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Plasma Shaping
Magnetically confined fusion plasmas such as those generated in tokamaks and stellarators are characterized by a typical shape. Plasma shaping is the study of the plasma shape in such devices, and is particularly important for next step fusion devices such as ITER. This shape is conditioning partly the performance of the plasma. Tokamaks, in particular, are axisymmetric devices, and therefore one can completely define the shape of the plasma by its cross-section. History Early fusion reactor designs tended to have circular cross-sections simply because they were easy to design and understand. Generally, fusion machines using a toroidal layout, like the tokamak and most stellarators, arrange their magnetic fields so the ions and electrons in the plasma travel around the torus at high velocities. However, as the circumference of a path on the outside of the plasma area is longer than one on the inside, this caused several effects that disrupted the stability of the plasma. Durin ...
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Magnetic Confinement Fusion
Magnetic confinement fusion (MCF) is an approach to generate thermonuclear fusion power that uses magnetic fields to confine fusion fuel in the form of a plasma (physics), plasma. Magnetic confinement is one of two major branches of controlled fusion research, along with inertial confinement fusion. Deuterium–tritium fusion, Fusion reactions for reactors usually combine light Atomic nucleus, atomic nuclei of deuterium and tritium to form an alpha particle (helium-4 nucleus) and a neutron, where the energy is released in the form of the kinetic energy of the reaction products. In order to overcome the Coulomb barrier, electrostatic repulsion between the nuclei, the fuel must have a temperature of hundreds of millions of kelvin, at which the fuel is fully Ionization, ionized and becomes a Plasma (physics), plasma. In addition, the plasma must be at a sufficient density, and the energy must remain in the reacting region for a sufficient time, as specified by the Lawson criterion (tri ...
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Plasma (physics)
Plasma () is a state of matter characterized by the presence of a significant portion of charged particles in any combination of ions or electrons. It is the most abundant form of ordinary matter in the universe, mostly in stars (including the Sun), but also dominating the rarefied intracluster medium and Outer space#Intergalactic space, intergalactic medium. Plasma can be artificially generated, for example, by heating a neutral gas or subjecting it to a strong electromagnetic field. The presence of charged particles makes plasma electrically conductive, with the dynamics of individual particles and macroscopic plasma motion governed by collective electromagnetic fields and very sensitive to externally applied fields. The response of plasma to electromagnetic fields is used in many modern devices and technologies, such as plasma display, plasma televisions or plasma etching. Depending on temperature and density, a certain number of neutral particles may also be present, in wh ...
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Tokamak
A tokamak (; ) is a device which uses a powerful magnetic field generated by external magnets to confine plasma (physics), plasma in the shape of an axially symmetrical torus. The tokamak is one of several types of magnetic confinement fusion, magnetic confinement devices being developed to produce controlled thermonuclear fusion power. The tokamak concept is currently one of the leading candidates for a practical fusion reactor for providing minimally polluting electrical power. The proposal to use controlled thermonuclear fusion for industrial purposes and a specific scheme using thermal insulation of high-temperature plasma by an electric field was first formulated by the Soviet physicist Oleg Lavrentiev in a mid-1950 paper. In 1951, Andrei Sakharov and Igor Tamm modified the scheme by proposing a theoretical basis for a thermonuclear reactor, where the plasma would have the shape of a torus and be held by a magnetic field. The first tokamak was built in the Soviet Union ...
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Stellarator
A stellarator confines Plasma (physics), plasma using external magnets. Scientists aim to use stellarators to generate fusion power. It is one of many types of magnetic confinement fusion devices. The name "stellarator" refers to stars because fusion mostly occurs in stars such as the Sun. It is one of the earliest human-designed fusion power devices. The stellarator was invented by American scientist Lyman Spitzer in 1951. Much of its early development was carried out by Spitzer's team at what became the Princeton Plasma Physics Laboratory (PPPL). Spitzer's Model A began operation in 1953 and demonstrated plasma confinement. Larger models followed, but demonstrated poor performance, losing plasma at rates far worse than theoretical predictions. By the early 1960s, hopes of producing a commercial machine faded, and attention turned to studying fundamental theory. By the mid-1960s, Spitzer was convinced that the stellarator was matching the Bohm diffusion rate, which suggested i ...
