MICE analysis meeting – BL analysis12 January 2010 1

Demonstrating the emittance – momentum

matrixA second look at

December’s beam line data

Mark Rayner

12 January 2009

AMDG

MICE analysis meeting – BL analysis12 January 2010 2

Introduction – The MICE beam line• Purpose: generate the elements of the “emittance-momentum matrix”

Study performance at every portion of a full cooling channel

• Can we use the TOFs to demonstrate the matrix elements?

Q1Q1 Q2Q2 Q3Q3 Q4Q4 Q5Q5 Q6Q6 Q7Q7 Q8Q8 Q9Q9DK solDK sol D2D2D1D1

TOF1TOF1TOF0TOF0TargetTarget

DiffuserDiffuser

Cooling channel Cooling channel and spectrometersand spectrometers

33 66 1010

140140

200200

240240

Initial Initial 4D 4D NN (mm) (mm)

Abso

rber

Abso

rber

PPzz (

MeV

/c)

(M

eV

/c)

DataData

MICE note 176 Apollonio, Cobb

MICE analysis meeting – BL analysis12 January 2010 3

Timing detectors TOF0 and TOF1

Tof-0

0.48 m

10 x 4cm scintillator barsx = 1.15 cmt = 50 ps

Tof-1

0.48 m

7 x 6cm scintillator barsx = 1.73 cmt = 50 ps

MICE analysis meeting – BL analysis12 January 2010 4

Beam characterization using the TOFs

PID

at the diffuserat the diffuser

emittance

phase ellipse orientation

beam size at TOF1at TOF1

emittance

phase ellipse orientation

longitudinalmomentum

path lengthtrans mom

z

g0

0

10

20

30

40

50

60

70

80

0 100 200 300 400 500

Momentum / MeV/c

Tim

e o

f fl

igh

t /

ns

e+

mu

pi

p

pi - mu

MICE analysis meeting – BL analysis12 January 2010 5

PID on December’s scaled decay beam line data

Kevin’s optics6-200

Runs 1380-1397 and 1391-1393

6-140(rescaled currents)Runs 1409-1411

Intermediate momentum beam line with scaled quad currents

Runs 1407-1408

MICE analysis meeting – BL analysis12 January 2010 6

Reconstruction procedure• 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 x0’ and y0’ from x1 and y1

• 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

Marco’s=6mm pabsorber=200 MeV/c centre of the -p matrix beam

MICE analysis meeting – BL analysis12 January 2010 7

6-200 momentum reconstructionMC truth (and hence the reconstructed detector response of the truth) and data have slightly different geometries and optics, but both have been designed by Marco to generate the 6-200 element of the -p matrix

Momentum is reconstructed just before TOF1The simulation contains only muonsSlide 5 shows show the data cut on t to select muons

Old geometry (May 2009, simulation) z = 796.61 cmNew geometry (December 2009, data) z = 779.91 cmDifference = 16.7 cm = 0.557 ns / c

Det. resp. t (blue) looks surprisingly good compared to the truth (light blue), but there is indeed a 70 ps error

MICE analysis meeting – BL analysis12 January 2010 8

x and y trace space

Truth Recon’d det. sim. Data

MICE analysis meeting – BL analysis12 January 2010 9

(Raw) RMS trace emittances from the 2D histograms

Binned truthx RMS trace emittance = 2.367800 mmy RMS trace emittance = 1.453120 mmTransverse 4d RMS trace emittance = 1.854912 mm

Reconstruction of detector response simulationx RMS trace emittance = 2.552532 mmy RMS trace emittance = 1.123380 mmTransverse 4d RMS trace emittance = 1.693359 mm

Datax RMS trace emittance = 2.309358 mmy RMS trace emittance = 0.933133 mmTransverse 4d RMS trace emittance = 1.467971 mm

MICE analysis meeting – BL analysis12 January 2010 10

Extra slides

MICE analysis meeting – BL analysis12 January 2010 11

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

• Positron calibration is necessary

x (mm)

y (mm)

s - L (mm)

s - L (mm)

py (

MeV

/c)

px (

MeV

/c)

MICE analysis meeting – BL analysis12 January 2010 12

Monte Carlo simulation• 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

Marco’s=6mm pabsorber=200 MeV/c centre of the e-p matrix beam

MICE analysis meeting – BL analysis12 January 2010 13

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

Marco’s=6mm pabsorber=200 MeV/c centre of the e-p matrix beam