Mark Rayner, Analysis meeting 9 September ‘08: Use of TOFs for Beam measurement, slide 1

Use of TOFs for Beam measurement

Analysis workshop, RAL 4 September 2008Mark Rayner

Mark Rayner, Analysis meeting 9 September ‘08: Use of TOFs for Beam measurement, slide 2

Early beam diagnostics with the TOFs: For each muon…

• Use timing measurements at TOF0 and TOF1 to measure momentum– Sigma P = x MeV/c [CM21]

• Given knowledge of…– Quad geometry and currents– Beam line geometry– Muon momentum

• …predict the transfer matrix for the muon between TOF0 and TOF1– Use a field map, and multiply together slice matrices

• Use TOF position measurements and the transfer matrix to deduce x’ and y’ – Test this in G4MICE first of all using Monte Carlo truth positions…– …then using detector response simulation positions

• Finally, create a phase plane with these (x, x’) measurements and measure the emittance, and other optical parameters

Mark Rayner, Analysis meeting 9 September ‘08: Use of TOFs for Beam measurement, slide 3

10 100 1000 104 105

0.1

100

105

108

101 1

10 100 1000 104 105

1

1000

106

109

101 2

10 100 1000 104 105

0.1

100

105

108

101 1

10 100 1000 104 105

1

1000

106

109

101 2

TOF0TOF1 transfer matrix as a function of momentum:

Units: metres and MeV/cTwo lines

Red-solid: FDF planeBlue-dashed: DFD plane

Mark Rayner, Analysis meeting 9 September ‘08: Use of TOFs for Beam measurement, slide 4

180 200 220 240 260 280 300 2.0

1.5

1.0

0.5

0.0

0.5

180 200 220 240 260 280 300

6

4

2

0

2

4

6

180 200 220 240 260 280 300

1.0

0.5

0.0

180 200 220 240 260 280 300

5

4

3

2

1

0

TOF0TOF1 transfer matrix as a function of momentum:

Units: metres and MeV/cTwo lines

Red-solid: FDF planeBlue-dashed: DFD plane

Mark Rayner, Analysis meeting 9 September ‘08: Use of TOFs for Beam measurement, slide 5

QuadTypeQC-FieldMap effective length

• Effective Length = g z / g(z=0)– At y=5cm, leff = 0.666m

– At y=10cm, leff = 0.662m

– At y=15cm, leff = 0.662m

– At y=20cm, leff = 0.661m

– At y=25cm, leff = 0.662m

y=25cmBx [Tesla]

z [m]

y=20cm

y=15cm

y=10cm

y=5cm

l

23.6 cm23.6 cm

17.82 cm17.82 cm

x

y

Mark Rayner, Analysis meeting 9 September ‘08: Use of TOFs for Beam measurement, slide 6

H. WiedemannParticle Accelerator Physics 1

Mark Rayner, Analysis meeting 9 September ‘08: Use of TOFs for Beam measurement, slide 7

Matrix elements

Focussing plane

Defocussing plane

Mark Rayner, Analysis meeting 9 September ‘08: Use of TOFs for Beam measurement, slide 8

Effective parameters

Focussing plane

Defocussing plane

Mark Rayner, Analysis meeting 9 September ‘08: Use of TOFs for Beam measurement, slide 9

Extra slides

Mark Rayner, Analysis meeting 9 September ‘08: Use of TOFs for Beam measurement, slide 10

TOF0

CherenkovTOF1

(Inside cage to shield from tracker

solenoid fringe fields)

Tracker solenoid

muon

phot

on

electron

Quadrupole triplet

~250 MeV/crealistic muon

beam

G4MICEWhat is ?

pair using truth–

true pz before TOF0

pair using truth–

true pz after TOF1

pair using recon.–

true pz before TOF0 pair using recon.

