The appreciation of stochastic motion in particle accelerators Page: 1 of 12
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The Appreciation of Stochastic Motion in Particle
University of Wisconsin-Madison, Madison, Wisconsin
Lawrence Berkeley Laboratory, Berkeley, California
August 3, 2003
A description is given of the analytic and numerical work, performed from
July 1955 through August 1956, so as to develop, and then study, the
process of making intense proton beams, suitable for colliding beams. It is
shown how this investigation led, in a most natural way, to the
realization that stochasticity can arise in a simple Hamiltonian system.
Furthermore, the criterion for the onset of stochasticity was understood,
and carefully studied, in two different situations. The first situation was
the proposed (and subsequently used) "stacking process" for developing
an intense beam, where stochasticity occurs as additional particles are
added to the intense circulating beam. The second situation occurs when
one seeks to develop "stochastic accelerators" in which particles are
accelerated (continuously) by a collection of radio frequency systems. It
was in the last connection that the well-known criterion for stochasticity,
resonance overlap, was obtained.
* Work supported by the Director, Office of Energy Research, Office of High Energy and Nuclear
Physics, Division of High Energy Physics of the US Department of Energy, under Contract No. DE-
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Symon, Keith & Sessler, Andrew. The appreciation of stochastic motion in particle accelerators, article, August 3, 2003; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc779420/m1/1/: accessed April 23, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.