Non-linear Dynamics

Le résumé fourni par la source

In most of Chapter 3 we discussed accelerator components that were represented by matrices. There, we also found the focal length of quadrupoles to depend on the momentum offset and cause the chromaticity to become non-zero. This effect becomes more important, the stronger the quadrupoles are. Therefore, in most accelerators, the chromaticity is corrected by adjusting sextupoles that are installed at locations with non-zero dispersion. This was described in detail in Section 8.5.4 . We found that compensating the chromaticity depends on the product of the integrated sextupole strength https://www.w3.org/1998/Math/MathML" display="inline"> k 2 L https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003463283/50980182-d9b8-447a-af84-943d2668dd44/content/math11_1.tif "/> and dispersion D x and correcting a large chromaticity requires strong sextupoles. This is particularly relevant for linear colliders with strong quadrupoles adjacent to the interaction point where the beta functions are extremely large. A second example is modern synchrotron light sources with their strongly focusing quadrupoles to keep the beta functions and dispersion small in order to minimize the emittance. Since the dispersion is small, the sextupoles must be very strong. But these very strong sextupoles do not only compensate the chromaticity, they also give non-linear kicks to particles with the correct momentum and thus distort their transverse motion, our topic for this chapter.

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