Distortion functions

Author: Collins, T. L.
Published: United States : [publisher not identified], 1984
Springfield, Va.: National Technical Information Service, [approximately 1984]
Physical Description: microfiche : negative ; 11 x 15 cm

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Summary

We have a set of distortion functions which are a new form of solution to the old problem of describing the non-linear beam shape that repeats. They have an exact formal similarity to our usual orbit distortion calculation, and therefore have the nice property that a modest arithmetic effort will yield a precise value at one point in the ring and twice that effort will give values at all points. This latter property permits an easy evaluation of the second-order tune shift from sextupoles - both types - which is very important. The distortion is expanded in orders which here means the power of the multipole. There is no reason why one cannot extend the calculations to higher orders but from the numerical examples one can see that practically the first order is enough (except for tune shift). The first order does describe most of the distortion for marginally acceptable beams. Higher order effects do appear as small, closed resonances but there is often not much distinction between second and still higher orders. In any case the nature of the expansion (and the examples) makes clear that small first order is a necessary and sufficient condition for good beams. One possible exception are higher-order coupling terms, n nu/sub x/-n nu/sub y/, from sextupoles.

Report Numbers

DE85007511; FNAL-84/114

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NTIS collection.

Note

DOE contract number: AC03-76SF00515
OSTI Identifier 5937597
Research organization: Fermi National Accelerator Lab., Batavia, IL (USA).

View MARC record | catkey: 47350778

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Distortion functions

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