Radiation Damping
Radiation damping in accelerator physics is a phenomenon where betatron oscillations and longitudinal oscillations of the particle are damped due to energy loss by synchrotron radiation. It can be used to reduce the beam emittance of a high-velocity charged particle beam. 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 the quantum fluctuations of the radiation for the moment). In longitudinal direction, the loss of particle impulse due to ra ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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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 ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Elementary Charge
The elementary charge, usually denoted by , is a fundamental physical constant, defined as the electric charge carried by a single proton (+1 ''e'') or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . In SI units, the coulomb is defined such that the value of the elementary charge is exactly or 160.2176634 zeptocoulombs (zC). Since the 2019 revision of the SI, the seven SI base units are defined in terms of seven fundamental physical constants, of which the elementary charge is one. In the centimetre–gram–second system of units (CGS), the corresponding quantity is . Robert A. Millikan and Harvey Fletcher's oil drop experiment first directly measured the magnitude of the elementary charge in 1909, differing from the modern accepted value by just 0.6%. Under assumptions of the then-disputed atomic theory, the elementary charge had also been indirectly inferred to ~3% accuracy from blackb ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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SLAC
SLAC National Accelerator Laboratory, originally named the Stanford Linear Accelerator Center, is a federally funded research and development center in Menlo Park, California, United States. Founded in 1962, the laboratory is now sponsored by the United States Department of Energy and administrated by Stanford University. It is the site of the Stanford Linear Accelerator, a 3.2 kilometer (2-mile) linear accelerator constructed in 1966 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, accelerator physics, astroparticle physics, and cosmology. The laboratory is under the programmatic direction of the United States Department of Energy Office of Science. History Founded in 1962 as the Stanford Linear Accelera ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Particle Beam Cooling
Particle beam cooling is the process of improving the quality of particle beams produced by particle accelerators, by reducing the emittance. Techniques for particle beam cooling include: * Stochastic cooling * Electron coolingI. Meshkov, Electron Cooling: Status and Perspectives, Physics of Particles and Nuclei, Vol. 25, Issue 6, pp. 631-661, 1994 * Ionization cooling * Laser cooling * Radiation damping Radiation damping in accelerator physics is a phenomenon where betatron oscillations and longitudinal oscillations of the particle are damped due to energy loss by synchrotron radiation. It can be used to reduce the beam emittance of a high-veloci ... * Buffer-gas cooling within RF quadrupoles References Accelerator physics {{Accelerator-stub ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Laurent Series
In mathematics, the Laurent series of a complex function f(z) is a representation of that function as a power series which includes terms of negative degree. It may be used to express complex functions in cases where a Taylor series expansion cannot be applied. The Laurent series was named after and first published by Pierre Alphonse Laurent in 1843. Karl Weierstrass had previously described it in a paper written in 1841 but not published until 1894. Definition The Laurent series for a complex function f(z) about an arbitrary point c is given by f(z) = \sum_^\infty a_n(z-c)^n, where the coefficients a_n are defined by a contour integral that generalizes Cauchy's integral formula: a_n =\frac\oint_\gamma \frac \, dz. The path of integration \gamma is counterclockwise around a Jordan curve enclosing c and lying in an annulus A in which f(z) is holomorphic ( analytic). The expansion for f(z) will then be valid anywhere inside the annulus. The annulus is shown in red in th ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Rigidity (electromagnetism)
In particle physics, rigidity R is a measure of the resistance of a particle to deflection by magnetic fields, defined as the particle's momentum divided by its charge. For a fully ionised nucleus moving at relativistic speed, this is equivalent to the energy per atomic number. It is an important quantity in accelerator physics and astroparticle physics. Definitions Motion within a magnetic field The concept of rigidity is derived from the motion of a charged particle within a magnetic field: two particles follow the same trajectory through a magnetic field if they have the same rigidity, even if they have different masses and charges. This situation arises in many particle accelerator and particle detector designs. If a charged particle enters a uniform magnetic field, with the field orientated perpendicular to the initial velocity, the Lorentz force accelerates the particle in the direction which is perpendicular to both the velocity and magnetic field vectors. The resultin ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Classical Electron Radius
