Mark 20121024

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Mark 20121024

  1. 1. Simulation and Analysis of the Data in TPS 2012/10/24 Cheng-Chin Chiang 江政錦 1
  2. 2. Personal DataPresent Position:Assistant Researcher in Beam Dynamics Group, NSRRCEducation:National Taiwan University (2004~2009), Ph.D. in PhysicsExperience:2004~2010(1)  Member of BELLE collaboration in KEK(2)  On call shift of BELLE sub-detector in KEK(3)  System manger of NTU High Energy Lab.(4)  Internal referee of Physical analysis group in BELLE collaboration2010~2012(5) Computer programming for TPS project 2
  3. 3. Working Experience at KEK-BELLE 3
  4. 4. KEK Campus (Tsukuba, Japan) 4
  5. 5. KEK-BELLE e +e- Collider•  Two separate rings for e+ and e-•  Energy in CM is 10.58GeV  Y(4S)•  Ring length 3Km 8.0 GeV e- Belle 3.5 GeV e+ 5
  6. 6. KEK e +e- Acceleratore+/e- Linac Straight Section Arc Section 6 e+ Generator of linac Electron Source of linac
  7. 7. The BELLE Detector Extreme Forward Calorimeter γ, π0 reconstruction e+- identification 7
  8. 8. My Working Place at KEKExtreme Forward Calorimeter Electronic-Hut BELLE control room Spring Autumn Kitty 8
  9. 9. Study the CP (Charge × Parity) ViolationFor example: B0→J/ψ K0 Decay -- B0 Decay(Time dependent CP violation) -- B0 Decay 9
  10. 10. The Challenge of CP Violation•  In theoretical calculations: - We need a good model to explain the behavior of B meson decays from experimental measurements Tree diagram Penguin diagram•  In experiment: - We need to produce the maximum number of B meson decays for good measurements in statistics (i.e. good luminosity). - We need good analysis methods and tools to evaluate the huge amount of experimental data 10
  11. 11. : B0 →ρ0ρ0 : Continuum 657 Million BB Data Measurement : b→c decays : Other charmless (B0→ρ0ρ0 Decay) B decaysMode Yield Eff.(%) Σ BF (x10-6) UL (x10-6) +23.6+10.1 +0.2ρ0ρ0 24.5−22.1−16.2 9.16 (fL=1) 1.0 0.4 ± 0.4 −0.3 <1.0 (fL=1) +67.4 +3.5ρ0ππ 112.5−65.6 ± 52.3 2.90 1.3 5.9−3.4 ± 2.7 <12.0 4π +61.2+27.7 161.2−59.4−25.1 1.98 2.5 +4.7+2.1 12.4 −4.6−1.9 <19.3 € +14.5+4.8 € ρ0f0 −11.8−12.9−3.6 9.81 … … <0.3€ € f0f0 +4.7 −7.7−3.5 ± 3.0 10.17 … … <0.1 € +37.0 € +1.9 f0ππ 6.3−34.7 ± 18.0 2.98 … 0.3−1.8 ± 0.9 <3.8 € 11 € € €
