1. Fanglei Lin JLEIC R&D Meeting, August 4, 2016
Alternate JLEIC Electron Collider Ring Designs --- Use New Magnets to Obtain a Small Emittance
Fanglei Lin
JLEIC R&D Meeting, August 4, 2016
F. Lin

2. Electron Ring Baseline Design Layout
Circumference of m = 2 x m arcs + 2 x straights 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

3. 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.

4. 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: 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: more quads, stronger quads, larger ring (possible), large chromaticities, chromaticity compensation scheme
Need combine non-linear dynamic studies

5. New Magnet FODO Arc Cell e-Ring
Complete electron collider ring optics
circumference of m = 2 x m arcs + 2 x m straights

6. 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
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

7. 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
Arc FODO cell (2 dipoles, 2 quads per cell)
length
15.2 (PEP-II cell length)
11.4 (half of ion ring 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 (including dispersion suppresser, no spin rotator) 42 44 58

8. Momentum Acceptance & Dynamic Aperture
First look of momentum acceptance and dynamics aperture at 5 GeV by using 2 sextupole families for linear chromaticity correction only, no errors.
Chromatic tunes and chromatic *
Dynamic aperture
(-7, +13)σp/p
±20 σx

9. New Magnet TME-like Arc Cell e-Ring
Complete electron collider ring optics
circumference of m = 2 x m arcs + 2 x m straights

10. 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
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

11. 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
Arc TME-like cell (4 dipoles, 4 quads per cell)
length
15.2 (PEP-II cell length)
11.4 (half of ion ring 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 (including dispersion suppresser, no spin rotator) 44 58 28

12. Momentum Acceptance & Dynamic Aperture
First look of momentum acceptance and dynamics aperture at 5 GeV by using 2 sextupole families for linear chromaticity correction only, no errors.
Chromatic tunes and chromatic *
Dynamic aperture
(-12, +12) σp/p
±10 σx

13. Summary of Three Optics Designs
±20σx
(-7.8, +5.6) σp/p
Optimized baseline e-ring design with FODO arc cells (PEP-II magnets)
±20 σx
(-7, +13)σp/p
New magnet e-ring design with FODO arc cells
±10 σx
(-12, +12)σp/p
New magnet e-ring design with TME-like arc cells

14. Thank You for Your Attention !

15. 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%.