Spin Tracking Studies for Polarimetry at the ILC Moritz Beckmann DESY - FLC visiting SLAC May-August 2010 IWLC, Geneva October 20, 2010 Moritz Beckmann IWLC Oct 20, 2010 1/ 16
Introduction • Polarization is planned to be measured at the ILC with 0.25 % uncertainty in the beam delivery system (BDS) • Compton polarimeters, beam energy 45-500 GeV • Longterm scale calibration of luminosity-averaged polarization at IP to 0.1% using e + e − collision data • Spin diffusion / depolarization must be understood to 0.1% (further) spin tracking studies required Moritz Beckmann IWLC Oct 20, 2010 2/ 16
Simulation • This study is performed for the ILC • Could be used for other projects (e.g. CLIC) as well, if fed with corresponding lattice / parameters Moritz Beckmann IWLC Oct 20, 2010 3/ 16
Spin tracking • Spin propagation in electromagnetic fields is described by T-BMT equation d � � s = � � r , t ) , � dt � Ω E ( � B ( � r , t ) , � p , m , a × � s • Rough approximation ( � E = 0 , � B � = 0): Spin precession ∝ orbit bending in magnetic field: θ spin = a γ · θ orbit 567 · θ orbit for electrons at 250 GeV ≈ a : anomalous gyro-magnetic moment, a. k. a. g − 2 2 γ = E m Moritz Beckmann IWLC Oct 20, 2010 4/ 16
Idealized Lattice • Using latest available lattice (ILC2007b), beam parameters from Reference Design Report (2007) • 10 000 particles, spins assumed ∝ � e z at the end of the linac • Perfect magnet alignment, no collision effects • Plot: longitudinal polarization along BDS UP/DP: positions of up-/downstream polarimeters • Dips due to dipoles: polarization vector rotates, but no significant depolarization Moritz Beckmann IWLC Oct 20, 2010 5/ 16
Idealized Lattice (cont’d) UP/DP: positions of up-/downstream polarimeters Caution: scaling of x-axes varies Moritz Beckmann IWLC Oct 20, 2010 6/ 16
Idealized Lattice (Zoom) • Spin fan-out due to lateral beam size in quadrupoles • Red lines: ± 0 . 1% (must know changes to this precision) Moritz Beckmann IWLC Oct 20, 2010 7/ 16
Special Issues in the Interaction Region • Important elements are not yet included in lattice • Detector magnets • Crab cavities (give the bunch a transverse kick to compensate for beamline crossing angle) • Additional cavity or achromaticity for travelling focus scheme to achieve higher luminosity • Effects of beam-beam collision have to be investigated • Disruption of beam ( ∼ 10 − 4 rad) • Spin flips due to emission of beamstrahlung Moritz Beckmann IWLC Oct 20, 2010 8/ 16
Alignment / Ground Motion • Magnet misalignments between polarimeters contribute to incomparability of measurements • Need to investigate effect of static misalignments and ground motion: • Polarization vector rotation ( θ spin = a γ · θ orbit ) • Spin fan-out due to poor focussing Moritz Beckmann IWLC Oct 20, 2010 9/ 16
Alignment / Ground Motion • Magnet misalignments between polarimeters contribute to incomparability of measurements • Need to investigate effect of static misalignments and ground motion: • Polarization vector rotation ( θ spin = a γ · θ orbit ) • Spin fan-out due to poor focussing • Compensation by feed-back correctors? → Requirements on alignment and BPM precision Need for additional correctors? Moritz Beckmann IWLC Oct 20, 2010 9/ 16
Static Misalignments • Initial sample, each element randomly misaligned (Gaussian-distributed random numbers, σ x , y = 2 µ m) • σ x , y = 2 nm in final focus region (0-50m in front of IP) • Plots shows three exemplary samples 0.805 long. polarization IP DP 0.8 0.795 0.79 not misaligned 0.785 misaligned 0.78 0 20 40 60 80 100 120 140 distance from IP [m] Moritz Beckmann IWLC Oct 20, 2010 10/ 16
Static Misalignments • Initial sample, each element randomly misaligned (Gaussian-distributed random numbers, σ x , y = 2 µ m) • σ x , y = 2 nm in final focus region (0-50m in front of IP) • Plots shows three exemplary samples • No feed-back correctors implemented yet • Dashed: after rotation of the momentum vectors at the IP such that < p t > = 0; spins rotated accordingly ( a γ ) • Orbit correction at IP: ∆P z P z (IP,DP) < 0 . 1% 0.805 long. polarization IP DP 0.8 0.795 0.79 not misaligned misaligned 0.785 misaligned, corrected 0.78 0 20 40 60 80 100 120 140 distance from IP [m] Moritz Beckmann IWLC Oct 20, 2010 10/ 16
