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24-449: The Alternating Gradient Synchrotron was built on the innovative concept of the alternating gradient, or strong-focusing principle , developed by Brookhaven physicists. This new concept in accelerator design allowed scientists to accelerate protons to energies that were previously unachievable. The AGS became the world's premiere accelerator when it reached its design energy of 33 billion electron volts (GeV) on July 29, 1960. Until 1968,

48-465: 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 magnetized by a large electric current in the coils of tubing wrapped around the poles. Another design is a Helmholtz coil layout but with the current in one of the coils reversed. At the particle speeds reached in high energy particle accelerators ,

72-437: A defocusing effect that can be countered with a convergent magnet 'lens'. This can be shown schematically as a sequence of divergent and convergent lenses. The quadrupoles are often laid out in what are called FODO patterns (where F focusses vertically and defocusses horizontally, and D focusses horizontally and defocusses vertically and O is a space or deflection magnet). Following the beam particles in their trajectories through

96-448: A variety of methods, depending on the phenomena of interest. 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

120-496: Is due to the laws of electromagnetism (the Maxwell equations ) which show that it is impossible for a quadrupole to focus in both planes at the same time. The image on the right shows an example of a quadrupole focusing in the vertical direction for a positively charged particle going into the image plane (forces above and below the center point towards the center) while defocusing in the horizontal direction (forces left and right of

144-415: Is summed up by a focusing strength κ {\displaystyle \kappa } which depends on the quadrupole gradient G {\displaystyle G} as well as the beam's rigidity [ B ρ ] = p / q {\displaystyle [B\rho ]=p/q} , where q {\displaystyle q} is the electric charge of the particle and

168-528: Is the relativistic momentum . The focusing strength is given by and particles in the magnetic will behave according to the ODE The same equation will be true for the y direction, but with a minus sign in front of the focusing strength to account for the field changing directions. The components of the ideal magnetic field in the plane transverse to the beam are given by the following (see also multipole magnet ). where K {\displaystyle K}

192-405: Is the field gradient of the normal quadrupole component and J {\displaystyle J} is the field gradient of the skew quadrupole component. The SI unit of the field gradients are T / m {\displaystyle \mathrm {T} /\mathrm {m} } . The field in a normal quadrupole is such that the magnetic poles are arranged with an angle of 45 degrees to

216-447: 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

240-596: The Alternating Gradient Synchrotron . Courant and Snyder found that the net effect of alternating the field gradient was that both the vertical and horizontal focusing of protons could be made strong at the same time, allowing tight control of proton paths in the machine. This increased beam intensity while reducing the overall construction cost of a more powerful accelerator. The theory revolutionised cyclotron design and permitted very high field strengths to be employed, while massively reducing

264-454: 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

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288-608: The AGS Booster. The AGS Booster then accelerates these particles for injection into the AGS. The AGS Booster also provides particle beams to the NASA Space Radiation Laboratory . It became increasingly clear that if further progress was to be made in high energy nuclear physics by experiments using artificially accelerated particles some new principle must be found that would cheapen the cost per GeV. It

312-546: The AGS was the highest energy accelerator in the world, slightly higher than its 28 GeV sister machine, the Proton Synchrotron at CERN , the European laboratory for high-energy physics. While 21st century accelerators can reach energies in the trillion electron volt region, the AGS earned researchers three Nobel Prizes and today serves as the injector for Brookhaven's Relativistic Heavy Ion Collider ; it remains

336-439: The amplitude of the free oscillations is to increase the frequency by increasing the restoring force, and although this is easy to achieve in the vertical direction by increasing the magnetic field gradient, the condition for horizontal stability is violated if n exceeds unity. The new principle discovered by Christofilos and Courant , Livingston and Snyder increases the frequency of the betatron oscillations by alternating

360-428: 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

384-401: The center point away from the center). If an F quadrupole and a D quadrupole are placed immediately next to each other, their fields completely cancel out (in accordance with Earnshaw's theorem ). But if there is a space between them (and the length of this has been correctly chosen), the overall effect is focusing in both horizontal and vertical planes. A lattice can then be built up enabling

408-413: The focusing arrangement, an oscillating pattern would be seen. The action upon a set of charged particles by a set of linear magnets (i.e. only dipoles, quadrupoles and the field-free drift regions between them) can be expressed as matrices which can be multiplied together to give their net effect, using ray transfer matrix analysis . Higher-order terms such as sextupoles, octupoles etc. may be treated by

432-543: The magnetic force term is larger than the electric term in the Lorentz force : and thus magnetic deflection is more effective than electrostatic deflection . Therefore a 'lattice' of electromagnets is used to bend, steer and focus a charged particle beam. The quadrupoles in the lattice are of two types: 'F quadrupoles' (which are horizontally focusing but vertically defocusing) and 'D quadrupoles' (which are vertically focusing but horizontally defocusing). This situation

456-564: The sign of the gradient of the magnetic field. The structure of the magnet is no longer uniform round the ring with a constant gradient but is broken up into sectors whose gradient is alternatively positive and negative. The work performed at the accelerator led to three Nobel Prizes in Physics : This particle physics –related article is a stub . You can help Misplaced Pages by expanding it . Strong focusing In accelerator physics strong focusing or alternating-gradient focusing

480-466: The size of the magnets needed by minimising the size of the beam. Most particle accelerators today use the strong-focusing principle. Modern systems often use multipole magnets, such as quadrupole and sextupole magnets , to focus the beam down, as magnets give a more powerful deflection effect than earlier electrostatic systems at high beam kinetic energies. The multipole magnets refocus the beam after each deflection section, as deflection sections have

504-409: The transport of the beam over long distances—for example round an entire ring. A common lattice is a FODO lattice consisting of a basis of a focusing quadrupole, 'nothing' (often a bending magnet), a defocusing quadrupole and another length of 'nothing'. A charged particle beam in a quadrupole magnetic field will experience a focusing / defocusing force in the transverse direction. This focusing effect

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528-535: The world's highest intensity high-energy proton accelerator. The AGS Booster , constructed in 1991, further augments the capabilities of the AGS, enabling it to accelerate more intense proton beams and heavy ions such as Gold . Brookhaven's linear particle accelerator (LINAC) provides 200 million electron volt (MeV) protons to the AGS Booster, and the Electron Beam Ion Source (EBIS) and Tandem Van de Graaff accelerators provide other ions to

552-445: Was first conceived by Nicholas Christofilos in 1949 but not published (Christofilos opted instead to patent his idea). In 1952, the strong focusing principle was independently developed by Ernest Courant , M. Stanley Livingston , Hartland Snyder and J. Blewett at Brookhaven National Laboratory , who later acknowledged the priority of Christofilos' idea. The advantages of strong focusing were then quickly realised, and deployed on

576-412: Was lucky for CERN that just at the time a European machine was being considered this new principle was discovered. The problem was simple enough. A cheaper machine could be built if the amplitudes of the free and forced oscillations of the accelerating particles could be decreased in some way so that the vacuum chamber size and the cross-section of the magnet ring could be reduced. The simplest way to reduce

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