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Weak Focusing
Weak focusing occurs in particle accelerators when charged particles are passing through uniform magnetic fields, causing them to move in circular paths due to the Lorentz force. Because of the circular movement, the orbits of two particles with slightly different positions may approximate or even cross each other. Because a particle beam has a finite emittance, this effect was used in cyclotrons and early synchrotrons to prevent the growth of deviations from the desired particle orbit. Due to its definition, it also occurs in the dipole magnets of modern accelerator facilities and must be considered in beam optics calculations. In modern facilities, most of the beam focusing is usually done by quadrupole magnets, using Strong focusing In accelerator physics strong focusing or alternating-gradient focusing is the principle that, using sets of multiple electromagnets, it is possible to make a particle beam simultaneously converge in both directions perpendicular to the direction ...
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Weak Focusing Dipole Sketch
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Particle Accelerators
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 ...
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Lorentz Force
In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge moving with a velocity in an electric field and a magnetic field experiences a force of \mathbf = q\,\mathbf + q\,\mathbf \times \mathbf (in SI unitsIn SI units, is measured in teslas (symbol: T). In Gaussian-cgs units, is measured in gauss (symbol: G). See e.g. )The -field is measured in amperes per metre (A/m) in SI units, and in oersteds (Oe) in cgs units. ). It says that the electromagnetic force on a charge is a combination of a force in the direction of the electric field proportional to the magnitude of the field and the quantity of charge, and a force at right angles to the magnetic field and the velocity of the charge, proportional to the magnitude of the field, the charge, and the velocity. Variations on this basic formula describe the magnetic force on ...
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Particle Beam
A particle beam is a stream of charged or neutral particles. In particle accelerators, these particles can move with a velocity close to the speed of light. There is a difference between the creation and control of charged particle beams and neutral particle beams, as only the first type can be manipulated to a sufficient extent by devices based on electromagnetism. The manipulation and diagnostics of charged particle beams at high kinetic energies using particle accelerators are main topics of accelerator physics. Sources Charged particles such as electrons, positrons, and protons may be separated from their common surrounding. This can be accomplished by e.g. thermionic emission or arc discharge. The following devices are commonly used as sources for particle beams: * Ion source * Cathode ray tube, or more specifically in one of its parts called electron gun. This is also part of traditional television and computer screens. * Photocathodes may also be built in as a part of an ...
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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 ...
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Cyclotron
A cyclotron is a type of particle accelerator invented by Ernest O. Lawrence in 1929–1930 at the University of California, Berkeley, and patented in 1932. Lawrence, Ernest O. ''Method and apparatus for the acceleration of ions'', filed: January 26, 1932, granted: February 20, 1934 A cyclotron accelerates charged particles outwards from the center of a flat cylindrical vacuum chamber along a spiral path. The particles are held to a spiral trajectory by a static magnetic field and accelerated by a rapidly varying electric field. Lawrence was awarded the 1939 Nobel Prize in Physics for this invention. The cyclotron was the first "cyclical" accelerator. The primary accelerators before the development of the cyclotron were electrostatic accelerators, such as the Cockcroft–Walton accelerator and Van de Graaff generator. In these accelerators, particles would cross an accelerating electric field only once. Thus, the energy gained by the particles was limited by the maximum elec ...
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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). Th ...
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Dipole Magnet
A dipole magnet is the simplest type of magnet. It has two poles, one north and one south. Its magnetic field lines form simple closed loops which emerge from the north pole, re-enter at the south pole, then pass through the body of the magnet. The simplest example of a dipole magnet is a ''bar magnet''. Bar Magnet" hyperphysics; http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html/ref> Dipole magnets in accelerators In particle accelerators, a dipole magnet is the electromagnet used to create a homogeneous magnetic field over some distance. Particle motion in that field will be circular in a plane perpendicular to the field and collinear to the direction of particle motion and free in the direction orthogonal to it. Thus, a particle injected into a dipole magnet will travel on a circular or helical trajectory. By adding several dipole sections on the same plane, the bending radial effect of the beam increases. In accelerator physics, dipole magnets are used to rea ...
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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 ...
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Strong Focusing
In accelerator physics strong focusing or alternating-gradient focusing is the principle that, using sets of multiple electromagnets, it is possible to make a particle beam simultaneously converge in both directions perpendicular to the direction of travel. By contrast, weak focusing is the principle that nearby circles, described by charged particles moving in a uniform magnetic field, only intersect once per revolution. Earnshaw's theorem shows that simultaneous focusing in two directions transverse to the beam axis at once by a single magnet is impossible - a magnet which focuses in one direction will defocus in the perpendicular direction. However, iron "poles" of a cyclotron or two or more spaced quadrupole magnets (arranged in quadrature) can alternately focus horizontally and vertically, and the net overall effect of a combination of these can be adjusted to focus the beam in both directions. Strong focusing was first conceived by Nicholas Christofilos in 1949 but not pub ...
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