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8.3. The upstream Cherenkov for --e separation
The upstream Cherenkov detector provides pion/muon/electron separation to insure a
clean muon beam for the MICE experiment. The purpose of the upstream Cherenkov is to
reduce backgrounds from the time of flight detector. At the position of the upstream
Cherenkov, the beam particles are essentially muons but there are contaminations from pions
and decay electrons. In the momentum range of interest to MICE, a pure time-of-flight
technique does not provide a sufficient muon-pion separation mainly at the high-momentum
end. In this sense, a Cherenkov device nicely complements the TOF counters.
8.3.1. Characteristics of the particle beams at the position of CKOV1
T.J. Roberts performed the simulation of the beam for Phase VI of the MICE
experiment (Aug 05 beam line design). He assumed that the RF is switched off and that the
absorbers are empty. The primary pions are generated in the ISIS production target and are
tracked as well as their secondaries along the transport beam line and through the whole
MICE setup. Most pions decay on the way before MICE. The dipole magnets and a thick
collimator on the beam line provide further purification of the beam towards an essentially
pure muon beam at the position of CKOV1. However, it is a fact that there will be a small
contamination by pions, but its exact importance also depends on the beam tune and on the
accuracy of the simulation (since the hadronic interactions were not yet taken into account).
Many of the muons, which traverse the diffuser, are within the acceptance of the
trackers and emerge downstream to cross the TOF2 detector planes. These are the so-called
"good muons". The present muon sample (16254 muons) corresponds to 107 primary pions
from the production target. A reasonable although small sample of pions at CKOV1 (381
pions) was obtained by tracking 40 107 pions from the target.
The pictures presented below show the beam spot distribution for good muons at the
position of CKOV1 (Figures 8.3.1 to 8.3.4).
Figure 8.3.1. Transverse distribution of the good muons at the entrance of CKOV1.
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Figures 8.3.2 (left) and 8.3.3 (right). X- and Y-distributions for the good muons at the
entrance of CKOV1.
Figure 8.3.4. Radial distributions of the pions and good muons traversing CKOV1 (semi-log
plot).
The momentum distributions of the muons and pions are shown in Figure 8.3.5. For
the muons the peak is at 230 MeV/c and corresponds to about 200 MeV/c at the central
absorber of MICE. It is seen that the broad pion distribution extends up to higher momenta
where particle discrimination is difficult for the TOF system.
Figure 8.3.5. Semilog plot of the momentum distributions of pions and good muons at the
entrance of CKOV1.
The good muon component of the beam is slightly divergent in both XZ and YZ
planes with a sigma of about 20 mrad as shown in Figures 8.3.6 and 8.3.7.
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Figures 8.3.6 (left) and 8.3.7 (right). Angular distributions of the pions (blue squares) and
good muons (red diamonds) at the position of CKOV1.
The immediate consequence is that the size of the beam spot will hardly increase over
the longitudinal thickness of the CKOV1 setup (about 70 cm).
8.3.2. General principles for the design of CKOV1
Many different conceptual designs for the particle identification by CKOV1 have
been studied. Given the low momentum range from 190 MeV/c up to about 370 MeV/c and
the fact that one has to distinguish pions from muons, it is immediately seen that no radiator
material exists with an index of refraction such as to make the device pion blind. The smallest
index for liquids is obtained for fluorocarbons (n=1.25) and the corresponding pion threshold
is 185 MeV/c. For solids, one candidate material is aerogel with an index of 1.07: the pion
threshold is now 365 MeV/c, but the muon threshold is 276 MeV/c making the device
insensitive to a large of fraction of the muons. Another possible choice would be "highdensity" aerogel with n=1.12: in this case, the pion threshold drops to 276 MeV/c while the
muon threshold is found to be 208 MeV/c.
Given the difficulty of the choice of a single radiator, we have performed the
conceptual design of a RICH type Cherenkov device with a water or fluorocarbon radiator.
Although it is a perfectly viable option, our conclusion is that its construction and operation
are more delicate in addition to the larger budget required.
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We finally imagined a "dual" radiator Cherenkov setup, made of two identical
detection units located "sequentially" along the beam line. The detection units have different
aerogel radiators of indices 1.07 and 1.12 respectively.
