1. Ion Collider Ring: Design and Polarization
V.S. Morozov for JLEIC study group
JLEIC Collaboration Meeting, JLab
October 5-7, 2016
F. Lin 1

2. Outline Baseline design of the ion collider ring Ion polarization
What is missing
Design updates
Injection parameters
Injection lattice
Vertical doglegs
Interaction region
Electron cooling
Next iteration of the design

3. Ion Collider Design Requirements
Provide the necessary beam parameters
20(8)-100 GeV protons, GeV/u ions
Focusing at the IP that supports luminosities above 1033 cm-2s-1
Sufficient beam and luminosity lifetime
Capability of operating multiple detectors
One full-acceptance detector incorporated
Small angle detection
Space for a second detector reserved
Polarization preservation and control using figure-8 geometry
Light ion (p, d, 3He, and possibly Li) polarization above 70%
Transverse and longitudinal polarization orientations adjustable at the IP
Sufficient polarization lifetime
Match the electron collider ring geometry
Same tunnel
Incorporate provisions for non-linear dynamics correction
Sextupole families
Chromatic correction scheme

4. Ion Collider Ring Layout
Circumference of m
Cost reduction by using super-ferric magnets
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

5. Ion Collider Ring Parameters
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
1 / 0.5
Horizontal / vertical rms beam size at IP *x,y µm
~30 / ~10
Maximum horizontal / vertical rms beam size x,y mm
4.8 / 3.4

6. Nonlinear Dynamics –I sextupoles pairs in the arcs (talk by G. Wei)
Momentum acceptance
Dynamic aperture IP y
p/p x

7. Arc Ends
Provide dispersion suppression and geometric match to the electron ring
Arc end upstream of IP
Shaped to provide 50 mrad crossing angle at the IP
Arc end downstream of IP
Shaped to provide 1.5 m separation from the electron beam
20 m
5 m
ions IP
10 m
2 m
ions

8. Element Count Dipoles: 133 Quadrupoles: 205 Sextupoles: 125
Regular: 127 super-ferric, B < 3.06 T
Special: 2 for IR (discussed later) + 4 cos() super-conducting, B < 4.7 T
Quadrupoles: 205
Regular: 155 with integrated field < 48 T (60 T/m)
Regular*: 44 with integrated field < 72 T (90 T/m, these may require separate design, e.g. increased length)
Special: 6 final-focusing quadrupoles (discussed later)
Sextupoles: 125
Maximum pole-tip field ~1.5 T

9. Aperture Specifications
Regular dipoles
Closed orbit allowance, COA = 1 cm
Sagitta of 4 m section, SG  1 cm
Horizontal rms beam size at injection, x inj = (xx inj + (Dxp/pinj)2)1/2  3 mm
Vertical rms beam size at injection, y inj = (yy inj)1/2  2 mm
Horizontal aperture, HA = 10 x inj + SG + COA = 5 cm
Vertical aperture, VA = 10 y inj + COA = 3 cm
Regular quadrupoles
HA = VA = 10 x inj + COA = 4 cm

10. Super-Ferric Magnets 3 T Cost effective Fast ramp rate
Cable-in-conduit conductor
Prototype winding (talk by P. McIntyre)

11. Ion Polarization Requirements
Major JLEIC ion complex components
Polarization design requirements
High polarization (~80%) of protons and light ions (d, 3He++, and possibly 6Li+++)
Both longitudinal and transverse polarization orientations available at all IPs
Sufficiently long polarization lifetime
Spin flipping
Ion
source
SRF linac
Booster
285 – 7062 MeV
(accumulator ring)
Ion collider ring
8-100 GeV/c
Cooling
A.M. Kondratenko et al.

12. Spin Motion in Figure-8 Ring
Properties of a figure-8 structure
Spin precessions in the two arcs are exactly cancelled
In an ideal structure (without perturbations) all solutions are periodic
The spin tune is zero independent of energy
A figure-8 ring provides unique capabilities for polarization control
It allows for stabilization and control of the polarization by small field integrals
Spin rotators are compact, easily rampable and give no orbit distortion
It eliminates depolarization problem during acceleration
Spin tune remains constant for all ion species avoiding spin resonance crossing
It provides efficient polarization control of any particles including deuterons
It is currently the only practical way to accommodate polarized deuterons
Electron quantum depolarization is reduced due to energy independent spin tune
It makes possible ultra-high precision experiments with polarized beams
It allows for a spin flipping system with a spin reversal time of ~1 s
n = 0

