Strong focusing

<h2 id="multipole-magnets">Multipole magnets</h2>

<p>Modern systems often use multipole magnets, such as <a href="/facts/Quadrupole_magnet/x2VmpLL8">quadrupole</a> and <a href="/facts/Sextupole_magnet/VQy9V0Ve">sextupole magnets</a>, to focus the beam down, as <a href="/facts/Magnet/vvrg6VSk">magnets</a> 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'.
</p><p>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.
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<h2 id="mathematical-modeling">Mathematical modeling</h2>
<p>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 <a href="/facts/Ray_transfer_matrix_analysis/k8MtAnYt">ray transfer matrix analysis</a>.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> Higher-order terms such as sextupoles, octupoles etc. may be treated by a variety of methods, depending on the phenomena of interest.
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<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Electron_gun/l6nahAeW">Electron gun</a> – uses cylindrical symmetric fields such as provided by a Wehnelt cylinder to focus an electron beam</li>
<li><a href="/facts/Maglev_(transport)/2o7UVAM5">Maglev</a> – has also been a suggested use of strong focusing</li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a href="http://bc1.lbl.gov/CBP_pages/educational/WoB/home.htm">Lawrence Berkeley National Laboratory: World of Beams</a> <a href="https://web.archive.org/web/20050302091712/http://bc1.lbl.gov/CBP_pages/educational/WoB/home.htm">Archived</a> 2005-03-02 at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>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. <a href="/wiki/Ernest_Courant" target="_blank">/wiki/Ernest_Courant</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>The Alternating Gradient Concept <a href="https://web.archive.org/web/20130402193938/http://www.bnl.gov/bnlweb/history/focusing.asp" target="_blank">https://web.archive.org/web/20130402193938/http://www.bnl.gov/bnlweb/history/focusing.asp</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Christofilos, N. C. (1950). "Focusing System for Ions and Electrons". US Patent No. 2,736,799. <a href="/wiki/Nicholas_Christofilos" target="_blank">/wiki/Nicholas_Christofilos</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>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. <a href="/wiki/Ernest_Courant" target="_blank">/wiki/Ernest_Courant</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>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. <a href="/wiki/Physical_Review" target="_blank">/wiki/Physical_Review</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>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. <a href="/wiki/Ernest_Courant" target="_blank">/wiki/Ernest_Courant</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
<li id="fn:7"><p>Beam focusing <a href="http://www-linux.gsi.de/~boine/vorlesung/skript/html/node9.html" target="_blank">http://www-linux.gsi.de/~boine/vorlesung/skript/html/node9.html</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li>
</ol>

Strong focusing open-in-new

Strong focusing