Beam Based Alignment of the SLC Final Focus Sextupoles*

The strong demagnification inherent in final focus systems requires local cancellation of the resulting chromaticity. Strong sextupole pairs separated by a -I transform are positioned x12 in betatron phase away from the Interaction Point (IP) in order to cancel chromatic aberrations primarily due to the final quadrupoles. Sextupole alignment is critical in order to provide orthogonal tuning of the chromaticity and, in the case of the SLC, to limit the third and higher order optical aberrations generated from misaligned and ‘nested’ horizontal and vertical sextupole pairs. Reported here is a novel technique for aligning the beam centroid to the sextupole centers, which uses measurements of the critically dependent parameter the beam size at the IP. Results for the SLC final focus sextupoles are presented, where a resolution of ~50 pm is achieved. I. MOTIVATION The motivation for achieving good static [l] sextupole alignment is actually two-fold in the SLC final focus. Tuning time is minimized by orthogonalizing chromaticity control with respect to IP beam waist adjustments Cp* ‘), dispersion control, and coupling correction. Furthermore, due to space requirements, the SLC final focus chromatic correction sections employ ‘nested’ horizontal and vertical sextupole pairs four per final focus [2]. The linear optics between the two sextupole pairs are designed to provide a -I transform to cancel geometric and chromatic dispersion aberrations. Misaligned sextupoles within the nested system generate skew and normal quadrupole fields which distort the -I transfcmn and so generate higher order optical aberrations which arc not all correctable. Therefore, it is critical to achieve static alignment of these sextupoles to within -200 l.tm for present SLC beam parameters. II. THE ALIGNMENT METHOD The scxtupole pairs are placed rr.Q in phase from the IP at points of large horizontal dispersion. Therefore, a horizontal sextupole offset will introduce a normal quadrupole field and generate horizontal IP dispersion and both horizontal and vertical waist shifts. A vertical offset will introduce a skew quadrupole field and generate vertical IP dispersion and coupling. The SLC final focus design provides orthogonal correction for each of these effects. By measuring the amount of IP waist, dispersion, and coupling change as a function of each sextupole strength, the horizontal and vertical sextupole * Work supported by Department of Energy contract DE-AC0376SF00515 offsets with respect to the final focus orbit are calculated. Alignment correction is implemented by closed orbit bumps with horizontal and vertical dipole corrector magnets within the tinal focus. A desirable quality of the technique is that the measurement olerances are consistent with the alignment goals if there are no measurable waist, dispersion, or coupling changes in the IP beam given significant sextupole strength changes, then the necessary alignment is achieved. For SLC, there are just two power supplies for the four sextupoles per tinal focus. The two X-sextupoles (horizontal chromaticity correction) are in series on one supply, while the Y-sextupoles are in series on a second supply. Fortunately, due to the -I transform between pairs, this is ideal the waist, dispersion, and coupling changes at the IP can be independently separated into symmetric and anti-symmetric components of sextupole pair misalignment in X and Y. Figure 1 illustrates the eight different observable misalignment components. The individual sextupole misalignments are simply linear combinations of these eight components. x-waist