1. Polarization studies for CEPC
Zhe Duan
Institute of High Energy Physics, CAS
Presented at eeFACT 2016
The Cockcroft Institute, UK, Oct 24th , 2016

2. Motivation
Energy calibration with polarized LEP was a major achievement from both accelerator and particle physics point of view.
What is the operation mode for energy CEPC?
What is the energy reach with useful self-polarization for energy CEPC? In particular, what about WW threshold?
eeFACT2016, The Cockcroft Institute, UK, Sep 2016

3. CEPC schemes & energy calibration
Single ring (pretzel orbit)
Similar to LEP
Energy calibration of one beam
Energy calibration only after physics
Partial double ring[1]+crab waist
Similar to FCC-ee
Energy calibration of both beams possible
Beam energy monitoring throughout each fill with non-colliding bunches
[1] M. Koratzinos, Proc. IPAC He named this idea as the “bowtie” scheme.
eeFACT2016, The Cockcroft Institute, UK, Sep 2016

4. CEPC self-polarization parameters
Wangdou & Wangdou
Parameters
Single Ring Z
PDR-Z
PDR-W
beam energy(GeV)
45.5 80
radius of curvature(km)
6.1
circumference(km) 54
bunch number
100
1100
400
momentum compaction factor
3.4e-5
3.5e-5
2.4e-5
energy spread(MeV) σε
22.75
72.
synchrotron tune Qz
0.097
0.039
0.057
polarization build-up time(hour)
44.9
2.67
spread of spin precessing rate σν=aγ σε
0.052
0.16
modulation index σ=σν /Qz
0.530
1.34
2.86
It was experimentally shown in LEP increased energy spread leads to reduced equilibrium polarization.
According to A. Blondel, 52MeV is tentatively regarded as the maximum energy spread allowing useful polarization for beam calibration. Need detailed simulation to justify.
eeFACT2016, The Cockcroft Institute, UK, Sep 2016

5. Operation mode of energy calibration @ Z-pole
5~10% polarization is needed for energy calibration. ~ 1/10 polarization build- up time is needed. Polarization asymmetric wigglers can further boost the process.
LEP type polarization wiggler is assumed, B+ / B- = 6.25.
Wigglers on, ~ 45min to reach 10% polarization.
In partial double ring scheme, a scheme similar to FCC-ee can be adopted. refer to M. Koratzinos, XPOL Workshop 2016.
Assume 50 non-colliding bunches (~1/20), wigglers switch on for 45 min and switch off, then every ~ 6 min one bunch is depolarized to continuously monitor beam energy, and replaced by a fresh injected bunch. This process is sustainable.
1 wiggler costs 8% SR power;
2 wigglers cost 10% SR power;
12 wigglers cost 20% SR power.
A lot of questions yet to be addressed
Optics and operation issues with wigglers
energy difference between colliding and non-colliding bunches need to be addressed.
Measured local energy vs. global energy model.
Most importantly, the predicted precision of energy calibration. …
eeFACT2016, The Cockcroft Institute, UK, Sep 2016

6. What is the energy range of useful beam polarization for energy calibration?
Simulation study of equilibrium beam polarization for a model ring of similar parameters to CEPC.
Focus is on the polarization beam energy 80GeV (W+W- threshold).
eeFACT2016, The Cockcroft Institute, UK, Sep 2016

7. Polarization simulation for a model ring
Arc FODO cells of phase advances 60/60 degrees, connected by straight FODO cells; Periodicity: 4. Circumference: m. No polarization wigglers yet.
Parameters \ Energy Range Z W
energy(GeV) / aγ
45.6 / 103.5
80.4/182.5
working point Qx/Qy
268.08/268.22
natual emittance(nm)
0.56
1.73
damping time (turn) τx/τy/τz
1293/1293/647
237/237/119
rms energy spread σε (10-4)
5.3
9.33
rms energy spread σε (MeV)
24.2
75.0
polarization build-up time(hour)
37.44
2.20
spread of spin precessing rate σν=aγ σε
0.055
0.170
eeFACT2016, The Cockcroft Institute, UK, Sep 2016

