1. Alignment study 19/May/2010 (S. Haino)

2. Summary on Alignment review Inner layers are expected to be kept “almost” aligned when AMS arrives at ISS Small shifts ( 30~50 μm ) in z-direction will be possible due to (1) Change of gravity (2) Shrink of foam support Momentum (or Energy) reference is needed for the absolute rigidity calibration

3. Alignment methods for AMS-PM Monitoring Layer 1N/9 movement 8-layer acceptance (8 Layers+ Layer 1N or 9) 10 3 ~10 4 protons (E > 10 GV) Incoherent alignment (ladder base alignment) Maximum acceptance (~ 0.5 m 2 sr) > 10 6 protons (E > 10 GV) Coherent alignment (momentum calibration) 9-layer +Ecal acceptance ( ~100 GeV)

4. Alignment monitoring Layer 1N Layer 9 dYdYdZdZ dθ xy MC data generated with Gbatch/PGTRACK Alignment accuracy estimated from Gaussian fitting error on the residual of layer 1N/9 hit Proton flux weight above 10 GV

5. Coherent alignment Check of absolute alignment for outer layers by comparing Rigidity measured by Tracker (R Tracker ) and Energy measured by Ecal (E Ecal ) on high energy e+ and e - sample Radiation energy loss makes P Tracker = | R Tracker | smaller w.r.t. E Ecal Alignment shift makes R Tracker shifted to the opposite direction for e+ and e -

6. Coherent alignment - simulation AMS-B Gbatch/PGTRACK simulation (For details please see presentation by P. Zuccon) 10 8 e - and e + each are injected in uniform Log 10 E distribution (10 < E < 500 GeV) isotropically from a plane 2.4m × 2.4m at Z = 1.8m Only trajectories which pass all the Tracker 9 layers are simulated Physics switches : LOSS= 1, DRAY= 1, HADR= 0, MULS= 1, BREM= 1, PAIR= 1

7. Ecal energy correction Absolute energy scale Linearity due to the shower leak Before After

8. E Ecal /P Tracker VS E gen In case Layer 1N is shifted by ΔY = ±20 μm

9. Coherent alignment - simulation Compare E Ecal /P Tracker distribution between R Tracker > 0 and R Tracker 80 GeV Flux weight applied assuming e - flux tuned by Fermi/LAT data e + flux tuned and extrapolated by Pamela data Simulated acceptance (full Ecal) : 0.025 m 2 sr Live data taking time : 100 days Kolmogorov probability ( P ) is calculated for the compatibility of two scaled histograms with R Tracker > 0 and R Tracker < 0

10. E Ecal /P Tracker comparison P: Kolmogorov probability In case Layer 1N is shifted by ΔY = ±20 μm : T = 100 days P: Kolmogorov probability

11. -Log P VS ΔY In case Layer 1N is shifted by ΔY : T = 100 days Estimated error ~5 μm

12. Alignment methods for AMS-PM Monitoring Layer 1N/9 movement 2~3 μm accuracy ( dY ) for 10 min. live time Incoherent alignment (ladder alignment) > 10 6 protons (E > 10 GV) for 1 ~ 2 days Study in progress Coherent alignment (momentum calibration) ~5 μm accuracy for 100 days live time

13. Backup slides

14. Alignment difference Between Pre-int. (2008) and Flight-int. (2009) Ext. planes seem rotating w.r.t. Int. planes by order of 100 μm/60 cm ~ 10 -2 degrees A small ( ~50 μm ) Z-shift found in Ext. planes No significant shift found for internal layers

15. Alignment difference between Pre-int.(2008) and Flight-int.(2009) Ladder Rotaion (dY/dX) Ladder Shift (dX)Ladder Shift (dY) Ladder Shift (dZ)

16. Alignment with test beam B-off runs with 400 GeV/c proton beam ( 4B70D0BF-4b710CBF, 58 points available) are reconstructed with straight tracks The following three parameters are tuned w.r.t. the CR alignment (2009) (1) Layer shift along z -axis : ~20 μm (2) Ladder shift along x -axis : 5~10 μm (3) Ladder shift along y -axis : 5~10 μm

17. Test beam alignment Ladder Shift (dX) RMS ~5 μm Layer Shift (dZ) RMS ~15 μm Ladder Shift (dY) RMS ~5 μm

18. Mean of (400GV)/Rigidity before alignment

19. Mean of (400GV)/Rigidity After alignment

20. Alignment study with B-off/on The 5 alignment applied to proton TB runs 1.Linear fitting on B-OFF runs 2.Curved fitting (1/R = 0 fixed) on B-OFF runs 3.Curved fitting (1/R free par.) on B-OFF runs 4.Curved fitting (R = 400 GV fixed) on B-ON runs 5.Curved fitting (1/R free par.) on B-ON runs

21. Alignment study with B-off/on

22. Alignment study with AMS-01 dZ = 31±44 μm

23. Alignment monitoring - simulation AMS-B Gbatch/PGTRACK simulation (For details please see presentation by P. Zuccon) 10 8 protons injected in uniform Log 10 R distribution (1 GV < R < 10 TV) isotropically from a plane 2.4m × 2.4m at Z = 1.8m Physics switches : LOSS= 1, DRAY= 1, HADR= 0, MULS= 1 Alignment accuracy estimated from Gaussian fitting error on the residual of layer 1N/9 hit weighted by proton flux above 10 GV

24. Geometry Layer8  Layer 1N Layer1 Layer 2,3 Layer 4,5 Layer 6,7 Layer 9 Ecal 65 × 65 cm 2 Layer 9

25. External layes are kept as they are

26.  Elena Vannuccini  In-flight alignment: STEP 1 Step 1  Correction for random displacements of the sensors ( incoherent alignment ) – Done with relativistic protons – Input trajectory evaluated from (misaligned) spectrometer fit measured step 1 Flight data Simulation X sideY side protons 7-100 GV (6x6y, all plane included in the fit) After incoherent alignment: residuals are centered width consistent with nominal resolution + alignment uncertainty (~1  m)  Elena Vannuccini 

27. In-flight alignment: STEP 2 step 2step 1 After Step1:  (possible) uncorrected global distortions might mimic a residual deflection  spectrometer systematic effect Step 2  Correction for global distortions of the system (coherent alignment) – Done with electrons and positrons – Energy determined with the calorimeter   E/E < 10 % above 5GeV Energy-rigidity match HOWEVER, the energy measured by the calorimeter can not be used directly as input of the alignment procedure, for two reasons: 1.Calorimeter calibration systematic uncertainty 2.Electron/positron Bremstrahlung above the spectrometer deflection offset calorimeter calibration uncertanty  Elena Vannuccini 

28. Bremsstrahlung effect From Bethe-Heitler model The probability distribution of z – depends on the amount of traversed material – does not depend on the initial momentum  it should be the same for electrons and positrons !! With real data: – Spectrometer systematic gives a charge-sign dependent effect – Calorimeter systematic has the same effect for both electrons and positrons * P0P0 P Spe P Cal ~P 0  t~0.1X 0  e ± e±