1. Beam line characterization with the TOFs1 Demonstrating the emittance-momentum matrix Mark Rayner, CM26 California, 24 March 2010 3610 140 200 240 Initial 4D  N (mm) Absorber p z (MeV/c) Cooling channel Q1Q2Q3Q4Q5Q6Q7Q8Q9 DK sol D2D1 TOF1TOF0 Target Diffuser GVA1BPM1 ,   12 Diffuser t

2. Beam line characterization with the TOFs2 Introduction  Purpose of the beam line:  Generate the emittance-momentum matrix elements in pion  muon decay beam lines  (3, 6, 10) mm  (140, 200, 240) MeV/c  Data taking in December  6 mm – 200 MeV/c element  Runs 1380 – 1393, Kevin Tilley’s optics, 6k target pulses  6 mm – 140 MeV/c element  Runs 1409 – 1411, KT’s optics re-scaled to the new momentum, 2k target pulses  Phase space reconstruction by TOF0 and TOF1  Longitudinal momentum resolution O(5 MeV/c)  Transverse position resolution O(2 cm)  Transverse momentum resolution O( p x max /70)  Dependent on p x max, the maximum un-scraped momentum of the optics in question  Comparison with Monte Carlo simulations  The 6-200 element has been simulated using G4BeamLine and G4MICE  This talk  Reconstruction algorithm  Distributions, means, covariance matrices, and emittances for 6-140 and 6-200 data  Analysis talk on Friday  What this means for future stages in MICE

3. Beam line characterization with the TOFs3 Selection of the muon peak 6-200 6-140 Intermediate momentum

4. Beam line characterization with the TOFs4 Reconstruction procedure Estimate the momentum p/E = S/  t Calculate the transfer matrix Deduce (x’, y’) at TOF1 from (x, y) at TOF0 Deduce (x’, y’) at TOF0 from (x, y) at TOF1 Assume the path length S  z TOF1 – z TOF0 s  l eff +  F +  D Track through through each quad, and calculate Add up the total path S = s 7 + s 8 + s 9 + drifts Q5Q6Q7Q8Q9 TOF1TOF0 z TOF1 – z TOF0 = 8 m

5. Beam line characterization with the TOFs5 Momentum reconstruction: 6-200 simulation Path length ! Measuring path length removes the bias on the momentum measurement

6. Beam line characterization with the TOFs6 Simulation/data comparison at TOF1 (6-200 matrix element) This simulation uses the geometry from before TOF1 was moved  z = – 16.7 cm = – 0.56 ns / c Muon time of flight Muon momentum

7. Beam line characterization with the TOFs7 6-140 (x, p x, y, p y, p z ) in mm and MeV/c 4296 -509.0 132.3 -20.37 5.77 4451 -5.34 1.32 168.8 15.13 -438.7 55.8 -7.03 13.65 1286 30.08 -8.49 14.085 0.136 212.8 x RMS normalized phase emittance = 5.30 mm y RMS normalized phase emittance = 1.78 mm Transverse 4d RMS normalized phase emittance = 3.07 mm Covariance matrix Means

8. Beam line characterization with the TOFs8 6-200 (x, p x, y, p y, p z ) in mm and MeV/c 3359 -610.0 205.8 18.99 -17.68 3600 1.17 -1.61 82.3 17.43 -107.6 -5.0 -5.84 11.81 602 16.64 -12.09 15.311 -0.407 258.1 x RMS normalized phase emittance = 5.37 mm y RMS normalized phase emittance = 2.25 mm Transverse 4d RMS normalized phase emittance = 3.48 mm Covariance matrix Means

9. Beam line characterization with the TOFs9 Momentum

10. Beam line characterization with the TOFs10 Horizontal phase space 3  fit

11. Beam line characterization with the TOFs11 Vertical phase space

12. Beam line characterization with the TOFs12 Horizontal spatial dispersion

13. Beam line characterization with the TOFs13 Horizontal momentum dispersion

14. Beam line characterization with the TOFs14 Vertical spatial dispersion

15. Beam line characterization with the TOFs15 Vertical momentum dispersion

16. Beam line characterization with the TOFs16 Conclusion  6-200 element  Trace space beam properties required at TOF1 (6-200)  = 261.8 MeV/c,  x = 2.55 mm,  y = 1.12 mm, and 4D  N = 1.69 mm  Takes into account binning effects  Trace space beam properties measured at TOF1 (6-200)  = 258.1 MeV/c,  x = 2.31 mm,  y = 0.93 mm, and 4D  N = 1.47 mm  Phase space beam properties measured at TOF1 (6-200)  = 258.6 MeV/c,  x = 5.37 mm,  y = 2.25 mm, and 4D  N = 3.48 mm  Phase space beam properties measured at TOF1 (6-140)  = 212.8 MeV/c,  x = 5.30 mm,  y = 1.78 mm, and 4D  N = 3.07 mm  Analysis talk on Friday  Simulation: how would these beams behave in Stage 6?  What about time?  Suggestion for the future data shifts  Observe >40k muons (~6k target pulses?) for each of the nine elements  Kevin Tilley’s re-scaled 6-200 optics  Optics derived from Marco’s genetic algorithm