  12. 12. Publications1.  C.C. Chiang et al. (Belle Collaboration), ``Measurement of B0 → ππππ decays and search for B → ρ0ρ0”, Phys. Rev. D, 78, 111102(R) (2008); arXiv:0808.2576.2.  C.C. Chiang et al. (Belle Collaboration), ``Measurement of B0 → ππππ decays and search for B → ρ0ρ0 at Belle”, in the Book ``Les Rencontres de physique de la Vallée dAoste”, Edited by M. Greco, ISBN 978-88-86409-56-8, p.365-378 (2008).3.  C.C. Chiang et al. (Belle Collaboration), ``b → d and other charmless B decays at Belle”, European Physical Society Europhysics Conference on High Energy Physics (2009), PoS(EPS-HEP2009) 207; http://pos.sissa.it/cgi-bin/reader/conf.cgi?confid=84.4.  C.C. Chiang et al. (Belle Collaboration), ``Search for B0 → K*0 anti-K*0, B0 → K*0 K*0 and B0 → KKππ decays”, Phys. Rev. D, 81, 071101(R) (2010); arXiv:1001.4595.5.  C.C. Chiang et al. (Belle Collaboration),``Improved Measurement of the Electroweak Penguin Process B → Xs l+l-“, 35th International Conference of High Energy Physics, PoS(ICHEP2010) 231; http://pos.sissa.it/cgi-bin/reader/conf.cgi?confid=120. 12
  13. 13. Working Experience at NSRRC 13
  14. 14. Optimize the TPS/BR Lattice FULL TPS booster b6p4d2 20. Linux version 8.23/08 28/09/12 10.28.00 10 x y DX10(m), DX 18. 16. 14. (a) Baseline Design: 12. 10. Qx= 14.3796, Qy= 9.3020 Cx= 1.0, Cy= 1.0 8. 6. 4. 2. 0.0 0.0 10. 20. 30. 40. 50. 60. 70. 80. 90. s (m) E / p0c = 0 . Table name = TWISS FULL TPS booster b6p4d2 20. Linux version 8.23/08 28/09/12 10.28.20 10 x y DX10 (m), DX (b) From Magnet Group Data: 18. 16. 14. 12. 10. Qx= 14.3781, Qy= 9.3057 8. 6. (ΔQx= -0.0015, ΔQy= +0.0037) 4. 2. Cx= 0.95, Cy= 1.25 0.0 0.0 10. 20. 30. 40. 50. 60. 70. 80. 90. s (m) E / p0c = 0 . Table name = TWISS FULL TPS booster b6p4d2 20. Linux version 8.23/08 28/09/12 10.28.30 10 x y DX10(m), DX 18. 16. 14. (c) New Re-Matching Result: 12. 10. Qx= 14.3799, Qy= 9.3027 8. 6. (ΔQx= +0.0003, ΔQy= +0.0007) Cx= 1.0, Cy= 1.0 4. 2. 0.0 0.0 10. 20. 30. 40. 50. 60. 70. 80. 90. s (m) 14 E / p0c = 0 . Table name = TWISS
  15. 15. Check the Dynamic Aperture (DA) for TPS/BR with 10 Random Machines E/E = 0% 14 Blue: baseline lattice (a) βx=14.926, βy=6.749 1 2 Red: new matched lattice (c) 12 3 4 10 βx=14.904, βy=6.683 5 6 7 8 The multipole field errors are adoptedy (mm) 9 8 10 1 2 in the lattice model. 6 3 4 5 4 6 7 The size of DA is related to the injection 8 2 9 10 efficiency. We do not yet consider the 0 close orbit distortion and orbit variations -30 -20 -10 0 x (mm) 10 20 30 due to ramping. E/E = -1.5% E/E = 1.5% 14 14 βx=15.942, βy=5.928 βx=13.898, βy=7.643 1 1 2 2 12 3 12 3 4 4 10 βx=15.928, βy=5.854 5 6 10 βx=13.872, βy=7.577 5 6 7 7 8 8y (mm) y (mm) 9 9 8 10 8 10 1 1 2 2 6 3 6 3 4 4 5 5 6 6 4 7 4 7 8 8 9 9 2 10 2 10 0 0 -30 -20 -10 0 x (mm) 10 20 30 -30 -20 -10 0 x (mm) 10 20 30 15
