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SLIDE #1m.rayner1@physics.ox.ac.uk Beam measurements using the MICE TOF counters Analysis meeting, 23 September 2008 Mark Rayner
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SLIDE #2m.rayner1@physics.ox.ac.uk The available data Tof-0 0.48 m 12 x 4cm scintillator bars s x = 1.15 cm s t = 50 ps Tof-1 0.48 m 8 x 6cm scintillator bars s x = 1.73 cm s t = 50 ps
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SLIDE #3m.rayner1@physics.ox.ac.uk What we would like to measure
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SLIDE #4m.rayner1@physics.ox.ac.uk The MICE beam line
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SLIDE #5m.rayner1@physics.ox.ac.uk Large aperture quadrupoles g [T/m] z [m] g [T/m] z [m] = 66.2 cml 23.6 cm 17.82 cm x y y=25cm B x [Tesla] z [m] y=20cm y=15cm y=10cm y=5cm OPERA G4MICE Gradient = 0.766458 T/m
![SLIDE Large aperture quadrupoles g [T/m] z [m] g [T/m] z [m] = 66.2 cml 23.6 cm cm x y y=25cm B x [Tesla] z [m] y=20cm y=15cm y=10cm y=5cm OPERA G4MICE Gradient = T/m](http://images.slideplayer.com./16/4955166/slides/slide_5.jpg "SLIDE Large aperture quadrupoles g [T/m] z [m] g [T/m] z [m] = 66.2 cml 23.6 cm cm x y y=25cm B x [Tesla] z [m] y=20cm y=15cm y=10cm y=5cm OPERA G4MICE Gradient = T/m")
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SLIDE #6m.rayner1@physics.ox.ac.uk Modelling the quadrupole fringe fields Effective focusing strength k [m -2 ] Central quadrupole gradient [T/m] Effective length l [m] Central quadrupole gradient [T/m] 150 MeV/c 200 250 300 150 Defocusing Focusing g [T/m] z [m] g [T/m] z [m] = G4MICE
![SLIDE Modelling the quadrupole fringe fields Effective focusing strength k [m -2 ] Central quadrupole gradient [T/m] Effective length l [m] Central quadrupole gradient [T/m] 150 MeV/c Defocusing Focusing g [T/m] z [m] g [T/m] z [m] = G4MICE](http://images.slideplayer.com./16/4955166/slides/slide_6.jpg "SLIDE Modelling the quadrupole fringe fields Effective focusing strength k [m -2 ] Central quadrupole gradient [T/m] Effective length l [m] Central quadrupole gradient [T/m] 150 MeV/c Defocusing Focusing g [T/m] z [m] g [T/m] z [m] = G4MICE")
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SLIDE #7m.rayner1@physics.ox.ac.uk Modelling the quadrupole fringe fields Effective phase advance W [radians] Central quadrupole gradient [T/m] 150 MeV/c 200 250 300 Defocusing Focusing Focusing transfer matrix Defocusing transfer matrix
![SLIDE Modelling the quadrupole fringe fields Effective phase advance W [radians] Central quadrupole gradient [T/m] 150 MeV/c Defocusing Focusing Focusing transfer matrix Defocusing transfer matrix](http://images.slideplayer.com./16/4955166/slides/slide_7.jpg "SLIDE Modelling the quadrupole fringe fields Effective phase advance W [radians] Central quadrupole gradient [T/m] 150 MeV/c Defocusing Focusing Focusing transfer matrix Defocusing transfer matrix")
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SLIDE #8m.rayner1@physics.ox.ac.uk Objective #1: Make sure it’s possible to solve for x’ Avoid 0 or p Aim for p/2 f–f/2f g or k z TOF0 TOF1 1 0.8 0.6 0.4 0.2 0 0.3 10.80.60.4 g 07 [T/m] Phase advance W / p 222.5 MeV/c 247.5 MeV/c 0.50.90.7
![SLIDE Objective #1: Make sure it’s possible to solve for x’ Avoid 0 or p Aim for p/2 f–f/2f g or k z TOF0 TOF g 07 [T/m] Phase advance W / p MeV/c MeV/c](http://images.slideplayer.com./16/4955166/slides/slide_8.jpg "SLIDE Objective #1: Make sure it’s possible to solve for x’ Avoid 0 or p Aim for p/2 f–f/2f g or k z TOF0 TOF g 07 [T/m] Phase advance W / p MeV/c MeV/c")
