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Momentum Compaction
The momentum compaction or momentum compaction factor is a measure for the momentum dependence of the recirculation path length for an object that is bound in cyclic motion (closed orbit). It is used in the calculation of particle paths in circular particle accelerators (like synchrotrons), and for astronomical objects that are bound by gravitation. For a perturbation theory, perturbed orbit, the momentum compaction factor is defined as the derivative of normalized path length difference to normalized momentum \alpha_p = \frac = \frac \frac =\frac \oint \frac\mathrms. Furthermore, the momentum compaction is closely connected to the so-called slip-factor \eta with the horizontal dispersion D_x and the gyroradius \rho \alpha_p = \frac+\eta wherein \gamma is the Lorentz factor. References {{Accelerator-stub Accelerator physics Equations of astronomy Momentum Orbits ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Momentum
In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass and is its velocity (also a vector quantity), then the object's momentum is : \mathbf = m \mathbf. In the International System of Units (SI), the unit of measurement of momentum is the kilogram metre per second (kg⋅m/s), which is equivalent to the newton-second. Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference, but in any inertial frame it is a ''conserved'' quantity, meaning that if a closed system is not affected by external forces, its total linear momentum does not change. Momentum is also conserved in special relativity (with a modified formula) and, in a modified form, in electrodynamics, quantum mechanics, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particle Accelerator
A 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. Other powerful accelerators are, RHIC at Brookhaven National Laboratory in New York and, formerly, the Tevatron at Fermilab, Batavia, Illinois. Accelerators are also used as synchrotron light sources for the study of condensed matter physics. Smaller particle accelerators are used in a wide variety of applications, including particle therapy for oncological purposes, radioisotope production for medical diagnostics, ion imp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Synchrotron
A 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. The most powerful modern particle accelerators use versions of the synchrotron design. The largest synchrotron-type accelerator, also the largest particle accelerator in the world, is the Large Hadron Collider (LHC) near Geneva, Switzerland, built in 2008 by the European Organization for Nuclear Research (CERN). It can accelerate beams of protons to an energy of 6.5 tera electronvolts (TeV or 1012 eV). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitation
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak interaction. As a result, it has no significant influence at the level of subatomic particles. However, gravity is the most significant interaction between objects at the macroscopic scale, and it determines the motion of planets, stars, galaxies, and even light. On Earth, gravity gives weight to physical objects, and the Moon's gravity is responsible for sublunar tides in the oceans (the corresponding antipodal tide is caused by the inertia of the Earth and Moon orbiting one another). Gravity also has many important biological functions, helping to guide the growth of plants through the process of gravitropism and influencing th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation Theory
In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In perturbation theory, the solution is expressed as a power series in a small parameter The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of \varepsilon usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, usually by keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction. Perturbation theory is used in a wide range of fields, and reaches its most sophisticated and advanced forms in quantum field theory. Perturbation theory (quantum mechanics) describes the use of this method in quantum mechanics. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbit
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion. For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World Scientific
World Scientific Publishing is an academic publisher of scientific, technical, and medical books and journals headquartered in Singapore. The company was founded in 1981. It publishes about 600 books annually, along with 135 journals in various fields. In 1995, World Scientific co-founded the London-based Imperial College Press together with the Imperial College of Science, Technology and Medicine. Company structure The company head office is in Singapore. The Chairman and Editor-in-Chief is Dr Phua Kok Khoo, while the Managing Director is Doreen Liu. The company was co-founded by them in 1981. Imperial College Press In 1995 the company co-founded Imperial College Press, specializing in engineering, medicine and information technology, with Imperial College London. In 2006, World Scientific assumed full ownership of Imperial College Press, under a license granted by the university. Finally, in August 2016, ICP was fully incorporated into World Scientific under the new impr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business international ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CERN
The European Organization for Nuclear Research, known as CERN (; ; ), is an intergovernmental organization that operates the largest particle physics laboratory in the world. Established in 1954, it is based in a northwestern suburb of Geneva, on the France–Switzerland border. It comprises 23 member states, and Israel (admitted in 2013) is currently the only non-European country holding full membership. CERN is an official United Nations General Assembly observer. The acronym CERN is also used to refer to the laboratory; in 2019, it had 2,660 scientific, technical, and administrative staff members, and hosted about 12,400 users from institutions in more than 70 countries. In 2016, CERN generated 49 petabytes of data. CERN's main function is to provide the particle accelerators and other infrastructure needed for high-energy physics research — consequently, numerous experiments have been constructed at CERN through international collaborations. CERN is the site of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gyroradius
The gyroradius (also known as radius of gyration, Larmor radius or cyclotron radius) is the radius of the circular motion of a charged particle in the presence of a uniform magnetic field. In SI units, the non-relativistic gyroradius is given by :r_ = \frac where m is the mass of the particle, v_ is the component of the velocity perpendicular to the direction of the magnetic field, q is the electric charge of the particle, and B is the strength of the magnetic field. The angular frequency of this circular motion is known as the gyrofrequency, or cyclotron frequency, and can be expressed as :\omega_ = \frac in units of radians/second. Variants It is often useful to give the gyrofrequency a sign with the definition :\omega_ = \frac or express it in units of hertz with :f_ = \frac. For electrons, this frequency can be reduced to :f_ = (2.8\times10^\,\mathrm/\mathrm)\times B. In cgs-units the gyroradius :r_ = \frac and the corresponding gyrofrequency :\omega_ = \frac include a factor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentz Factor
The Lorentz factor or Lorentz term is a quantity expressing how much the measurements of time, length, and other physical properties change for an object while that object is moving. The expression appears in several equations in special relativity, and it arises in derivations of the Lorentz transformations. The name originates from its earlier appearance in Lorentzian electrodynamics – named after the Dutch physicist Hendrik Lorentz. It is generally denoted (the Greek lowercase letter gamma). Sometimes (especially in discussion of superluminal motion) the factor is written as (Greek uppercase-gamma) rather than . Definition The Lorentz factor is defined as :\gamma = \frac = \frac = \frac , where: *''v'' is the relative velocity between inertial reference frames, *''c'' is the ''speed of light in a vacuum'', * is the ratio of ''v'' to ''c'', *''t'' is coordinate time, * is the proper time for an observer (measuring time intervals in the observer's own frame). This is t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Accelerator Physics
Accelerator physics is a branch of applied physics, concerned with designing, building and operating particle accelerators. As such, it can be described as the study of motion, manipulation and observation of relativistic charged particle beams and their interaction with accelerator structures by electromagnetic fields. It is also related to other fields: * Microwave engineering (for acceleration/deflection structures in the radio frequency range). *Optics with an emphasis on geometrical optics (beam focusing and bending) and laser physics (laser-particle interaction). *Computer technology with an emphasis on digital signal processing; e.g., for automated manipulation of the particle beam. *Plasma physics, for the description of intense beams. The experiments conducted with particle accelerators are not regarded as part of accelerator physics, but belong (according to the objectives of the experiments) to, e.g., particle physics, nuclear physics, condensed matter physics or ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