  16. 16. Estimate Eddy Current Effect in TPS/BR The beam is injected from linac The beam energy is increased in to TPS/BR at 150 MeV TPS/BR from 150 MeV to 3 GeV (DESY formula) (S.Y. Lee’s formula) 0.2 3 2 K2 (S.Y. Lee) x (S.Y. Lee) 0.18 K2 (SLS) 1.5 y (S.Y. Lee) Energy 2.5 0.16 1 x (SLS) y (SLS) 0.14 0.5 2 Chromaticity Energy (GeV) 0.12K2 (1/m3) 0 0.1 1.5 -0.5 0.08 -1 0.06 ΔK2(at Dipole) vs. Time 1 -1.5 Chromaticity vs. Time 0.04 -2 0.5 0.02 -2.5 0 0 -3 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 Time (ms) Time (ms) Check DA for the worst (Eddy) case (at 23 ms) 16
  17. 17. Check DA with 100 Random Machines TPS/BR Original lattice model E/E = -1.5% E/E = 0% E/E = 1.5% 14 14 14 dynap dynap dynap chamber chamber chamber 12 12 12 10 10 10 y (mm) y (mm) y (mm) 8 8 8 6 6 6 4 4 4 2 2 2 0 0 0 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 x (mm) x (mm) x (mm) w/ Eddy effect (worst case) E/E = -1.5% E/E = 0% E/E = 1.5% 14 14 14 dynap dynap dynap chamber chamber chamber 12 12 12 10 10 10y (mm) y (mm) y (mm) 8 8 8 6 6 6 4 4 4 2 2 2 0 0 0 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 x (mm) x (mm) x (mm) 17
  18. 18. Apply Sextupole Magnets for Chromaticity Correction During TPS/BR Ramping Chromaticity = (+1.07, +1.50) 0 2 K2 (Eddy current effect, DESY formula) -1 K2 EDDY vs. K2 SD 1 K2 (SD sextupole strength) K2 (SF sextupole strength) K2 (SD Sextupole Strength) (1/m^3) -2 0 -3 -1 K2 (1/m3) -4 € -2 -5 ’check.log’ u 1:(2.0*$2) fit result: a1=-28.2654, b1=-0.012603 -3 -6 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 K2 (Sextupole Strength Induced by Eddy Current Effect) (1/m^3) -4 K2 SD = (−28.2654) × K2 EDDY − 0.0126 -5 K2 (SF, SD) vs. Time Chromaticity = (+1.07, +1.50) 0.5 ’check.log’ u 1:(2.0*$3) fit result: a2=2.27689, b1=0.00534554 -6 0.45 0 20 40 60 80 100 120 140 160 0.4 K2 EDDY vs. K2 SF Time (ms) K2 (SF Sextupole Strength) (1/m^3) (For a ramping period) 0.35€ 0.3 0.25 0.2 0.15 € 0.1 MAD Chromaticity (ξx , ξy ) ~ (+1, +1) 0.05 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 K2 (Sextupole Strength Induced by Eddy Current Effect) (1/m^3) 18 K2 SF = (2.2769) × K2 EDDY + 0.0053 €
  19. 19. Check DA with 100 Random Machines w/ Eddy effect (worst case) + sext. corrections E/E = -1.5% E/E = 0% E/E = 1.5% 14 14 14 dynap dynap dynap chamber chamber chamber 12 12 12 10 10 10y (mm) y (mm) y (mm) 8 8 8 6 6 6 4 4 4 2 2 2 0 0 0 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 x (mm) x (mm) x (mm) In summary, applying sextupole magnets in TPS/BR during the energy ramping allows us to improve the DA. 19
