Polarization studies for CEPC Zhe Duan Institute of High Energy Physics, CAS Presented at eeFACT 2016 The Cockcroft Institute, UK, Oct 24th , 2016 zhe.duan@ihep.ac.cn

Motivation Energy calibration with polarized beam @ LEP was a major achievement from both accelerator and particle physics point of view. What is the operation mode for energy calibration @ CEPC? What is the energy reach with useful self-polarization for energy calibration @ CEPC? In particular, what about WW threshold? eeFACT2016, The Cockcroft Institute, UK, 24-27 Sep 2016

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 2015. He named this idea as the “bowtie” scheme. eeFACT2016, The Cockcroft Institute, UK, 24-27 Sep 2016

CEPC self-polarization parameters Wangdou 20160325 & Wangdou 20160329 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, 24-27 Sep 2016

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, 24-27 Sep 2016

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 level @ beam energy 80GeV (W+W- threshold). eeFACT2016, The Cockcroft Institute, UK, 24-27 Sep 2016

Polarization simulation for a model ring Arc FODO cells of phase advances 60/60 degrees, connected by straight FODO cells; Periodicity: 4. Circumference: 57436.8m. 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, 24-27 Sep 2016

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-2002-044, 2002. [2] E. Forest, KEK Report KEK-2010-39, 2010. [3] Z. Duan, M. Bai, D. P. Barber and Q. Qin, NIM A793 (2015) 81. eeFACT2016, The Cockcroft Institute, UK, 24-27 Sep 2016

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 orbit @ quadrupoles = 56.6 μm. (νx, νy)=(268.124, 268.261) rms tilt of n0-axis = 0.98 mrad @ aγ=182.5 eeFACT2016, The Cockcroft Institute, UK, 24-27 Sep 2016

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, 24-27 Sep 2016

Polarization around 80GeV, different Qz eeFACT2016, The Cockcroft Institute, UK, 24-27 Sep 2016

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, 24-27 Sep 2016

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, 24-27 Sep 2016

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, 24-27 Sep 2016

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, 24-27 Sep 2016

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, 24-27 Sep 2016

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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=268.22 for the bare lattice, νB = 197.33, 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.