Transcript Emittance measurement using the TOFs • • The question: can we use position measurements from two TOFs to measure transverse emittance? – Question: x-emittance, y-emittance,

Emittance measurement using the TOFs
•
•
The question: can we use position measurements from two TOFs to measure
transverse emittance?
– Question: x-emittance, y-emittance, transverse emittance, and the trace space
(geometric) or phase space (normalized) definition?
• Supplementary question: If muons come from pion decays in the PSI solenoid
where there is a strong magnetic vector potential, will the muon beam have
angular momentum? If so, then 1-d emittance is not conserved. Ignore today.
– Alpha, beta, gamma also interesting. Anything else?
Proposed method
– Step 1: Do a simulation to determine the transfer matrix between the TOFs using MC
truth
• Caveat: Equivalent to relying on a 1st order Taylor expansion. Cannot express the
increase in emittance and decrease in energy expected in the Cherenkov
– Step 2: Measure the positions in both TOFs
• Error = slab width / root 12 ~ 2 cm
– Step 3: Deduce the conjugate momentum in both planes using the simulated transfer
matrix and the measured positions
– Step 4: Get whichever optical beam properties you like in the plane of either TOF from
the new phase space distributions
Mark Rayner 14/8/08
Analysis Meeting: Emittance
measurement using the TOFs
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Clues on the probable beam just before TOF 0
•
• 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
Mark Rayner 14/8/08
•
CM15 Transport half width plot
25
Half width x / cm
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
norm. em. 7.1 mm after the diffuser
20
Diffuser
TOF0
15
10
5
z/m
0
Half width y / cm
•
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
-5
-10
-15
-20
-25
•
– 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%
Analysis Meeting: Emittance
measurement using the TOFs
2
Use G4MICE to simulate the entire process
•
•
Which beam?
– Gaussian/Top-hat (?) muons starting just before TOF0 in the Stage 6 setup
• Switch to real setup when choice/position of two detectors decided
– Initial mean phase space vector: Pz 250 MeV/c, otherwise zero
– Initial moments matrix: L = 0, alphas = 0, beta x = 1.9 m, beta y = 3.3 m, RMS Pz = 10% [Kevin]
• Sigma({x, y}) = {28, 37} (mm)½ * Sqrt( normalized emittance )
– Will fill the TOFs [Sigma(y) = 200 mm] at 30 mm normalized emittance
– Will only fill a single slab width [Sigma(y) = 20 mm] at 0.3 mm normalized emittance
– Vary initial normalized emittance: 0.5mm, 1mm, 2.5mm, 5mm, 7.5mm, 10mm, 15mm, 20mm, 30mm,
40mm
Trial analysis
– Step 1: Use MC truth to get the transfer matrix
• Problem: G4MICE step length only approximates path through quadrupoles leading to a
spread in the G4MICE calculated transfer matrix elements even in a linear channel. Use mean
of these and compare to pen and paper prediction.
– Step 2: Use G4MICE digitization of the simulated detector response for the positions
– Step 3: Solve for conjugate momenta as before
• Caveat: Using the same simulation for Step 1 and Step 2 is cheating! Errors in e.g. G4MICE
quadrupole model won’t show up
– Step 4: Get the optical beam parameters by fitting bivariate Gaussians and also using standard
statistical formulae
• Compare with same analysis of truth data
Mark Rayner 14/8/08
Analysis Meeting: Emittance
measurement using the TOFs
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Beam line parameters table from Kevin
Kevin’s data
Element
Position
Effective
Length
Field
Strength
s
k = (e/p)*dB/dx
[p=(250–11–3)~235MeV]
m
m
T/m
m
m-2
TOF0 centre
20.8116
Drift Space
20.8624
CKOV1
21.0624
Drift Space
21.5674
Q35 Qd - Q7
24.9637
Drift Space
25.6237
Q35 Qd - Q8
26.1237
Drift Space
26.7837
Q35 Qd - Q9
27.2837
Drift Space.
