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Ideally Hard Superconductor
An ideally hard superconductor is a type II superconductor material with an infinite pinning force. In the external magnetic field it behaves like an ideal diamagnet if the field is switched on when the material is in the superconducting state, so-called "zero field cooled" (ZFC) regime. In the field cooled (FC) regime, the ideally hard superconductor screens perfectly the change of the magnetic field rather than the magnetic field itself. Its magnetization behavior can be described by Bean's critical state model. The ideally hard superconductor is a good approximation for the melt-textured high temperature superconductors ( HTSC) used in large scale HTSC applications such as flywheels, HTSC bearings, HTSC motors, etc. See also *Frozen mirror image method *Bean's critical state model Bean's critical state model, introduced by C. P. Bean in 1962, gives a macroscopic explanation of the irreversible magnetization behavior ( hysteresis) of hard Type-II superconductors. Assumptions ...
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Type II Superconductor
In superconductivity, a type-II superconductor is a superconductor that exhibits an intermediate phase of mixed ordinary and superconducting properties at intermediate temperature and fields above the superconducting phases. It also features the formation of magnetic field vortices with an applied external magnetic field. This occurs above a certain critical field strength ''Hc1''. The vortex density increases with increasing field strength. At a higher critical field ''Hc2'', superconductivity is destroyed. Type-II superconductors do not exhibit a complete Meissner effect. History In 1935, Rjabinin and Shubnikov experimentally discovered the Type-II superconductors. In 1950, the theory of the two types of superconductors was further developed by Lev Landau and Vitaly Ginzburg in their paper on Ginzburg–Landau theory. In their argument, a type-I superconductor had positive free energy of the superconductor-normal metal boundary. Ginzburg and Landau pointed out the possibilit ...
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Pinning Force
Pinning force is a force acting on a pinned object from a pinning center. In solid state physics, this most often refers to the vortex pinning, the pinning of the magnetic vortices ( magnetic flux quanta, Abrikosov vortices) by different kinds of the defects in a type II superconductor. Important quantities are the ''individual'' maximal pinning force, which defines the depinning of a single vortex, and an ''average'' pinning force, which defines the depinning of the correlated vortex structures and can be associated with the critical current density (the maximal density of non-dissipative current). The interaction of the correlated vortex lattice with system of pinning centers forms the magnetic phase diagram of the vortex matter in superconductors. This phase diagram is especially rich for high temperature superconductors ( HTSC) where the thermo-activation processes are essential. The pinning mechanism is based on the fact that the amount of grain boundary area is reduced whe ...
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Diamagnet
Diamagnetic materials are repelled by a magnetic field; an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagnetic materials are attracted by a magnetic field. Diamagnetism is a quantum mechanical effect that occurs in all materials; when it is the only contribution to the magnetism, the material is called diamagnetic. In paramagnetic and ferromagnetic substances, the weak diamagnetic force is overcome by the attractive force of magnetic dipoles in the material. The magnetic permeability of diamagnetic materials is less than the permeability of vacuum, ''μ''0. In most materials, diamagnetism is a weak effect which can be detected only by sensitive laboratory instruments, but a superconductor acts as a strong diamagnet because it repels a magnetic field entirely from its interior. Diamagnetism was first discovered when Anton Brugmans observed in 1778 that bismuth was re ...
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Bean's Critical State Model
Bean's critical state model, introduced by C. P. Bean in 1962, gives a macroscopic explanation of the irreversible magnetization behavior ( hysteresis) of hard Type-II superconductors. Assumptions Hard superconductors often exhibit hysteresis in magnetization measurements. C. P. Bean postulated for the Shubnikov phase an extraordinary shielding process due to the microscopic structure of the materials. He assumed lossless transport with a critical current density ''Jc(B)'' ''(Jc(B→0) = const.'' and ''Jc(B→∞) = 0)''. An external magnetic field is shielded in the Meissner phase (''H < Hc1'') in the same way than in a soft superconductor. In the Shubnikov phase ''(Hc1 < H < Hc2)'', the critical current flows below the surface within a depth necessary to reduce the field in the inside of the superconductor to ''Hc1''.


Explanation of the irreversible magnetization


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Approximation
An approximation is anything that is intentionally similar but not exactly equality (mathematics), equal to something else. Etymology and usage The word ''approximation'' is derived from Latin ''approximatus'', from ''proximus'' meaning ''very near'' and the prefix ''ad-'' (''ad-'' before ''p'' becomes ap- by assimilation (phonology), assimilation) meaning ''to''. Words like ''approximate'', ''approximately'' and ''approximation'' are used especially in technical or scientific contexts. In everyday English, words such as ''roughly'' or ''around'' are used with a similar meaning. It is often found abbreviated as ''approx.'' The term can be applied to various properties (e.g., value, quantity, image, description) that are nearly, but not exactly correct; similar, but not exactly the same (e.g., the approximate time was 10 o'clock). Although approximation is most often applied to numbers, it is also frequently applied to such things as Function (mathematics), mathematical functio ...
