1. Preservation and Control of Ion Polarization in MEIC
A.M. Kondratenko, M.A. Kondratenko
Science and Technique Laboratory Zaryad, Novosibirsk, Russia
Yu.N. Filatov
Moscow Institute of Physics and Technology, Dolgoprydny, Russia
V.S. Morozov, Ya.S. Derbenev, F. Lin, and Y. Zhang
Jefferson Lab, Newport News, VA, USA
MEIC Collaboration Meeting
October 5-7, 2015
F. Lin

2. Outline Introduction Figure 8 or racetrack?
Spin dynamics in a Figure-8 ring
Polarization preservation during acceleration
Polarization control in the collider ring
Spin stability criterion and zero-integer spin resonance
Initial spin tracking results
Conclusions

3. Ion Polarization Requirements
Major MEIC 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
to future high-energy
collider ring
Ion
source
SRF linac
Booster
285 – 7062 MeV
(accumulator ring)
Medium-energy collider ring
8-100 GeV/c
Cooling

4. Spin Resonances in Conventional Ring
Spin tune (number of spin precession per turn) in a conventional ring
A spin resonance occurs whenever the spin precession becomes synchronized with the frequency of spin perturbing fields
Imperfection resonances due to alignment and field errors
Intrinsic resonances due to betatron oscillations
Coupling and higher-order resonances

5. Racetrack Resonances
Racetrack booster Ep = 1.22 – 8 GeV, Ed = 2.03 – 8.16 GeV
Protons
~13 imperfection resonances
~26 intrinsic resonances require full solenoidal Siberian snake, ~30 Tm
Many higher-order resonances
Deuterons
0 imperfection resonances
1 or 2 intrinsic resonances can be avoided
Higher-order resonances can be accelerated through
Racetrack collider ring Ep = 8 – 100 GeV, Ed = 8.16 – 100 GeV
~175 imperfection resonances
~350 intrinsic resonances require two full dipole Siberian snakes, ~50 Tm
7 imperfection resonances can be crossed individually
~12 intrinsic resonances is a problem
Many higher-order resonances ruin polarization and polarization lifetime

6. Figure-8 vs Racetrack Booster
Figure-8 booster
Same optics for all polarized and unpolarized ion beams
Universally good and simple solution for polarization of any particles
No restriction on the field ramp rate
Additional arc bending angle of 150
Additional integrated dipole field BL = B ~ 70 Tm
Extra space for quadrupoles, etc.
Racetrack booster
Proton & He3 polarization: OK
Requires ~10 m long Siberian snake with ~30 Tm longitudinal field integral
Snake field must ramp with energy
Different optics for each ion species
Allows one to shorten circumference by about 10 m
Deuteron polarization: OK with fast ramp
Can be handled with care
Field ramp rate must be >~1 T/s
Betatron tune jumps may be needed to cross spin resonances (this technique changes the optics during jumps)

7. Figure-8 vs Racetrack Collider Ring
Figure 8 collider ring
Same optics for all polarized and unpolarized ion beams
Good for polarization
Stable optics during acceleration and spin manipulation
Additional arc bending angle of 163.4
Additional integrated dipole field BL ~ 950 Tm
Extra space for quadrupoles, etc.
Racetrack collider ring
Proton polarization: probably OK but challenging
Problem with optics stability especially at low energies
Requires two full dipole Siberian snakes with a total field integral of ~50 Tm
Figure-8 features can be preserved
At low energies of ~8 GeV, the snakes introduce a significant tune shift (~0.2), which must be compensated; the tune shift changes nonlinearly with energy ~ -2
Deuteron polarization: realistically NO
Cannot be preserved unless the ramp time to 100 GeV/c is less than ~1 s
At the present acceleration rate, polarization is lost by ~10 GeV/c
Even if polarization is preserved during acceleration, there is no guarantee of sufficient polarization lifetime; in fact, it will most likely be short.

8. Spin Motion in a 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

9. Polarization Control Concept
Local spin rotator determines spin tune and local spin direction
Polarization is stable if  >> w0
w0 is the zero-integer spin resonance strength
B||L of only 3 Tm provides deuteron polarization stability up to 100 GeV
A conventional ring at 100 GeV would require B||L of 1200 Tm or BL of 400 Tm

10. 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

11. Solenoid Matching in Booster
Booster lattice without solenoid
Booster lattice with solenoid
No correction needed
solenoid

