The appreciation of stochastic motion in particle accelerators Page: 2 of 12
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Some fifty years ago, when designers of particle accelerators began
to make extensive numerical calculations of particle orbits in proposed
machines, phenomena were often observed that would now be called
"chaotic". The term used in the accelerator community was "stochastic".
Such phenomena were observed both in horizontal and vertical particle
motions transverse to the design orbit, and in longitudinal motion along
the orbit. They occurred in certain cases when nonlinear forces were
Although stochastic behavior was familiar to accelerator designers,
such behavior generally occurs in regions of phase space outside the
stable region where accelerator design calls for particles to be. As a result
there is very little mention of stochastic behavior in the accelerator
literature. We are unaware of any paper devoted specifically to his topic.
The only paper we have found which mentions this topic in any detail is
one by the present authors written in 1956 as a Midwestern Universities
Research Organization, MURA report (Internal MURA Report 130, April
16, 1956), and published also in the Proceedings of the CERN Symposium
on High Energy Accelerators and Pion Physics, 1956 (Ref.1). Even that
paper devotes to the topic only about half a page out of 15.
II. Longitudinal Particle Motion
With the advent of alternating gradient (AG) focusing, and the
invention of fixed field alternating gradient (FFAG) focusing, it became
possible, for the first time, to seriously contemplate colliding beam
devices. What was required was a method of building up an intense beam
by means of radio frequency manipulation of particles. Thus attention
was focused upon the longitudinal motion of particles, work described in
1956.1 Most particularly, prior to that time, attention was directed upon
the small amplitude motion of particles being accelerated. Now, for the
first time, attention had to be paid to large amplitude motion and, even,
to the motion of particles not being accelerated.
In Ref 1, we treated the longitudinal motion of a particle under the
action of the radio-frequency accelerating voltages applied across an
accelerating gap. Thus we only had one accelerating gap per turn. This is
a very simple problem to calculate numerically, and with suitable
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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/m1/2/: accessed April 25, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.