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%