1. Non-linear Beam Dynamics Studies for JLEIC Electron Collider Ring
Fanglei Lin, Vasiliy Morozov, Guohui Wei, Yuhong Zhang (JLAB)
Yunhai Cai, Yuri Nosochkov (SLAC)
Min-Huey Wang
JLEIC Collaboration Meeting Spring 2017
April 3-5, 2017
F. Lin

2. Outline
The goal of the study is to identify the lattice design of the electron collider ring with the best overall properties: low emittance, adequate chromatic correction and large dynamic aperture (DA)
Optimized baseline design based on FODO arc cells and PEP-II magnets
Recap of chromaticity compensation and update on DA
Design based on TME-like arc cells and new magnets
Chromaticity compensation and DA
Design based on short FODO arc cells and new magnets
Conclusions and Outlook

3. Recap of the Optimized Baseline Design
PEP-II type FODO arc cells and PEP-II magnets
Circumference: C = m = 2 x m arcs + 2 x m straights
Natural chromaticity: [xH, xV] = [-113, -120]
Optimized for minimum emittance
Emittance at 5 GeV (from Elegant) without chromaticity correction blocks (CCB)
Before optimization: ge = 138 mm-rad, e = 14 nm-rad
After optimization: ge = 92 mm-rad, e = 9.5 nm-rad (8.9 nm-rad from MAD)
Complete ring without non-linear chromaticity correction blocks
IP, b*=10/2cm

4. Chromatic Sextupoles – Optimized Baseline
Linear chromaticity correction: conventional 2-family sextupoles in 108o arc cells (30 cells with sextupoles per arc  compensation of high order effects due to ~2p phase advance in every 10 cells)
Non-linear correction: Chromaticity Correction Blocks (CCB) on each side of IP, where sextupoles are set nearly in phase with the FFQ for correction of non-linear chromaticity e-
R=155m RF
Spin rotator
Arc, 261.7
81.7
Forward e- detection IP
Tune trombone & Straight FODOs
Future 2nd IP
CCB
Arc sextupoles
Future CCB
for 2nd IP

5. CCB Schemes FODO type CCB, ex = 19.4 nm SBCC (scheme-6), ex = 8.3 nm
Interleaved –I sextupole pairs in regular FODO arc cells  no impact on emittance, but strong sextupoles, residual non-linear effects, insufficient correction, small off-energy DA
Compact CCB with 3 interleaved sextupoles  adequate chromaticity correction, but residual non-linear effects, small DA, large emittance (~15 5 GeV)
FODO type CCB with non-interleaved –I sextupoles pairs and high b finctions  adequate chromaticity correction and DA, but large emittance (>15 nm-rad)
SuperB type CCB (SBCC) with non-interleaved –I sextupole pairs and missing dipoles  adequate correction and DA, lowest 8.3 nm-rad emittance (with short dipoles) ‒ Best -I S2 S1
FODO type CCB, ex = 19.4 nm
SBCC (scheme-6), ex = 8.3 nm

6. Correction and DA Update – Optimized Baseline
Best SBCC option with short dipoles (scheme-6), ex = GeV
Tune vs Dp/p
b* vs Dp/p
Qx = 48.22
Qy = 50.16
No errors: DA = ±23sx×72sy (LEGO)
PEP-2 MP field errors (except FFQ): DA = ±20sx×46sy
10 seeds
Dp/p=0

7. Summary – Optimized Baseline Design
Chromaticity Correction Schemes
x/x,0
DA: x/σx , y/σy
Range of (p/p)/σ
p/p=0
p/p=0.4%
Linear correction: conventional 2-family arc sextupoles (v1)
Non-linear: no dedicated correction 1
±20, ±48
0, 0
  9
Linear correction: conventional 2-family arc sextupoles
Non-linear: interleaved –I sext pairs in regular arc cells (v1a)
Non-linear: FODO type CCB with 2 non-interleaved –I sextupole pairs, optimized phase advance (v1b3)
2.1
±15, ±40
±4.5, ±10
  9
Non-linear: FODO type CCB with 2 non-interleaved –I sextupole pairs, optimized phase advance, reduced beta functions for lower emittance (v1d2)
1.7
±17, ±41
±5, ±10
Non-linear: compact CCB with 3 interleaved sextupoles, optimized phase advance
±8.5, ±18
±5, ±7.3
Non-linear: SuperB type scheme (SBCC) with regular length dipoles and large bending angles (scheme-3 )
1.4
±25, ±60
±10, ±15
Non-linear: SBCC with short dipoles and small bending angles (scheme-6, optimized, ring geometry not yet matched)
0.93
±23, ±72
±7, ±26
11
Best option

