1. Emittance–momentum matrix1 Demonstrating the emittance-momentum matrix Mark Rayner, MICE Video Conference, 21 January 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. Emittance–momentum matrix2 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 –6 mm, and an intermediate momentum Runs 1407 – 1408, KT’s optics re-scaled to the new momentum, 1k 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

3. Emittance–momentum matrix3 Selection of the muon peak 6-200 6-140 Intermediate momentum

4. Emittance–momentum matrix4 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. Emittance–momentum matrix5 Momentum reconstruction: 6-200 simulation Path length ! Measuring path length removes the bias on the momentum measurement

6. Emittance–momentum matrix6 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. Emittance–momentum matrix7 Horizontal (x,x’) trace space Vertical (y,y’) trace space Simulation/data comparison at TOF1 (6-200 matrix element) Simulation (truth) Data 1, 2, and 3  fits

8. Emittance–momentum matrix8 Conclusion 6-200 element –Beam properties required at TOF1 = 261.8 MeV/c,  x = 2.55 mm,  y = 1.12 mm, and 4D  N = 1.69 mm Takes into account binning effects –Beam properties measured at TOF1 = 258.6 MeV/c,  x = 2.31 mm,  y = 0.93 mm, and 4D  N = 1.47 mm –Given the complexity of the beam line, this is not a bad start! Next analysis steps –Refinements of the simulation are possible in both G4BeamLine and G4MICE –Simulate the other matrix elements Suggestion for the data taking in February –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 –Demonstrating the emittance-momentum matrix would be a nice step forward!