1. JLEIC Electron Collider Ring Design and Polarization
Fanglei Lin
JLEIC Collaboration Meeting Fall 2016
October 5-7, 2016
F. Lin

2. Outline Electron collider design goal
Electron collider ring baseline design
Electron collider ring baseline design optimization
Electron collider ring new design options
Electron polarization design and simulation

3. Electron Collider Design Goal
Electron beam parameters
3-10 GeV energy
3A beam current up to 6-7 GeV
~1cm bunch length
small emittance
< 10MW total synchrotron radiation power
70% or above polarization
Longitudinal polarization at collision points with a long polarization lifetime
Forward electron detection
Up to two detectors
Provision for correction of beam nonlinearity

4. CEBAF - Full Energy Injector
CEBAF fixed target program
5-pass recirculating SRF linac
Exciting science program beyond 2025
Can be operated concurrently with the JLEIC
e- collider ring
Wien Filters and solenoids provide vertically polarized electron beam to the JLEIC.
CEBAF will provide for JLEIC
Up to 12 GeV electron beam
High repetition rate (up to 1497 MHz)
High polarization (>85%)
Good beam quality
See Jiquan Guo’s talk: Electron injection scheme from CEBAF to the collide ring

5. Transfer Line Design requirements Realization
No significant emittance growth
Room for matching and diagnostic region, compression chicane if needed, a spreader step if needed
PEP-II magnets (cost)
Realization
Utilizes PEP-II LER 156 dipoles and 68 quadrupoles
Dipoles are grouped six as one in FODO cells with 120 phase advance
Total length of transfer line is meters
Injection scheme --- PEP-II-like design
Dispersion free injection insertion
Septum + DC + RF kickers
Vertical injection avoiding parasitic interaction with circulating
ion beams in the horizontal plane, simplifying the problem of
masking the detector from particle loss during injection
Courtesy of Y. Roblin

6. Electron Ring Baseline Design Layout
Circumference of m = 2 x m arcs + 2 x straights
Figure-8 crossing angle 81.7 e-
R=155m RF
Spin rotator
CCB
Arc, 261.7
81.7
Forward e- detection IP
Tune trombone & Straight FODOs
Future 2nd IP
310 m
784 m

7. Normal Arc FODO Cell
Complete FODO (Each arc has 34 such normal FODO cell)
Length 15.2 m (arc bending radius 155 m)
2 dipoles + 2 quadrupoles + 2 sextupoles
108/108 x/y betatron phase advance
Dipoles
Magnetic/physical length 5.4/5.68 m
Bending angle 48.9 mrad (2.8), bending radius m
GeV
Sagitta 3.3 cm
Quadrupoles
Magnetic/physical length 0.56/0.62 m
-11.6 and 12.8 T/m field 10 GeV
0.58 and mm radius
Sextupoles
Magnetic/physical length 0.25/0.31 m
-176 and 88 T/m2 field 10 GeV
for chromaticity compensation only in two arcs
(strengths will be determined in DA simulations)
BPMs and Correctors
Physical length 0.05 and 0.3 m

8. Baseline Optics Parameters
Electron beam momentum
GeV/c 10
Circumference m
Arc’s net bend
deg
261.7
Straights’ crossing angle
81.7
Arc/straight length
754.84/322.3
Beta stars at IP *x,y cm
10/2
Detector space
-3 / 3.2
Maximum horizontal / vertical  functions x,y
949/692
Maximum horizontal / vertical dispersion Dx,y
1.9 / 0
Horizontal / vertical betatron tunes x,y
45.(89) / 43.(61)
Horizontal / vertical chromaticitiesx,y
-149 / -123
Momentum compaction factor 
2.2 10-3
Transition energy tr
21.6
Hor./ver. emittance x,y (normalized/un-normalized)
µm rad
1093 / 219 (0.056/0.011)

