In accelerator physicsstrong 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.[1][2]
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 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 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 the focusing arrangement, an oscillating pattern would be seen.
Mathematical modelingedit
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.[7] Higher-order terms such as sextupoles, octupoles etc. may be treated by a variety of methods, depending on the phenomena of interest.
See alsoedit
Electron gun – uses cylindrical symmetric fields such as provided by a Wehnelt cylinder to focus an electron beam
Maglev – has also been a suggested use of strong focusing
Referencesedit
^Courant, E. D.; Snyder, H. S. (Jan 1958). "Theory of the alternating-gradient synchrotron" (PDF). Annals of Physics. 3 (1): 360–408. Bibcode:2000AnPhy.281..360C. doi:10.1006/aphy.2000.6012.
^Blewett, J. P. (1952). "Radial Focusing in the Linear Accelerator". Physical Review. 88 (5): 1197–1199. Bibcode:1952PhRv...88.1197B. doi:10.1103/PhysRev.88.1197.
Lawrence Berkeley National Laboratory: World of Beams 2005-03-02 at the Wayback Machine
April 12, 2024
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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 Sextupole electromagnet as used within the storage ring of the Australian Synchrotron to focus and steer the electron beamEarnshaw 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 1 2 Strong focusing was first conceived by Nicholas Christofilos in 1949 but not published Christofilos opted instead to patent his idea 3 In 1952 the strong focusing principle was independently developed by Ernest Courant M Stanley Livingston Hartland Snyder and J Blewett at Brookhaven National Laboratory 4 5 who later acknowledged the priority of Christofilos idea 6 The advantages of strong focusing were then quickly realised and deployed on 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 the size of the magnets needed by minimising the size of the beam Most particle accelerators today use the strong focusing principle Contents 1 Multipole magnets 2 Mathematical modeling 3 See also 4 References 5 External linksMultipole magnets edit nbsp Quadrupole electromagnet from the storage ring of the Australian Synchrotron serves much the same purpose as the sextupole magnets 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 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 the focusing arrangement an oscillating pattern would be seen Mathematical modeling editThe 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 7 Higher order terms such as sextupoles octupoles etc may be treated by a variety of methods depending on the phenomena of interest See also editElectron gun uses cylindrical symmetric fields such as provided by a Wehnelt cylinder to focus an electron beam Maglev has also been a suggested use of strong focusingReferences edit Courant E D Snyder H S Jan 1958 Theory of the alternating gradient synchrotron PDF Annals of Physics 3 1 360 408 Bibcode 2000AnPhy 281 360C doi 10 1006 aphy 2000 6012 The Alternating Gradient Concept Christofilos N C 1950 Focusing System for Ions and Electrons US Patent No 2 736 799 Courant E D Livingston M S Snyder H S 1952 The Strong Focusing Synchrotron A New High Energy Accelerator Physical Review 88 5 1190 1196 Bibcode 1952PhRv 88 1190C doi 10 1103 PhysRev 88 1190 hdl 2027 mdp 39015086454124 Blewett J P 1952 Radial Focusing in the Linear Accelerator Physical Review 88 5 1197 1199 Bibcode 1952PhRv 88 1197B doi 10 1103 PhysRev 88 1197 Courant E D Livingston M S Snyder H S Blewett J 1953 Origin of the Strong Focusing Principle Physical Review 91 1 202 203 Bibcode 1953PhRv 91 202C doi 10 1103 PhysRev 91 202 2 Beam focusingExternal links editLawrence Berkeley National Laboratory World of Beams Archived 2005 03 02 at the Wayback Machine Retrieved from https en wikipedia org w index php title Strong focusing amp oldid 1217015817, wikipedia, wiki, book, books, library,