13. Zero-Integer Spin Resonance & Spin Stability Criterion
The total zero-integer spin resonance strength is composed of
coherent part due to closed orbit excursions
incoherent part due to transverse and longitudinal emittances
Spin stability criterion
the spin tune induced by the 3D spin rotator must significantly exceed the strength of the zero-integer spin resonance
for proton beam
for deuteron beam

14. Pre-Acceleration & Spin Matching
Polarization in Booster stabilized and preserved by a single weak solenoid
0.6 Tm at 8 GeV/c
d / p = / 0.01
Longitudinal polarization in the straight with the solenoid
Conventional 8 GeV accelerators require B||L of ~30 Tm for protons and ~100 Tm for deuterons
beam from Linac
Booster
to Collider Ring
BIIL

15. Spin Dynamics in Booster
Acceleration in figure-8 booster with transverse quadrupole misalignments
0.3 Tm (maximum) spin stabilizing solenoid
Spin tracking simulation using Zgoubi (developed by F. Meot, BNL)
protons
x0 = y0 = 1 cm
p/p = -0.1%, 0, +0.1%
deuterons
x0 = y0 = 1 cm
p/p = 0

16. Polarization Control in Ion Collider Ring
3D spin rotator: control of the radial, vertical, and longitudinal spin components
Module for control of the radial component (fixed radial orbit bump)
Module for control of the vertical component (fixed vertical orbit bump)
Module for control of the longitudinal component
3D spin rotator IP
ions

17. Spin Dynamics in Ion Collider Ring
100 GeV/c figure-8 ion collider ring with transverse quadrupole misalignments
Example of vertical proton polarization at IP. The 1st 3D rotator:  = 10-2 , ny=1. The 2nd 3D rotator is used for compensation of coherent part of the zero-integer spin resonance strength
1st 3D rotator for control
2nd 3D rotator for compensation
Zgoubi
without compensation
with compensation

18. Spin Flip
Adiabaticity criterion: spin reversal time must be much longer than spin precession period
 flip >> 1 ms for protons and 0.1 s for deuterons
Vertical (hy) & longitudinal (hz) spin field components as set by the spin rotator vs time  Spin tune vs time (changes due to piece-wise linear shape)
Vertical & longitudinal components of proton polarization vs time at 100 GeV/c

19. What Is Missing
Beam acceleration and formation scheme (talks by J. Guo and T. Satogata)
Transition energy crossing scheme
Vertical doglegs for stacking electron and ion beam lines in the arcs
Crab crossing scheme (talk by S. Sosa)
Optimized IR integration
Optimization of the electron cooling section (talk by S. Benson)
Detector solenoid and compensation (talk by G. Wei)
Engineering details (talks by T. Michalski and P. McIntyre)
Each 8 m dipole represented as 4 m pieces
Realistic space for components such as RF

20. Space Charge Limit Limit on transverse normalized emittances Assuming
Longitudinally-uniform transversely-Gaussian bunch
Longitudinally- and transversely-Gaussian bunch
Assuming
Ring circumference of
Beam current of 0.5 A and 52/56 filled buckets  charge per bunch
Momentum
Bunch length
Space-charge tune shift
Resulting emittances

21. Momentum Spread at Injection
Assumptions
rms momentum spread at 100 GeV/c is
rms bunch length at 100 GeV/c is
each injection bunch is split into 64 collision bunches
normalized longitudinal emittance is conserved in the bunch splitting process
rms bunch length at 8 GeV/c injection is
Relative momentum spread at injection is

22. Emittance Evolution due to IBS (I)
Starting with

23. Emittance Evolution due to IBS (II)
Starting with

24. Bunch Splitting
Injection and acceleration with long bunches from the Booster
Each long bunch is split into multiple small bunches for collision
Simulations in progress (talk by T. Satogata)

25. Beta Squeeze
Geometric beam emittance is larger at injection than in collision mode; therefore, maximum beta functions in detector region and CCB’s must be reduced to fit the beam in the dynamic and physical apertures.
Geometric emittance is ~32 times greater at injection than at 100 GeV (~1 8 GeV/c vs GeV/c)
Nominally, beta functions should be reduced by the same factor of ~32
Constraints
Global betatron tunes fixed
Phase advance from the CCB fixed
Dispersion suppressed

