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Poloidal
The terms toroidal and poloidal refer to directions relative to a torus of reference. They describe a three-dimensional coordinate system in which the poloidal direction follows a small circular ring around the surface, while the toroidal direction follows a large circular ring around the torus, encircling the central void. The earliest use of these terms cited by the Oxford English Dictionary is by Walter M. Elsasser (1946) in the context of the generation of the Earth's magnetic field by currents in the core, with "toroidal" being parallel to lines of latitude and "poloidal" being in the direction of the magnetic field (i.e. towards the poles). The OED also records the later usage of these terms in the context of toroidally confined plasmas, as encountered in magnetic confinement fusion. In the plasma context, the toroidal direction is the long way around the torus, the corresponding coordinate being denoted by in the slab approximation or or in magnetic coordinates; the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poloidal–toroidal Decomposition
In vector calculus, a topic in pure and applied mathematics, a poloidal–toroidal decomposition is a restricted form of the Helmholtz decomposition. It is often used in the spherical coordinates analysis of solenoidal vector fields, for example, magnetic fields and incompressible fluids. Definition For a three-dimensional vector field F with zero divergence : \nabla \cdot \mathbf = 0, this F can be expressed as the sum of a toroidal field T and poloidal vector field P :\mathbf = \mathbf + \mathbf where r is a radial vector in spherical coordinates (''r'', ''θ'', ''φ''). The toroidal field is obtained from a scalar field, ''Ψ''(''r'', ''θ'', ''φ''), as the following curl, : \mathbf = \nabla \times (\mathbf \Psi(\mathbf)) and the poloidal field is derived from another scalar field Φ(''r'', ''θ'', ''φ''), as a twice-iterated curl, : \mathbf = \nabla \times (\nabla \times (\mathbf \Phi (\mathbf)))\,. This decomposition is symmetric in that the curl of a toroid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zonal Flow (plasma)
In toroidally confined fusion plasma experiments the term zonal flow means a plasma flow within a magnetic surface primarily in the poloidal direction. This usage is inspired by the analogy between the quasi-two-dimensional nature of large-scale atmospheric and oceanic flows, where zonal means latitudinal, and the similarly quasi-two-dimensional nature of low-frequency flows in a strongly magnetized plasma. Zonal flows in the toroidal plasma context are further characterized by * being localized in their radial extent transverse to the magnetic surfaces (in contrast to global plasma rotation), * having little or no variation in either the poloidal or toroidal direction—they are ''m'' = ''n'' = 0 modes (where ''m'' and ''n'' are the poloidal and toroidal mode numbers, respectively), * having zero real frequency when analyzed by linearization around an unperturbed toroidal equilibrium state (in contrast to the geodesic acoustic mode branch, which has finite frequency). * Arising ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torus
In geometry, a torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution. If the axis of revolution is tangent to the circle, the surface is a horn torus. If the axis of revolution passes twice through the circle, the surface is a spindle torus. If the axis of revolution passes through the center of the circle, the surface is a degenerate torus, a double-covered sphere. If the revolved curve is not a circle, the surface is called a '' toroid'', as in a square toroid. Real-world objects that approximate a torus of revolution include swim rings, inner tubes and ringette rings. Eyeglass lenses that combine spherical and cylindrical correction are toric lenses. A torus should not be confused with a '' solid torus'', which is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torus
In geometry, a torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution. If the axis of revolution is tangent to the circle, the surface is a horn torus. If the axis of revolution passes twice through the circle, the surface is a spindle torus. If the axis of revolution passes through the center of the circle, the surface is a degenerate torus, a double-covered sphere. If the revolved curve is not a circle, the surface is called a '' toroid'', as in a square toroid. Real-world objects that approximate a torus of revolution include swim rings, inner tubes and ringette rings. Eyeglass lenses that combine spherical and cylindrical correction are toric lenses. A torus should not be confused with a '' solid torus'', which is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zonal And Poloidal
In magnetic confinement fusion the zonal direction primarily connotes the poloidal direction (i.e. the short way around the torus), the corresponding coordinate being denoted by ''y'' in the slab approximation or ''θ'' in magnetic coordinates. However, in the fusion context, usage is restricted to the context of zonal plasma flows and there will in general be a toroidal component in such flows as well. Thus, although the term zonal has come into use in plasma physics to emphasize an analogy with zonal flows in geophysics, it does not uniquely identify the direction of flow, unlike the case in geophysics. See also * Toroidal and poloidal * Zonal and meridional Zonal and meridional flow are directions and regions of fluid flow on a globe. Zonal flow follows a pattern along latitudinal lines, latitudinal circles or in the west–east direction. Meridional flow follows a pattern from north to south ... * Zonal flow (plasma) * Zonal flow Orientation (geometry) Magnetic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toroidal Coord