– true pz after TOF1

MeV/c

2 2 2AIR

smp

t c s

Mark Rayner, Analysis meeting 9 September ‘08: Use of TOFs for Beam measurement, slide 11

G4MICE quad fields – transverse plane

0

0.05

0.1

0.15

0.2

0 0.1 0.2 0.3

x / m

By

/ T

TypeQC -1 * TypeQC-FieldMap TypeIV 1 T/m

0

0.05

0.1

0.15

0.2

0.25

0 0.1 0.2 0.3 0.4

r / m

Br

/ T

TypeQC -1 * TypeQC-FieldMap TypeIV 1 T/m

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 0.2 0.4 0.6 0.8

z / m

By

/ T

at

x=5c

m

QC HardEdge QC Enge IV HardEdge IV Enge QC Field-Map

23.6 cm23.6 cm

17.82 cm17.82 cm

Mark Rayner, Analysis meeting 9 September ‘08: Use of TOFs for Beam measurement, slide 12

TOF 0 TOF 1 PDG calculations

Energy and momentumdetails thickness density dE/dx (min I) dE mass E before p before E after p after dp

cm g cm-3 MeV g-1 cm2 MeV MeV c-2 MeV MeV MeV MeV MeVTOF0 scintillator polyvinyltoluene 5 1.03 1.97 10.12 105.66 271 249.5535 260.88 238.5253 11.02819Ckov aerogel silica aerogel 8 0.2 1.74 2.78 105.66 260.88 238.5253 258.1 235.4816 3.043762Air air dry, 1 atm 730 1.20E-03 1.82 1.6 105.66 258.1 235.4816 256.5 233.7268 1.754785TOF1 scintillator polyvinyltoluene 5 1.03 1.97 10.12 105.66 256.5 233.7268 246.38 222.5737 11.15306

Lorentz and timeE average p average beta gamma dtMeV MeV microseconds

TOF0 265.94 244.0394361 0.917648477 6.3322692 1.816236508Ckov 259.49 237.0034609 0.913343331 6.031219 2.91967607Air 257.3 234.6041871 0.91179241 5.9299811 266.8736115TOF1 251.44 228.1502661 0.907374587 5.660227 1.83680113

ScatteringX0 X0 RMS theta RMS thetag cm-2 cm mrad degrees

TOF0 43.9 42.62135922 27.02095823 1.5481882Ckov 27.25 136.25 19.21043782 1.1006779Air 36.62 30516.66667 11.9337395 0.6837535TOF1 43.9 42.62135922 29.23004715 1.6747598

Mark Rayner, Analysis meeting 9 September ‘08: Use of TOFs for Beam measurement, slide 13

Beam line parameters table from Kevin

Kevin’s data Trace space transfer matrix approximation

Element PositionEffective Length

Field Strength

sk = (e/p)*dB/dx

[p=(250–11–3)~235MeV] Omega (phase advance)

= s * Sqrt Mag k

m m T/m m m-2

TOF0 centre 20.8116

Drift24.9637 – 20.8116 – 0.33

= 3.8221

Drift Space 20.8624

CKOV1 21.0624

Drift Space 21.5674

Q35 Qd - Q7 24.9637 0.66 0.88758 QD 0.66 1.133 0.748

Drift Space 25.6237 Drift26.1237 – 24.9637 – 0.66 =

0.5

Q35 Qd - Q8 26.1237 0.66 -1.34275 QF 0.66 -1.714 1.131

Drift Space 26.7837 Drift27.2837 – 26.1237 – 0.66 =

0.5

Q35 Qd - Q9 27.2837 0.66 1.14749 QD 0.66 1.464 0.966

Drift Space. 27.9437Drift

28.8437 – 27.2837 – 0.33 = 1.23TOF1 centre 28.8437

Q35 dimensions: Pole tip radius (the radial distance between the central axis of the quadrupole and its pole tip) 17.82 cmVertical ½ aperture 23.6 cm, Horizontal ½ aperture 23.6 cm