26. Collision Mode Betatron tunes: x = 24.22, y = 23.16 y = 7.5

27. Injection Mode
* increased by a factor of 30 to (3 m, 0.6 m), max reduced by a factor of ~26
Betatron tunes: x = 24.22, y = 23.16
x = 12.5
y = 7.5
x = 8.5
y = 5.5

28. (dipole x aperture – sagitta), quad aperture
Beam Size at Injection
Assuming pinj = 8 GeV/c, x inj norm = y inj norm = 1 m, p/pinj = 110-3
quad y aperture
(dipole x aperture – sagitta), quad aperture
dipole y aperture

29. Multipole Effect at Injection
Preliminary study by G. Wei
Multipole data from TAMU
Assuming pinj = 8 GeV/c, x inj norm = y inj norm = 1 m, p/pinj = 110-3
injection
injection
11y
12x

30. General Considerations
Doglegs for vertically stacking the electron and ion collider beam lines in the arc sections
Constraints
Cannot interleave net rotations about different axis to avoid breaking the figure-8 spin symmetry
Have to manage horizontal and vertical dispersions
Minimize total length and magnet strengths for a given size of the vertical step (in the following assumed to be 1 m, need engineering feedback)
Dogleg options
Single step, e.g. bend down + ~2 vertical betatron phase advance + bend up
Two step (á la CEBAF), e.g. down/up dipole step +  vertical betatron phase advance + down/up dipole step
Combined vertical and horizontal bends, e.g. down/up dipole step + horizontally bending section with  vertical betatron phase advance + down/up dipole step

31. Dogleg Option I: Single Step
Achromatic
Can provide relatively large vertical step size
Size dominated by the space necessary to accumulate the 2 vertical betatron phase advance  to reduce it, use 1.6 m long (2 x regular) quadrupoles with maximum gradient of 52.3 T/m at 100 GeV/c
Yuri: it may be worth inserting another quadrupole

32. Dogleg Option II: Two Step
Achromatic
More efficient for a relatively small vertical step size
Lengths of the dipole pairs contribute significantly to the total size
Use 1.6 m long (2 x regular) quads with maximum gradient of 50.0 T/m at 100 GeV/c

33. Dogleg Option III: Combined
Achromatic for vertical dispersion, matched directly to a regular arc FODO cell and suppresses horizontal dispersion
(-) Involves a larger number of quadrupole families
Provides horizontal bend of one regular arc FODO cell
More efficient for a relatively small vertical step size
Lengths of the dipole pairs contribute significantly to the total size
(+) May be a better geometric match to the electron beam line  smaller tunnel
Use 1.6 m long (2 x regular) quads with maximum gradient of 46.1 T/m at 100 GeV/c

34. Detector Region Optimization
Zero dispersion slope at the secondary focus (later talk by V. Morozov)
limit x and y
D’ ~ 0
~14.4 m
4 m
x , y < ~0.6 m
middle of straight
D = 0, D’ = 0

35. Optimized Detector Region Geometry
Use another dipole after the 2nd spectrometer dipole with same-size but opposite-sign bending angle to straighten out the dispersion slope
Keep the beam position and angle at the end point fixed
Three dispersion-suppression/
geometry-control dipoles
|56 mrad| ( GeV)
cannot be much smaller
2nd spectrometer dipole
56 mrad ( GeV)
length of this straight
controls overall height
geometrically fixed point
“3rd” spectrometer dipole
-56 mrad ( GeV)
i beam
length of this straight
controls overall length
e beam

36. Detector Region LayoutIP e-
Compton polarimetry
forward ion detection
ions
forward e- detection
dispersion suppressor/
geometric match
spectrometers

37. Electron Cooling Section
Space reserved for two 30 m long cooling solenoids in one straight
Solenoids of opposite fields for coupling compensation and spin dynamics
Recent electron cooling design developments necessitate modifications
Ion  functions of ~100 m
No ion quadrupoles between the solenoids
ions
cooling solenoid
match

38. Next Iteration Incorporate Vertical doglegs
Impacts the footprint, need to know electron ring layout (talks by F. Lin and Y. Nosochkov)
Crab cavities
Optimized detector region
Optimized cooling section
Detector solenoid
More accurate dipole design
Realistic space for RF cavities
Possibly reduced * with strong cooling