9. Synchrotron Radiation Parameters
Beam current up to 3 A at 6.95 GeV
Synchrotron radiation power is under 10 MW at high energies
Beam energy
GeV 3 5
6.95
9.3 10
Beam current A
1.4
0.95
0.71
Total SR power MW
0.16
2.65
Linear SR power density (arcs)
kW/m
2.63
9.9
Energy loss per turn
MeV
0.11
0.88
3.3
10.6
14.1
Energy spread
10-3
0.27
0.46
0.66
0.82
0.91
Transverse damping time ms
376 81 26 14
Longitudinal damping time
188 41 13 7
Normalized Emittance um 30
137
425
797
1093

10. Summary of Baseline Design
2.2km electron collider ring was design reuse of PEP-II HER magnets mostly
Two arcs are composed of 15.2m long FODO cells, dispersion suppression sections and spin rotators
FODO cell and dispersion suppression (PEP-II magnets)
dipole 5.4m, bending angle 2.8, bending radius 110.5m, sagitta 3.3 cm, GeV, can reach GeV with only ~0.2% saturation
Quadrupole 0.56m, field gradient <13 10 GeV with saturation <0.4%, gradient ~ GeV with saturation up to ~6%
108/108 x/y betatron phase advance in FODO cell
Spin rotators have new dipoles, solenoids and quads 10 GeV).
Straight FODO cells, tune trombone and matching sections use PEP-II 0.73m-long PEP-II quads and some new quads
Chromaticity compensation block, RF sections and detector region use new dipoles and quads.
Arcs contribute ~90% emittance and ~30-40% chromaticities.

11. 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, 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: small dipole bending angle results in small emittance and no sagitta issue
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: possible more quads, stronger quads, possible larger ring, large chromaticities, efficient chromaticity compensation scheme
Need combine non-linear dynamic studies

12. Optimized Optics of Matching Section
Baseline design
Regular arc FODO cell: each dipole bending angle , phase advance
Matching section: each dipole bending angle
Optimized design: “missing magnet”-like dispersion suppressor + beta function matching
Matching section dipole bending angles
Regular arc bending angle
8 extra dipoles (4 FODO cells) are needed
Regular arc FODO cell
Spin rotator
Matching section
Baseline
Regular arc FODO cell
Spin rotator
New

13. Optimized Optics of Spin Rotator
Baseline design
Lattice in the two dipole sets was not optimized to have a small emittance contribution.
Optimized design
Lattice in the two dipole sets is optimized to a DBA-like optics, which has a smaller emittance than that in the baseline design.
Baseline
Dipole set
2nd sol. + decoupling quads
1st sol. + decoupling quads
New
Dipole set
2nd sol. + decoupling quads
1st sol. + decoupling quads

14. Normalized Horizontal Emittance (m)
10 GeV
Section
Normalized Horizontal Emittance (m)
Baseline design
Optimized design *
Regular FODO cells in two arcs
476
569
Matching sections between FODO cells and spin rotators
389 6
Spin rotators
119 84
Straight with IP (CCB + Chicane) 85
Straight without IP
Total
1068
745
Extra space needed (m)
111

15. Summary of Optimized Baseline Design
Optimized electron collider ring with reduced-emittance ring (for nonlinear dynamics studies) circumference of m=2x811.84m arcs + 2x280.92m straights
Overall geometry of the ring does not change significantly
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)
In the baseline design: chromaticities: (H,V) = (-149 , -123)
Geometric horizontal emittance x = GeV, energy spread p/p = 5 GeV
In the baseline design: geometric horizontal emittances x = 14 5 GeV, energy spread p/p = 5 GeV
Note that chromaticities and emittances may vary in different chromaticity compensation schemes
See Yuri Nosochkov’s talk: Electron Collider Ring Chromatic Compensation and Dynamic Aperture

16. IP Region Optics Optimization
Baseline Design
Optimized Design IP e-
forward e-
detection region
FFQs
Compton polarimetry region
x(m), y(m)
Dx(m)
x(m), y(m)
Dx(m) e-
forward e-
detection region
FFQs
Compton polarimetry region IP
Shorter up- and downstream detector space: from (-3, 3.2)m down to (-2.6, 1.6)m
Smaller beta functions at FFQs, resulting in smaller beam sizes
Softer bends in the middle of chicane to reduce the synchrotron background to the Compton polarimetry detectors