  20. 20. Establish Analysis Tools (MIA&ICA)•  To prepare the analysis tools for TPS commissioning, we apply MIA (Model Independent Analysis) [1] and ICA (Independent Component Analysis) [2] in turn-by-turn BPM data mining. [1] Y. T. Yan et al., Report No. SLAC-PUB-11209 (2005). [2] X. Huang et al., Phys. Rev. ST Accel. Beams 8, 064001 (2005).•  MIA or ICA are fast analyses (one-shot) for BPM beam signal, which are used to measure the lattice parameters such as beta, phase advance, dispersion, betatron and synchrotron tunes.•  We test MIA and ICA methods with TPS/BR simulation data and TLS /SR experimental data.•  For TPS/BR analysis, we have included the multipole errors, eddy current effects, and BPM noise in track simulation. 20
  21. 21. The Principle of MIA •  We decompose the equal time covariance matrix of turn-by- turn BPM data with Singular Value Decomposition (SVD): ⎛ x1 (1) x1 (2)  x1 (1000) ⎞ ⎜ ⎟ ⎜ x 2 (1) x 2 (2)  x 2 (1000) ⎟ For 60 BPMs and 1000 turns: X(t) = ⎜     ⎟ ⎜ ⎟ ⎝ x 60 (1) x 60 (2)  x 60 (1000)⎠ CX = X(t)X(t)T = UΛU T (decomposed with SVD) € ⎛ S1 ⎞ Dx Dispersion Spatial Temporal ⎜ ⎟ ⎜ S2 ⎟ ⎜ S3 ⎟ νx Betatron motion€ ∴ X = U(U X) = ( A1 T A2 A3 A4 A5 )⎜ ⎟ ⎜ S4 ⎟ Dx νx 2νx ⎜ S5 ⎟ 2νx Sextupole terms ⎜ ⎟ ⎝  ⎠ 21
  22. 22. Extract Beta, Phase, Dsipersion and Tunes from the First Three of Largest Singular ValuesFor horizontal betatron motion: Dx = A1 × const. 2 2 ⎛ s1 ⎞ βx = (A2 + A3 ) × const. ⎜ ⎟ ⎜ s2 ⎟ ⎛ ⎞ −1 A2X = U(U T X) = ( A1 A2 A3  0)⎜ s3 ⎟ ⎜ ⎟ ∴ φx = tan ⎜ ⎟ ⎝ A3 ⎠ ⎜  ⎟ ⎜ ⎟ ⎝ 0 ⎠ ν syn. = FFT(s1) ⎛ βx1 βx1 ⎞ ⎜ aDx1 sin(ν x φ1 ) cos(ν x φ1 ) ⎟ ν x = FFT(s2,3 ) ⎜ M M ⎟ ⎜ βx 2 βx 2 ⎟ aDx 2 sin(ν x φ 2 ) cos(ν x φ 2 ) ⎟= ⎜ M M Spatial Matrix ⎜    ⎟ ⎜ ⎜ aDxm βxm sin(ν x φ m ) βxm € cos(ν x φ m ) ⎟ ⎟ € (a = constant, Dx= dispersion) ⎝ M M ⎠ ⎛ λ λ1 λ1 ⎞ ⎜ 1 sin(2πν syn. • 0) sin(2πν syn. • 1)  sin(2πν syn. • N)⎟ ⎜ N N N ⎟ ⎜ λ2 cos(2πν x • 0) λ2 cos(2πν x • 1)  λ2 ⎟ cos(2πν x • N) ⎟ Temporal Matrix×⎜ N ⎜ λ N N ⎟ (νsyn.=synchrotron tune) λ3 λ3 ⎜ 3 sin(2πν x • 0 sin(2πν x • 1)  sin(2πν x • N) ⎟ ⎜ N N N ⎟ 22 ⎝     ⎠
  23. 23. Ramping Effects vs. Turn Number 3 Ramping Energy 9 10 1 6 7 8 9 10 Ramping RF Voltage Beam Energy 8 5 7 4 2.5 0.8 6 3 RF Voltage (MV) 2 RF VoltageEnergy (GeV) 0.6 1.5 5 2 4 0.4 1 2 3 1 1-10000 turn 1-10000 turn 10001-20000 turn 10001-20000 turn 20001-30000 turn 20001-30000 turn 1 30001-40000 turn 30001-40000 turn 40001-50000 turn 0.2 40001-50000 turn 0.5 50001-60000 turn 50001-60000 turn 60001-70000 turn 60001-70000 turn 70001-80000 turn 70001-80000 turn 80001-90000 turn 80001-90000 turn 90001-100660 turn 90001-100660 turn 0 0 0 20000 40000 60000 80000 100000 0 20000 40000 60000 80000 100000 Turn Number Turn Number Ramping Sextupole Strength K2 2 SF sextupole strength 1 1 2 3 4 5 6 7 8 9 10 It takes about 100,660 turns 0 to accomplish a ramping cycle. Eddy current effect, DESY formula -1 K2 (1/m^3) -2 Eddy Effect Each color represents specific ramping period -3 1-10000 turn SD sextupole strength 10001-20000 turn 20001-30000 turn -4 (for every 10,000 turns). 30001-40000 turn 40001-50000 turn 50001-60000 turn -5 60001-70000 turn 70001-80000 turn 80001-90000 turn 90001-100660 turn -6 0 20000 40000 60000 80000 100000 23 Turn Number
