Luminosity (scattering Theory)
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Luminosity (scattering Theory)
In scattering theory and accelerator physics, luminosity (''L'') is the ratio of the number of events detected (''dN'') in a certain period of time (''dt'') to the cross-section (''σ''): : L = \frac\frac. It has the dimensions of events per time per area, and is usually expressed in the cgs units of cm−2· s−1 or the non-SI units of b−1·s−1. In practice, ''L'' is dependent on the particle beam parameters, such as beam width and particle flow rate, as well as the target properties, such as target size and density. A related quantity is integrated luminosity (''L''int), which is the integral of the luminosity with respect to time: : L_\mathrm = \int L \ dt. The luminosity and integrated luminosity are useful values to characterize the performance of a particle accelerator. In particular, all collider experiments aim to maximize their integrated luminosities, as the higher the integrated luminosity, the more data is available to analyze. Examples of collider l ...
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Scattering Theory
In mathematics and physics, scattering theory is a framework for studying and understanding the scattering of waves and particles. Wave scattering corresponds to the collision and scattering of a wave with some material object, for instance sunlight scattered by rain drops to form a rainbow. Scattering also includes the interaction of billiard balls on a table, the Rutherford scattering (or angle change) of alpha particles by gold atomic nucleus, nuclei, the Bragg scattering (or diffraction) of electrons and X-rays by a cluster of atoms, and the inelastic scattering of a fission fragment as it traverses a thin foil. More precisely, scattering consists of the study of how solutions of partial differential equations, propagating freely "in the distant past", come together and interact with one another or with a boundary condition, and then propagate away "to the distant future". The direct scattering problem is the problem of determining the distribution of scattered radiation/ ...
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Tevatron
The Tevatron was a circular particle accelerator (active until 2011) in the United States, at the Fermi National Accelerator Laboratory (also known as ''Fermilab''), east of Batavia, Illinois, and is the second highest energy particle collider ever built, after the Large Hadron Collider (LHC) of the European Organization for Nuclear Research (CERN) near Geneva, Switzerland. The Tevatron was a synchrotron that accelerated protons and antiprotons in a ring to energies of up to 1 TeV, hence its name. The Tevatron was completed in 1983 at a cost of $120 million and significant upgrade investments were made during its active years of 1983–2011. The main achievement of the Tevatron was the discovery in 1995 of the top quark—the last fundamental fermion predicted by the Standard Model of particle physics. On July 2, 2012, scientists of the CDF and DØ collider experiment teams at Fermilab announced the findings from the analysis of around 500 trillion collisions produced from ...
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Beta Function (accelerator Physics)
The beta function in accelerator physics is a function related to the transverse size of the particle beam at the location s along the nominal beam trajectory. It is related to the transverse beam size as follows:https://www.cockcroft.ac.uk/wp-content/uploads/2014/12/Neil_3.pdf \sigma(s) = \sqrt where * s is the location along the nominal beam trajectory * the beam is assumed to have a Gaussian shape in the transverse direction * \sigma(s) is the width parameter of this Gaussian * \epsilon is the RMS geometrical beam emittance, which is normally constant along the trajectory when there is no acceleration Typically, separate beta functions are used for two perpendicular directions in the plane transverse to the beam direction (e.g. horizontal and vertical directions). The beta function is one of the Courant–Snyder parameters (also called Twiss parameters). Beta star The value of the beta function at an interaction point is referred to as beta star. The beta function is t ...
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Cross Section (physics)
In physics, the cross section is a measure of the probability that a specific process will take place when some kind of radiant excitation (e.g. a particle beam, sound wave, light, or an X-ray) intersects a localized phenomenon (e.g. a particle or density fluctuation). For example, the Rutherford scattering, Rutherford cross-section is a measure of probability that an alpha particle will be deflected by a given angle during an interaction with an atomic nucleus. Cross section is typically denoted (sigma) and is expressed in units of area, more specifically in barn (unit), barns. In a way, it can be thought of as the size of the object that the excitation must hit in order for the process to occur, but more exactly, it is a parameter of a stochastic process. In classical physics, this probability often converges to a deterministic proportion of excitation energy involved in the process, so that, for example, with light scattering off of a particle, the cross section specifies the ...
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Solid Angle
In geometry, a solid angle (symbol: ) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point. The point from which the object is viewed is called the ''apex'' of the solid angle, and the object is said to ''subtend'' its solid angle at that point. In the International System of Units (SI), a solid angle is expressed in a dimensionless unit called a '' steradian'' (symbol: sr). One steradian corresponds to one unit of area on the unit sphere surrounding the apex, so an object that blocks all rays from the apex would cover a number of steradians equal to the total surface area of the unit sphere, 4\pi. Solid angles can also be measured in squares of angular measures such as degrees, minutes, and seconds. A small object nearby may subtend the same solid angle as a larger object farther away. For example, although the Moon is much small ...