Figure 8.3.8. Threshold curves for aerogel n=1.07 (upper picture) and aerogel n=1.12 (lower
picture) as a function of momentum. Red curves are for muons, blue for pions and green for
electrons.
The nominal photoelectrons yields per centimeter of radiator have been computed
with the formula [Review of Particles Properties]
N p.e.  90 sin 2  c
where
cos  c 
1
n
The coefficient "90" takes into account the emission spectrum of Cherenkov light and
the spectral response of a typical bialkali photocathode. At =1, a n=1.07 aerogel generates
11.4 photoelectrons per cm thickness, while the n=1.12 aerogel produces 18.3 photoelectrons
per cm.
The principle of operation is sketched in Figure 8.3.8.
The radiators of indices n=1.07 and n=1.12 define three momentum regions labelled
I, II and III defined by the respective thresholds for muons and pions. If the detection unit #1
has a radiator n=1.07 while the unit #2 has one with n=1.12, it is visible that unit#1 alone will
signal muons in the momentum region I (207 < p < 276 MeV/c). In the momentum region II
(276 MeV/c < p < 365 MeV/c), the units #1 and #2 will fire in coincidence for muons only.
Above 365 MeV/c, muons and pions will generate light in both units. It is known however
that the muon momenta in MICE will not exceed 350 MeV/c, but in any case, the high
momentum particles could be eliminated with a momentum cut defined by the tracker.
8.3.3. Description of the detection units defining CKOV1
8.3.3.1. External views, overall dimensions and internal structure.
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A detection unit is represented in Figure 8.3.9. It has a square transverse cross section
and the four lateral faces are equipped with one photomultiplier.
Figure 8.3.9. Perspective view of one detection unit for CKOV1. Two such units are
located sequentially along the beam line. The particles enter from the left in the green
plate (radiator box).The housing of one photomultiplier has been removed.
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Figure 8.3.10. Side view and external dimensions (in millimeters) of a detection unit. The
beam particles are travelling along the z-axis.
Figure 8.3.11. Front view and external dimensions (in millimeters) of a detection unit.
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As written above, the whole CKOV1 device is constructed by putting two identical
detection units one after the other along the beam line. The longitudinal thickness is shown in
Figure 8.3.12.
Figure 8.3.12. Side view and longitudinal thickness of the whole CKOV1 device.
A longitudinal cut reveals the inner elements of a detection unit (Figure 8.3.13). All
these elements will now be described sequentially.
Figure 8.3.13. Cut of a detection unit passing through the beam axis and the axes of two
opposite photomultipliers.
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The four PMT support plates define a square box, which is closed on both side by
plastic windows attached to the front and back flanges. The 20-mm thick aerogel radiator is
contained in a recess carved out of the entrance plastic window. The aerogel material is
separated from the main volume by a 3-mm thick optical glass window. The Cherenkov light
produced in the radiator is channelled to the four photomultipliers by thin walled conical
mirrors.
8.3.3.2. The main vessel (Figure 8.3.14)
Although the main vessel could be entirely constructed from aluminium plates, we
prefer to build it from 15-mm thick standard steel plates. Before assembly they are plated
with a thin layer of electroless nickel to protect against corrosion. The advantage of steel is to
provide a cheap shielding from stray magnetic fields. The aerogel type proposed below
(section 8.3.3.4) is claimed to be non hygroscopic: it is thus not necessary for the main vessel
to be gas tight and even welded.
All four PMT support plates are identical and are simply bolted to the front and back
flanges. Appropriate recesses are foreseen to automatically provide with the required lighttightness for the photomultipliers.
Figure 8.3.14. The main vessel
8.3.3.3. The aerogel box
The aerogel box also serves as the entrance window. It is carved out of a single 30mm thick black polyacetal (Delrin) plate. All inner faces of the box are covered with 3-mm
thick aluminised optical glass. This is intended to reflect towards the main volume the
Cherenkov photons back scattered by the radiator material. A longitudinal cut through the
aerogel box is shown in figure 8.3.15. Apart from the optical glass window, the total
longitudinal thickness of inactive (absorptive) material is 5 mm (2 mm plastic and 3 mm
glass).
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Figure 8.3.15. Cut through the window and aerogel box.