Static Misalignments (cont’d) • Collimators in BDS absorb up to 1000 particles due to missing orbit correction (will be moved in front of upstream polarimeter according to SB-2009 proposal) • Observed changes in polarization consistent with statistical effects ( ≤ 2 σ ) • ∆ P z of corrected beams = ∆ P z from collimators ⇒ Orbit correction at IP: ∆P z P z (UP,IP) < 0 . 1% 0.805 0.805 long. polarization UP IP 0.8 0.8 0.795 0.795 collimators 0.79 0.79 not misaligned not misaligned misaligned 0.785 misaligned 0.785 misaligned, corrected 0.78 0.78 -1800 -1700 -1600 -1500 -1400 -1300 0 10 20 30 40 50 60 70 80 distance from IP [m] distance from IP [m] Moritz Beckmann IWLC Oct 20, 2010 11/ 16
Static Misalignments: IP [rad] 0.22 100 θ = a γ ⋅ θ 0.2 spin orbit spin 0.18 80 θ 0.16 0.14 60 • Orbit and helicity 0.12 0.1 40 vector rotation are 0.08 strongly correlated 20 0.06 0.04 0 0.02 • Provisional -3 × 10 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 [rad] θ feed-back (lower orbit 40 [rad] plot) recovers 0.22 = a θ γ ⋅ θ 35 0.2 spin orbit longitudinal spin 0.18 30 polarization 0.16 θ 25 0.14 20 0.12 • Assumption: Spins 0.1 15 0.08 ∝ � e z at the end of 10 0.06 the linac 5 0.04 0.02 0 × 10 -3 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 [rad] θ orbit Moritz Beckmann IWLC Oct 20, 2010 12/ 16
Ground motion A. Hartin, PST 2009 • Plot: IP beam y-position and helicity with ground motion model for “noisy” site without correction • Nominal beam size σ y at IP: 5.7 nm Moritz Beckmann IWLC Oct 20, 2010 13/ 16
Summary • A spin tracking framework for high energy linear colliders has been set up • First studies have been performed for the ILC, where an understanding of polarisation to the permille-level is required Moritz Beckmann IWLC Oct 20, 2010 14/ 16
Summary • A spin tracking framework for high energy linear colliders has been set up • First studies have been performed for the ILC, where an understanding of polarisation to the permille-level is required • Alignment in whole BDS is crucial, but causes mainly helicity vector rotation → reversible • Provisional orbit correction at the IP ⇒ same P z at polarimeters and IP w. r. t. tolerances • Need to specify the polarization requirements on beam position monitors and alignment systems → more investigations Moritz Beckmann IWLC Oct 20, 2010 14/ 16
Outlook • Include more details into the simulation • Detector magnets • Crab cavities • Travelling focus scheme • Collision effects • Ground motion • Feed-back systems in lattice • Interface to polarimeter simulations • Develop calibration strategies Moritz Beckmann IWLC Oct 20, 2010 15/ 16
Thanks for your attention! Moritz Beckmann IWLC Oct 20, 2010 16/ 16
Backup slides Moritz Beckmann IWLC Oct 20, 2010 17/ 16
Static Misalignments: Upstream Polarimeter θ orbit : angle between reference orbit and actual particle orbit • Effects from misalignments are small, though visible (distribution offset from zero) • Depolarization ∼ 10 − 7 Moritz Beckmann IWLC Oct 20, 2010 18/ 16
Static Misalignments: Downstream Polarimeter 0.12 [rad] 12 θ = a γ ⋅ θ spin orbit 0.1 spin 10 θ 0.08 8 6 0.06 4 0.04 2 • Less correlation than 0.02 0 at the IP, effect of -3 × 10 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 [rad] θ extraction line orbit 0.12 24 [rad] quadrupoles? 22 = a θ γ ⋅ θ spin orbit 20 0.1 spin 18 • needs further 16 θ 0.08 14 investigation 12 0.06 10 8 0.04 6 4 0.02 2 0 × 10 -3 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 [rad] θ orbit Moritz Beckmann IWLC Oct 20, 2010 19/ 16
Effects of Energy spread • Sample as in the beginning, no misalignments • No difference due to energy spread visible Moritz Beckmann IWLC Oct 20, 2010 20/ 16
Effects of Energy spread • Sample as in the beginning, no misalignments • No difference due to energy spread visible Moritz Beckmann IWLC Oct 20, 2010 21/ 16
Detector magnets • Detectors contain • solenoid for tracking devices • dipole (anti-DID) to compensate for (detector) effects of crossing angle Moritz Beckmann IWLC Oct 20, 2010 22/ 16
Detector magnets • Detectors contain • solenoid for tracking devices • dipole (anti-DID) to compensate for (detector) effects of crossing angle • Additional correction kickers required to align beam at IP and behind detector • Parameters (solenoid field etc.) vary for different detector concepts Moritz Beckmann IWLC Oct 20, 2010 22/ 16
Detector magnets: Orbit Correction Simple model of SiD, first-order orbit correction • Mean x position < 0 . 03 mm • Plot for polarization not available due to technical problems Moritz Beckmann IWLC Oct 20, 2010 23/ 16
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