12. Polarization Control with 3D Spin Rotator
“3D spin rotator” rotates the spin about any chosen direction in 3D and sets the stable polarization orientation
nx control module (constant radial orbit bump)
z1 =  nx/sin y
L 8 m x  1.6 cm By max= 3 T
ny control module (constant vertical orbit bump)
z2 =  ny/sin x
L 8 m y  1.6 cm Bx max= 3 T
nz control module
z3 =  nz
zi, x, y – are the spin rotation angles of solenoid field, radial-field dipole and vertical-field dipole respectively.
Control of radial (nx) spin component
Control of vertical (ny) spin component
Control of longitudinal (nz) spin component IP z x z y

13. Polarization Control in the Collider Ring
Placement of the 3D spin rotator in the collider ring
Integration of the 3D spin rotator into the collider ring’s lattice
Seamless integration into virtually any lattice
Spin-control solenoids
Vertical-field dipoles
Radial-field dipoles
Lattice quadrupoles

14. Solenoid Strengths
Momentum dependence of the solenoid strengths for deuterons, d = 10-4
Momentum dependence of the solenoid strengths for protons, p = 10-2
Radial
Vertical
Longitudinal
Bz1
Bz2
Bz3
Radial
Vertical
Longitudinal
Bz1
Bz2
Bz3

15. Spin Flipping
Necessary for the physics program to reduce systematic uncertainties
The universal 3D spin rotator can be used to flip the polarization
Consider e.g. multiple polarization reversals at the IP at 100 GeV/c
Polarization is flipped by reversing the fields of the solenoids in the radial and longitudinal spin control modules
Polarization is preserved if
The spin tune is kept constant during spin manipulation
The rate of change of the polarization direction is slow compared to the spin precession rate
> 0.1 ms for protons and > 10 ms for deuterons
Polarization
Protons
Deuterons
Bz2, T
Bz3, T
Vertical ny = 1
2.19
-1.49
Vertical ny = -1
-2.19
1.49
Longitudinal nz = 1
1.88
-0.06
Longitudinal nz= -1
-1.88
0.06

16. 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

17. Spin Response Function of Collider Ring
The coherent part of zero- integer spin resonance induced by perturbing radial field hx() can be calculated using periodical response function F():
F() is calculated from linear optics
Perturbing radial fields arise, for example, due to dipole roll errors, vertical quads misalignments, etc.
Such perturbing fields result in vertical closed orbit distortion

18. RMS Vertical Closed Orbit Distortion
Assuming certain rms vertical closed orbit distortion, we statistically calculate vertical orbit offset in the quadrupoles and resonance strength
rms vertical closed orbit distortion for random misalignment of all quads
Assuming that orbit distortion in the arcs < 100 m

19. Coherent Part of Resonance Strength
2 T  2 m control solenoids allow setting p = and d = 10-4
Sufficient for polarization stabilization and control
The coherent part of the zero-integer spin resonance strength is determined by closed orbit distortions.
Orbit distortion does not exceed 100 m

20. Incoherent Part of Resonance Strength
Effect of higher-order resonances due to incoherent tune spread requires study similarly to the case of two Siberian snakes
The incoherent part of the zero-integer spin resonance strength is determined by emittances of betatron and synchrotron oscillations and depends on magnetic lattice
In an ideal lattice, the incoherent part is determined primarily by the emittance of vertical betatron oscillations
Incoherent part of the resonance strength is determined by the second order and has vertical direction
Assuming normalized vertical beam emittance of 0.07 m rad

21. Spin-Tracking Perfect Figure-8 Ring
Spin tracking using Zgoubi in collaboration with F. Meot of BNL
MEIC lattice, no errors, 60 GeV/c proton, initial spin nz = 1, reference orbit
Proton on one-sigma phase-space trajectories in both x and y

22. Stabilization against Error Effects
One arc dipole rolled by 0.2 mrad, no closed orbit correction
After addition of a 1 spin rotator solenoid in the straight (s  310-3)

23. Acceleration
With 0.2 mrad dipole roll, no orbit correction, no spin rotator, 200103 turns
After addition of a 5 spin rotator in the straight (s  1.410-2), 300103 turns

24. Conclusions & Future Plans
Schemes have been developed for MEIC based on the figure-8 design that
eliminate resonant depolarization problem during acceleration
allow polarization control by small fields without orbit perturbation
provide for seamless integration of the polarization control into the ring lattice
efficiently control the polarization of any particles including deuterons
allow adjustment of any polarization at any orbital location
allow spin manipulation during experiments
make possible ultra-high precision experiments with polarized beams
allow for straightforward adjustment of spin dynamics for any experimental needs
Initial spin tracking results support the validity of the developed concepts
Future work
Systematic comparison of figure-8 and racetrack booster options
Spin tracking to validate the statistical model and verify developed schemes
Development of efficient numerical techniques for spin calculations
Optimization of response function at the IP by tuning the lattice
Spin flipping development