8. Simulation method
Simulation code: fortran scripts calling PTC[1] as a library
First order normal form[2] to obtain and , then apply DK formula (first order spin resonance only)
Monte-Carlo simulation of depolarization rate[3] (higher order spin resonances included)
Lattice imperfection introduction and correction
In MADX, vertical misalignment errors are introduced for each quadrupole (2736 quads in total), with a rms ymis = 50μm ~ 120 μm.
Near each quad, there is a zero-length BPM & and a H/V corrector of 0.05 m. BPM error is not introduced yet.
Realistic trajectory & closed orbit correction is not implemented (refer to Sergey Sinyatkin’s talk ). MICADO algorithm is used to correct vertical orbit only, only successful cases with typical final rms VCO and tilt of n0-axis are selected and exported to PTC lattice format, and launched for polarization simulation.
Harmonic closed orbit spin matching is not implemented yet.
[1] F. Schmit, E. Forest and E. McIntosh, CERN-SL , 2002.
[2] E. Forest, KEK Report KEK , 2010.
[3] Z. Duan, M. Bai, D. P. Barber and Q. Qin, NIM A793 (2015) 81.
eeFACT2016, The Cockcroft Institute, UK, Sep 2016

9. One particular error seed
Initially all quads are vertical misaligned by 50 μm rms, then corrected with MICADO using 300 correctors.
rms vertical closed orbit = 57.9 μm.
rms vertical closed quadrupoles = 56.6 μm.
(νx, νy)=( , )
rms tilt of n0-axis = 0.98 aγ=182.5
eeFACT2016, The Cockcroft Institute, UK, Sep 2016

10. Polarization around 80 GeV
Note:
stepsize is aγ=0.1
Qz is the synchrotron tune.
ξ = a γ σδ / Qz is the modulation index.
eeFACT2016, The Cockcroft Institute, UK, Sep 2016

11. Polarization around 80GeV, different Qz
eeFACT2016, The Cockcroft Institute, UK, Sep 2016

12. Polarization scan over energy
Fix fractional part of aγ = 0.5, Qz = 0.11
Enhanced imperfection
resonances around
85 GeV due to optics
structure.
eeFACT2016, The Cockcroft Institute, UK, Sep 2016

13. 210 error seeds
Initially all quads are vertical misaligned by 50 μm ~ 120 μm rms, then corrected with MICADO using 300 ~ 500 correctors.
Some statistics of corrected machines.
Qz is fixed to be 0.11, larger than Wang Dou’s parameter list.
@80GeV
eeFACT2016, The Cockcroft Institute, UK, Sep 2016

14. Simulated beam polarization @ 80 GeV
Sub-100 μm rms vertical closed orbit at quadrupoles is necessary but not sufficient for useful self-polarization, if no harmonic closed orbit spin matching is adopted. Tight requirements on allowed misalignment errors - > Beam-based alignment.
eeFACT2016, The Cockcroft Institute, UK, Sep 2016

15. Simulated beam polarization @ 80 GeV
If closed orbit harmonic spin matching is taken into account, the rms tilt of n0-axis needs to be reduced to smaller than 3 mrad for useful polarization.
eeFACT2016, The Cockcroft Institute, UK, Sep 2016

16. Discussion
Possible operation mode of energy calibration for Z-pole is discussed. A lot of detailed questions to address.
Simulation of beam polarization at 80 GeV indicates very tight requirements on misalignment error or closed orbit harmonic spin matching. Larger synchrotron tune will help.
~50 μm rms misalignment error has been achieved at recent light source facilities. But according to Jorg Wenninger, in LHC, over three year the typical rms misalignment of quadrupoles is ~ 200 μm, corresponding to a movement of ~ 0.17 μm per day.
We have no idea yet what will be like in CEPC, but this indicates possible frequent re-alignment is required.
Going to even larger circumference will relieve these requirements, as in FCC-ee. But the misalignment tolerance from other optics requirements is also demanding.
eeFACT2016, The Cockcroft Institute, UK, Sep 2016

17. eeFACT2016, The Cockcroft Institute, UK, 24-27 Sep 2016
Thank you for your attention!
eeFACT2016, The Cockcroft Institute, UK, Sep 2016

18. eeFACT2016, The Cockcroft Institute, UK, 24-27 Sep 2016
Backup
eeFACT2016, The Cockcroft Institute, UK, Sep 2016

19. Analysis of the cause of the very large tilt of n_0 axis around 85GeV (aγ=197) (cont.)
where 2π νB is the total phase advance accumulated through all dipole cells that precess spin vectors,
and [νB] = [νy] νB / νy
In the model lattice of CEPC,
P=4, M=296, νy= for the bare lattice, νB = , therefore, [νB]=197
Super strong imperfection resonance (and thus a large tilt of n0-axis) occurs at aγ=197,
aγ=192, 196, 200, … are locations of very strong imperfection resonance (and also large tilt of n0-axis)
Note that the contribution of vertical correctors and vertical offset in quadrupoles could enhance n0 tilt at some other locations, but when a lot of random seeds are plotted on the same figure, the contribution from vertical closed orbit in quadrupoles looks more evident.