Neutral-beam injectionNeutral-beam injection (NBI) is one method used to heat plasma inside a fusion device consisting in a beam of high-energy neutral particles that can enter the magnetic confinement field. When these neutral particles are ionized by collision with the plasma particles, they are kept in the plasma by the confining magnetic field and can transfer most of their energy by further collisions with the plasma. By tangential injection in the torus, neutral beams also provide momentum to the plasma and current drive, one essential feature for long pulses of burning plasmas.
Singular value decompositionIn linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any matrix. It is related to the polar decomposition. Specifically, the singular value decomposition of an complex matrix M is a factorization of the form where U is an complex unitary matrix, is an rectangular diagonal matrix with non-negative real numbers on the diagonal, V is an complex unitary matrix, and is the conjugate transpose of V.
LU decompositionIn numerical analysis and linear algebra, lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix decomposition). The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix form of Gaussian elimination. Computers usually solve square systems of linear equations using LU decomposition, and it is also a key step when inverting a matrix or computing the determinant of a matrix.
Cyclotron radiationCyclotron radiation is electromagnetic radiation emitted by non-relativistic accelerating charged particles deflected by a magnetic field. The Lorentz force on the particles acts perpendicular to both the magnetic field lines and the particles' motion through them, creating an acceleration of charged particles that causes them to emit radiation as a result of the acceleration they undergo as they spiral around the lines of the magnetic field.
QR decompositionIn linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of an orthonormal matrix Q and an upper triangular matrix R. QR decomposition is often used to solve the linear least squares problem and is the basis for a particular eigenvalue algorithm, the QR algorithm. Any real square matrix A may be decomposed as where Q is an orthogonal matrix (its columns are orthogonal unit vectors meaning ) and R is an upper triangular matrix (also called right triangular matrix).
Plasma (physics)Plasma () is one of four fundamental states 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, being mostly associated with stars, including the Sun. Extending to the rarefied intracluster medium and possibly to intergalactic regions, plasma can be artificially generated by heating a neutral gas or subjecting it to a strong electromagnetic field.
Decision problemIn computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the input values. An example of a decision problem is deciding by means of an algorithm whether a given natural number is prime. Another is the problem "given two numbers x and y, does x evenly divide y?". The answer is either 'yes' or 'no' depending upon the values of x and y. A method for solving a decision problem, given in the form of an algorithm, is called a decision procedure for that problem.
Cholesky decompositionIn linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced ʃəˈlɛski ) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations. It was discovered by André-Louis Cholesky for real matrices, and posthumously published in 1924. When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations.
Electron cyclotron resonanceElectron cyclotron resonance (ECR) is a phenomenon observed in plasma physics, condensed matter physics, and accelerator physics. It happens when the frequency of incident radiation coincides with the natural frequency of rotation of electrons in magnetic fields. A free electron in a static and uniform magnetic field will move in a circle due to the Lorentz force. The circular motion may be superimposed with a uniform axial motion, resulting in a helix, or with a uniform motion perpendicular to the field (e.
Attosecond physicsAttosecond physics, also known as attophysics, or more generally attosecond science, is a branch of physics that deals with light-matter interaction phenomena wherein attosecond (10−18 s) photon pulses are used to unravel dynamical processes in matter with unprecedented time resolution. Attosecond science mainly employs pump–probe spectroscopic methods to investigate the physical process of interest.
Synchrotron radiationSynchrotron radiation (also known as magnetobremsstrahlung radiation) is the electromagnetic radiation emitted when relativistic charged particles are subject to an acceleration perpendicular to their velocity (a ⊥ v). It is produced artificially in some types of particle accelerators or naturally by fast electrons moving through magnetic fields. The radiation produced in this way has a characteristic polarization, and the frequencies generated can range over a large portion of the electromagnetic spectrum.
TokamakA tokamak (ˈtoʊkəmæk; токамáк) 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.
MeasurementMeasurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind. The scope and application of measurement are dependent on the context and discipline. In natural sciences and engineering, measurements do not apply to nominal properties of objects or events, which is consistent with the guidelines of the International vocabulary of metrology published by the International Bureau of Weights and Measures.
Generalized functionIn mathematics, generalized functions are objects extending the notion of functions. There is more than one recognized theory, for example the theory of distributions. Generalized functions are especially useful in making discontinuous functions more like smooth functions, and describing discrete physical phenomena such as point charges. They are applied extensively, especially in physics and engineering. A common feature of some of the approaches is that they build on operator aspects of everyday, numerical functions.
System identificationThe field of system identification uses statistical methods to build mathematical models of dynamical systems from measured data. System identification also includes the optimal design of experiments for efficiently generating informative data for fitting such models as well as model reduction. A common approach is to start from measurements of the behavior of the system and the external influences (inputs to the system) and try to determine a mathematical relation between them without going into many details of what is actually happening inside the system; this approach is called black box system identification.
SynchrotronA synchrotron is a particular type of cyclic particle accelerator, descended from the cyclotron, in which the accelerating particle beam travels around a fixed closed-loop path. The magnetic field which bends the particle beam into its closed path increases with time during the accelerating process, being synchronized to the increasing kinetic energy of the particles. The synchrotron is one of the first accelerator concepts to enable the construction of large-scale facilities, since bending, beam focusing and acceleration can be separated into different components.
Generalized inverseIn mathematics, and in particular, algebra, a generalized inverse (or, g-inverse) of an element x is an element y that has some properties of an inverse element but not necessarily all of them. The purpose of constructing a generalized inverse of a matrix is to obtain a matrix that can serve as an inverse in some sense for a wider class of matrices than invertible matrices. Generalized inverses can be defined in any mathematical structure that involves associative multiplication, that is, in a semigroup.
Particle acceleratorA particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams. Large accelerators are used for fundamental research in particle physics. The largest accelerator currently active is the Large Hadron Collider (LHC) near Geneva, Switzerland, operated by the CERN. It is a collider accelerator, which can accelerate two beams of protons to an energy of 6.5 TeV and cause them to collide head-on, creating center-of-mass energies of 13 TeV.
Signal processingSignal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing signals, such as sound, , potential fields, seismic signals, altimetry processing, and scientific measurements. Signal processing techniques are used to optimize transmissions, digital storage efficiency, correcting distorted signals, subjective video quality and to also detect or pinpoint components of interest in a measured signal. According to Alan V. Oppenheim and Ronald W.
X-rayX-ray radiation, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 nanometers to 10 picometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz (3e16Hz to 3e19Hz) and energies in the range 124 keV to 145 eV, respectively. X-ray wavelengths are shorter than those of UV rays and typically longer than those of gamma rays.