The classical electron radius is a combination of fundamental Physical quantity, physical quantities that define a length scale for problems involving an electron interacting with electromagnetic radiation. It links the classical electrostatic self-interaction energy of a homogeneous charge distribution to the electron's rest mass energy. According to modern understanding, the electron has no internal structure, and hence no size attributable to it. Nevertheless, it is useful to define a length that characterizes electron interactions in atomic-scale problems. The CODATA value for the classical electron radius is : r_\text = \frac\frac = where e is the elementary charge, m_ is the electron mass, c is the speed of light, and \varepsilon_0 is the vacuum permittivity, permittivity of free space. This is about three times larger than the proton radius, charge radius of the proton. The classical electron radius is sometimes known as the Hendrik Lorentz, Lorentz radius or the Thoms ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Radius Of Curvature
In differential geometry, the radius of curvature, , is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof. Definition In the case of a space curve, the radius of curvature is the length of the curvature vector. In the case of a plane curve, then is the absolute value of : R \equiv \left, \frac \ = \frac, where is the arc length from a fixed point on the curve, is the tangential angle and is the curvature. Formula In two dimensions If the curve is given in Cartesian coordinates as , i.e., as the graph of a function, then the radius of curvature is (assuming the curve is differentiable up to order 2) R =\left, \frac \\,, where y' = \frac\,, y'' = \frac, and denotes the absolute value of . If the curve is given parametrically by functions and , then the radiu ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Momentum
In Newtonian mechanics, momentum (: momenta or momentums; 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 (from Latin '' pellere'' "push, drive") 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 dimensionally 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 of reference, it is a ''conserved'' quantity, meaning that if a closed system is not affected by external forces, its total momentum does not change. Momentum is also conserved in special relativity (with a mo ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Lorentz Factor
The Lorentz factor or Lorentz term (also known as the gamma factor) is a dimensionless quantity expressing how much the measurements of time, length, and other physical properties change for an object while it moves. 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 Lorentz ether theory, Lorentzian electrodynamics – named after the Netherlands, 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: * is the relative velocity between inertial reference frames, * is the speed of light in vacuum, * is the ratio of to , * is coordinate time, * is the proper time for an observer (measuring time intervals in ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Vacuum Permittivity
Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric constant, or the distributed capacitance of the vacuum. It is an ideal (baseline) physical constant. Its CODATA value is: It is a measure of how dense of an electric field is "permitted" to form in response to electric charges and relates the units for electric charge to mechanical quantities such as length and force. For example, the force between two separated electric charges with spherical symmetry (in the vacuum of classical electromagnetism) is given by Coulomb's law: F_\text = \frac \frac Here, ''q''1 and ''q''2 are the charges, ''r'' is the distance between their centres, and the value of the constant fraction 1/(4π''ε''0) is approximately . Likewise, ''ε''0 appears in Maxwell's equations, which describe the properties of electr ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Wiggler (synchrotron)
A wiggler is an insertion device in a synchrotron. It is a series of magnets designed to periodically laterally deflect ('wiggle') a beam of charged particles (invariably electrons or positrons) inside a storage ring of a synchrotron. These deflections create a change in acceleration which in turn produces emission of broad synchrotron radiation tangent to the curve, much like that of a bending magnet, but the intensity is higher due to the contribution of many magnetic dipoles in the wiggler. Furthermore, as the wavelength (λ) is decreased this means the frequency (ƒ) has increased. This increase of frequency is directly proportional to energy, hence, the wiggler creates a wavelength of light with a larger energy. A wiggler has a broader spectrum of radiation than an undulator. Typically the magnets in a wiggler are arranged in a Halbach array. The design shown above is usually known as a Halbach wiggler. History The first suggestion of a wiggler magnet to produce sy ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |