1. Mark Rayner – Analysis SessionCM25, 4 November 20091 Beam characterization by the TOFs Mark Rayner The University of Oxford MICE CM25

2. Mark Rayner – Analysis SessionCM25, 4 November 20092 Compressed schematic view of the upstream beam line TRP Q7Q8Q9Diffuser x, y, z p x, p y, p z I7I7 I8I8 I9I9 IDID D2 RFAbsorber t 1 x 1, y 1 t 0 x 0, y 0 t ? t ? ? Stages II - VI  x,  y , , , 

3. Mark Rayner – Analysis SessionCM25, 4 November 20093 Beam characterization using the TOFs PID at the diffuser emittance phase ellipse orientation beam size at TOF1 emittance phase ellipse orientation longitudinal momentum path length trans mom z g0g0

4. Mark Rayner – Analysis SessionCM25, 4 November 20094 Momentum measurement by the TOFs ‏Muon energy approximately constant between TOFs  p/E = s/t  s = path length between TOF0 and TOF1 (~8m)  t = time of flight (~29ns at 250 MeV/c) ‏Predicted resolution  4.7 MeV/c at 250 MeV/c ‏Bias on the measurement  Time of flight mis-calibration by 10 ps: 0.57 MeV/c bias  Path length over/underestimation by 10 mm: 2.1 MeV/c bias

5. Mark Rayner – Analysis SessionCM25, 4 November 20095 Digression: positron TOF0 – TOF1 calibration ‏Positrons all travel at c  Used to calibrate TOF0 relative to TOF1:  t=  z/c  However their path exceeds the longitudinal displacement and cannot be individually determined ‏Need a careful Monte Carlo  Input positron calibration beam from G4BL simulation – not yet simulated ‏Instead get a rough idea – uniformly populate phase space  For a paraxial beam in a quadrupole channel, contributions to (s-L) from x and y may be separated… x y pxpx pypy

6. Mark Rayner – Analysis SessionCM25, 4 November 20096 Path length – L as a function of transverse phase space x (mm) y (mm) s - L (mm) p y (MeV/c) p x (MeV/c) y = p y = 0 x = p x = 0

7. Mark Rayner – Analysis SessionCM25, 4 November 20097 Conclusion to the digression ‏Positron path lengths can exceed L by 70mm  (230ps bias on time of flight)  Any more and they are scraped  However the majority of transmitted phase space has (s-L) ~ O(10mm)  [30ps bias] ‏A Monte Carlo simulation is required  Which part of phase space is occupied by the positron beam?

8. Mark Rayner – Analysis SessionCM25, 4 November 20098 Beam characterization using the TOFs PID at the diffuser emittance phase ellipse orientation beam size at TOF1 emittance phase ellipse orientation longitudinal momentum path length trans mom z g0g0

9. Mark Rayner – Analysis SessionCM25, 4 November 20099 Monte Carlo simulation ‏Marco’s  =6mm p absorber =200 MeV/c centre of the e-p matrix beam  Mean Pz = 270 MeV/c at TOF0 (see left histogram) ‏P/E=s/t where s=true path length  Measures true p before TOF1 with RMS error 0.65 MeV/c  See right histogram  Width and bias due to dE/dx in the air between TOF0 and TOF1

10. Mark Rayner – Analysis SessionCM25, 4 November 200910 Should we simply approximate s=  z? ‏P/E=  z/t  RMS error 3.38 MeV/c  Bias -4.06 MeV/c  Due to the width of the  =s-  z distribution

11. Mark Rayner – Analysis SessionCM25, 4 November 200911 Monte Carlo: Full demonstration of P reconstruction ‏Iterative calculation of increasingly good s=  z+  and P  Begin with P from P/E=  z/t 1 Calculate a linear transfer map at P from TOF0 to TOF1 (top hat quadrupoles) 2 Deduce x 0 ’ and y 0 ’ from x 1 and y 1 3 Integrate ds while tracking the initial trace space vector through the beam line 4 Make a better estimate of P from P/E=s/t 5 Make a small Bethe-Bloch correction for the energy loss in air between the TOFs

12. Mark Rayner – Analysis SessionCM25, 4 November 200912 Result of the full Monte Carlo

13. Mark Rayner – Analysis SessionCM25, 4 November 200913 Momentum measurement conclusion ‏This method eliminates path length bias ‏It is implemented as a G4MICE application  It should replace the current p/E=  z/t automatic momentum reconstruction  Emittance measurement is a natural by-product at minimal extra cost  An online monitoring GUI can be produced to plot p and  in real time ‏It initially requires  Quadrupole currents I 7, I 8 and I 9  Quadrupole and TOF positions z 0, z 7, z 8, z 9, z 1  Eventually easily obtained from from the database ‏For individual muon P measurements it requires  t, x 0, y 0, x 1, y 1, PID ‏This method will not work with positrons  Therefore TOF calibration must use simulation of positron beam

14. Mark Rayner – Analysis SessionCM25, 4 November 200914 TOF0 x mm: x’ radians Truth Reconstruction All Monte Carlos from a realistic G4BeamLine 6mm emittance 200 MeV/c centre of absorber momentum beam simulated in G4MICE Note that this method has also reconstructed x0’ and y0’ We can just as easily deduce (x1’, y1’) from (x0, y0)

15. Mark Rayner – Analysis SessionCM25, 4 November 200915 TOF1 x mm: x’ radians Truth Reconstruction

16. Mark Rayner – Analysis SessionCM25, 4 November 200916 TOF0 y mm: y’ radians Truth Reconstruction

17. Mark Rayner – Analysis SessionCM25, 4 November 200917 TOF1 y mm: y’ radians Truth Reconstruction

18. Mark Rayner – Analysis SessionCM25, 4 November 200918 Work in progress ‏Software  Currently debugging momentum bias correction/emittance measurement with the new data and new calibration  Online reconstruction featuring these innovations  Add TOF0-TOF1 calibration to overall TOF calibration procedure ‏Physics  Extrapolation of beam size at diffuser – easy!   O T  O  Where O is just a drift transfer matrix ‏Simulation  Require positron simulation with TOF calibration optics ‏Shifts  Measure emittance at the elements of the emittance-momentum matrix  Beam size at the diffuser  Compare measured Twiss parameters with the design optics