  24. 24. 6-D Phase Space for a Ramping Cycle X vs. PX Y vs. PY -ct vs. ΔE/E BPM1 {X-PX} - plane BPM1 {Y-PY} - plane BPM1 {T-PT} - plane 0.0006 0.002 1-10000 turn 1-10000 turn 0.0006 10001-20000 turn 10001-20000 turn 20001-30000 turn 20001-30000 turn 30001-40000 turn 0.0015 30001-40000 turn 0.0004 40001-50000 turn 40001-50000 turn 0.0004 50001-60000 turn 50001-60000 turn 60001-70000 turn 60001-70000 turn 70001-80000 turn 0.001 70001-80000 turn 80001-90000 turn 80001-90000 turn 0.0002 90001-100660 turn 90001-100660 turn 0.0002 0.0005BPM1 PX/P0 PY/P0 dE/E 0 0 0 -0.0002 -0.0005 . -0.0002 1-10000 turn 10001-20000 turn 20001-30000 turn 30001-40000 turn -0.001 40001-50000 turn -0.0004 -0.0004 50001-60000 turn . 60001-70000 turn -0.0015 70001-80000 turn 80001-90000 turn -0.0006 90001-100660 turn -0.0006 -0.002 -0.003 -0.002 -0.001 0 0.001 0.002 0.003 -0.004 -0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004 0 0.02 0.04 0.06 0.08 0.1 . X (m) Y (m) -ct (m) . 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 . . . Each color represents specific tracking period (for every 10,000 turns).BPM60 24
  25. 25. Reconstruct TPS/BR Lattice Parameters with MIA Reconstructed value at BPM Model 20 30 20 30 18 (a) (b) 18 (c) (d) 25 25 16 x = 0.380 16 y = 0.302 14 20 14 20 Power (Model: 0.3796) (Model: 0.3020) Power(m) (m) 12 12 15 15 10 10 x y 8 10 8 10 6 6 5 5 4 4 2 0 2 0 0 50 100 150 200 250 300 350 400 450 500 0 0.1 0.2 0.3 0.4 0.5 0 50 100 150 200 250 300 350 400 450 500 0 0.1 0.2 0.3 0.4 0.5 s (m) Horizontal Tune s (m) Vertical Tune 0.7 30 (e) (f) 0.6 25 The reconstructed values of βx, βy and horizontal 0.5 20 = 0.025 dispersion Dx at BPMs are shown as red dots in 0.4 s PowerDx (m) 0.3 15 (Model: 0.0250) (a), (c) and (e), respectively. The gray lines are 0.2 10 model values along the TPS booster. The 0.1 5 reconstructed tunes for νx, νy and νs are shown -0.1 0 0 in (b), (d) and (f), respectively. 0 50 100 150 200 250 300 350 400 450 500 0 0.1 0.2 0.3 0.4 0.5 s (m) Synchrotron Tune 25
