1. JLEIC Electron Ring Nonlinear Dynamics Work Plan
F. Lin, V.S. Morozov
Teleconference with SLAC
January 26, 2016
F. Lin

2. Outline JLEIC electron collider ring for nonlinear dynamics studies
Not the baseline design
Reduced-emittance optics design: some sections have been optimized to reduce the emittance by ~30%
Review of submitted proposal
IR design for both rings
Beam dynamics for ion ring only, but can be applied to electron ring
Discussion of chromaticity compensation options
Discussion of short-term plans

3. Reduced-Emittance Electron Ring
Circumference of m = 2 x m arcs + 2 x straights
Chromaticities: (H,V) = (-138, -125)
Figure-8 crossing angle 81.7
Reduced-emittance ring layout is very similar to the baseline design layout (below). e-
R=155m RF
Spin rotator
CCB
Arc, 261.7
81.7
Forward e- detection IP
Tune trombone & Straight FODOs
Future 2nd IP

4. Electron Ring Optics Parameters
Electron beam momentum
GeV/c 10
Circumference m
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
0.78 / 0
Horizontal / vertical betatron tunes x,y
47.(49) / 49.(15)
Horizontal / vertical chromaticitiesx,y
-138 / -125
Momentum compaction factor 
1.9 10-3
Transition energy tr
22.7
Energy spread
10-3
0.9
Hor./ver. emittance x,y
µm rad
779 / 156 (0.040/0.008)
Energy 5GeV
0.45
Hor./ver. emittance x,y 5GeV
97 / 19 (0.01/0.002)

5. Normal Arc FODO Cell
Complete FODO (Each arc has 39 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 (every 5 cells create five –I (3) sextupole pairs)
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
-13.0 and 12.8 T/m field 10 GeV
0.65 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

6. Reduced-Emittance Sections
End of arc
Dispersion suppression
Matching between arcs and spin rotators
Spin rotator
Regular arc FODO cell
Spin rotator
Dipole set
2nd sol. + decoupling quads
1st sol. + decoupling quads

7. Chromaticity Compensation
Upstream local Chromaticity Compensation Block (CCB)
Two 5m-long dipoles and four 2m-long dipoles with a maximum field GeV
13 quads (7 families) have a maximum field ~25 10 GeV
4 sextupoles (2 families) are used for a compensation of local chromaticities from the FFQs
SXT1
SXT2
SXT1
SXT2
Ion CCB
From V. Morozov Re Im
h21000
0.04
h30000
-0.013
h10110
-0.18
h10020
1.85
0.09
h10200
2.04
-0.09

8. Compton polarimetry region
IP Region
IP region
Final focusing quads with maximum field gradient ~63 T/m
Four 3m-long dipoles (chicane) with GeV for low-Q2 tagging with small momentum resolution, suppression of dispersion and Compton polarimeter IP e-
forward e-
detection region
FFQs
Compton polarimetry region
x(m), y(m)
Dx(m)

9. Complete Electron Ring Optics
Along the ion beam direction (in order to match the ion ring optics design easily)
ion e- IP
Upstream CCB

10. Complete Electron Ring Optics
Along the electron beam direction e- IP
Upstream CCB

11. Milestones of Submitted Proposal
MDI and IR Studies:
Quarter 1: Further optimization of the detector region design. Achieve a scheme with acceptable detector background levels that meshes smoothly with the nearby accelerator requirements.
Quarter 2: Collaborate with the JLab group to optimize the chromaticity correction scheme. This potentially impacts details of the IR layout and requires a certain amount of design iteration.
Quarter 3: With the latest data in hand, continue to refine the IR masking design to maintain low detector background levels. Develop a vacuum chamber for the interaction region that satisfies detector and accelerator requirements.
Quarter 4: Evaluate the effect of lattice imperfections and alignment errors on the performance of the IR design, background etc. Investigate vacuum pumping requirements in the IR region.
Nonlinear Beam dynamics:
Quarter 1-2: Ongoing optimization of the hadron-ring lattice, including examining variants as the design evolves. Goals for the acceptance are about 8 sigma in the transverse dimensions and about 0.4% in energy spread. Development of the beam diagnostics and correction concepts.
Quarter 3-4: Once estimates for the magnet field harmonics become available, investigate the effect of these on the acceptance of the lattice. Ultimately these results will be used to generate magnet specifications. Compensation of the detector solenoid effects.
From V. Morozov

12. Chromaticity Compensation Options
All potential schemes work in a similar way
Sextupoles placed in a dispersive region generate a chromatic  wave with a phase such that it cancels the chromatic kick of the final focusing blocks
Sextupoles are positioned in a way that cancels their unwanted nonlinear effects
Additional sextupoles are used to compensate the residual chromaticity
Compensation scheme options
Minus-identity sextupole pairs in the arcs: chromatic beta waves add up, geometric kicks cancel
CCB proposed by JLab: –I sextupole pairs and sextupoles at low-x locations (upstream CCB only now, downstream CCB has to be in the arc)
Distributed sextupole scheme: multiple –I pairs (every 5 arc FODO cells) build up a chromatic wave (slides 13,14)
Distributed sextupole scheme with -beat: lower-strength sextupoles
General considerations when selecting a scheme
Larger  functions at sextupole locations mean lower sextupole strengths and generally better chromatic compensation but cause larger amplitude-dependent tune shift
Smaller  functions generally mean smaller amplitude dependent tune spread but require stronger sextupoles and cause larger higher-order chromaticities
We probably need to find a balance of the two effects
Electron emittance growth has to be minimized
Modified based on V. Morozov’s ion compensation options

13. Chromaticity Compensation
Compensation of momentum dependence of betatron tunes (primarily due to strong focusing at IP) using properly-phased sextupole families
Distributed sextupole compensation strategy
Build-up chromatic  wave in the arcs to cancel FFB’s chromatic kick
Arc FODO cells (39 cells each arc) with 108 phase advance in x/y
Five sextupole families, each with an even number of magnets
 phase advance between individual sextupoles of each family
n+/2 phase advance from the last sextupole of each family to IP
Option of exciting  beat in the arcs if needed (last consideration)
Compensation of residual linear chromaticity
Two sextupole families, each with a multiple of 4 magnets (4 arc FODD cells)
/2 (108  90) phase advance between individual sextupoles of each family
Control of chromatic driving terms ((2), D(2), / ) and cancellation of geometric resonance driving terms to first order in sextupole strength
FFB IP 
/2 
Modified based on V. Morozov’s ion compensation options

14. Chromatic Amplitude Functions
Adjust sextupole strengths & phase advance by minimizing W function at IP
Compensate residual linear chromaticity by two additional families
Before compensation
After sextupole compensation
From V. Morozov

15. Comparison to KEKB

16. Suggested Short-Term Goals
Down selection of a chromaticity compensation scheme
A quick check and comparison of most promising schemes by analysis of nonlinear parameters and tracking
Use linear matrices for matching and adjusting the phase advance, enough flexibility is built into the lattice for an actual optical implementation later
Determine optimum -function values at the sextupole locations
Relevant questions to think about
Consider compensating both FFBs using the nearest arc at the expense of chromatic smear at the IP
Optimization of betatron tunes
Evaluate the need for geometric sextupoles and octupoles
Error sensitivity study
Use PEP-II magnet multipole field errors, misalignment and rotation parameters
First use BPMs and correctors included in the lattice next to each quadrupole
Part of the diagnostics and correction scheme development
From V. Morozov