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Beam Emittance
In accelerator physics, emittance is a property of a charged particle beam. It refers to the area occupied by the beam in a position-and-momentum phase space. Each particle in a beam can be described by its position and momentum along each of three orthogonal axes, for a total of six position and momentum coordinates. When the position and momentum for a single axis are plotted on a two dimensional graph, the average spread of the coordinates on this plot are the emittance. As such, a beam will have three emittances, one along each axis, which can be described independently. As particle momentum along an axis is usually described as an angle relative to that axis, an area on a position-momentum plot will have dimensions of length × angle (for example, millimeters × milliradian). Emittance is important for analysis of particle beams. As long as the beam is only subjected to conservative forces, Liouville's Theorem shows that emittance is a conserved quantity. If t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moment (mathematics)
In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph. If the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total mass) is the center of mass, and the second moment is the moment of inertia. If the function is a probability distribution, then the first moment is the expected value, the second central moment is the variance, the third standardized moment is the skewness, and the fourth standardized moment is the kurtosis. The mathematical concept is closely related to the concept of moment in physics. For a distribution of mass or probability on a bounded interval, the collection of all the moments (of all orders, from to ) uniquely determines the distribution (Hausdorff moment problem). The same is not true on unbounded intervals (Hamburger moment problem). In the mid-nineteenth century, Pafnuty Chebyshev became the first person to think systematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron Cooling
Electron cooling is a method to shrink the emittance (size, divergence, and energy spread) of a charged particle beam without removing particles from the beam. Since the number of particles remains unchanged and the space coordinates and their derivatives (angles) are reduced, this means that the phase space occupied by the stored particles is compressed. It is equivalent to reducing the temperature of the beam. See also stochastic cooling. The method was invented by Gersh Budker at INP, Novosibirsk, in 1966 for the purpose of increasing luminosity of hadron colliders. It was first tested in 1974 with 68 MeV protons at NAP-M storage ring at INP. It is used at both operating ion colliders: the Relativistic Heavy Ion Collider and in the Low Energy Ion Ring at CERN. Basically, electron cooling works as follows: * A beam of dense quasi-monoenergetic electrons is produced and merged with the ion beam to be cooled. * The velocity of the electrons is made equal to the average velocity ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Cooling
Stochastic cooling is a form of particle beam cooling. It is used in some particle accelerators and storage rings to control the emittance of the particle beams in the machine. This process uses the electrical signals that the individual charged particles generate in a feedback loop to reduce the tendency of individual particles to move away from the other particles in the beam. The technique was invented and applied at the Intersecting Storage Rings, and later the Super Proton Synchrotron (SPS), at CERN in Geneva, Switzerland, by Simon van der Meer, a physicist from the Netherlands. It was used to collect and cool antiprotons—these particles were injected into the Proton-Antiproton Collider, a modification of the SPS, with counter-rotating protons and collided at a particle physics experiment. For this work, van der Meer was awarded the Nobel Prize in Physics in 1984. He shared this prize with Carlo Rubbia of Italy, who proposed the Proton-Antiproton Collider. This exper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadrupole Magnet
Quadrupole magnets, abbreviated as Q-magnets, consist of groups of four magnets laid out so that in the planar multipole expansion of the field, the dipole terms cancel and where the lowest significant terms in the field equations are quadrupole. Quadrupole magnets are useful as they create a magnetic field whose magnitude grows rapidly with the radial distance from its longitudinal axis. This is used in particle beam focusing. The simplest magnetic quadrupole is two identical bar magnets parallel to each other such that the north pole of one is next to the south of the other and vice versa. Such a configuration will have no dipole moment, and its field will decrease at large distances faster than that of a dipole. A stronger version with very little external field involves using a ''k''=3 Halbach cylinder. In some designs of quadrupoles using electromagnets, there are four steel pole tips: two opposing magnetic north poles and two opposing magnetic south poles. The steel is mag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Excitation (accelerator Physics)
