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Nuclear fusion
From Wikipedia, the free encyclopedia
In physics and nuclear chemistry, nuclear fusion is the process by which multiple nuclei join together to form a heavier nucleus. It is accompanied by the release or absorption of energy depending on the masses of the nuclei involved. Iron and nickel nuclei have the largest binding energies per nucleon of all nuclei and therefore are the most stable. The fusion of two nuclei lighter than iron or nickel generally releases energy while the fusion of nuclei heavier than iron or nickel absorbs energy; vice-versa for the reverse process, nuclear fission.
Overview
In astrophysics, fusion reactions power the stars and produce all but the lightest elements. Whereas the fusion of light elements in the stars releases energy, production of the heaviest elements absorbs energy, so that it can only take place in the extremely high-energy conditions of supernova explosions. In technical applications, fusion of light elements provides the energy of thermonuclear explosions, and research is being performed with the goal of making fusion power a viable means of producing electricity.
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.
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 repulsion can be overcome by the nuclear force which is stronger at close distances.
When a nucleon such as a proton or neutron is added to a nucleus, the nuclear 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 area-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.[1] 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. 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 0.01 MeV. In comparison, the energy needed to remove an electron from hydrogen is 13.6 eV, about 750 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 0.01 MeV. Converting the units between electronvolts and kelvins shows that the barrier would be overcome at a temperature in excess of 120 milion Kelvins, obviously a very high temperature.
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 0.01 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 s 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 <sv> times the product of the reactant number densities:
f = n_1 n_2 \langle \sigma v \rangle
If a species of nuclei is reacting with itself, such as the DD reaction, then the product n1n2 must be replaced by (1 / 2)n2.
\langle \sigma v \rangle increases from virtually zero at room temperatures up to meaningful magnitudes at temperatures of 10 – 100 keV. At these temperatures, well above typical ionization energies (13.6 eV in the hydrogen case), the fusion reactants exist in a plasma state.
The significance of <sv> as a function of temperature in a device with a particular energy confinement time is found by considering the Lawson criterion. |