Toroidal describes something which resembles or relates to a torus or toroid: Mathematics *Torus *Toroid, a surface of revolution which resembles a torus *Toroidal polyhedron *Toroidal coordinates, a three-dimensional orthogonal coordinate system *Toroidal and poloidal coordinates, directions relative to a torus of reference *Toroidal graph, a graph whose vertices can be placed on a torus such that no edges cross *Toroidal grid network, where an n-dimensional grid network is connected circularly in more than one dimension Engineering *Toroidal inductors and transformers, a type of electrical device *Toroidal and poloidal, directions in magnetohydrodynamics *Toroidal engine, an internal combustion engine with pistons that rotate within a toroidal space *Toroidal CVT, a Continuously variable transmission#Toroidal or roller-based CVT (Extroid CVT), type of continuously variable transmission *Toroidal reflector, a parabolic reflector which has a different focal distance depending on t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tokamak
A tokamak (; russian: токамáк; otk, 𐱃𐰸𐰢𐰴, Toḳamaḳ) is a device which uses a powerful magnetic field to confine plasma in the shape of a torus. The tokamak is one of several types of magnetic confinement devices being developed to produce controlled thermonuclear fusion power. , it was the leading candidate for a practical fusion reactor. Tokamaks were initially conceptualized in the 1950s by Soviet physicists Igor Tamm and Andrei Sakharov, inspired by a letter by Oleg Lavrentiev. The first working tokamak was attributed to the work of Natan Yavlinsky on the T-1 in 1958. It had been demonstrated that a stable plasma equilibrium requires magnetic field lines that wind around the torus in a helix. Devices like the z-pinch and stellarator had attempted this, but demonstrated serious instabilities. It was the development of the concept now known as the safety factor (labelled ''q'' in mathematical notation) that guided tokamak development; by arrang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordinate System
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the ''x''-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and ''vice versa''; this is the basis of analytic geometry. Common coordinate systems Number line The simplest example of a coordinate system is the identification of points on a line with real numbers using the '' number line''. In this system, an arbitrary point ''O'' (the ''origin'') is chosen on a given line. The coordinate of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oxford English Dictionary
The ''Oxford English Dictionary'' (''OED'') is the first and foundational historical dictionary of the English language, published by Oxford University Press (OUP). It traces the historical development of the English language, providing a comprehensive resource to scholars and academic researchers, as well as describing usage in its many variations throughout the world. Work began on the dictionary in 1857, but it was only in 1884 that it began to be published in unbound fascicles as work continued on the project, under the name of ''A New English Dictionary on Historical Principles; Founded Mainly on the Materials Collected by The Philological Society''. In 1895, the title ''The Oxford English Dictionary'' was first used unofficially on the covers of the series, and in 1928 the full dictionary was republished in 10 bound volumes. In 1933, the title ''The Oxford English Dictionary'' fully replaced the former name in all occurrences in its reprinting as 12 volumes with a one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Walter M
Walter may refer to: People * Walter (name), both a surname and a given name * Little Walter, American blues harmonica player Marion Walter Jacobs (1930–1968) * Gunther (wrestler), Austrian professional wrestler and trainer Walter Hahn (born 1987), who previously wrestled as "Walter" * Walter, standard author abbreviation for Thomas Walter (botanist) ( – 1789) Companies * American Chocolate, later called Walter, an American automobile manufactured from 1902 to 1906 * Walter Energy, a metallurgical coal producer for the global steel industry * Walter Aircraft Engines, Czech manufacturer of aero-engines Films and television * ''Walter'' (1982 film), a British television drama film * Walter Vetrivel, a 1993 Tamil crime drama film * ''Walter'' (2014 film), a British television crime drama * ''Walter'' (2015 film), an American comedy-drama film * ''Walter'' (2020 film), an Indian crime drama film * '' W*A*L*T*E*R'', a 1984 pilot for a spin-off of the TV series ''M*A*S*H'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Earth's Magnetic Field
Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magnetic field is generated by electric currents due to the motion of convection currents of a mixture of molten iron and nickel in Earth's outer core: these convection currents are caused by heat escaping from the core, a natural process called a geodynamo. The magnitude of Earth's magnetic field at its surface ranges from . As an approximation, it is represented by a field of a magnetic dipole currently tilted at an angle of about 11° with respect to Earth's rotational axis, as if there were an enormous bar magnet placed at that angle through the center of Earth. The North geomagnetic pole actually represents the South pole of Earth's magnetic field, and conversely the South geomagnetic pole corresponds to the north pole of Earth's mag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latitude
In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pole, with 0° at the Equator. Lines of constant latitude, or ''parallels'', run east–west as circles parallel to the equator. Latitude and '' longitude'' are used together as a coordinate pair to specify a location on the surface of the Earth. On its own, the term "latitude" normally refers to the ''geodetic latitude'' as defined below. Briefly, the geodetic latitude of a point is the angle formed between the vector perpendicular (or '' normal'') to the ellipsoidal surface from the point, and the plane of the equator. Background Two levels of abstraction are employed in the definitions of latitude and longitude. In the first step the physical surface is modeled by the geoid, a surface which approximates the mean sea level over t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