Quantum excitation is the effect in circular accelerators or storage rings whereby the discreteness of photon emission causes the charged particles (typically electrons) to undergo a random walk or diffusion process. Mechanism An electron moving through a magnetic field emits radiation. The expected amount of radiation can be calculated using the classical power. Considering quantum mechanics, however, this radiation is emitted in discrete packets of photons. For this description, the distribution of number of emitted photons and also the energy spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ... for the electron should be determined instead. In particular, the spectrum of a bending magnet is given by : S(\xi)=\frac\xi\int_0^\infty K_(\bar \xi) d\bar \xi The diffusion c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radiation Damping
Radiation damping in accelerator physics is a way of reducing the beam emittance of a high-velocity charged particle beam by synchrotron radiation. The two main ways of using radiation damping to reduce the emittance of a particle beam are the use of ''undulators'' and ''damping rings'' (often containing undulators), both relying on the same principle of inducing synchrotron radiation to reduce the particles' momentum, then replacing the momentum only in the desired direction of motion. Damping rings As particles are moving in a closed orbit, the lateral acceleration causes them to emit synchrotron radiation, thereby reducing the size of their momentum vectors (relative to the design orbit) without changing their orientation (ignoring quantum effects for the moment). In longitudinal direction, the loss of particle impulse due to radiation is replaced by accelerating sections ( RF cavities) that are installed in the beam path so that an equilibrium is reached at the design energy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Root Mean Square
In mathematics and its applications, the root mean square of a set of numbers x_i (abbreviated as RMS, or rms and denoted in formulas as either x_\mathrm or \mathrm_x) is defined as the square root of the mean square (the arithmetic mean of the squares) of the set. The RMS is also known as the quadratic mean (denoted M_2) and is a particular case of the generalized mean. The RMS of a continuously varying function (denoted f_\mathrm) can be defined in terms of an integral of the squares of the instantaneous values during a cycle. For alternating electric current, RMS is equal to the value of the constant direct current that would produce the same power dissipation in a resistive load. In estimation theory, the root-mean-square deviation of an estimator is a measure of the imperfection of the fit of the estimator to the data. Definition The RMS value of a set of values (or a continuous-time waveform) is the square root of the arithmetic mean of the squares of the values, or th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pepper Pot Mask-Based Emittance Measurement
Pepper or peppers may refer to: Food and spice * Piperaceae or the pepper family, a large family of flowering plant ** Black pepper * ''Capsicum'' or pepper, a genus of flowering plants in the nightshade family Solanaceae ** Bell pepper ** Chili pepper * Sichuan pepper, a strong spice *"Alder pepper", the flower of ''Alnus alnobetula'' Music * Pepper (band), a rock-reggae band originally from Hawaii * The Peppers, a French male instrumental group * "Pepper" (song), a 1996 song by Butthole Surfers * "Pepper", an instrumental song by Linkin Park from ''LP Underground 12'' People and fictional characters * Pepper (name), a list of people and fictional characters with either the given name or surname * Peppers (name), a list of people with the surname Science and technology * Pepper (cryptography), a secret value added before hashing * Pepper (robot), a humanoid robot by Aldebaran Robotics and SoftBank Mobile * PPAPI or Pepper Plugin API, an interface for web browser plugi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transpose
In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix by producing another matrix, often denoted by (among other notations). The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley. In the case of a logical matrix representing a binary relation R, the transpose corresponds to the converse relation RT. Transpose of a matrix Definition The transpose of a matrix , denoted by , , , A^, , , or , may be constructed by any one of the following methods: # Reflect over its main diagonal (which runs from top-left to bottom-right) to obtain #Write the rows of as the columns of #Write the columns of as the rows of Formally, the -th row, -th column element of is the -th row, -th column element of : :\left mathbf^\operatorname\right = \left mathbf\right. If is an matrix, then is an matrix. In the case of square matrices, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadrupole Scan Beamline
A quadrupole or quadrapole is one of a sequence of configurations of things like electric charge or current, or gravitational mass that can exist in ideal form, but it is usually just part of a multipole expansion of a more complex structure reflecting various orders of complexity. Mathematical definition The quadrupole moment tensor ''Q'' is a rank-two tensor—3×3 matrix. There are several definitions, but it is normally stated in the traceless form (i.e. Q_ + Q_ + Q_ = 0). The quadrupole moment tensor has thus nine components, but because of transposition symmetry and zero-trace property, in this form only five of these are independent. For a discrete system of \ell point charges or masses in the case of a gravitational quadrupole, each with charge q_\ell, or mass m_\ell, and position \vec_\ell = \left(r_, r_, r_\right) relative to the coordinate system origin, the components of the ''Q'' matrix are defined by: : Q_ = \sum_\ell q_\ell\left(3r_ r_ - \left\, \vec_\ell \rig ... [...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 th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