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SLIDE #9m.rayner1@physics.ox.ac.uk Objective #2: Minimize the error on x’: Make the beam fill Tof-1 1 0.8 0.6 0.4 0.2 0 1.20.80.60.4 g 07 [T/m] Phase advance W / p 222.5 MeV/c 247.5 MeV/c 1.0 01020304050 0 10 20 30 40 50 b 0 [m] b 1 [m] g or k z TOF0 TOF1 (1.1, 1.1, 1.1) T/m (0.55, 1.1, 0.55) T/m
![SLIDE Objective #2: Minimize the error on x’: Make the beam fill Tof g 07 [T/m] Phase advance W / p MeV/c MeV/c b 0 [m] b 1 [m] g or k z TOF0 TOF1 (1.1, 1.1, 1.1) T/m (0.55, 1.1, 0.55) T/m](http://images.slideplayer.com./16/4955166/slides/slide_9.jpg "SLIDE Objective #2: Minimize the error on x’: Make the beam fill Tof g 07 [T/m] Phase advance W / p MeV/c MeV/c b 0 [m] b 1 [m] g or k z TOF0 TOF1 (1.1, 1.1, 1.1) T/m (0.55, 1.1, 0.55) T/m")
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SLIDE #10m.rayner1@physics.ox.ac.uk = /2 and 1 = 0 : Set each quad separately (0.9, –1.1, 0.4) T/m 1 0.8 0.6 0.4 0.2 0 1.20.80.60.4 g 09 [T/m] Phase advance W / p 222.5 MeV/c 247.5 MeV/c 1.0 01020304050 0 10 20 30 40 50 b 0 [m] b 1 [m] a 0 =1 a 0 =0
![SLIDE = /2 and 1 = 0 : Set each quad separately (0.9, –1.1, 0.4) T/m g 09 [T/m] Phase advance W / p MeV/c MeV/c b 0 [m] b 1 [m] a 0 =1 a 0 =0](http://images.slideplayer.com./16/4955166/slides/slide_10.jpg "SLIDE = /2 and 1 = 0 : Set each quad separately (0.9, –1.1, 0.4) T/m g 09 [T/m] Phase advance W / p MeV/c MeV/c b 0 [m] b 1 [m] a 0 =1 a 0 =0")
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SLIDE #11m.rayner1@physics.ox.ac.uk Quad behaviour changes over the range of muon momenta k [m -2 ] l [m] W [radians] Q7 g 0 = + 0.9 T/m Q8 g 0 = – 1.1 T/m Q9 g 0 = + 0.4 T/m 235 MeV/c +10% –10% 1.20 1.00 0.715 0.704 0.78 0.70 0.92 0.83 0.812 0.805 1.30 1.05 0.58 0.50 0.655 0.625 0.50 0.44 -17%-2%-10% -19% +6% -10% -14%-5%-12%
![SLIDE Quad behaviour changes over the range of muon momenta k [m -2 ] l [m] W [radians] Q7 g 0 = T/m Q8 g 0 = – 1.1 T/m Q9 g 0 = T/m 235 MeV/c +10% –10% %-2%-10% -19% +6% -10% -14%-5%-12%](http://images.slideplayer.com./16/4955166/slides/slide_11.jpg "SLIDE Quad behaviour changes over the range of muon momenta k [m -2 ] l [m] W [radians] Q7 g 0 = T/m Q8 g 0 = – 1.1 T/m Q9 g 0 = T/m 235 MeV/c +10% –10% %-2%-10% -19% +6% -10% -14%-5%-12%")
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SLIDE #12m.rayner1@physics.ox.ac.uk Predicted transfer matrix vs. momentum M 12 [m] M 21 [m -1 ]M 22 M 11 M(p) = –0.8 –1.2 –0.41 2 0 –0.7 –0.4 220250 220250 220250 220250 –0.34
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SLIDE #13m.rayner1@physics.ox.ac.uk Truth test of the transfer matrix method z [m] Quadrupole Gradient [T/m]
![SLIDE Truth test of the transfer matrix method z [m] Quadrupole Gradient [T/m]](http://images.slideplayer.com./16/4955166/slides/slide_13.jpg "SLIDE Truth test of the transfer matrix method z [m] Quadrupole Gradient [T/m]")
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SLIDE #14m.rayner1@physics.ox.ac.uk Conclusion Proposed quadrupole gradients: –g 7 = 0.9 T/m, g 8 = –1.1 T/m, g 9 = 0.4 T/m Mean phase advance = /2 Final betatron function = initial betatron function Error on x = 1.7 cm Error on x’ = 0.0187 radians –Due to slab width = 0.0108 radians –Due to scattering in the Cherenkov = 0.0150 radians (8 cm, X0 = 136 cm) –Due to tracking in the quadrupoles = 0.0027 radians Due to non-linearities –Negligible while p ~ p z Due to the quadrupole momentum measurement error = 0.0027 radians –Error due to Landau width in the Cherenkov = 0.9 MeV/c ( p = 3MeV/c) [G4MICE] –Error due to 70 ps time of flight resolution = 3.3 MeV/c –Total momentum measurement error = 3.4 MeV/c Approximate trace space area resolution = 0.3 mm