27.9437
TOF1 centre
Trace space transfer matrix approximation
0.66
0.66
0.66
28.8437
0.88758
-1.34275
1.14749
Drift
24.9637 – 20.8116 – 0.33
= 3.8221
QD
0.66
Drift
26.1237 – 24.9637 – 0.66 = 0.5
QF
0.66
Drift
27.2837 – 26.1237 – 0.66 = 0.5
QD
0.66
Drift
28.8437 – 27.2837 – 0.33
= 1.23
Omega (phase advance)
= s * Sqrt Mag k
1.133
0.748
-1.714
1.131
1.464
0.966
Q35 dimensions: Pole tip radius (the radial distance between the central axis of the quadrupole and its pole tip) 17.82 cm
Vertical ½ aperture 23.6 cm, Horizontal ½ aperture 23.6 cm
Mark Rayner 14/8/08
Analysis Meeting: Emittance
measurement using the TOFs
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Mathematica output: trace space transfer matrices
Mark Rayner 14/8/08
Analysis Meeting: Emittance
measurement using the TOFs
5
Gaussian beam 7.5mm
MC truth G4MICE detector simulation of TOF hits with x’ reconstructed using MC transfer matrix
x’
x’
x/m
x/m
TOF 0
TOF 1
x’
x’
Mark Rayner 14/8/08
Analysis Meeting: Emittance
measurement using the TOFs
x/m
6
x/m
Extra slides
Mark Rayner 14/8/08
Analysis Meeting: Emittance
measurement using the TOFs
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TOF 0  TOF 1 PDG calculations
Energy and momentum
details
TOF0
Ckov
Air
TOF1
scintillator
aerogel
air
scintillator
thickness
cm
polyvinyltoluene
silica aerogel
dry, 1 atm
polyvinyltoluene
Lorentz and time
E average p average
MeV
MeV
TOF0
265.94
244.0394361
Ckov
259.49
237.0034609
Air
257.3
234.6041871
TOF1
251.44
228.1502661
5
8
730
5
beta
density
dE/dx (min I) dE
mass
E before p before E after
p after
dp
g cm-3
MeV g-1 cm2 MeV
MeV c-2 MeV
MeV
MeV
MeV
MeV
1.03
1.97
10.12
105.66
271 249.5535
260.88 238.5253 11.02819
0.2
1.74
2.78
105.66
260.88 238.5253
258.1 235.4816 3.043762
1.20E-03
1.82
1.6
105.66
258.1 235.4816
256.5 233.7268 1.754785
1.03
1.97
10.12
105.66
256.5 233.7268
246.38 222.5737 11.15306
gamma
0.917648477 6.3322692
0.913343331 6.031219
0.91179241 5.9299811
0.907374587 5.660227
dt
microseconds
1.816236508
2.91967607
266.8736115
1.83680113
Scattering
X0
X0
RMS theta RMS theta
g cm-2
cm
mrad
degrees
TOF0
43.9
42.62135922 27.02095823 1.5481882
Ckov
27.25
136.25 19.21043782 1.1006779
Air
36.62
30516.66667 11.9337395 0.6837535
TOF1
43.9
42.62135922 29.23004715 1.6747598
Mark Rayner 14/8/08
Analysis Meeting: Emittance
measurement using the TOFs
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Transverse covariance matrix before TOF 0
mass
Pz
beta x
beta y
MeV
MeV
mm
mm
105.66
250
1900
3300
Norm em Cov xx
mm
(mm)2
0.5 401.508
1 803.016
2 1606.032
5 4015.08
10 8030.16
20 16060.32
30 24090.48
40 32120.64
Mark Rayner 14/8/08
Cov PxPx Cov yy
(MeV)2
(mm)2
6.951316 697.356
13.90263 1394.712
27.80526 2789.424
69.51316 6973.56
139.0263 13947.12
278.0526 27894.24
417.0789 41841.36
556.1053 55788.48
Analysis Meeting: Emittance
measurement using the TOFs
Cov PyPy
(MeV)2
4.002273
8.004545
16.00909
40.02273
80.04545
160.0909
240.1364
320.1818
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