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Differential Of A Function
In calculus, the differential represents the principal part of the change in a function ''y'' = ''f''(''x'') with respect to changes in the independent variable. The differential ''dy'' is defined by :dy = f'(x)\,dx, where f'(x) is the derivative of ''f'' with respect to ''x'', and ''dx'' is an additional real variable (so that ''dy'' is a function of ''x'' and ''dx''). The notation is such that the equation :dy = \frac\, dx holds, where the derivative is represented in the Leibniz notation ''dy''/''dx'', and this is consistent with regarding the derivative as the quotient of the differentials. One also writes :df(x) = f'(x)\,dx. The precise meaning of the variables ''dy'' and ''dx'' depends on the context of the application and the required level of mathematical rigor. The domain of these variables may take on a particular geometrical significance if the differential is regarded as a particular differential form, or analytical significance if the differential i ...
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High Luminosity Large Hadron Collider
The High Luminosity Large Hadron Collider (HL-LHC; formerly referred to as HiLumi LHC) is an upgrade to the Large Hadron Collider, operated by the European Organization for Nuclear Research (CERN), located at the French-Swiss border near Geneva. From 2011 to 2020, the project was led by Lucio Rossi. In 2020, the lead role was taken up by Oliver Brüning. The upgrade started as a design study in 2010, for which a European Framework Program 7 grant was allocated in 2011, with goal of boosting the accelerator's potential for new discoveries in physics. The design study was approved by the CERN Council in 2016 and HL-LHC became a full-fledged CERN project. The upgrade work is currently in progress and physics experiments are expected to start taking data at the earliest in 2028. The HL-LHC project will deliver proton-proton collisions at 14 TeV with an integrated luminosity of for both ATLAS and CMS experiments, for LHCb, and for ALICE. In the heavy-ion sector, the integra ...
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Lead
Lead is a chemical element with the Symbol (chemistry), symbol Pb (from the Latin ) and atomic number 82. It is a heavy metals, heavy metal that is density, denser than most common materials. Lead is Mohs scale of mineral hardness#Intermediate hardness, soft and malleable, and also has a relatively low melting point. When freshly cut, lead is a shiny gray with a hint of blue. It tarnishes to a dull gray color when exposed to air. Lead has the highest atomic number of any stable nuclide, stable element and three of its isotopes are endpoints of major nuclear decay chains of heavier elements. Lead is toxic, even in small amounts, especially to children. Lead is a relatively unreactive post-transition metal. Its weak metallic character is illustrated by its amphoteric nature; lead and lead oxides react with acids and base (chemistry), bases, and it tends to form covalent bonds. Compounds of lead are usually found in the +2 oxidation state rather than the +4 state common with lighte ...
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SuperKEKB
SuperKEKB is a particle collider located at KEK (''High Energy Accelerator Research Organisation'') in Tsukuba, Ibaraki Prefecture, Japan. SuperKEKB collides electrons with positrons at the centre-of-momentum energy close to the mass of the Υ(4S) resonance making it a second-generation B-factory for the Belle II experiment. The accelerator is an upgrade to the KEKB accelerator, providing approximately 40 times higher luminosity, due mostly to superconducting quadrupole focusing magnets. The accelerator achieved "first turns" (first circulation of electron and positron beams) in February 2016. First collisions occurred on 26 April 2018. At 20:34 on 15 June 2020, SuperKEKB achieved the world’s highest instantaneous luminosity for a colliding-beam accelerator, setting a record of 2.22×1034 cm−2s−1. Description The SuperKEKB design reuses many components from KEKB. Under normal operation, SuperKEKB collides electrons at 7 GeV with positrons at 4 GeV (compared to KEKB at 8 G ...
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KEKB (accelerator)
KEKB was a particle accelerator used in the Belle experiment to study CP violation. KEKB was located at the ''KEK'' (''High Energy Accelerator Research Organisation'') in Tsukuba, Ibaraki Prefecture, Japan. It has been superseded by its upgrade, the SuperKEKB accelerator (located at the same site). The SuperKEKB is a luminosity upgrade of KEKB. SuperKEKB had its first particle collisions in 2018. The SuperKEKB accelerator produces particle beams for the Belle II experiment, which is an upgrade of the Belle experiment (located at the same site as Belle). The Belle experiments studied b-quark hadrons to research CP violation. KEKB was called a B-factory for its copious production of B-mesons which provide a golden mode to study and measure the CP violation due to its property of decaying into other lighter mesons. KEKB was basically an asymmetric electron–positron collider, with electrons having the energy of 8 GeV and positrons having the energy of 3.5 GeV, giving 10.58 GeV c ...
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SLAC
SLAC National Accelerator Laboratory, originally named the Stanford Linear Accelerator Center, is a United States Department of Energy National Laboratory operated by Stanford University under the programmatic direction of the U.S. Department of Energy Office of Science and located in Menlo Park, California. It is the site of the Stanford Linear Accelerator, a 3.2 kilometer (2-mile) linear accelerator constructed in 1966 and shut down in the 2000s, that could accelerate electrons to energies of 50 GeV. Today SLAC research centers on a broad program in atomic and solid-state physics, chemistry, biology, and medicine using X-rays from synchrotron radiation and a free-electron laser as well as experimental and theoretical research in elementary particle physics, astroparticle physics, and cosmology. History Founded in 1962 as the Stanford Linear Accelerator Center, the facility is located on of Stanford University-owned land on Sand Hill Road in Menlo Park ...
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Electron
The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron's mass is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum ( spin) of a half-integer value, expressed in units of the reduced Planck constant, . Being fermions, no two electrons can occupy the same quantum state, per the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: They can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer ...
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