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Quasisymmetry
In magnetic confinement fusion, quasisymmetry (sometimes hyphenated as quasi-symmetry) is a type of continuous symmetry in the magnetic field strength of a stellarator. Quasisymmetry is desired, as Noether's theorem implies that there exists a conserved quantity in such cases. This conserved quantity ensures that particles stick to the flux surface, resulting in better confinement and neoclassical transport. It is currently unknown if it is mathematically possible to construct a quasi-symmetric magnetic field which upholds magnetohydrodynamic force balance, which is required for stability. There are stellarator designs which are very close to being quasisymmetric, and it is possible to find solutions by generalizing the magnetohydrodynamic force balance equation.{{Cite journal , last1=Rodríguez , first1=E. , last2=Bhattacharjee , first2=A. , date=January 2021 , title=Solving the problem of overdetermination of quasisymmetric equilibrium solutions by near-axis expansions. I. Genera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stellarator
A stellarator is a plasma device that relies primarily on external magnets to confine a plasma. Scientists researching magnetic confinement fusion aim to use stellarator devices as a vessel for nuclear fusion reactions. The name refers to the possibility of harnessing the power source of the stars, such as the Sun. It is one of the earliest fusion power devices, along with the z-pinch and magnetic mirror. The stellarator was invented by American scientist Lyman Spitzer of Princeton University in 1951, and much of its early development was carried out by his team at what became the Princeton Plasma Physics Laboratory (PPPL). Lyman's Model A began operation in 1953 and demonstrated plasma confinement. Larger models followed, but these demonstrated poor performance, losing plasma at rates far worse than theoretical predictions. By the early 1960s, any hope of quickly producing a commercial machine faded, and attention turned to studying the fundamental theory of high-energy plasma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Omnigeneity
Omnigeneity (sometimes also called omnigenity) is a property of a magnetic field inside a magnetic confinement fusion reactor. Such a magnetic field is called omnigenous if the path a single particle takes does not drift radially inwards or outwards on average. A particle is then confined to stay on a flux surface. All tokamaks are exactly omnigenous by virtue of their axisymmetry, and conversely an unoptimized stellarator is generally ''not'' omnigenous. Because an exactly omnigenous reactor has no neoclassical transport (in the collisionless limit), stellarators are usually optimized in a way such that this criterion is met. One way to achieve this is by making the magnetic field quasi-symmetric, and the Helically Symmetric eXperiment takes this approach. One can also achieve this property without quasi-symmetry, and Wendelstein 7-X is an example of a device which is close to omnigeneity without being quasi-symmetric. Theory The drifting of particles across flux surfaces ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helically Symmetric Experiment
The Helically Symmetric Experiment (HSX, stylized as Helically Symmetric eXperiment), is an experimental plasma confinement device at the University of Wisconsin–Madison, with design principles that are intended to be incorporated into a fusion reactor. The HSX is a modular coil stellarator which is a toroid-shaped pressure vessel with external electromagnets which generate a magnetic field for the purpose of containing a plasma. It began operation in 1999. Background A stellarator is a magnetic confinement fusion device which generates all required magnetic fields to confine high temperature plasma by external magnetic coils. In contrast, in tokamaks and reversed field pinches, the magnetic field is created by the interaction of external magnets and an electrical current flowing through the plasma. The lack of this large externally driven plasma current makes stellarators suitable for steady-state fusion power plants. However, due to non- axisymmetric nature of the fields, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NCSX Modular Coils And Reference Plasma
The National Compact Stellarator Experiment, NCSX in short, was a magnetic fusion energy experiment based on the stellarator design being constructed at the Princeton Plasma Physics Laboratory (PPPL). NCSX was one of a number of new stellarator designs from the 1990s that arose after studies illustrated new geometries that offered better performance than the simpler machines of the 1950s and 1960s. Compared to the more common tokamak, these were much more difficult to design and build, but produced far more stable plasma, the main problem with successful fusion. The design proved to be too difficult to build, repeatedly running over its budget and timelines. The project was eventually cancelled on 22 May 2008, 0.04. ;Magnet coils: * 18 modular coils (6 each of types A, B, C) of wound copper wire, cooled with liquid nitrogen (LN2), * 18 toroidal coils, solid copper cooled with LN2, * 6 pairs of poloidal field coils, solid copper cooled with LN2, * 48 trim coils. csx.pppl.gov/ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Confinement Fusion
Magnetic confinement fusion is an approach to generate thermonuclear fusion power that uses magnetic fields to confine fusion fuel in the form of a plasma. Magnetic confinement is one of two major branches of fusion energy research, along with inertial confinement fusion. The magnetic approach began in the 1940s and absorbed the majority of subsequent development. Fusion reactions combine light atomic nuclei such as hydrogen to form heavier ones such as helium, producing energy. In order to overcome the electrostatic repulsion between the nuclei, they must have a temperature of tens of millions of degrees, creating a plasma. In addition, the plasma must be contained at a sufficient density for a sufficient time, as specified by the Lawson criterion (triple product). Magnetic confinement fusion attempts to use the electrical conductivity of the plasma to contain it through interaction with magnetic fields. The magnetic pressure offsets the plasma pressure. Developing a suitable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous Symmetry