8. Work Plan – since 2016 Fall Meeting
Optimize SBCC for low emittance in the optimized baseline design ‒ Done
Can emittance be further reduced?
Implement the SBCC in the low emittance design with TME-like arc cells and new magnets; match ring’s geometry; optimize chromaticity correction; check dynamic aperture
If DA is good, continue with studies in bullet # 4
Otherwise  study the low emittance design with short FODO-arc-cell and new magnets; optimize chromaticity correction; check dynamic aperture
Further studies
Replace thin-lens trombones with quadrupole adjustment, verify performance
Tune scan to find optimal tune for maximum DA
Effects of misalignment and field errors on DA
Implement orbit correction scheme (BPMs and correctors)
Specify tolerances
Effects of non-linear field errors on DA
Regular magnets: start with the PEP-II specs
FF quads: specify tolerances
Next  bullet # 2: study performance of ring design based on TME arc cells

9. Design Based on TME Arc Cells
Matched geometry, C = m = 2 x m arcs + 2 x m straights
Low emittance TME-like arc cells with new magnets
Low emittance SBCC scheme
Two options studied: 4 high-b SBCCs or 2 high-b + 2 low-b SBCCs
5 GeV: e = 3.2 nm-rad, ge = 30.9 mm-rad without SBCCs,
e = 3.0 nm-rad, ge = 29.4 mm-rad with 4 high-b SBCCs IP
SBCC
Design with 4 high-b SBCCs
Design with 2 high-b + 2 low-b SBCCs

10. Arc Cell and SBCC – TME Design
SD,SF,SF,SD
TME-like arc cell with new magnets
Length 22.8 m (same as ion ring arc cell)
Arc bending radius m (as in the baseline)
Phase advance 270o / 90o (x/y)
4 dipoles
Length 4 m, bending angle 2.1o
Field GeV
Sagitta 1.83 cm
4 quadrupoles
Length 0.56 m
Gradient GeV
4 sextupoles (2 families)
Arc IP S1 S2
Low emittance SBCC (high-b)
Short dipoles with small bending angles  low H-function  low emittance contribution
Two non-interleaved –I sextupole pairs per SBCC with sufficiently high beta functions
Optimized phase advance (np + Dm) from SBCC sextupoles to FFQs for best correction of non-linear chromaticity

11. Chromaticity Correction – TME design
Non-linear correction: previously designed low emittance SBCC
4 high-b SBBCs ‒ for nominal IP and future 2nd IP
2 high-b SBCCs (near IP) + 2 low-b SBCCs ‒ lower natural chromaticity
Linear correction (in arcs):
Conventional 2-family sextupoles in 24 TME cells per arc (non-linear compensation properties due to ~2p phase advance in every 4 cells )
-I sextupole pairs (non-interleaved or interleaved); various options as shown in the table
X, Y indicate X or Y sextupoles in a given cell; empty cells have no sextupoles
90o between same family pairs to cancel 1st order chromatic beta
Sextupole strengths of “1” and “2” families in scheme 3d are fixed at X1 = X2/2 and Y1 = Y2/2
Cell # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 3a X Y 3b 3c 3d X1 X2 Y1 Y2 3e 3f

12. Correction Performance and DA – TME design
Schemes with –I pairs in arcs require strong arc sextupoles
Large local chromatic beta variation in arcs leading to non-linear chromaticity and poor correction with insufficient momentum range
Best performance with:
Conventional 2-family arc sextupoles ‒ lowest sextupole strengths and chromatic non-linearities
2 high-b SBCCs (to correct FFQ) + 2 low-b SBCCs ‒ lowest natural chromaticity
Tune vs Dp/p
15σx
29σy
Dynamic aperture w/o errors
Qx = 65.22
Qy = 35.16
Dynamic aperture is smaller than in the optimized baseline design

13. Short Summary – TME Design
Chromaticity Compensation Schemes
Arc Sexts
K2 (1/m3)
x , x
DA: x/σx , y/σy
(p/p)/σ
=0
=0.4%
Linear correction: conventional 2-family arc sextupoles
Non-linear: 4 high-b SBCCs – 2 SBCCs for FFQ correction, 2 other SBCCs not used for correction
14.71,
-159, -196
-9, +5
Non-linear: 4 high-b SBCCs – all used for correction
13.93,
8.8, 23
7, 12
-12, +12
Linear correction: conventional 2-family arc sextupoles, but different position of focusing sextupoles in TME cell
Non-linear: 4 high-b SBCCs – 2 SBCCs for FFQ correction, 2 other SBCCs for local correction
43.81, -9.61
Non-linear: 2 high-b SBCCs for FFQ correction, 2 low-b SBBCs not used for correction
10.13,
-145, -166
15, 29
7, 14
30.53, -7.25
-9, +9
Linear correction: -I pairs in arcs (schemes 3a, 3b)
29.71,
-5, +5
Best option
Lowest 3 nm-rad emittance, but DA of 15s w/o errors may not be large enough !
Next  bullet # 3: study performance of ring design based on short FODO cells

