1. Update on MEIC Nonlinear Dynamics Work
V.S. Morozov
Teleconference with SLAC
March 24, 2015
F. Lin

2. Outline Update on the MEIC ion collider ring design
Review of milestones
Discussion of chromaticity compensation options
Discussion of short-term plans

3. Ion Collider Ring Figure-8 ring with a circumference of 2153.9 m
Two 261.7 arcs connected by two straights crossing at 81.7
geom. match #3
disp. supp./
disp. supp./
geom. match #2
norm.+
SRF
Arc, 261.7
tune
tromb.+
match
elec. cool.
R = m
81.7
future 2nd IP
Polarimeter
det. elem.
disp. supp.
ions
beam exp./
match IP
disp. supp./
geom. match #3
disp. supp./
geom. match #1

4. Ion Collider Ring Parameters
All design goals achieved
Resulting collider ring parameters
Proton energy range
GeV
20(8)-100
Polarization %
> 70
Detector space m
-4.6 / +7
Luminosity
cm-2s-1
> 1033
Circumference m
Straights’ crossing angle
deg
81.7
Horizontal / vertical beta functions at IP *x,y cm
10 / 2
Maximum horizontal / vertical beta functions x,y max
~2500
Maximum horizontal dispersion Dx
3.28
Horizontal / vertical betatron tunes x,y
24(.38) / 24(.28)
Horizontal / vertical natural chromaticitiesx,y
-101 / -112
Momentum compaction factor 
6.45  10-3
Transition energy tr
12.46
Normalized horizontal / vertical emittance x,y
µm rad
0.35 / 0.07
Horizontal / vertical rms beam size at IP *x,y µm
~20 / ~4
Maximum horizontal / vertical rms beam size x,y mm
2.8 / 1.3

5. Arc FODO Cell Basic building block of the arcs Dipoles Quadrupoles
Length of 22.8 m = 1.5  electron FODO cell lengths (26 cells per arc)
Betatron phase advance of 90 in each plane
Dipoles
Magnetic/physical length of 8/8.28 m (implemented as two 4 m long pieces)
Bending angle of 73.3 mrad (4.2), bending radius of m, sagitta of 18.3 mm
Field of 3.06 T at 100 GeV/c
x aperture = (4 cm+sagitta/2) = 5 cm, y aperture = 3 cm (10 + 1 cm orbit allowance)
Quadrupoles
Magnetic/physical length of 0.8/0.9 m
Field gradients of 52.7/-52.9 T/m at 100 GeV/c
Field of 2.1/-2.1 T at 40 mm radius
Sextupole/corrector package next to each quadrupole
Magnetic/physical length of 0.5/0.6 m
3 T at 40 mm focusing sextupole adds 34.8/-7.1 units of x/y chromaticity
3 T at 40 mm defocusing sextupole adds -3.7/18.1 units of x/y chromaticity
BPM next to each quadrupole
Physical length of 0.15 m

6. Ion IR Optics IR design features Modular design
Based on triplet Final Focusing Blocks (FFB)
Asymmetric design to satisfy detector requirements and reduce chromaticity
Spectrometer dipoles before and after downstream FFB, second focus downstream of IP
No dispersion at IP, achromatic optics downstream of IP
detector
elements
match/
beam compression IP
match/
beam expansion
geom. match/
disp. suppression
FFB
FFB
ions

7. Complete Ion Collider Ring Lattice
Optics of a complete ring with all sections incorporated and matched
ions
Arc 1
Straight 2 IP
Arc 2
Straight 1

8. Milestones of Funded 1-Year Grant
First and Second quarters
Optimization of the detector region design
Comparison of different non-linear compensation schemes and selection of the optimal one
Optimization of the non-linear dynamics compensation scheme
Third and fourth quarters
Continuation of the momentum acceptance and dynamic aperture optimization
Consideration of lattice imperfections: magnet field errors and misalignments
Development of the beam diagnostics and correction scheme

9. 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.

10. 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
Distributed sextupole scheme: multiple –I pairs build up a chromatic wave
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

11. 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 with 90 phase advance in x/y
Two 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
Compensation of ~1/6 residual linear chromaticity
Two sextupole families, each with a multiple of 4 magnets
/2 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 

12. 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

13. Suggested Short-Term Goals
Note: a postdoc, Guohui Wei, joining whose main focus will be on this work
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,
First use BPMs and correctors included in the lattice next to each quadrupole
Part of the diagnostics and correction scheme development
Somewhat longer-term goals
Consider impact of magnet multipole components, can collaborate with P. McIntyre of Texas A&M University