1. ELIC Low Beta Optics with Chromatic Corrections Hisham Kamal Sayed 1,2 Alex Bogacz 1 1 Jefferson Lab 2 Old Dominion University

2. Hisham K. Sayed EIC Meeting Hampton University 2008 2 Chromaticity effects Chromaticity is the derivative of the betatron tunes versus fractional momentum offset If chromaticity & momentum spread become large enough that the betatron tunes overlap a nonlinear resonance  particle loss Δp/p >0 Δp/p=0 Δp/p<0 quadrupole Δp/p >0 Δp/p=0 Δp/p<0 quadrup ole Sextupo les

3. Hisham K. Sayed EIC Meeting Hampton University 2008 3 ELIC have very large values of β max (~ 3/32 km for electron ring) at the ultra strong final focus quadrupoles  high sensitivity to the misalignments and field errors. Low β* (~ 5/5 mm for electron ring) & small momentum compaction  huge chromatic aberrations and large momentum acceptance. Why chromaticity correction is important for ELIC? Effect of chromaticity and momentum offset on beta functions around IR’d Beta x,y

4. Hisham K. Sayed EIC Meeting Hampton University 2008 4 The final focus chromatic correction system Pairs of sextupoles. Sextupoles in each pair are placed at –I (minus identity transformation in transverse phase space) from each other  the resulting adverse spherical aberrations induced by the sextupoles are cancelled. There must be dispersion at the sextupoles  the sextupole strengths are at a minimum. Dispersion needs to be generated around the IR and terminated at the matching section QdQd QfQf S` d S`` d S` f S`` f

5. Hisham K. Sayed EIC Meeting Hampton University 2008 5 IP Matching Two IR’s for ELIC Electron Ring IP Matching Quadrupoles

6. Hisham K. Sayed EIC Meeting Hampton University 2008 6 IR Dispersion wave and 1.2 o degrees chicane with vertical crossing Dispersion wave generated and confined with 4 vertical dipoles Dispersion is zero at IP Dipole parameters L[cm]=110 B[kG]=4.5 IP Dipoles

7. Hisham K. Sayed EIC Meeting Hampton University 2008 7 Vertical layout of the electron IR IP Longitudinal direction (m) Vertical direction (cm) 20 m50 m

8. Hisham K. Sayed EIC Meeting Hampton University 2008 8 β Chromaticity correction with sextupoles β- functions around the interaction region, the green arrows represent the sextupoles pairs. The phase advance, showing the –I transformation between the sextupoles pairs Vertical dispersion Horizontal dispersion

9. Hisham K. Sayed EIC Meeting Hampton University 2008 9 Phase space in vertical plane before and after applying the correction scheme Initial phase space phase space after two pass through 2 IR’s No correction phase space after two pass through 2 IR’s after correction Vertical plane Δp/p~0.0006 Y Y`

10. Hisham K. Sayed EIC Meeting Hampton University 2008 10 The tunes versus the momentum offset Tune variation due to passing through two IR’s for horizontal and vertical directions Target  The tunes should show a reduced nonlinear behavior with the change in momentum offset

11. Hisham K. Sayed EIC Meeting Hampton University 2008 11 Momentum compaction versus momentum offset Momentum compaction variation due to passing through two IR’s for horizontal and vertical directions Target  smaller change in compaction factor with the change in the momentum offset

12. Hisham K. Sayed EIC Meeting Hampton University 2008 12 The chromaticity versus the momentum offset Chromaticity variation due to passing through two IR’s for horizontal and vertical directions Target  fixed chromaticity for different Dp/p

13. Hisham K. Sayed EIC Meeting Hampton University 2008 13 Conclusion & Future Work A novel design for the interaction region and matching section for EIC electron ring presented (A. Bogacz). A scheme for correcting inherent lattice chromaticity was implemented into the design The scheme was verified via multi-particle tracking simulation through the lattice using a matrix based optics code OptiM. Presented results show a proof-of-principle for an effective chromaticity correction scheme. Further simulations and optimization will be carried out with more robust tracking package ELEGANT. Dynamic aperture studies will be carried out. Considering adding octupoles to correct higher order effects and spherical aberrations from sextupoles (S. Derbenev)