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Stochastic Cooling of Particle Beams pp 5–34Cite as

Simplified Theory, Time-Domain Picture

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Part of the book series: Lecture Notes in Physics ((LNP,volume 866))

Abstract

The arrangement for cooling of the horizontal beam size is sketched in Fig. 2.1. Assume, for the moment, that there is only one particle circulating. Unavoidably, it will have been injected with some small error in position and angle with respect to the ideal orbit (centre of the vacuum chamber). As the focusing system continuously tries to restore the resultant deviation, the particle oscillates around the ideal orbit. The feedback system observes via antennae barycentre errors (transverse offsets or momentum deviations) of successive groups (or samples) of by-flying particles. Signals are sent to other antennae further downsream to correct the barycentre errors. Stochastic cooling works by correcting barycentre errors over many turns in the ring. High system bandwidths correspond to short samples, large statistical barycentre errors, and therefore fast cooling.

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Notes

  1. 1.

    The bandwidth/pulse length relation was introduced by Nyquist and independently by Küpfmüller in 1928. This theorem is closely-related to the more general sampling theorem of communication theory which states: If a function S(t) contains no frequencies higher than W cycles per second, it is completely described by its values S(mT s ) at sampling points spaced by Δt=T s =1/2W (i.e. taken at the ‘Nyquist rate’ 2W; see, for example, J. Betts [6, 7]).

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  1. CERN, Geneva, Switzerland

    Dieter Möhl

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  1. Dieter Möhl
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Möhl, D. (2013). Simplified Theory, Time-Domain Picture. In: Stochastic Cooling of Particle Beams. Lecture Notes in Physics, vol 866. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34979-9_2

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