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Phys
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (. ...
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High Temperature Superconductors
High-temperature superconductors (abbreviated high-c or HTS) are defined as materials that behave as superconductors at temperatures above , the boiling point of liquid nitrogen. The adjective "high temperature" is only in respect to previously known superconductors, which function at even colder temperatures close to absolute zero. In absolute terms, these "high temperatures" are still far below ambient, and therefore require cooling. The first high-temperature superconductor was discovered in 1986, by IBM researchers Bednorz and Müller, who were awarded the Nobel Prize in Physics in 1987 "for their important break-through in the discovery of superconductivity in ceramic materials". Most high-c materials are type-II superconductors. The major advantage of high-temperature superconductors is that they can be cooled by using liquid nitrogen, as opposed to the previously known superconductors which require expensive and hard-to-handle coolants, primarily liquid helium. A ...
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High-temperature Superconductivity
High-temperature superconductors (abbreviated high-c or HTS) are defined as materials that behave as superconductors at temperatures above , the boiling point of liquid nitrogen. The adjective "high temperature" is only in respect to previously known superconductors, which function at even colder temperatures close to absolute zero. In absolute terms, these "high temperatures" are still far below ambient, and therefore require cooling. The first high-temperature superconductor was discovered in 1986, by IBM researchers Bednorz and Müller, who were awarded the Nobel Prize in Physics in 1987 "for their important break-through in the discovery of superconductivity in ceramic materials". Most high-c materials are type-II superconductors. The major advantage of high-temperature superconductors is that they can be cooled by using liquid nitrogen, as opposed to the previously known superconductors which require expensive and hard-to-handle coolants, primarily liquid helium. ...
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Flywheels
A flywheel is a mechanical device which uses the conservation of angular momentum to store rotational energy; a form of kinetic energy proportional to the product of its moment of inertia and the square of its rotational speed. In particular, assuming the flywheel's moment of inertia is constant (i.e., a flywheel with fixed mass and second moment of area revolving about some fixed axis) then the stored (rotational) energy is directly associated with the square of its rotational speed. Since a flywheel serves to store mechanical energy for later use, it is natural to consider it as a kinetic energy analogue of an electrical inductor. Once suitably abstracted, this shared principle of energy storage is described in the generalized concept of an accumulator. As with other types of accumulators, a flywheel inherently smooths sufficiently small deviations in the power output of a system, thereby effectively playing the role of a low-pass filter with respect to the mechanical velocity ...
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Journal Of Applied Physics
The ''Journal of Applied Physics'' is a peer-reviewed scientific journal with a focus on the physics of modern technology. The journal was originally established in 1931 under the name of ''Physics'', and was published by the American Physical Society for its first 7 volumes. In January 1937, ownership was transferred to the American Institute of Physics "in line with the efforts of the American Physical Society to enhance the standing of physics as a profession". The journal's current editor-in-chief is André Anders (Lawrence Berkeley National Laboratory). According to the ''Journal Citation Reports'', the journal has a 2021 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... of 2.877. References External links * Physics journals Weekly journals Publications ...
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Frozen Mirror Image Method
Frozen mirror image method (or method of frozen images) is an extension of the method of images for magnet- superconductor systems that has been introduced by Alexander Kordyuk in 1998 to take into account the magnetic flux pinning phenomenon. The method gives a simple representation of the magnetic field distribution generated by a magnet (a system of magnets) outside an infinitely flat surface of a perfectly hard (with infinite pinning force) type-II superconductor in more general field cooled (FC) case, i.e. when the superconductor goes into superconducting state been already exposed to the magnetic field. The difference from the mirror image method, which deals with a perfect type-I superconductor (that completely expels the magnetic field, see the Meissner effect), is that the perfectly hard superconductor screens the variation of the external magnetic field rather than the field itself. Description The name originates from the replacement of certain elements in the origin ...
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Superconductivity
Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike an ordinary metallic conductor, whose resistance decreases gradually as its temperature is lowered even down to near absolute zero, a superconductor has a characteristic critical temperature below which the resistance drops abruptly to zero. An electric current through a loop of superconducting wire can persist indefinitely with no power source. The superconductivity phenomenon was discovered in 1911 by Dutch physicist Heike Kamerlingh Onnes. Like ferromagnetism and atomic spectral lines, superconductivity is a phenomenon which can only be explained by quantum mechanics. It is characterized by the Meissner effect, the complete ejection of magnetic field lines from the interior of the superconductor during its transitions into the sup ...
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