Beam momentum measurement
using TOFs: progress report
Analysis meeting, 18 December 2007
Mark Rayner – Oxford/RAL
Set N
Analysis meeting: Beam momentum measurements using TOFs
Tuesday, 18 December 2007
Slide 1 of 10
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G4MICE: Stage 2 Volumes
75cm
SpecVirt
65cm
5cm
40cm
Upstream
Shield
SpecVirt11
20cm
1m
SpecVirt7
75cm
50cm
70cm
25cm
SpecVirt10
SpecVirt6
SpecVirt2
75cm
SpecVirt3
Special Virtual Planes
25cm
20cm
-14.4m
18cm
-14.05m
-14.55m
0cm
-13.7m
-11.4m
21cm
20cm
Q7
Q8
-9.65m
-6.53m
Q9
-7.9m
-6.39m
-6.67m
-14.6m
-14m
Active Area Tof-0 Cherenkov
-12m
-10m
Analysis meeting: Beam momentum measurements using TOFs
Tuesday, 18 December 2007
-8m
Active area Tof-1
-6m
Slide 2 of 10
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 N  N det VN
  xx  xx '  xy  xy ' 


 x'x'  x' y  x' y ' 

V2  
 yy  yy ' 



 y ' y ' 

Analysis meeting: Beam momentum measurements using TOFs
Tuesday, 18 December 2007
Slide 3 of 10
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Trans phase space
y
py
-100 MeV – 100 MeV
py / MeV
y / cm
Analysis meeting: Beam momentum measurements using TOFs
Tuesday, 18 December 2007
-40 cm – 40 cm
Slide 4 of 10
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Trans phase space
x
px
-100 MeV – 100 MeV
px / MeV
x / cm
Analysis meeting: Beam momentum measurements using TOFs
Tuesday, 18 December 2007
-40 cm – 40 cm
Slide 5 of 10
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Long. phase space
Analysis meeting: Beam momentum measurements using TOFs
Tuesday, 18 December 2007
Slide 6 of 10
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• How is G4MICE TOF physics currently coded?
– Simulation
• PID, (t, x, y, z, E, px, py, pz), station number, slab number, DE
– Digitization
• PMT ADC and TDC counts
– Reconstruction
• (t, x, y, z)
Analysis meeting: Beam momentum measurements using TOFs
Tuesday, 18 December 2007
Slide 7 of 10
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How G4MICE is currently coded: Digitization
TOF Detector Response
• Geant4 simulates energy loss and scattering
• ‘TofHit’s are created as Geant4 steps through scintillator slabs
• Then for each of the TofHit’s PMTs
  x hit  x PMT
DEhit
nPE  Q.E.PMT
exp 
– Signal is calculated using:
10 keV
 140 cm
• Q.E.PMT (Quantum efficiency) = 0.25
?
• ADC = nPE / 0.125
• 10 keV takes into account solid angle for getting to a PMT too




– # photons per keV getting to captured solid angle < TIR
– Signal arrival time at the PMT is a Gaussian
• Mean:
thit 
x hit - x PMT
1.7 108 ms -1
– Should take into account diagonal path
» Error O(1.7 ns) [half slab at 45 degrees]
• Standard deviation (time resolution): 100 ps
• TDC = t / 25 ps
dE/dx~2 MeV/cm in scintillator
2.5cm
5MeV
5000/10=500
125=lots
n(polystyrene) = 1.59
• Coded in DetResp/TOF/ in class TofDigits
• Constants stored in Interface/src/dataCards.cc
Analysis meeting: Beam momentum measurements using TOFs
Tuesday, 18 December 2007
Slide 8 of 10
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How G4MICE is currently coded: Reconstruction
TofSlabHit
• Reconstructed time:
L/2
(TDC count left/top PMT  25 ps) 
1.7 108 ms 1
– Error depends on beam emittance
Right PMTs
Left PMTs
L=40cm
Top PMTs
Bottom PMTs
Analysis meeting: Beam momentum measurements using TOFs
Tuesday, 18 December 2007
Slide 9 of 10
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TOF1
TOF0
Analysis meeting: Beam momentum measurements using TOFs
Tuesday, 18 December 2007
Slide 10 of 10
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Extra slides:
Analysis meeting: Beam momentum measurements using TOFs
Tuesday, 18 December 2007
Slide 11 of 10
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Momentum measurement
uncertainties
• p = b g(b) m0 c
– assume PID ascertains m0
• Timing uncertainty
– Technical challenge: progress being made in Milano
• One counter = scintillator with 2 PMTs
– “…a conservative request for single counters timing resolution is 60–70 ps”
» MICE Note 145
• Other factors:
– 2 planes per station
» Rotated so as to yield ‘space points’
– Multiple space points per muon possible/likely
• t1–t0 will be larger still
• Path length uncertainty
– Software challenge: challenges remain…
• Multiple scattering in Tof-0, Cerenkov, Tof-1 and air
• Focusing in quadrupoles Q7, Q8 and Q9
• Limited transverse position resolution
Analysis meeting: Beam momentum measurements using TOFs
Tuesday, 18 December 2007
Slide 12 of 10
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Path length between Tof-0 and Tof-1
•
Is a straight line between the Tof centres good enough?
–
–
–
0.48 m
zTof-1 – zTof-0 = 8.0255 m in G4MICE
200 MeV/c muons, speed = 0.88 c
With no forces acting on the muon
• Path distance corner to opposite corner = 8 m + 2.9 cm
• Maximum possible timing error = 87 ps
–
Not negligible
0.48 m
Tof-1
(same design for Tof-2)
muons
Tof-0
3 slab hits
2 space points
2 slab hits
1 space point
1 ps  1012 s
Diagrams and dimensions from MICE Technical Reference
Analysis meeting: Beam momentum measurements using TOFs
Tuesday, 18 December 2007
Slide 13 of 10
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• Pencil beam
– x=y=3cm, x’=y’=0
• Quads OFF
• Monochromatic
– 200 MeV/c
Analysis meeting: Beam momentum measurements using TOFs
Tuesday, 18 December 2007
Slide 14 of 10
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Beam parameters at Tof-0
MICE Beam Line Design, Kevin Tilley, 16-XI-07
Analysis meeting: Beam momentum measurements using TOFs
Tuesday, 18 December 2007
Slide 15 of 10
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• Divergent beam
– x=y=7cm, x’=y’=0.2mrad
• Quads OFF
• Monochromatic
– 200 MeV/c
Analysis meeting: Beam momentum measurements using TOFs
Tuesday, 18 December 2007
Slide 16 of 10
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Quadrupoles
• Magnet type
Field gradient
[T/m]
– Q35
• Field gradients set by Beam line review:
– 0.9 – 1.5 T/m
• Effective length Dz
Q7
0.89
Q8
-1.35
Q9
1.15
– 0.66 m
• Pole tip radius xmax
– 17.82 cm
• Rough estimate transverse momentum kick
Dp  300 MeV/c B y [T] Dz [m]
– 2 MeV/c per transverse cm displaced from design axis at each Q35
• Corresponding angular kick at 200 MeV/c
– 0.6 degrees per transverse cm displaced
• Rough estimate path increase over 8m
– 3 cm at half pole width
Analysis meeting: Beam momentum measurements using TOFs
Tuesday, 18 December 2007
Slide 17 of 10
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• Divergent beam
– x=y=7cm, x’=y’=0.2mrad
• Quads ON
Quads set correctly!
– 1 T/m each quad
– Monochromatic
– 200 MeV/c
Analysis meeting: Beam momentum measurements using TOFs
Tuesday, 18 December 2007
Slide 18 of 10
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