8.3.3.4. The aerogel radiators.
The chosen aerogel radiators are non hygroscopic and have indices of refraction of
1.07 and 1.12. They are manufactured by Matsushita (Japan) and are delivered as square tiles
of 115 mm x 115 mm x 11.5 mm. One essential property of aerogels is the (bulk) scattering of
photons, which occurs inside the material. It means that a fraction of the photons are scattered
away from their original travel direction. The angular distribution of scattering is of the dipole
type (a + b cos2 ) and will be later approximated by an isotropic distribution with respect to
the original direction. The probability of scattering is parameterised by a scattering length
Lscatt measured by L. Cremaldi (Mississipi). The wavelength dependence of the scattering
length for various aerogel is represented in figure 8.3.16. Direct measurement of the true
internal absorption in aerogel is difficult but the scarce available measurements indicate it is
less than a couple of percents for n=1.03.
In the case of MICE, the optical performances have been evaluated at a single
wavelength of 400 nm. We have thus used the experimentally measured values for the
scattering lengths i.e. 10.76 mm and 7.54 mm for the aerogels n=1.07 and n=1.12
respectively. The internal absorption was neglected.
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Figure 8.3.16. Left: wavelength dependence of the scattering lengths of aerogels
n=1.03, n=1.07 and n=1.12. Right: measured transmission curves of the same
aerogels. The continuous lines are fits based on the Debye-Rayleigh approximation.
See section 8.3.4.
The transverse size of the radiator is determined by the transverse beam spot of the
good muons. The latter is shown in figure 8.3.3. It is seen that a radiator of 220-mm radius
contains all MC good muons. In practice, it is constructed as a 4 x 4 square array of the above
mentioned aerogel tiles. A reduction of the size of the radiator generates losses in the PID
capabilities. They are shown in a semilog plot in figure 8.3.17.
Figure 8.3.17. Semilog plot of the PID losses as a function of the size of a square
radiator.
8.3.3.5. The optical glass window
The downstream side of the aerogel box is closed with a square 3-mm thick Schott
B270 glass window. It is used as a mechanical wall to avoid the aerogel from falling inside
the main vessel and as a precaution during assembly and handling.
The optical transparency of the B270 glass is shown in Figure 8.3.18 for a sample 10mm thick.
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Figure 8.3.18. Transmission of a 10-mm thick sample of the Schott B270 glass
The square glass window is covered with an evaporated reflecting layer outside the
beam spot for good muons i.e. at distances from the center larger than 220 mm. This is
essential to reflect back scattered or diffused photons. The composition of the reflecting layer
is explained below (Figure 8.3.20).
It was checked that the large number of photons generated by pions, muons and
electrons in the n=1.5 glass are trapped inside the glass. The contribution of the few leaking
photons towards the mirrors and the PMTs is negligible.
8.3.3.6. The conical mirrors.
They are the interfaces between the radiator and the photomultipliers. On one side,
they have to exactly match the 200-mm diameter PMTs while on the other side they have to
enclose the useful area (circular beam spot for good muons) of the radiator, which lies in a
plane perpendicular to the PMT effective area.
For each PMT it can be shown by geometry that it exists a particular straight cone
with an elliptical cross section, which fulfils these conditions. The cone is then cut by two
orthogonal planes at 45 degrees with respect to the x- and y- axes. The construction is
repeated for all PMTs at 90 degrees from one another.
Figure 8.3.19. 3D view of the conical mirrors.
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The conical mirrors are constructed from 3-mm thick polycarbonate (Lexan) sheets.
The originally flat sheets are thermally formed in a mould at about 150 °C to the proper
shape.
They are the covered with a reflecting layer of Aluminium, silicon oxyde SiO2 and
hafnium oxyde HfO2. It guarantees a reflectivity of the order of 92% at 400 nm (Figure
8.3.20).
The mirrors are supported by a lightweight modular structure (not shown here) fitting
exactly in the main vessel. This support can be built from aluminium plates or more elegantly
from honeycomb composites.
Figure 8.3.20. Reflectivity of the reflecting layer for the mirrors and the optical
window.
For completeness, the possibility of replacing the reflecting surfaces by diffusing
paint has been studied. Further details and a comparison with reflectors are given below.
8.3.3.7. The PMT assembly
We will use the low background 200-mm diameter EMI9356KA photomultipliers.