In mathematics, continuous symmetry is an intuitive idea corresponding to the concept of viewing some Symmetry in mathematics, symmetries as Motion (physics), motions, as opposed to discrete symmetry, e.g. reflection symmetry, which is invariant under a kind of flip from one state to another. However, a discrete symmetry can always be reinterpreted as a subset of some higher-dimensional continuous symmetry, e.g. reflection of a 2 dimensional object in 3 dimensional space can be achieved by continuously rotating that object 180 degrees across a non-parallel plane. Formalization The notion of continuous symmetry has largely and successfully been formalised in the mathematical notions of topological group, Lie group and Group action (mathematics), group action. For most practical purposes continuous symmetry is modelled by a ''group action'' of a topological group that preserves some structure. Particularly, let f:X\to Y be a function, and ''G'' is a group that acts on ''X'' then a su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noether's Theorem
Noether's theorem or Noether's first theorem states that every differentiable symmetry of the action of a physical system with conservative forces has a corresponding conservation law. The theorem was proven by mathematician Emmy Noether in 1915 and published in 1918. The action of a physical system is the integral over time of a Lagrangian function, from which the system's behavior can be determined by the principle of least action. This theorem only applies to continuous and smooth symmetries over physical space. Noether's theorem is used in theoretical physics and the calculus of variations. It reveals the fundamental relation between the symmetries of a physical system and the conservation laws. It also made modern theoretical physicists much more focused on symmetries of physical systems. A generalization of the formulations on constants of motion in Lagrangian and Hamiltonian mechanics (developed in 1788 and 1833, respectively), it does not apply to systems that cann ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 the poloidal magnetic flux 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 axis. The total flux passing through flux surface itself is zero, as magnetic field lines are everywhere tangent to the surface. Flux surfaces can either be rational or irrational, depending on the behavior of magnetic field lines on the flux surface. Ratio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neoclassical Transport
Neoclassical transport, also known as neoclassical diffusion and often associated with banana orbits, is a type of diffusion seen in fusion power reactors that have an overall toroidal layout (like a donut). It is a modification of classical diffusion, adding in effects due to the geometry of the reactor that give rise to new diffusion effects. Description Classical transport models a plasma in a magnetic field as a large number of particles traveling in helical paths around a line of force. In typical reactor designs, the lines are roughly parallel, so particles orbiting adjacent lines may collide and scatter. This results in a random walk process which eventually leads to the particles finding themselves outside the magnetic field. Neoclassical transport adds the effects of the geometry of the fields. In particular, it considers the field inside the tokamak and similar toroidal arrangements, where the field is stronger on the inside curve than the outside simply due to the ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetohydrodynamics
Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magnetofluids include plasmas, liquid metals, salt water, and electrolytes. The word ''magnetohydrodynamics'' is derived from ' meaning magnetic field, ' meaning water, and ' meaning movement. The field of MHD was initiated by Hannes Alfvén, for which he received the Nobel Prize in Physics in 1970. The fundamental concept behind MHD is that magnetic fields can induce currents in a moving conductive fluid, which in turn polarizes the fluid and reciprocally changes the magnetic field itself. The set of equations that describe MHD are a combination of the Navier–Stokes equations of fluid dynamics and Maxwell’s equations of electromagnetism. These differential equations must be solved simultaneously, either analytically or numerically. History The first record ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subset
In mathematics, Set (mathematics), set ''A'' is a subset of a set ''B'' if all Element (mathematics), elements of ''A'' are also elements of ''B''; ''B'' is then a superset of ''A''. It is possible for ''A'' and ''B'' to be equal; if they are unequal, then ''A'' is a proper subset of ''B''. The relationship of one set being a subset of another is called inclusion (or sometimes containment). ''A'' is a subset of ''B'' may also be expressed as ''B'' includes (or contains) ''A'' or ''A'' is included (or contained) in ''B''. A ''k''-subset is a subset with ''k'' elements. The subset relation defines a partial order on sets. In fact, the subsets of a given set form a Boolean algebra (structure), Boolean algebra under the subset relation, in which the join and meet are given by Intersection (set theory), intersection and Union (set theory), union, and the subset relation itself is the Inclusion (Boolean algebra), Boolean inclusion relation. Definition If ''A'' and ''B'' are sets and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National Compact Stellarator Experiment
The National Compact Stellarator Experiment, NCSX in short, was a magnetic fusion energy experiment based on the stellarator design being constructed at the Princeton Plasma Physics Laboratory (PPPL). NCSX was one of a number of new stellarator designs from the 1990s that arose after studies illustrated new geometries that offered better performance than the simpler machines of the 1950s and 1960s. Compared to the more common tokamak, these were much more difficult to design and build, but produced far more stable plasma, the main problem with successful fusion. The design proved to be too difficult to build, repeatedly running over its budget and timelines. The project was eventually cancelled on 22 May 2008, 0.04. ;Magnet coils: * 18 modular coils (6 each of types A, B, C) of wound copper wire, cooled with liquid nitrogen (LN2), * 18 toroidal coils, solid copper cooled with LN2, * 6 pairs of poloidal field coils, solid copper cooled with LN2, * 48 trim coils. csx.pppl.gov/Me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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