17. New Electron Collider Ring Option I
FODO arc cell design using new magnets, same bending radius in the arc cells as the baseline design
Complete electron collider ring with circumference of m = 2 x m arcs + 2 x m straights

18. New Magnet FODO Arc Cell
Arc FODO cell (Each arc has 54 such normal FODO cells)
Length 11.4 m (half of ion ring arc cell)
arc bending radius m (same as in the baseline)
108/108 x/y betatron phase advance
Dipole
Magnetic/physical length 3.6/3.88 m
Bending angle 36.7 mrad (2.1), bending radius 98.2 m
GeV 12 GeV)
Sagitta 1.65 cm
Quadrupoles
Magnetic/physical length 0.56/0.62 m
17.5 T/m field 10 GeV (21 12 GeV)
mm 10 GeV ( GeV)
Sextupoles
Magnetic/physical length 0.25/0.31 m
-624 and 262 T/m2 field 10 GeV for chromaticity compensation
of the whole ring
1.2 T and mm 10 GeV (1.4 T and GeV)
BPMs and Correctors
Physical length 0.05 and 0.3 m
New
Baseline

19. Comparison of e-Ring Parameters
Baseline design (FODO arc cell) w/ PEP-II magnets
Optimized baseline design (FODO arc cell) w/ PEP-II magnets
New design (FODO arc cell) w/ new magnets
Ring circumference m
2154
2186
2182
Bending angle per arc / figure-8 crossing angle
deg
261.7 / 81.7
Beta stars at IP *x,y cm
10 / 2
Hor. / ver. chromaticities x,y
-149 / -123
-113 / -120
-127 / -140
Momentum compaction factor 
10-3
2.2
1.9
1.1 (reduce bunch length or V_peak )
Energy 5 and 10 GeV
10-4
4.6 / 9.1
4.5 / 9.0
4.6 / 9.3
Normalized 5 and 10 GeV
rad
137 / 1093
93 / 740
54 / 433
Hori. beam sizes at 5 and 10 GeV m
38 / 75
31 / 62
24 / 47
Energy loss per 5 and 10 GeV
MeV
0.88 / 14.1
0.82 / 13.1
0.89 / 14.4
Total SR 5 and 10 GeV MW
2.7 / 10
2.5 / 9.2
2.7 / 10.2
Arc FODO cell length
15.2 (PEP-II cell length)
11.4 (half of ion arc cell)
dipole length / sagitta
m / cm
5.4 / 3.3
3.6 / 1.65
dipole bending angle / radius
deg / m
2.8 / 110.5
2.1 / 98.2
quad 10 & 12 GeV
m / T/m
0.56 / 13 / 15.6
0.56 / 17.5 / 21
cells per arc 42 44 58

20. New Electron Collider Ring Option II
Theoretical-Minimum-Emittance(TME)-like arc cell design using new magnets, same bending radius in the arc cells as the baseline design
Complete electron collider ring with circumference of m = 2 x m arcs + 2 x m straights

21. New Magnet TME-like Arc Cell
Arc TME-like cell (Each arc has 26 such normal TME-like cells)
Length 22.8 m (same as ion ring arc cell)
arc bending radius m (same as in the baseline)
270/90 x/y betatron phase advance
Dipole
Magnetic/physical length 4.0/4.28 m
Bending angle 36.7 mrad (2.1), bending radius m
GeV 12 GeV)
Sagitta 1.83 cm
Quadrupoles
Magnetic/physical length 0.56/0.62 and 1.0/1.06 m
20 T/m field 10 GeV (24 12 GeV)
mm 10 GeV ( GeV)
Sextupoles
Magnetic/physical length 0.25/0.31 m
400 and 604 T/m2 field 10 GeV for chromaticity compensation of the whole ring
0.72 T and mm 10 GeV (0.86 T and GeV)
BPMs and Correctors
Physical length 0.05 and 0.25 m