The mechanical assembly is straightforward and was already described for CKOV2 (Figure
8.3.21 and section 8.5 of the Technical Reference Document). In principle, they could be
equipped with mumetal shielding but their actual location in the beam line is not affected by
stray fields.
It should be stressed that a noise-free operation of the PMTs requires a positive highvoltage. This is simply to keep the photocathode at ground potential since it is in the vicinity
of the metallic pieces of the main vessel.
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Figure 8.3.21. Cut through the axis of a photomultiplier assembly.
8.3.3.8. The supporting structure in the beam area
To be defined later.
8.3.4. Optical performances, detection efficiency and purity matrix
The assessment of the optical performances of CKOV1 uses the particle files
simulated with GEANT4 [TJR 05] for MICE Step VI, RF off and empty absorbers for an
average momentum of 230 MeV/c. See section 8.3.1 above.
8.3.4.1. Basic data
The figure 8.3.22 shows the distributions of Cherenkov angles in aerogel for the
indices n=1.07 and n=1.12.
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Figure 8.3.22. Distributions of Cherenkov angles for the indices of refraction of the aerogel
radiators (n=1.07 for the upper graph, n=1.12 for the lower graph). The green curves and
traingles represent the distribution of Cherenkov angles for the photons induced by muons in
the glass window.
For the same two indices, the figure 8.3.22 shows the photoelectron yields, using the
standard formula for "normal response" bialkali photocathodes [see section 8.3.2 above and
the Review of Particles Properties] (convoluted with the spectral Cherenkov emission) and
(temporarily) assuming 100% light collection efficiency in CKOV1.
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Figure 8.3.22. Distributions of the number of photoelectrons for the indices of refraction of
the aerogel radiators (n=1.07 for the upper graph, n=1.12 for the lower graph).The green
curves and triangles represent the distribution of the number of photoelectrons induced by
muons in the glass window.
8.3.4.2. Optical simulation
The tracking of the photons inside the detection units of CKOV1 was performed in three
steps:
a) generation of the Cherenkov cones corresponding to the simulated pion and muon files.
This step takes into account the variable path length of the particle inside the radiator.
The actual number of photoelectrons Np.e. detected in the photomultiplier and induced
by the particles in a radiator is given by
N p.e.   Global L N 0 sin 2  c
where L is the thickness of the radiator,
c is the Cherenkov angle and
N0 = 90 photoelectrons cm-1 is a constant whose value takes into account the
spectrum of Cherenkov light convoluted with the response of a standard bialkali
photocathode (see section 8.3.2 above).
The global detection efficiency Global is the product of two factors
 Global   Geom   Phys
where Geom is the geometric light collection probability, or the probability that a given ray
ends up with the proper angle to hit a PMT; and
Phys is the physical attenuation factor due to all physical processes (reflections,
scattering, absorption) occurring along the ray path.
The photons generated are uniformly distributed along the particle path inside the
aerogel. This is justified by the theoretical relation [Paul99]

d2 N
2  
1
 2 1  2 2 
dz d
 
 n  
since 1 and the effective  is peaked at around 400 nm due to the response of the PMTs
(giving a constant n()).
b) tracking of the "photoelectron rays" using the ZEMAX-EE software (Engineering Edition,
version Nov. 2005).
Its results is a large ray database summarizing the detailed history of any photon, from the
emission to the detection.
This commercial software allows very realistic descriptions of all surfaces,
coatings, scatterings, diffusions, reflections and refractions within the CKOV1 setup.
1) The transmission of a photon of wavelength  through an aerogel slab of
thickness L is parameterized as follows
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 CL 
T  A exp  4 
  
where the value of the "clarity" C is obtained from experimental data (C=0.01
m cm-1). In the wavelength range 250 to 700 nm, the parameters A and C are given
in the following table. They were obtained by fitting the experimental data
represented in Figure 8.3.16. In this table, the L values gives the aerogel thicknesses
used for the measurements
4
A
C
L (mm)
n=1.03
0.990
0.041
105
n=1.07
0.988
0.252
115
n=1.12
0.970
0.638
115
n=1.12
0.917
1.216
230
2) the scattering probability of photons in aerogel is obtained from the Debye-Rayleigh
relation
1
C
 4
Lscat 
For example, at =400 nm, the scattering lengths Lscat are 7.56 and 10.54 mm for the
aerogel n=1.12 and n=1.07 respectively. It follows that most photons are scattered many times
in a 20-mm thick radiator.
