Emittance–momentum matrix 1

Demonstrating the emittance-momentum matrix

Mark Rayner, MICE Video Conference, 21 January 2010

3 6 10

140

200

240

Initial 4D N (mm)

Abs

orbe

r pz (

MeV

/c)

Cooling

channel

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9DK sol D2D1

TOF1TOF0Target

Diffuser

GVA1 BPM1

,

1 2

Diffuser

t

Emittance–momentum matrix 2

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(pxmax/70)

• Dependent on pxmax, 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

Emittance–momentum matrix 3

Selection of the muon peak

6-200

6-140

Intermediate

momentum

Emittance–momentum matrix 4

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 zTOF1 – zTOF0

s leff + F + D

Track through through each quad,

and calculate

Add up the total pathS = s7 + s8 + s9 + drifts

Q5 Q6 Q7 Q8 Q9

TOF1TOF0

zTOF1 – zTOF0 = 8 m

Emittance–momentum matrix 5

Momentum reconstruction: 6-200 simulation

Path length

!

Measuring path length removes the bias on the momentum measurement

Emittance–momentum matrix 6

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 matrix 7

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 matrix 8

Conclusion• 6-200 element

– Beam properties required at TOF1

• <pz> = 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

• <pz> = 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!