1. 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

2. 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

3. Electron Collider Ring
Baseline ring circumference of m = 2 x m arcs + 2 x straights
Chromaticities : (x , x) = (-149 , -123)
Geometric horizontal emittance x = 14 nm-rad (uncoupled) and energy spread p/p = 5 GeV
Reduced-emittance ring (for nonlinear dynamics studies only) circumference of m = 2 x m arcs + 2 x 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 = 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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
128
Linear compensation + interleaved –I sextupole pairs for FF correction
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
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
236
Linear compensation + dedicated Jlab chromaticity compensation blocks (CCBs) in arcs for FF correction
±8.5,±18
±5,±7.3
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.

13. 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 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

14. 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%.

15. 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

16. Thank You for Your Attention !

17. Back Up

18. 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