1. Progress in Testing a Hybrid Multi-Bend Achromat Lattice in JLEIC Electron Ring
Fanglei Lin, Yuri Nosochkov
Vasiliy Morozov, Yuhong Zhang, Guohui Wei
JLEIC R&D Meeting, June 29, 2017
F. Lin

2. Outline Motivation Brief history of Hybrid Multi-Bend Achromat (HMBA)
SuperB
ESRF
JLEIC HMBA design option
Optics
Emittance
Estimated circumference
Chromaticity budget
Summary

3. Motivation / Application / Potential Issues
Reduce the emittance of electron beam in the JLEIC electron collider ring
Small emittance => reduce beam sizes at IP => boost the luminosity
Small emittance => enlarge * => reduce maximum beta functions and beam sizes at FFQs => reduce FFQs’ apertures
Hybrid Multi-Bend Achromat (HMBA) lattice
Philosophy :
dispersion bump for efficient chromaticity correction with less and relatively weak sextupoles
Small dispersion and horizontal beta function on dipoles
Application : SuperB and ESRF
Expected potential issues
Strong arc quadrupoles
Long arc length

4. Super B
From Yuri Nosochkov based on the latest SuperB HER lattice (per M. Biagini)

5. From Pantaleo Raimondi at IPAC’17

6. ESRF
From Pantaleo Raimondi at IPAC’17

7. JLEIC HMBA Cell 1
HMBA cell 1 : L = m,  = 225 mrad (12.89), HMBA cell bending radius is m ( m in the baseline and short-arc-cell lattices)
Dipole: total 8 dipoles
Two 4.5m, 45mrad and six 2.25m, 22.5mrad
All dipoles have the same bending radius of 100m (close to 110.5m in the baseline and 98.2 in the short-arc-cell lattices)
Quadrupole, total 11 quadrupoles in 6 families
Four 0.3 m and seven 0.5 m
Maximum strength is ~17 T/m at 5 GeV with a pole tip field 0.83 T at 5cm radius
Sextupole, total 4 in 2 families
Two 0.15 m and two 0.3 m
Strength will be determined
BPM and Correctors
Three 0.05m bpms and three 0.3 m H/V correctors
Phase advances are
H/V : 3 / 

8. Cell 1 Optics (H/V : 3 / ) SF SD

9. JLEIC HMBA Cell 2
HMBA cell 2 : L = m,  = 135 mrad (7.74), HMBA cell bending radius is m ( m in the baseline and short-arc-cell lattices)
Dipole: total 6 dipoles
Two 4.5m, 45mrad and four 1.125m, 11.25mrad
All dipoles have the same bending radius of 100m (close to 110.5m in the baseline and 98.2 in the short-arc-cell lattices)
Quadrupole, total 9 quadrupoles in 5 families
Four 0.3 m, four 0.5 m and one 0.7 m
Maximum strength is ~18 T/m at 5 GeV with a pole tip field 0.91 T at 5cm radius
Sextupole, total 4 in 2 families
Two 0.15 m and two 0.3 m
Strength will be determined
BPM and Correctors
Three 0.05m bpms and three 0.3 m H/V correctors
Phase advances are adjusted in two sets
H/V : 2.5 / 0.5 (90)
H/V : 2.6 / 0.6 (108)

10. Cell 2 Optics (H/V : 2.5 / 0.5) SF SD

11. Cell 2 Optics (H/V : 2.6 / 0.6) SF SD

12. Super HMBA Cell Optics Cell 1: 3 /  Cell 2: 2.5 / 0.5

13. Cell w/ Phase advance (H / V) Normalized Emittance (m)
3 GeV
5 GeV
10 GeV
HMBA cell 1 : 3 / 
2.2
10.1
80.9
HMBA cell 2 : 2.5 / 0.5 ( and 2.6 / 0.6 )
1.4 (1.9)
6.5 (8.7)
51.6 (69.5)
HMBA cell 1 + 2
1.9 (2.1)
8.7 (9.6)
69.9 (76.6)
Short FODO cell : 0.6 / 0.6
10.0
46.4
371.6
Note that:
The emittance is reduced by a factor of 5 for the HMBA cell.
The total emittance will be finally determined (maybe dominated) by other sections (such as dispersion suppression, SBCCs, spin rotators) if they have relatively large contribution.

14. Estimated Geometry Super HMBA cell : cell 1 + cell 2
Length m, bending angle , average arc radius m.
Estimated one arc bending angle:
20.63x(8+2) + 17  = 249.7
then crossing angle is 69.7
Estimated one arc length:
67.34* * *2 = m
IF each straight is ~220m, then the total circumference will be 2.5km.
2 spin rotators
2 SBCCs
Disp. Supp. for injection and matching
Sextupole pairs for chromaticity compensation
2 spin rotators
2 SBCCs

15. Optics of HMBA and FODO Cells

16. Cell w/ Phase Advance H / V
Chromaticity
Cell w/ Phase Advance H / V
Chromaticity H / V
HMBA cell 1 : 3 / 
-2.27 / -1.44
HMBA cell 2 : 2.5 / 0.5 ( and 2.6 / 0.6 )
-1.64 / (-1.85 / -1.39)
HMBA cell 1 + 2
-3.91 / (-4.12 / -2.83)
Short FODO : 0.6 / 0.6
-0.44 / -0.44
Chromaticities per cell: HMBA/FODO ~ 9
Number of cells per arc : HMBA/FODO ~ 10/50 = 1/5
Number of sextupoles per arc :
HMBA/FODO = ((4+4)*8)/((1+1)*40) =0.8
Beta functions * dispersion at sextupole locations (assume all sextupoles have the same length):
SF : HMBA/FODO ~ 0.95
SD : HMBA/FODO ~ 0.8
Total chromaticity from cells only : HMBA/FODO ~ 1.8
Total optic compensation factor :
HMBA/FODO ~
The sextupole strengths in the HMBA cell will be 2.4 to 2.8 times stronger than those in the FODO cell. This may induce strong nonlinear motion and limit the dynamic aperture. Need study the chromaticity compensation scheme.

17. Summary
A Hybrid Multi-Bend Achromat (HMBA) type optics design is explored for the JLEIC electron collider ring.
The result, in term of reducing the emittance, is very promising. There is about a factor of 5 reduction, comparing to a FODO cell design.
It requires strong quadrupole strengths and may, very possible, end up with a large circumference.
It needs a chromaticity compensation study to demonstrate an adequate dynamic aperture.

18. Back Up

19. From Yuri on Jan 31, 2017

20. ρ = 61.5 m
ρ = 61.3 m

21. ρ = 74.5 m
ρ = 61.3 m