The angular distribution of the scattered photons is assumed isotropic for simplicity
(instead of the more realistic dipole-type a + b cos2  ).
3) the genuine photon absorption is experimentally very small (<4% per cm) but has been
taken into account here. It corresponds to an absorption length of 245 mm at l=400 nm.
4) for the particular study of diffusing paints instead of mirrors, we use the experimental
data obtained by E. Forton [Forton 00]. There are three components: the lambertian diffuse
scattering of photons on the surfaces (about 25% at all wavelengths and angles of incidence),
an angle-dependent specular component and a rather large absorption.
All other optical properties (internal transmittance of B270 glass, reflectivities of
mirrors if present) were given above.
c) analysis of the ray database
The global detection efficiency Global is the product of two factors
 Global   Geom   Phys
where Geom is the geometric light collection probability, or the probability that a given ray
ends up with the proper angle to hit a PMT (Figure 8.3.23); and
Phys is the physical attenuation factor due to all physical processes (reflections,
scattering, absorption) occurring along the ray path (Figure 8.3.24).
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1000
3000
Geometrical efficiency
Geometrical efficiency
800
2000
600
400
1000
200
0
0.00
0.20
0.40
0.60
0.80
0
0.00
1.00
0.20
0.40
0.60
0.80
1.00
Figure 8.3.23. Distributions of the geometrical light collection probability for the good
muons. Left: for aerogel n=1.07. Right: for aerogel n=1.12.
500
Physical at tenuation
Physical attenuation
400
4000
300
200
2000
100
0
0.00
0.20
0.40
0.60
0.80
0
0.00
1.00
0.20
0.40
0.60
0.80
1.00
Figure 8.3.24. Distributions of the physical attenuation factor for the good muons. Left: for
aerogel n=1.07. Right: for aerogel n=1.12.
The global detection efficiency of a given event is then the product of the geometrical light
collection probability and the physical attenuation factor. The distributions of Global for the
two types of aerogel are shown in Figure 8.3.25. The curves were generated with the full
momentum bin of good muons having an average momentum of 230 MeV/c.
2000
200
Global efficiency
Global ef f iciency
1000
100
0
0.00
0.20
0.40
0.60
0.80
1.00
0
0.00
0.20
0.40
0.60
0.80
1.00
Figure 8.3.25. Distributions of the global detection efficiency for the good muons. Left: for
the aerogel n=1.07. Right: for the aerogel n=1.12.
8.3.4.3. Trigger configurations and detection efficiency for muons
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Up to now the detection units for CKOV1 were separately studied. Based on the ray
databases for the two aerogels, it is possible to study the various trigger configurations. The
whole CKOV1 is sketched as shown in Figure 8.3.26.
p
Beam
n = 1.07
n = 1.12
I
II
Thresholds muons 265
pions
365
210
MeV/c
275
MeV/c
CKOV1
Figure 8.3.27. Sketch of the whole CKOV1 setup.
Given that the detection units I and II could generate a signal or not, there are four
theoretical trigger configurations, labelled in the upper row of Table 8.3.1. It is obvious that
the configuration I on / II off should never occur since the Cherenkov momentum threshold is
lower for n=1.12 than for n=1.07 except for inefficiencies of unit II.
Particle
MC sample
I off / II off
I on/II off
I off / II on
I on / II on
Muons
16244
0.19 %
0%
94.68 %
5.13 %
Pions
380
45.14 %
0%
27.03 %
27.82 %
Table 8.3.1. Trigger configurations generated by pions and good muons. No electronic
threshold nor momentum cut were applied.
It is seen that the inefficiency for the detection of good muons amounts to 0.19 %.
