- Strong focusing
accelerator physicsstrong focusing or alternating-gradient focusing is the principle that the net effect on a particle beamof charged particles passing through alternating field gradients is to make the beam converge. 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 theoremshows that simultaneous focussing in two directions at once is impossible. However, ridged poles of a cyclotronor two or more spaced quadrupole magnets (arranged in quadrature) alternately focus horizontally and vertically. [ [http://www.bnl.gov/bnlweb/history/focusing.asp The Alternating Graident Concept ] ]
Strong focusing was first invented at
Brookhaven National Laboratoryand deployed on the Alternating Gradient Synchrotronthere. The theory was developed in 1957 by E. D. Courant and H. S. Snyder. [ [http://ab-abp-rlc.web.cern.ch/ab-abp-rlc/AP-literature/Courant-Snyder-1958.pdf Theory of 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. All current cyclotrons use strong focusing.
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 focussing arrangement, an oscillating pattern would be seen.
The effect of a set of focusing magnets can be expressed as a matrix. [ [http://www-linux.gsi.de/~boine/vorlesung/skript/html/node9.html Beam focusing ] ]
Electron gunuses cylindrical symmetric fields such as provided by a Wehnelt cylinderto focus an electron beam
Maglevhas also been a suggested use of strong focusing
* [http://bc1.lbl.gov/CBP_pages/educational/WoB/home.htm Lawrence Berkeley National Laboratory: World of Beams]
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