22. Comparison of e-Ring Parameters
Optimized baseline design (FODO arc cell) w/ PEP-II magnets
New design (FODO arc cell) w/ new magnets
New design (TME arc cell) w/ new magnets
Ring circumference m
2186
2182
2167
Bending angle per arc / figure-8 crossing angle
deg
261.7 / 81.7
Beta stars at IP *x,y cm
10 / 2
Hor. / ver. chromaticities x,y
-113 / -120
-127 / -140
-152 / -150
Momentum compaction factor 
10-3
1.9
1.1 (reduce bunch length or V_peak)
0.5 (reduce bunch length or V_peak)
Energy 5 and 10 GeV
10-4
4.5 / 9.0
4.6 / 9.3
4.5 / 9.1
Normalized 5 and 10 GeV
rad
93 / 740
54 / 433
31 / 247
Hori. beam sizes at 5 and 10 GeV m
31 / 62
24 / 47
18 / 36
Energy loss per 5 and 10 GeV
MeV
0.82 / 13.1
0.89 / 14.4
0.89 / 13.4
Total SR 5 and 10 GeV MW
2.5 / 9.2
2.7 / 10.2
2.5 / 9.5
Arc TME-like cell length
15.2 (PEP-II cell length)
11.4 (half of ion arc cell)
22.8 (ion ring arc cell)
dipole length / sagitta
m / cm
5.4 / 3.3
3.6 / 1.65
4.0 / 1.83
dipole bending angle / radius
deg / m
2.8 / 110.5
2.1 / 98.2
2.1 / 109.1
quad 10 & 12 GeV
m / T/m
0.56 / 13 / 15.6
0.56 / 17.5 / 21
0.56, 1.0 / 20 / 24
cells per arc 44 58 28

23. Electron Polarization Requirements
Major JLEIC electron complex components
Polarization design requirements
Electron polarization of 70% or above with sufficiently long lifetime
Longitudinal polarization at IP(s)
Spin flipping
electron collider ring
3 – 10 GeV/c
CEBAF

24. Electron Polarization Strategies
Highly vertically polarized electron beams are injected from CEBAF
avoid spin decoherence, simplify spin transport from CEBAF to MEIC, alleviate the detector background
Polarization is designed to be vertical in the JLEIC arc to avoid spin diffusion and longitudinal at collision points using spin rotators
Universal spin rotator (fixed orbit) rotates the electron polarization from 3 to 12GeV
Desired spin flipping is implemented by changing the source polarization
Polarization configuration with figure-8 geometry removes electron spin tune energy dependence
Significantly suppress the synchrotron sideband resonance
Continuous injection of electron bunch trains from the CEBAF is considered to
preserve and/or replenish the electron polarization, especially at higher energies
Spin matching in some key regions is considered to further improve polarization lifetime
Compton polarimeter is considered to measure the electron polarization
Two long opposite polarized bunch trains (instead of alternate polarization between bunches) simplify the Compton polarimetry …
Empty buckets
2.1 ns
476 MHz
Polarization (Up)
Polarization (Down)
bunch train & polarization pattern (in arcs)

25. Universal Spin Rotator (USR)
Schematic drawing of USR
Solenoid decoupling & Lattice function IP
Arc
Half
Solenoid
Quad. Decoupling Insert
P. Chevtsov et al., Jlab-TN
Parameters of USR for JLEIC
Dipole set
2nd sol. + decoup. quads
1st sol. + decoup. quads E
Solenoid 1
Arc Dipole 1
Solenoid 2
Arc Dipole 2
Spin Rotation
BDL
GeV
rad
T·m 3
π/2
15.7
π/3
π/6
4.5
π/4
11.8
23.6 6
0.62
12.3
2π/3
1.91
38.2 9 π
62.8 12
24.6
4π/3
76.4

26. Electron Polarization Configuration
Unchanged polarization in two arcs by having opposite solenoid field directions in two spin rotators in the same long straight section
figure-8 removes spin tune energy dependence and reduces the synchrotron sideband resonances
First order spin perturbation in the solenoids for off-momentum particles vanishes with opposite longitudinal solenoid fields in the pair of spin rotators in the same long straight
Sokolov-Ternov self-polarization process has a net depolarization effect, but the polarization lifetime is still large with highly-polarized injected electron beams
Two polarization states coexist in the collider ring and have the same polarization degradation IP
Spin Rotator e-
Magnetic field
Polarization
Polarization orientation
Arc IP
Solenoid field

