1. Update on study of chromaticity correction schemes for ion ring
Y. Nosochkov

2. 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)

3. 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

4. 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

5. 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.

6. 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

7. 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]

8. 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

9. 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]

10. 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

11. 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

12. 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

13. 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
SFIPU
3.841
3.167
4.273
SDIPU
4.035
-5.527
-5.602
SFIPD
0.969
8.297
9.549
SDIPD
-1.993
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.

14. 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.