The good muon detection sensitivity to an electronic threshold and/or to a high
momentum cut aimed at removing the high-energy pions is summarized in Table 8.3.2.
a) without electronic threshold
No momentum cut
With momentum cut
p < 365 MeV/c
I off / II off
0.19 %
I on/II off
0%
I off / II on
94.68 %
I on / II on
5.13 %
0.19 %
0%
94.64 %
5.13 %
b) with an electronic threshold of 1 photoelectron
I off / II off I on/II off
I off / II on I on / II on
No momentum cut
2.08 %
0%
95.84 %
2.02 %
With momentum cut
2.08 %
95.85 %
2.02 %
p < 365 MeV/c
Table 8.3.2. Sensitivity of good muon detection to electronic thresholds and/or to a
momentum cut.
For a given electronic threshold it is seen that a high-momentum cut does not change
the fraction of good muon detection. On the other hand, an electronic threshold of 1
photoelectron decreases the good muon detection efficiency from 99.81 % to 97.86 %. The
inefficiency rises from 0.19 % to more than 2 %.
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The same results can also be expressed in terms of a purity matrix i.e. as the
percentage of good muons for a given trigger configuration. This is summarized in Table
8.3.3. The content of each cell of the table is given by
Purity  1 
Nr. Pions
Nr. Pions  Nr. Muons
a) without electronic threshold
No momentum cut
With momentum cut
p < 365 MeV/c
I off / II off
87.819 %
I on/II off
0%
I off / II on
99.983 %
I on / II on
99.683 %
80.819 %
0%
99.984 %
100 %
b) with an electronic threshold of 1 photoelectron
I off / II off I on/II off
I off / II on I on / II on
No momentum cut
98.607 %
0%
99.983 %
99.351 %
With momentum cut
98.607 %
99.988 %
100 %
p < 365 MeV/c
Table 8.3.3. Purity matrix of the trigger configurations for good muons.
It is seen that the "useful" muon trigger configurations "I off / II on" and "I on / II on"
are contaminated by pions at the level of 3.2 10-3 % at most when there is no electronic
threshold.
The previous results were obtained with particle files at a nominal momentum of 230
MeV/c. Within the momentum bin (RMS of about 20 MeV/c) and the limited statistics
available at the extreme momenta, it is possible to deduce the momentum dependence of the
detection efficiency.
The figure 8.3.28 represents the contributions of the momentum bins to the three
different trigger configurations assuming an electronic threshold of 1 photoelectron. The
undetected events corresponding to the "I off/ II off" configurations are present at low
momentum only.
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Figure 8.3.28. Momentum dependence of the trigger configurations assuming an electronic
threshold of 1 photoelectron.
The statistics is rather poor above 280 MeV/c.
The momentum dependence of the muon detection efficiency is given in Figure
8.3.29. Apart from the low momentum component, it is essentially constant at 99.5% above
230 MeV/c. But it should be remembered that the present statistics is very poor away from the
average momentum of 230 MeV/c.
Figure 8.3.29. Momentum dependence of the muon detection efficiency for an electronic
threshold corresponding to 1 photoelectron.
8.3.4.4. Comparison of diffusing and reflecting optics.
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We found it interesting to explore the possibility of replacing all mirror surfaces in
CKOV1 with pure diffusing surfaces. Several publications suggest the use of white paper,
Tyvek foils (kind of Teflon) or special white paints. To our best knowledge, these solutions
were never applied to Cherenkov detectors. It was found that there are very few
measurements of the absolute reflectance and scattering for all these materials. It is however
easy to find data relative to a given coating [Stoll 96 and Stoll 97].
The absolute reflectance, scattering and absorption of a commercial white paint made
by Bicron were measured by E. Forton [Forton 00]. The angular distribution of a
monochromatic light measured at a fixed angle of incidence is interpreted as the sum of two
components:
- a scattered ("Lambertian") component varying with cos whereis the angle of detection.
- a specular component obeying to the normal reflection law.
Examples of such angular distributions are shown in Figure 8.3.30.
Figure 8.3.30. Angular distributions of the light scattered/reflected by the Bicron white paint.
Left:  = 450 nm, incidence 40°. Right:  = 600 nm, incidence=70°. Blue dots are data points
and the red curve is the model (see text).
In figure 8.3.30, the peak corresponds to the specular component and the broad
"background" is the scattered part. The different components depend on the wavelength, on
the angle of incidence. They are shown in figure 8.3.31 for the Bicron white paint illuminated
at 400 nm.
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§8 page 22/24
Figure 8.3.31. The scattered, reflected and absorbed components as functions of the angle of
incidence. The measurements were done at 400 nm.
