fusion of four protons into one alpha particle, with the release of two positrons, two neutrinos (which changes two of the protons into neutrons), and energy, but several individual reactions are involved, depending on the mass of the star. For stars the size of the sun or smaller, the proton-proton chain dominates. In heavier stars, the CNO cycle is more important. Both types of processes are responsible for the creation of new elements as part of stellar nucleosynthesis. At the temperatures and densities in stellar cores the rates of fusion reactions are still extremely slow. For example, at solar core temperature (T ~ 15 MK) and density (~120 g/cm3), the energy release rate is only ~0.1 microwatt/cm3 - millions of times less than the rate of energy release of ordinary candela and thousands of times less than the rate at which a human body generates heat. Thus, reproduction of stellar core conditions in a lab for nuclear fusion power production is completely impractical. 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, and therefore less startup effort. Another concern is the production of neutrons, which activate the reactor structure radiologically, but also have the advantages of allowing volumetric extraction of the fusion energy and tritium breeding. Reactions that release no neutrons are referred to as aneutronic. In order to be useful as a source of energy, a fusion reaction must satisfy several criteria. It must: Few reactions meet these criteria. The following are those with the largest cross sections: p (protium), D (deuterium), and T (tritium) are shorthand notation for the main three isotopes of hydrogen. 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-11B because it is roughly as difficult to burn but produces substantially more neutrons through D-D side reactions. There is also a p-7Li reaction, but the cross section is far too low except possible for Ti > 1 MeV, but at such high temperatures an endothermic, direct neutron-producing reaction also becomes very significant. Finally there is also a p-9Be reaction, which is not only difficult to burn, but 9Be can be easily induced to split into two alphas 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: n + 6Li → T + 4He n + 7Li → T + 4He + n To evaluate the usefulness of these reactions, in addition to the reactants, the products, and the energy released, one needs to know something about the cross section. Any given fusion device will have a maximum plasma pressure that it can sustain, and an economical device will always operate near this maximum. Given this pressure, the largest fusion output is obtained when the temperature is chosen so that <σv>/T² is a maximum. This is also the temperature at which the value of the triple product nTτ required for ignition is a minimum. This optimum temperature and the value of <σv>/T² at that temperature is given for a few of these reactions in the following table. Note that many of the reactions form chains. For instance, a reactor fueled with T and 3He will create some D, which is then possible to use in the D + 3He reaction if the energies are "right". An elegant idea is to combine the reactions (8) and (9). The 3He from reaction (8) can react with 6Li in reaction (9) before completely thermalizing. This produces an energetic proton which in turn undergoes reaction (8) before thermalizing. A detailed analysis shows that this idea will not really work well, but it is a good example of a case where the usual assumption of a Maxwellian plasma is not appropriate. Neutronicity, confinement requirement, and power density
Bremsstrahlung losses The ions undergoing fusion will essentially never occur alone but will be mixed with electrons that neutralize the ions' electrical charge and form a plasma. The electrons will generally have a temperature comparable to or greater than that of the ions, so they will collide with the ions and emit Bremsstrahlung. The Sun and stars are opaque to Bremsstrahlung, but essentially any terrestrial fusion reactor will be optically thin at relevant wavelengths. Bremsstrahlung is also difficult to reflect and difficult to convert directly to electricity, so the ratio of fusion power produced to Bremsstrahlung radiation lost 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. * The actual ratios of fusion to Bremsstrahlung power will likely be significantly lower for several reasons. For one, the calculation assumes that the energy of the fusion products is transmitted completely to the fuel ions, which then lose energy to the electrons by collisions, which in turn lose energy by Bremsstrahlung. However because the fusion products move much faster than the fuel ions, they will give up a significant fraction of their energy directly to the electrons. Secondly, the plasma is assumed to be composed purely of fuel ions. In practice, there will be a significant proportion of impurity ions, which will lower the ratio. In particular, the fusion products themselves must remain in the plasma until they have given up their energy, and will remain some time after that in any proposed confinement scheme. Finally, all channels of energy loss other than Bremsstrahlung have been neglected. The last two factors are related. On theoretical and experimental grounds, particle and energy confinement seem to be closely related. In a confinement scheme that does a good job of retaining energy, fusion products will build up. If the fusion products are efficiently ejected, then energy confinement will be poor, too. The temperatures maximizing the fusion power compared to the Bremsstrahlung are in every case higher than the temperature that maximizes the power density and minimizes the required value of the fusion triple product. This will not change the optimum operating point for D-T very much because the Bremsstrahlung fraction is low, but it will push the other fuels into regimes where the power density relative to D-T is even lower and the required confinement even more difficult to achieve. For D-D and D-3He, Bremsstrahlung losses will be a serious, possibly prohibitive problem. For 3He-3He, p-6Li and p-11B the Bremsstrahlung losses appear to make a fusion reactor using these fuels 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 PDF. See also | |||||||||||
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