![SLIDE Conclusion Proposed quadrupole gradients: –g 7 = 0.9 T/m, g 8 = –1.1 T/m, g 9 = 0.4 T/m Mean phase advance = /2 Final betatron function = initial betatron function Error on x = 1.7 cm Error on x’ = radians –Due to slab width = radians –Due to scattering in the Cherenkov = radians (8 cm, X0 = 136 cm) –Due to tracking in the quadrupoles = radians Due to non-linearities –Negligible while p ~ p z Due to the quadrupole momentum measurement error = radians –Error due to Landau width in the Cherenkov = 0.9 MeV/c ( p = 3MeV/c) [G4MICE] –Error due to 70 ps time of flight resolution = 3.3 MeV/c –Total momentum measurement error = 3.4 MeV/c Approximate trace space area resolution = 0.3 mm](http://images.slideplayer.com./16/4955166/slides/slide_14.jpg "SLIDE Conclusion Proposed quadrupole gradients: –g 7 = 0.9 T/m, g 8 = –1.1 T/m, g 9 = 0.4 T/m Mean phase advance = /2 Final betatron function = initial betatron function Error on x = 1.7 cm Error on x’ = radians –Due to slab width = radians –Due to scattering in the Cherenkov = radians (8 cm, X0 = 136 cm) –Due to tracking in the quadrupoles = radians Due to non-linearities –Negligible while p ~ p z Due to the quadrupole momentum measurement error = radians –Error due to Landau width in the Cherenkov = 0.9 MeV/c ( p = 3MeV/c) [G4MICE] –Error due to 70 ps time of flight resolution = 3.3 MeV/c –Total momentum measurement error = 3.4 MeV/c Approximate trace space area resolution = 0.3 mm")
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SLIDE #15m.rayner1@physics.ox.ac.uk z [m] Quadrupole Gradient [T/m] Monte Carlo simulation of reconstructing the trace space phase plane just before TOF 1 10,000 (1,000) muons incident on TOF 0 –Both with and without the Cherenkov = 250 MeV/c –Top Hat distribution, half width 20% (small) Beam fills TOF 0 –Gaussian x, RMS = 10 cm Horizontal emittance = 1 mm (small) Alpha = 0 Small beam first…
![SLIDE z [m] Quadrupole Gradient [T/m] Monte Carlo simulation of reconstructing the trace space phase plane just before TOF 1 10,000 (1,000) muons incident on TOF 0 –Both with and without the Cherenkov = 250 MeV/c –Top Hat distribution, half width 20% (small) Beam fills TOF 0 –Gaussian x, RMS = 10 cm Horizontal emittance = 1 mm (small) Alpha = 0 Small beam first…](http://images.slideplayer.com./16/4955166/slides/slide_15.jpg "SLIDE z [m] Quadrupole Gradient [T/m] Monte Carlo simulation of reconstructing the trace space phase plane just before TOF 1 10,000 (1,000) muons incident on TOF 0 –Both with and without the Cherenkov = 250 MeV/c –Top Hat distribution, half width 20% (small) Beam fills TOF 0 –Gaussian x, RMS = 10 cm Horizontal emittance = 1 mm (small) Alpha = 0 Small beam first…")
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SLIDE #16m.rayner1@physics.ox.ac.uk Format of the next slides No Ckov Cherenkov TRUTH RECON RECON – TRUTH
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SLIDE #17m.rayner1@physics.ox.ac.uk Momentum reconstruction
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SLIDE #18m.rayner1@physics.ox.ac.uk Momentum reconstruction
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SLIDE #19m.rayner1@physics.ox.ac.uk x’ reconstruction
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SLIDE #20m.rayner1@physics.ox.ac.uk x’ reconstruction
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SLIDE #21m.rayner1@physics.ox.ac.uk Momentum reconstruction
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SLIDE #22m.rayner1@physics.ox.ac.uk Momentum reconstruction