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ITER
ITER (initially the International Thermonuclear Experimental Reactor, ''iter'' meaning "the way" or "the path" in Latin) is an international nuclear fusion research and engineering megaproject aimed at creating energy through a fusion process similar to that of the Sun. It is being built next to the Cadarache facility in southern France. Upon completion of the main reactor and first plasma, planned for 2033–2034, ITER will be the largest of more than 100 fusion reactors built since the 1950s, with six times the plasma volume of JT-60SA in Japan, the largest tokamak operating today. The long-term goal of fusion research is to generate electricity; ITER's stated purpose is scientific research, and technological demonstration of a large fusion reactor, without electricity generation. ITER's goals are to achieve enough fusion to produce 10 times as much thermal output power as thermal power absorbed by the plasma for short time periods; to demonstrate and test technologies that wo ...
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Axisymmetric
Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation. Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated 90°, however the only geometric objects that are fully rotationally symmetric at any angle are spheres, circles and other spheroids. Formal treatment Formally the rotational symmetry is symmetry with respect to some or all rotations in -dimensional Euclidean space. Rotations are direct isometries, i.e., isometries preserving orientation. Therefore, a symmetry group of rotational symmetry is a subgroup of (see Euclidean group). Symmetry with respect to all rotations about all points implies translational symmetry with respect to all translations, so space is homogeneous, and the ...
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Cross Section (geometry)
In geometry and science, a cross section is the non-empty intersection (set theory), intersection of a solid body in three-dimensional space with a Plane (geometry), plane, or the analog in higher-dimensional spaces. Cutting an object into slices creates many parallel cross-sections. The boundary of a cross-section in three-dimensional space that is parallel to two of the Cartesian coordinate system, axes, that is, parallel to the plane determined by these axes, is sometimes referred to as a contour line; for example, if a plane cuts through mountains of a raised-relief map parallel to the ground, the result is a contour line in two-dimensional space showing points on the surface of the mountains of equal elevation. In technical drawing a cross-section, being a Planar projection, projection of an object onto a plane that intersects it, is a common tool used to depict the internal arrangement of a 3-dimensional object in two dimensions. It is traditionally crosshatched with th ...
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Flux Surface
In magnetic confinement fusion, a flux surface is a surface on which magnetic field lines lie. Since the magnetic field is divergence-free (and magnetic nulls are undesirable), the Poincare-Hopf theorem implies that such a surface must be either a torus, or a knot. In the tokamak and the stellarator flux surfaces have toroidal shapes, whereas the more exotic knotatron has a knotted flux surface. Flux surfaces are typically characterized by the poloidal magnetic flux In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted or . The SI unit of magnetic flux is the we ... or the toroidal magnetic flux. The poloidal flux is the magnetic flux passing through a ribbon going from the magnetic axis (the centre of the device) to the flux surface, and the toroidal flux is the magnetic flux passing through a circle which encloses the magnetic axi ...
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Equatorial Plane
The celestial equator is the great circle of the imaginary celestial sphere on the same plane as the equator of Earth. By extension, it is also a plane of reference in the equatorial coordinate system. Due to Earth's axial tilt, the celestial equator is currently inclined by about 23.44° with respect to the ecliptic (the plane of Earth's orbit), but has varied from about 22.0° to 24.5° over the past 5 million years due to Milankovitch cycles and perturbation from other planets. An observer standing on Earth's equator visualizes the celestial equator as a semicircle passing through the zenith, the point directly overhead. As the observer moves north (or south), the celestial equator tilts towards the opposite horizon. The celestial equator is defined to be infinitely distant (since it is on the celestial sphere); thus, the ends of the semicircle always intersect the horizon due east and due west, regardless of the observer's position on Earth. At the poles, the celestial ...
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Last Closed Flux Surface
A last is a mechanical form shaped like a human foot. It is used by shoemakers and cordwainers in the manufacture and repair of shoes. Lasts come in many styles and sizes, depending on the exact job they are designed for. Common variations include simple one-size lasts used for repairing soles and heels, custom-purpose mechanized lasts used in modern mass production, and custom-made lasts used in the making of bespoke footwear. Lasts are made of firm materialshardwoods, cast iron, and high-density plasticsto withstand contact with wetted leather and the strong forces involved in reshaping it. Since the early 19th century, lasts typically come in pairs to match the separate shapes of the right and left feet. The development of an automated lasting machine by the Surinamese-American Jan Ernst Matzeliger in the 1880s was a major development in shoe production, immediately improving quality, halving prices, and eliminating the previous putting-out systems surrounding shoemaking ...
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