14. Design Based on Short FODO Arc Cells
Short FODO arc cells for low emittance, and new magnets
Circumference: C = m = 2 x m arcs + 2 x m straights
Natural chromaticity: [xH, xV] = [-116, -147]
Two SBCCs near IP for non-linear chromaticity correction
Emittance at 5 GeV (from Elegant): e = 5.5 nm-rad, ge = 54 mm-rad
SBCCs
1x
3x
2y
4y IP

15. Arc Cell and SBCC – Short FODO Design
FODO arc cell with new magnets
Length 11.4 m (half of ion ring arc cell)
Arc bending radius m (as in the baseline)
Phase advance 108o (x & y)
2 dipoles
Length 3.6 m, bending angle 2.1
GeV
Sagitta 1.65 cm
2 quadrupoles
Length 0.56 m
21 12 GeV
2 sextupoles (2-family)
New
Arc IP
Spin rotator
SBCC
FODO cells S1 S2
Low emittance SBCC
Short dipoles with small bending angles  low H-function  low emittance contribution
Two non-interleaved –I sextupole pairs per SBCC with sufficiently high beta functions
Optimized phase advance from SBCC sextupoles to FFQs for best correction of non-linear chromaticity

16. Correction Performance – Short FODO Design
4 sextupole families in two SBCCs
K2L = 2.2, -4.5, -2.6, 3.9 (1/m2)
Optimized phase advance from sextupoles to IP 1x=3.7531, 2y=4.2535, 3x=5.2434, 4y=6.2413
Conventional 2-family arc sextupoles (opposite polarities in two arcs)
50 cells with x/y sextupoles per arc
K2 = 14.7 and 6.0 (1/m3), L = 0.25 m
Sufficiently large momentum range
W functions IP
 13σ
Tune vs Dp/p
b* vs Dp/p
Qx = 57.22
Qy = 55.16

17. Dynamic Aperture – Short FODO Design
Dynamic aperture at IP, no magnet errors, sx = 23.4 mm, sy = GeV
38σx
70σy
So far, the best overall dynamic aperture (w/o errors)

18. Work Plan – Updated
Optimize SBCC for low emittance in the optimized baseline design ‒ Done
Can emittance be further reduced?
Implement the SBCC in the low emittance design with TME-like arc cells and new magnets; match ring’s geometry; optimize chromaticity correction; check dynamic aperture ‒ Done
If DA is good, continue with studies in bullet # 4 ‒ DA is “not good enough”
Otherwise  study the low emittance design with short FODO-arc-cell and new magnets; optimize chromaticity correction; check dynamic aperture ‒ Done
Further studies for the short FODO-arc-cell design
Replace thin-lens trombones with quadrupole adjustment, verify performance
Tune scan to find optimal tune for maximum DA
Effects of misalignment and field errors on DA
Implement orbit correction scheme (BPMs and correctors)
Specify tolerances
Effects of non-linear field errors on DA
Regular magnets: start with the PEP-II field quality
FF quads: specify tolerances

19. Conclusions and Outlook
The study confirms that the SBCC scheme with sufficiently short dipoles provides an adequate non-linear chromaticity correction and yields a low emittance contribution in all the studied designs of the electron collider ring
The optimized baseline design based on PEP-II magnets provides adequate chromaticity correction and DA, but a relatively high emittance of ~9 5 GeV
The design based on TME-like arc cells with new magnets provides the lowest emittance of 3 nm-rad, but requires strong arc sextupoles leading to stronger non-linearities and smaller dynamic aperture
The design based on short FODO arc cells with new magnets appears to be the best option so far. It provides a relatively low emittance of 5.5 nm-rad, adequate chromatic compensation and the best dynamic aperture (without errors).
The plan for further studies is to focus on the short FODO ring design including: finalizing the optics; implementing orbit correction system; optimizing the tune for maximum DA; and investigating the impact of magnet errors and tolerance specification

20. Non-linear Beam Dynamics Studies for JLEIC Electron Collider Ring
Thank You

21. Non-linear Beam Dynamics Studies for JLEIC Electron Collider Ring
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22. PEP-II Measured Multipole Field Errors
Systematic errors (DBN/Bref)
Dipole at R = 30 mm
N= E-5
Quadrupole at R = 44.9 mm
N= E-3
E-4
E-4
E-3
E-3
E-3
Sextupole at R = mm
N= E-2
E-2
Random errors (DBN/Bref)
Dipole at R = 30 mm
N= E-5
E-5
E-5
E-5
Quadrupole at R = 44.9 mm
N= E-4
E-4
E-4
E-4
E-4
E-5
Sextupole at R = mm
N= E-3
E-3