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SLIDE #23m.rayner1@physics.ox.ac.uk x’ reconstruction
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SLIDE #24m.rayner1@physics.ox.ac.uk x’ reconstruction
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SLIDE #25m.rayner1@physics.ox.ac.uk Trace space reconstruction
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SLIDE #26m.rayner1@physics.ox.ac.uk Extra slides
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SLIDE #27m.rayner1@physics.ox.ac.uk TOF 0 TOF 1 PDG calculations
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SLIDE #28m.rayner1@physics.ox.ac.uk H. Wiedemann Particle Accelerator Physics 1
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SLIDE #29m.rayner1@physics.ox.ac.uk TOF0 Cherenkov TOF1 (Inside cage to shield from tracker solenoid fringe fields) Tracker solenoid muon photon electron Quadrupole triplet ~250 MeV/c realistic muon beam What is ? p air using truth – true p z before TOF0 p air using truth – true p z after TOF1 p air using recon. – true p z before TOF0 p air using recon. – true p z after TOF1 MeV/c
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SLIDE #30m.rayner1@physics.ox.ac.uk Beam line parameters table from Kevin Tilley Kevin’s dataTrace space transfer matrix approximation ElementPosition Effective Length Field Strength s k = (e/p)*dB/dx [p=(250–11–3)~235MeV] Omega (phase advance) = s * Sqrt Mag k mmT/mmm -2 TOF0 centre20.8116 Drift 24.9637 – 20.8116 – 0.33 = 3.8221 Drift Space20.8624 CKOV121.0624 Drift Space21.5674 Q35 Qd - Q724.96370.660.88758QD0.661.1330.748 Drift Space25.6237Drift26.1237 – 24.9637 – 0.66 = 0.5 Q35 Qd - Q826.12370.66-1.34275QF0.66-1.7141.131 Drift Space26.7837Drift27.2837 – 26.1237 – 0.66 = 0.5 Q35 Qd - Q927.28370.661.14749QD0.661.4640.966 Drift Space.27.9437 Drift 28.8437 – 27.2837 – 0.33 = 1.23 TOF1 centre28.8437 Q35 dimensions: Pole tip radius (the radial distance between the central axis of the quadrupole and its pole tip) 17.82 cm Vertical ½ aperture 23.6 cm, Horizontal ½ aperture 23.6 cm
![SLIDE Beam line parameters table from Kevin Tilley Kevin’s dataTrace space transfer matrix approximation ElementPosition Effective Length Field Strength s k = (e/p)*dB/dx [p=(250–11–3)~235MeV] Omega (phase advance) = s * Sqrt Mag k mmT/mmm -2 TOF0 centre Drift – – 0.33 = Drift Space CKOV Drift Space Q35 Qd - Q QD Drift Space Drift – – 0.66 = 0.5 Q35 Qd - Q QF Drift Space Drift – – 0.66 = 0.5 Q35 Qd - Q QD Drift Space Drift – – 0.33 = 1.23 TOF1 centre Q35 dimensions: Pole tip radius (the radial distance between the central axis of the quadrupole and its pole tip) cm Vertical ½ aperture 23.6 cm, Horizontal ½ aperture 23.6 cm](http://images.slideplayer.com./16/4955166/slides/slide_30.jpg "SLIDE Beam line parameters table from Kevin Tilley Kevin’s dataTrace space transfer matrix approximation ElementPosition Effective Length Field Strength s k = (e/p)*dB/dx [p=(250–11–3)~235MeV] Omega (phase advance) = s * Sqrt Mag k mmT/mmm -2 TOF0 centre Drift – – 0.33 = Drift Space CKOV Drift Space Q35 Qd - Q QD Drift Space Drift – – 0.66 = 0.5 Q35 Qd - Q QF Drift Space Drift – – 0.66 = 0.5 Q35 Qd - Q QD Drift Space Drift – – 0.33 = 1.23 TOF1 centre Q35 dimensions: Pole tip radius (the radial distance between the central axis of the quadrupole and its pole tip) cm Vertical ½ aperture 23.6 cm, Horizontal ½ aperture 23.6 cm")
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SLIDE #31m.rayner1@physics.ox.ac.uk Optical lens triplet f - ½ f f LL
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