First, one observes that the scattered component corresponds to a constant 30% of the
incident light. Second, one sees that, at small angles of incidence, the reflection is very small
while most of the incident light is absorbed. On the contrary, at large angles of incidence i.e.
when approaching the grazing condition, the specular component becomes dominant.
Instead of modifying the Zemax software for the optical evaluation of diffusing
surfaces, we assumed we had always the maximal light yield ("scattered" + "reflected") from
the diffuser. The assumption is equivalent to absorption of 20 %, a scattered contribution of
25% and a specular contribution of 55% (corresponding to the situation at 75° in figure
8.3.31). The optical evaluation thus represents the most optimistic case.
The distribution of the geometrical efficiency is the same as for mirrors: it means that
the light collection of the proposed optical system does not depend on the direction of the
incident light.
On the contrary, the distributions of the physical efficiencies show that the diffusing
surfaces induce a greater attenuation of the incoming light compared to the mirror surfaces.
The same conclusion is reached for the global efficiency represented in figure 8.3.32.
Figure 8.3.32. Distributions of global detection efficiencies for mirror (blue) and diffusing
(red) surfaces. The red curve and dots correspond to the most optimistic case for absorption.
The consequence of this poorer detection efficiency for diffusing surfaces is an
increased inefficiency (6.34 %) of the whole CKOV1 as seen from Table 8.3.4 for an
electronic threshold of 1 photoelectron. The numbers in italics correspond to the mirror case.
The purity matrix remains essentially the same for the two types of surfaces (Table 8.3.5).
No momentum cut
I off / II off
6.34 %
(2.08 %)
I on/II off
0.04 %
(0 %)
I off / II on
92.58 %
(95.84 %)
I on / II on
1.04 %
(2.02 %)
With momentum cut
p < 365 MeV/c
6.34 %
0.04 %
92.58 %
1.04 %
Table 8.3.4. Trigger configurations for good muons with diffusing surfaces when applying an
electronic threshold of 1 photoelectron. The numbers in parenthesis represent the situation
for mirror surfaces with the same threshold.
No momentum cut
I off / II off
99.524 %
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I on/II off
0%
I off / II on
99.979 %
I on / II on
99.120 %
22
§8 page 23/24
With momentum cut
p < 365 MeV/c
(98.607 %)
(99.983 %)
(99.351 %)
98.607 %
99.988 %
100 %
Table 8.3.5. Purity matrix for good muons with diffusing surfaces when applying an
electronic threshold of 1 photoelectron. The numbers in parenthesis represent the situation
for mirror surfaces with the same threshold.
As a general conclusion, the diffusing surfaces are definitely worse than mirror
surfaces even with the most optimistic assumption of a small absorption.
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201 MHz
Details
The
focus
Final
of
coilsTracker
the
Cherenkov
Cavity
in the
AFC module
Solenoid
Detector
Conceptual
Design
§8 page 24/24
8.3.5. Dimensions and tolerances
Table 8.3.6. Overall dimensions of CKOV1
Directions
along Oz (beam axis)
along Oy (vertical)
along Ox (horizontal)
Dimensions (mm)
713
1226
1226
Table 8.3.7 Tolerances
Item
Support frame
Steel vessel
PMT magnetic shielding
Optical parts
Surface flatness (mirrors
and windows)
Tolerances (mm)
± 2.5 mm
± 0.5 mm
± 0.1 mm
± 0.1 mm
± 0.01 mm
8.3.6. References
[Forton 00] E. Forton, Optical properties of diffusing panels and wavelength shifting fibers
for large volume scintillation detectors, MSc thesis, Louvain-la-Neuve, 2000 (in French).
[Paul 99] P.W.Paul, The aerogel radiator of the Hermes RICH, PhD thesis, Caltech, 1999.
[Stoll 96] S.P. Stoll, An investigation of the reflective properties of Tyvek papers and
Tetratex PTFE films, Brookhaven Phenix Note #245, 1996.
[Stoll 97] S.P. Stoll, Comparison of new and old Tyvek Style 1055B,
Note #245 Addendum, 1997.
[TJR 05] T.J. Roberts, MICE collaboration meeting, Rutherford Appleton Laboratory,
October 2005.
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