Emittance–momentum matrix1 Demonstrating the emittance-momentum matrix Mark Rayner, MICE Video Conference, 21 January Initial 4D  N (mm) Absorber p z (MeV/c) Cooling channel Q1Q2Q3Q4Q5Q6Q7Q8Q9 DK sol D2D1 TOF1TOF0 Target Diffuser GVA1BPM1 ,   12 Diffuser t

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 element has been simulated using G4BeamLine and G4MICE

Emittance–momentum matrix3 Selection of the muon peak Intermediate momentum

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

Emittance–momentum matrix5 Momentum reconstruction: simulation Path length ! Measuring path length removes the bias on the momentum measurement

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

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

Emittance–momentum matrix8 Conclusion element –Beam properties required at TOF1 = 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 = 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 optics Optics derived from Marco’s genetic algorithm –Demonstrating the emittance-momentum matrix would be a nice step forward!