Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 1

Use of TOFs for Beam measurement & RF phasing

Analysis workshop, RAL 4 September 2008Mark Rayner

Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, 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– Deduce using small amplitude particles in G4MICE– Verify by solving Hill’s equations– Try higher amplitudes– Find a simple procedure for matching transfer matrices to muons

• 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 workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 3

• Energy loss– 10.1 +/- 1.4 MeV per TOF

station– 2.8 +/- 0.9 MeV in the Ckov– 1.8 MeV in the 8m of air

• Scattering– 1.8 +/- 1.1 degrees per TOF– 1.4 +/- 0.8 degrees per

Ckov

• Focussing– 4.6 +/- 2.6 degrees in Q789

~m

┴ =1mm

~250 MeV/crealistic muon

beam

Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 4

Simple momentum reconstruction

• Data available from time of flight counters– Time of flight– Displacement

• Estimate p in the air between TOF0 and TOF1

• Momentum losses from PDG dE/dx for minimum ionizing particles– Estimate p before TOF0– Estimate p after TOF1

1 0t t t 2 2 2s L x y

2 2 2AIR

smp

t c s

0 0TOF AIR AIR CKOV TOFp p p p p 1 1TOF AIR TOFp p p

8mL xys

0t 1t

TOF0 TOF1

Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 5

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 workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 6

Deducing the transfer matrix from G4MICE Monte Carlo truth

• E.g. a 1150mm drift

• Cherenkov

• Quadrupoles

Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 7 7

Gaussian 0.5mmRectangular 1mmGaussian 7.5mm

Cherenkov ‘matrix elements’

• X plane, 0.8m ‘drift’

Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 8

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 workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 9

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 workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 10

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 workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 11

Gaussian beam 7.5mmMC truth G4MICE detector simulation of TOF hits with x’ reconstructed using MC transfer matrix

TOF 0 TOF 1x / m

x’

x / m

x’

x / m

x’

x / m

x’

Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 12

Errors – some initial thoughts

• The question: can we use position measurements from two TOFs to measure transverse emittance?– Error = slab width / root 12 ~ 2 cm

• Error on x’?

180 200 220 240 260 280 3000.0

0.1

0.2

0.3

0.4

180 200 220 240 260 280 3000.00

0.05

0.10

0.15

0.20

0.25

Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 13

TOF1& cage

Tracker Solenoid 1

Tracker 1

PhotonMuon

Electron

Focus coilRF

H2 absorber

Extrapolating the time

• Time extrapolation to tracker reference plane (or RF cavity) required for– Defining a neutrino factory like bunched, stable beam– Measuring longitudinal emittance

• Necessary to track each muon on the basis of– Tracker (and TOF?) x, px, y, py, t, pz measurements– Magnetic (and electric) field maps– Energy loss models

Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 14

Extrapolation of t, Pz to TRP

• Time of flight pz ~ intrinsic beam line pz

• t<500ps would be desirable in the tracker reference plane– Chris got 77ps using only the

tracker pz (tracker 24ps, material 12ps, TOF 70ps)

– A back of an envelope calculation suggests TOFs can achieve 30ps using TOF reconstructed pz with perfect tracking

• TOF pz may be complementary to tracker pz>6MeV/c when pt<10 MeV/c– 38% of muons when there is no

diffuser, E=200MeV/c, n=2mm, =33.3cm (John Cobb, CM19)

pz

[MeV/c]Before TOF0

After TOF1

Intrinsic to beam line

2.8 3.5

Due to TOF 4.4 4.7

Total 5.2 5.8

Resolution of the tracker

Smearing due to

stochastic processes

Both + 50ps TOF timing resolution

Chris Rogers, Thesis

Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 15

Extra slides

Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 16

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 workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 17

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

Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 18

Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 19

TOF1 Sigma X [m] and Sigma X’, 250 MeV/c, dp/p = 10%

• Initial beam– 1 mm – alpha=0

180 200 220 240 260 280 300

0 .0

0 .1

0 .2

0 .3

0 .4

180 200 220 240 260 280 300

0 .00

0 .05

0 .10

0 .15

0 .20

0 .25

Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 20

-25

-20

-15

-10

-5

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ha

lf w

idth

x /

cm

Ha

lf w

idth

y /

cm

TOF0 Diffuser

norm. em. 7.1 mm after the diffuser

z / m

Clues on the probable beam just before TOF 0

• Kevin’s assumptions at the target– Pions have mean Pz 444 MeV/c– Each variable is assume to have

a top hat distribution due to scraping

• x 5.1 mm, x’ 0.033• y 2.0 mm, y’ 0.014• Pz 2.5%

– Could use G4MICE to figure out the muon optical functions

– Haven’t done this yet• Average muon momentum /

MeV?– Tune dipoles for 208.58 after

diffuser– 222.87 before diffuser– 250 before TOF0

• -11 in each TOF• -3 in the Cherenkov• -2 in the 8 m air

• CM15 Transport half width plot

– Cov x’x’ = cov xx * (beta/Pz)2

– Marco: beta before diffuser 83 cm

• (Half width)2 / beta is constant• Beta x TOF0 190 cm• Beta y TOF0 332 cm

– Gradients ~ 0 so alphas ~ 0• Kevin’s muon beam assumption

– dp/p ~ 10%