Update on study of chromaticity correction schemes for ion ring Y. Nosochkov 02-12-2015

02/12/2015 Goals Compare performance of the present chromaticity correction block (CCB) with other CCB options Consider an alternative CCB design with –I sextupole pairs As an additional option, consider 60 and 90 degree arc cells Keep the ring optics unchanged except CCB and arcs Optimize CCB sextupole strengths and phase positions for larger chromatic bandwidth and larger dynamic aperture (Min-Huey, in progress) As a starting point, use thin sextupoles, and thin phase trombones for phase adjustment of the CCB sextupoles No adjustment of betatron tune at this point (future study)

Ring with the original CCB (Oct 2014) 02/12/2015 Ring with the original CCB (Oct 2014) Q=[25.79, 26.27] x =[-224, -233] IP1 CCB CCB IP2 Dm/2p (x,y) bpeak to IP [6.35, 5.66] [2.26, 3.53] Optimal Dm/2p should be near 1/4+n/2

Add thin sextupoles to the original lattice 02/12/2015 Add thin sextupoles to the original lattice CCB 60° arc cells 12 SD, 12 SF per arc IP sext nearly –I between two X-sextupoles, single Y-sextupole

Alternative CCB based on –I sextupole pairs 02/12/2015 Alternative CCB based on –I sextupole pairs Two –I pairs of sextupoles for X and Y correction on each side of IP to compensate sextupole non-linear geometric aberrations. Make large ratio of X and Y beta at the sextupoles for orthogonal chromaticity correction. Place sextupoles in phase with the Final Focus quadrupoles (separated by np) to compensate 1st order chromatic beta perturbation (W-function) from the FF. This will help correcting the 2nd order term of chromatic tune shift. Small optimization of phase at the sextupoles can also reduce the 3rd order term of chromatic tune shift. Drawback: longer CCB as compared to the original.

CCB with –I sextupole pairs and 60° arc cells 02/12/2015 CCB with –I sextupole pairs and 60° arc cells 60° arc cells 6 SD, 6 SF per arc IP sext -I -I Lower dispersion at the sextupoles compared to original Long CCB

Ring with -I pairs CCB and 60° arcs 02/12/2015 Ring with -I pairs CCB and 60° arcs Q=[28.41, 27.86] x =[-235, -280] CCB Dm/2p (x,y) bpeak to IP [7.75, 5.25] [3.75, 2.75]

CCB with –I sextupole pairs and 90° arc cells 02/12/2015 CCB with –I sextupole pairs and 90° arc cells 90° arc cells -I -I 8 SD, 8 SF per arc Lower dispersion at the sextupoles compared to original IP sext IP sext Long CCB

Ring with -I pairs CCB and 90° arcs 02/12/2015 Ring with -I pairs CCB and 90° arcs Q=[30.62, 28.74] x =[-235, -279] CCB Dm/2p (x,y) bpeak to IP [7.75, 4.75] [3.75, 2.75]

Preliminary comparison of chromaticity correction – W-function 02/12/2015 Preliminary comparison of chromaticity correction – W-function original W-function (~db/(bd)) is better corrected at IP in the modified lattices due to more optimal phase advance between CCB sextupoles and IP -I, 60° arcs -I, 90° arcs

02/12/2015 Chromatic tune Wider bandwidth in the modified lattices due to more optimal phase advance at CCB. Bandwidth is limited by the half-integer resonances. original -I, 60° arcs -I, 90° arcs

02/12/2015 Chromatic beta at IP Smaller chromatic variation of beta functions in the modified lattices due to better suppression of W-functions at IP. original -I, 60° arcs -I, 90° arcs

02/12/2015 Initial setting of sextupole strengths based on MAD (before further optimization) K-values assuming L=0.3 m sextupoles, but based on thin sextupole approximation CCB Original -I with 60° arcs -I with 90° arcs SF 8.511 15.007 7.938 SD -49.531 -19.187 -25.042 SFIPU 3.841 3.167 4.273 SDIPU 4.035 -5.527 -5.602 SFIPD 0.969 8.297 9.549 SDIPD -1.993 -10.747 -10.223 Large difference between the original and –I schemes is likely due to difference in the IP sextupole phase positions. These settings may change after further optimization.

02/12/2015 Short summary Optimizing phase positions of the CCB sextupoles improves the chromaticity correction (bandwidth and chromatic beta variation) In order to compare “apple-to-apple” with the original CCB lattice, the latter should be adjusted for an optimal phase at the CCB sextupoles (Min-Huey, in progress) Further optimization of sextupole strengths and phase advance is in progress including the impact on dynamic aperture (Min-Huey) Optimizing the betatron tune can further improve the chromatic performance.