27. Polarization Simulation
Spin tune 5 GeV
Longitudinal field spin tuning solenoid is inserted in the straight where the polarization is longitudinal.
500 particles Monte-Carlo simulation using SLICKTRACK (developed by D.P. Barber).
Main field errors, quads vertical misalignment and dipole role, are introduced.
Preliminary spin tracking
10 particles Monte-Carlo simulation using Zgoubi (developed by F. Meot, BNL).
Initial polarization is longitudinal.
Perfect machine, no errors.
Optimum Spin Tune with a 3Tm solenoid
Figure-8 JLEIC collider ring has no synchrotron sideband resonances !
Nasty, nasty sidebands !
Oscillation of spin components is due to the misaligned initial spin direction and invariant spin field.
This can be experimentally calibrated by adjusting the spin rotator settings.

28. Continuous Injection
Continuous injection (or top-off injection or trickle injection) has been applied in many modern electron storage ring light sources to maintain a constant beam current, and colliders (such as PEP-II, SuperB) to gain the average luminosity
Average luminosity is always near the peak luminosity
The collider looks like a “DC” accelerator allowing an improved operational consistency
JLEIC considers the continuous injection of the electron beams to
Obtain a high average luminosity
Reach a high equilibrium polarization
Note that
If the beam lifetime is shorter than the polarization lifetime, continuous injection maintains the beam current and improves the polarization as well
If the beam lifetime is longer than the polarization lifetime, beam lifetime has to been shorten (collimation, scraping, or reduce the dynamic aperture)
From John T. Seeman, SLAC-PUB-5933, Sep. 1992
Lost or Extracted
P0 (>Pt) Pt

29. Polarization w/o Cont. Injection
Averaged Pol.
Time (arbitrary scale)
Relative Polarization (%)
Injection pattern on polarization
Energy (GeV)
inj (min)
opt_meas (min)
(Pave/Pi)max * 3 12
160
0.94 5 8 60
0.88 7 4 20
0.85 9
0.8 6
0.89 10
0.5
2.5
0.86
: Initial polarization
: Injection time
: Depolarization time
: Measurement time

30. Polarization w Cont. Injection
Polarization w/ continuous injection
Equilibrium polarization
A relatively low average injected beam current of tens-of-nA level can maintain a high equilibrium polarization in the whole energy range.

31. Summary and Outlook Summary Outlook
The 2.2km baseline design of the JLEIC electron collider ring is summarized.
The optimization of the electron ring baseline design to reduce the emittance is reported.
Two electron collider ring design options to significantly reduce the emittance are discussed.
Electron polarization design and simulation results are reported.
Outlook
Finish the study of chromaticity compensation schemes to help determine the electron collider ring design
Perform a complete nonlinear beam dynamics study considering effect of misalignment, field errors and multipole fields, specify alignment and strength error tolerances
Perform electron spin tracking to study higher-order resonances, spin effect of the detector solenoid and beam-beam effect on the spin

32. Thank You for Your Attention !

33. Back Up

34. Magnet Inventory of MEIC e-Ring
Magnet category
PEP-II HER magnet
New magnet
Number
Max. Strength
Dipole
168
0.3 T 34
0.64 T
Quadrupole
263
17 T/m
151
25 T/m
Sextupole
104
600 T/m2(?) 32
600 T/m2
Skew quadrupole 12
2.33 T/m
BPM
331
Corrector
283
0.02 T 48
MEIC (total)
Dipoles: 202
Quads: 414
Sextupoles: 136
Skew quads: 12
Correctors: 331
PEP-II (total, from SuperB CDR)
Dipoles: 200
Quads: 291
Sextupoles: 104
Skew quads: 12
Correctors: 283
Study of PEP-II magnets will be discussed in Tommy Hiatt’s talk.