  26. 26. The Principle of ICA •  We diagonalize the non-equal time covariance matrices of turn-by- turn BPM data: ⎛ x1 (1) x1 (2)  x1 (1000) ⎞ ⎜ ⎟ ⎜ x 2 (1) x 2 (2)  x 2 (1000) ⎟ For 60 BPMs and 1000 turns: X(t) = ⎜     ⎟ ⎜ ⎟ ⎝ x 60 (1) x 60 (2)  x 60 (1000)⎠ whitening ⎛ Λ1 0 ⎞⎛U1T ⎞ CX (τ = 0) = X(t)X(t)T = (U1,U 2 )⎜ ⎟⎜ T ⎟, ⎝ 0 Λ 2 ⎠⎝U 2 ⎠ € CX (τ k ≠ 0) = X(t)X(t + τ k )T , k = 1,2,3... The Jacobi-like joint diagonalization is applied to find out a unitary matrix W which is a joint diagonalizer for all the auto-covariance matrices:€ s = W T (Λ−1/ 2U1T )X (temporal) 1 ⇒ CX (τ k ) = WDkW T , A = (Λ−1/ 2U1T ) −1W 1 (spatial) (k = 1,2,3...) 26
  27. 27. Reconstruct TLS/SR Lattice Parameters with ICA •  We practice the ICA in experimental turn-by-turn data for TLS/SR. •  The horizontal and vertical tunes of TLS/SR model are 0.310 and 0.277, respectively; the horizontal and vertical tunes from measurement are 0.302 and 0.180, respectively. Horizontal singular values Vertical singular values 36 36 Mode 1: βx Mode 1: βy 34 34 Mode 2: βx Mode 2: βy 32 32 Mode 3: βx There are horizontal betatron log(SVy) Mode 3: βy There are vertical betatron log(SV ) x 30 30 couplings, the magnitude of couplings, the magnitude of Mode 5: βy Mode 4: βx coupling is about 10-3 of vertical 28 coupling is about 10-7 of 28 betatron oscillation. horizontal betaton oscillation. 26 Mode 7: Dx 26 24 24 22 22 0 10 20 30 40 50 60 0 10 20 30 40 50 60 SVx Index SVy Index 25 25 1.4 1.2 20 20 1Reconstructed value at BPM 15 15 Dx (m) (m) (m) 0.8Model value at BPM y x 0.6 10 10Model 5 5 0.4 0.2 0 0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 0 20 40 60 80 100 120 s (m) s (m) s (m) 27
  28. 28. Summary of MIA&ICA•  We have successfully extracted lattice parameters, like beta, phase advance, dispersion and tunes with MIA or ICA for TPS/BR and TLS /SR.•  We have included MIA&ICA analysis codes in MATLAB based system.•  The property of MIA&ICA is fast analysis, so we can measure the machine status within seconds. It is suitable for TPS/BR analysis.•  The MIA&ICA provides another information for LOCO, which would be helpful in machine measurement and modeling. 28
  29. 29. Injection Study for TPS/SR•  In order to reduce the radiation level, we study the tolerance of injected beam condition•  Use Tracy-II for 6-D tracking. The lattice model includes the injection kicker strength, septum arrangement, chamber limits, multipole field errors (10 random machines are used), close orbit distortion and its correction by applying correctors, etc.•  We generate a thousand particles as a bunch of a beam and track these particles for a thousand turns•  Check the survival rate of a beam bunch and record the lost information of particles, including lost position, lost plane and lost turn number. These information are useful for radiation protection. 29
