First Look at Nonlinear Dynamics in the Electron Collider Ring Fanglei Lin, Min-Huey Wang (SLAC), Yuri M. Nosochkov (SLAC), Vasiliy S. Morozov, Guohui Wei, Yuhong Zhang JLEIC Collaboration Meeting Spring 2016 March 29-31, 2016 F. Lin

Outline Introduction of the electron ring for the nonlinear dynamics studies Primary results (@ 5 GeV) for various compensation schemes Linear chromaticity compensation only Linear chromaticity compensation + interleaved –I sextupole pairs for final focusing correction Linear chromaticity compensation + non-interleaved –I sextupole pairs and strength & phase adjustments for final focusing correction Linear chromaticity compensation + non-interleaved –I sextupole pairs and strength & phase adjustments for final focusing correction + reducing beta functions at –I pairs to lower the emittance growth Linear chromaticity compensation + dedicated Jlab chromaticity compensation blocks (CCBs) in arcs for final focusing correction Electron collider ring design options for control of the emittance Conclusion and Outlook

Electron Collider Ring Baseline ring circumference of 2154.28 m = 2 x 754.84 m arcs + 2 x 322.3 straights Chromaticities : (x , x) = (-149 , -123) Geometric horizontal emittance x = 14 nm-rad (uncoupled) and energy spread p/p = 4.5e-4 @ 5 GeV Reduced-emittance ring (for nonlinear dynamics studies only) circumference of 2185.54 m = 2 x 811.84 m arcs + 2 x 280.92 straights Optimized matching and spin rotator sections, replaced CCB w/ FODO cells, reduced beta functions in BES, reduced number of straight FODO cells and phase advance Chromaticities: (H,V) = (-113, -120) Geometric horizontal emittance x = 9.5 nm-rad (uncoupled) and energy spread p/p = 4.5e-4 @ 5 GeV Note that chromaticities and emittances may vary in different chromaticity compensation schemes e- R=155m RF Spin rotator CCB Arc, 261.7 81.7 Forward e- detection IP Tune trombone & Straight FODOs Future 2nd IP

Chromaticity Compensation Scheme I Compensation scheme I (v1) 2 sextupole families for linear chromaticity correction only, 30 cells in each arc (SR solenoids off) No local final focusing chromatic correct (large beam smear at IP) Emittance and chromaticities do not change Simulation results: Tune foot print Frequency map Dynamic aperture Amplitude dependent tune ±20σx

Chromaticity Compensation Scheme II Compensation scheme II (v1a) 2 sextupole families for linear chromaticity correction, 20 cells in each arc (SR solenoids off) 2 –I interleaved pairs in each X & Y in each arc for final focusing chromatic correction, phase advances were adjusted to 90o from –I sextupoles to IP using thin trombones (TT) Emittance and chromaticities do not change Simulation results Tune foot print Frequency map Dynamic aperture Amplitude dependent tune ±20σx

Chromaticity Compensation Scheme III Compensation scheme III (v1b3) 2 sextupole families for linear chromaticity correction, 20 cells in each arc (SR solenoids off) One –I non-interleaved pairs in each X & Y in each arc for final focusing chromatic correction, -I sextupole strengths and phases advances were adjusted to improve the chromatic tune and * using thin trombones Tunes were also adjusted using a thin trombone Chromaticities increase from (-113, -120) to (-127,-145) Emittance increases from 9.5 to 20.2 nm-rad Tune foot print Frequency map Dynamic aperture Amplitude dependent tune ±15σx

Chromaticity Compensation Scheme III Compensation scheme III (v1b3) 2 sextupole families for linear chromaticity correction, 20 cells in each arc (SR solenoids on) One –I non-interleaved pairs in each X & Y in each arc for final focusing chromatic correction, -I sextupole strengths and phases advances were adjusted to improve the chromatic tune and * using thin trombones Tunes were also adjusted using a thin trombone Chromaticities increase from (-113, -120) to (-127,-145) Emittance increases from 9.5 to 20.2 nm-rad Tune foot print Frequency map Dynamic aperture Amplitude dependent tune ±15σx

Chromaticity Compensation Scheme IV Compensation scheme IV (v1d2) 2 sextupole families for linear chromaticity correction, 20 cells in each arc (SR solenoids off) One –I non-interleaved pairs in each X & Y in each arc for final focusing chromatic correction, -I sextupole strengths and phases advances were adjusted to improve the chromatic tune and * using thin trombones Tunes were also adjusted using a thin trombone Reduce beta functions at the –I pairs to lower the emittance growth Chromaticities increase from (-113, -120) to (-121, -133) Emittance increase from 9.5 to 16.2 nm-rad Tune foot print Frequency map Dynamic aperture Amplitude dependent tune ±17σx

