1. Electron Polarization In MEIC
Pavel Chevtsov

2. Outline MEIC Electron Polarization Requirements
MEIC Electron Polarization Design
Universal Spin Rotator
Spin dynamics in MEIC Electron Ring
Summary

3. Electron Polarization Requirements
High (>80%) polarization of stored high-current electron beam
Sufficiently long polarization lifetime (>10 min) in 3 to 11 GeV energy range
Longitudinal polarization available at all interaction points
Alternating bunch-to-bunch polarization
Comparably high polarization of a stored positron beam through S-T self-polarization effect
Sufficiently fast self-polarization at low positron beam energies (~3 GeV)

4. Electron Polarization Design Choices
High electron polarization through full-energy injection from CEBAF
Over 80% electron beam polarization from CEBAF’s state-of-the-art polarized source/injector
High polarization well preserved during acceleration in the multi-pass recirculated SRF Linac of CEBAF
Polarization direction coming out of CEBAF easily controlled by two Wien filters in the CEBAF injector
Longitudinally-polarized electron beam injected from CEBAF into a long straight section of the MEIC electron collider ring
After polarization degradation, beam replaced by new bunches from CEBAF.
Possibility of continuous top-off injection from CEBAF

5. Electron Polarization Design Choices
Maintaining high electron beam polarization
S-T self-polarization by making the spin anti-parallel to bending magnetic field in the arcs
Spin-tune superconducting solenoid(s) in straight(s) to adjust the spin tune for polarization stability
Longitudinal electron polarization at IP’s using spin rotators
Four 90º spin rotators at the ends of the arcs
Upstream spin rotator rotates spin from vertical to longitudinal
Downstream spin rotator rotates spin back to vertical
Spin rotators work over entire energy range

6. Electron Polarization In Figure-8 Collider Ring

7. Impact of Figure-8 Shape
Figure-8 shape chosen exclusively due to its unique advantages for ion polarization
Electron collider ring matches ion figure-8 footprint to share same tunnel and accommodate interaction points
No complications due to figure-8 shape for electrons, potentially advantageous due to energy-independent zero spin tune
SC solenoids in the straights (where spin is longitudinal) to improve polarization stability s x

8. Self-Polarization Time
Positron Beam
Positrons can be accelerated in CEBAF as effective as electrons with similar beam quality
Both polarized and unpolarized positron sources being developed for fixed target program
Only unpolarized positron source can provide sufficiently high beam current
Positron beam polarized by S-T self-polarization
Polarization time too long at low energies (<6 GeV). Shortening polarization time by
Using small damping ring to enhance S-T effect
Accelerating to high (~7 GeV) energy for quick self-polarization and subsequent deceleration
Self-Polarization Time
GeV
Hours 3
14.6 4
3.5 5
1.1 7
0.21 9
0.06

9. Spin Flip and Polarization Lifetime
From CEBAF and at IP’s
spin
In arcs
Polarization
depolarization
Bunch trains with alternating polarization from CEBAF by changing polarization of photo-injector’s driving laser
S-T effect could cause significant depolarization of wrong-direction polarization
Depolarized beam can be replaced periodically by injection from CEBAF, provided polarization lifetime is not too short (>10 min)
Possibility of multiple spin flips by spin resonance crossing

10. Universal Spin Rotator
Spin rotator rotates spin from vertical to longitudinal
works in whole 3 to 11 GeV energy range
same orbit geometry for different energies
Universal spin rotator (USR) composed of two solenoid interspersed with arc bending dipoles
Fixed dipole bending angles  no orbit change, solenoid strengths adjusted for different energies
x-y coupling compensated for each solenoid individually
E (GeV) 1
BL1 (Tm) 1 2
BL2 (Tm) 2 3
/2
15.7
/3
/6
4.5
/4
11.8
23.6 6
0.62
12.3
2/3
1.91
38.2 9 
62.8 12
24.6
4/3
76.4

11. Solenoid Coupling Compensation
Transport matrix of a solenoid
X-Y decoupling scheme
(V. Livinenko & A. Zholents, 1980)
(H. Sayed)
BdL = 28.7 T m e- v
Decoupling
insertion L
L/2
solenoid m
solenoid m
decoupling quad insert
M = T
- T

12. Spin Dynamics
Analytic estimate of equilibrium electron polarization gives ~85%
Preliminary tracking results (D. Barber) consistent with ~85%
More detailed depolarization/polarization studies including spin matching underway (in collaboration with Profs. D. Barber and A. Kondratenko).

13. Summary Electron polarization requirements
High polarization (>80%)
Sufficient polarization lifetime
Longitudinal polarization at IP’s
Alternating bunch-to-bunch polarization / spin-flipping
High electron polarization by full-energy injection from CEBAF
High degree of polarization maintained by S-T effect and by spin tune control with spin-tune solenoids
Longitudinal polarization at IP’s provided by four spin rotators in the entire 3 to 11 GeV/c energy range without affecting orbit
No complications due to figure-8 shape, potential advantage
Possibility of polarized positron beam with unpolarized positron source and S-T self-polarization
Alternating polarization by flipping polarization at the source
Detailed spin tracking and simulations underway in collaboration with Profs. D. Barber and A. Kondratenko