  30. 30. Schematic Layout of TPS/SR Injection 3.6 2.8 3.6 K1 K2 K3 Bumped K4 Stored beam stored beam 0.6 Injected beam 0.6 0.6 0.6 Kicker magnet 0.8 0.8 Unit:(m) Pulsed septum DC septum (AC septum) K3 K4 K1 K2e- t1~T0t0= 0 t1=T0Injection pt. Injection pt. 30
  31. 31. QL1 K1 K2 400 800 K3 K4 QL1 68 mm 54 mm 600 600 [-34, +34] [-20, +34] 600 600 700 3000 1100 1100 3000 700 Middle of R1 straight Injection pointSimplified model for chamber x’limit used in injection simulations. Septum wallThe chamber limits in long and 3 mmshort straight sections are: Bumped beam acceptance[x = ±34 mm, y = ±5 mm] Acceptance Bumped stored beam x Injected beam Stored beam Beam stay clear = 20.0 mm Xoffset = 23.8 mm 31
  32. 32. Phase Space (Px/P0 vs. x) Choose one of the random machines and scan injected beam position in horizontal. 4 4 4 4 Xoffset = 23.8 mm Xoffset = 24.8 mm Xoffset = 25.8 mm Xoffset = 26.8 mm Px / P0 (x10-3) Px / P0 (x10-3) Px / P0 (x10-3) Px / P0 (x10-3) 3 3 3 3 2 2 2 2 1 1 1 1 0 0 0 0 Turn 0 Turn 0 Turn 0 Turn 0 -1 Turn 1 -1 Turn 1 -1 Turn 1 -1 Turn 1 Turn 2 Turn 2 Turn 2 Turn 2 Turn 3 Turn 3 Turn 3 Turn 3 -2 Turn 4 -2 Turn 4 -2 Turn 4 -2 Turn 4 Turn 5 Turn 5 Turn 5 Turn 5 Turn 6 Turn 6 Turn 6 Turn 6 Turn 7 Turn 7 Turn 7 Turn 7 -3 Turn 8 -3 Turn 8 -3 Turn 8 -3 Turn 8 Septum Septum Septum Septum Septum Septum Septum Septum -4 -4 -4 -4 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 x (mm) x (mm) x (mm) x (mm) 4 4 4 4 Xoffset = 27.8 mm Xoffset = 28.8 mm Xoffset = 29.8 mm Xoffset = 30.8 mm Px / P0 (x10-3) Px / P0 (x10-3) Px / P0 (x10-3) Px / P0 (x10-3) 3 3 3 3 2 2 2 2 1 1 1 1 0 0 0 0 Turn 0 Turn 0 Turn 0 Turn 0 -1 Turn 1 -1 Turn 1 -1 Turn 1 -1 Turn 1 Turn 2 Turn 2 Turn 2 Turn 2 Turn 3 Turn 3 Turn 3 Turn 3 -2 Turn 4 -2 Turn 4 -2 Turn 4 -2 Turn 4 Turn 5 Turn 5 Turn 5 Turn 5 Turn 6 Turn 6 Turn 6 Turn 6 Turn 7 Turn 7 Turn 7 Turn 7 -3 Turn 8 -3 Turn 8 -3 Turn 8 -3 Turn 8 Septum Septum Septum Septum Septum Septum Septum Septum -4 -4 -4 -4 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 x (mm) x (mm) x (mm) x (mm) 4 4 4 Xoffset = 31.8 mm Xoffset = 32.8 mm Xoffset = 33.8 mm Px / P0 (x10-3)Px / P0 (x10-3) Px / P0 (x10 ) 3 3 3 -3 2 2 2 1 0 1 0 1 0 Only show 9 turns -1 Turn 0 Turn 1 Turn 2 Turn 3 -1 Turn 0 Turn 1 Turn 2 Turn 3 -1 Turn 0 Turn 1 Turn 2 Turn 3 Turn 4 Results -2 Turn 4 -2 Turn 4 -2 Turn 5 Turn 5 Turn 5 Turn 6 Turn 6 Turn 6 Turn 7 Turn 7 Turn 7 -3 -3 -3 Turn 8 Turn 8 Turn 8 Septum Septum Septum Septum Septum Septum -4 -4 -4 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 x (mm) x (mm) x (mm) 32

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