Chromaticity Compensation Scheme V 2 sextupole families for linear chromaticity correction, 30 cells in each arc (SR solenoids on) One chromaticity compensation block (CCB) in each arc for final focusing chromatic correction, phase advances were adjusted from –I sextupoles to IP using thin trombones (TT) Tunes were also adjusted using a thin trombone Chromaticities increase from (-113, -120) to (-132, -152) Emittance increase from 9.5 to 16.9 nm-rad (can be further reduced by adjusting beta functions) Dynamic aperture ±8.5σx

Chromatic * Only linear chrom sext Interleaved distributed –I pairs Compact CCB Non-interleaved –I pairs with lower emittance Best correction with compact CCB and non-interleaved –I pairs. From Y. Nosochkov

Luminosity vs. Chromatic * Luminosity formula Integrated Luminosity ratio considering chromatic * due to the momentum spread here Consider Assume ion chromatic * dose not change too much

Summary Table Compensation Scheme x/x,0 x/σx , y/σy (p/p)/σp/p L/L0 Touschek lifetime (h) On momentum Off momentum (at 0.4%) Linear chromaticity compensation only 1 ±20,±48 0,0 -6.7 , +6.7 0.99498 128 Linear compensation + interleaved –I sextupole pairs for FF correction 1.00079 Linear compensation + non-interleaved –I sextupole pairs and strength & phase adjustments for FF correction 2.1 ±15,±40 ±4.5,±10 -8.9 , +8.9 1.00235 308 Linear compensation + non-interleaved –I sextupole pairs and strength & phase adjustments for FF correction + beta function control at –I pairs to lower emittance growth 1.7 ±17,±41 ±5,±10 1.00075 236 Linear compensation + dedicated Jlab chromaticity compensation blocks (CCBs) in arcs for FF correction ±8.5,±18 ±5,±7.3 1.00245 240 x,0 is the reduced uncoupled horizontal emittance 9.5nm-rad, not the emittance in the baseline design 14nm-rad. Touschek lifetime is calculated from MAD-X and will be benchmarked with ELEGANT or other codes.

Approaches of Reducing Emittance All following options have been investigated Optimizing of sections, such as matching section, spin rotator, etc., to reduce the emittance contribution (30%) Pros: do not change the optics of the rest of the ring, except some particular sections Cons: ~110m additional space and 16 quads are needed Adding (dipole) damping wigglers (50% @ 5 GeV) Pros: do not change the baseline design, fast damping Cons: need wigglers, more radiation power, larger energy spread (a factor of 2), high RF peak power if keep the same bunch length, not suitable at higher energies, may affect the polarization lifetime Offsetting the beam in quads (~ 7 to 8 mm) in arcs (48%) Pros: do not change the baseline design Cons: larger energy spread (a factor of 2), longer (maybe) bunch length, have to center the sextupoles New magnets (instead of PEP-II magnets) ring but still FODO cell arcs (50%) Pros: dipole has no sagitta issue with a small bending angle Cons: all new magnets, large chromaticities, strong sextupoles for chromaticity compensation due to small dispersion Different types of arc cell, such as DBA, TME (> 50%) Pros: much smaller emittance comparing to the FODO cell Cons: more quads, stronger quads, larger ring (possible), large chromaticities, chromaticity compensation scheme Need combine non-linear dynamic studies

Coupled Emittance In an electron storage ring without vertical bending and coupling, the natural horizontal emittance can be calculated by and the natural vertical emittance usually is a few orders of magnitude smaller than the horizontal one. A coupling effect can be introduced to a flat electron ring to obtain a non-flat beam. Assume the emittance coupling ratio k= y/x , then Here x,0 is the natural horizontal emittance. They satisfy x + y =x,0, and it has x/x,0=1/(1+k). JLEIC requires non-flat electron beams with k=y/x=1:5. Then x/x,0=0.83. I used the uncoupled natural horizontal emittance x,0 for the calculation of horizontal beam size, and x,0/5 for the calculation of vertical beam size. The beam sizes are overestimated by ~10%.

Conclusion and Outlook We have initiated non-linear beam dynamic studies for the JLEIC electron collider ring. Primary simulation results at 5 GeV are presented for a few chromaticity compensation schemes. Luminosity vs. chromatic * and Touschek lifetime were calculated (need further check). We consider a possible growth of emittance in the electron ring due to compensation of non-linear dynamics issues. We consider that non-linear dynamics studies should be combined with optimization of electron ring design for reducing the emittance. Outlook Continue and finish studies of various compensation schemes Determine the best compensation scheme for the electron ring considering control of emittance growth Study effects of alignment and field errors and orbit correction scheme

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Correction of b* chromatic variation in electron ring Only linear chrom sext Interleaved distributed –I pairs Compact CCB Non-interleaved –I pairs with lower emittance Best correction with compact CCB and non-interleaved –I pairs. From Y. Nosochkov