Exploring Areas for Improved Performance of
Cherenkov Counters in Super-TIGER
Jonah Eaton
Dr. Thomas Hams
Dr. Makoto Sasaki
Dr. Melissa Kiehl
April 1st, 2010
I. Introduction
The universe is filled with unresolved questions, how the universe began, why
does there seem to be more matter than anti-matter and so many more. One such
question surrounds the origins of cosmic rays. Super-TIGER is a balloon-borne
experiment to answer just that question. This research paper will discuss the physics,
general design, and methods for improved efficiency of the Cherenkov counters within
Super-TIGER. Specifically, this paper will explain the physics involved with high energy
particles, their role in Cherenkov radiation, and explore the general design and purpose
of the Cherenkov counter and the greater Super-TIGER experiment. Finally, this paper
will discuss how manipulating the shape, depth, and materials of the counter, and
changing the number, position and efficiency of the Photomultiplier Tubes (PMT), can
significantly increase the light collection and thus improve the performance of the
Cherenkov counter. Thus this paper will introduce factors of the Cherenkov counter to
adjust, and with the background physics knowledge, speculate how this may modify the
light collection efficiency before the counter is tested within a Monte-Carlo computer
simulation.
II. Super-TIGER
NASA Internship - This paper’s main subject of discussion is the Super-TIGER
experiment, a cosmic-ray experiment being conducted primarily by the Washington
University, NASA Goddard Space Flight Center, the California Institute of Technology,
and the University of Minnesota (de Nolfo, et al., 2009b). I have been fortunate enough
to receive an internship at the NASA Goddard under Dr. Thomas Hams in the High
Energy Astrophysics division during the summer of 2008, and have since returned for
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 2
the summer of 2009, and presently the 2009-2010 school year as part of the Howard
County Intern/Mentor program. During this period, I have gained general experience
about cosmic rays and their detection, primarily in the Super-TIGER and the BESS-
Polar experiments. Both of these are balloon-borne, high-altitude and long-duration
experiments designed to gather data on cosmic rays.
Cosmic Rays - One of the most perplexing phenomena in the universe is the
existence of cosmic rays. In brief, cosmic rays are high energy particles traveling around
in the universe, although they are mostly confined to our galaxy (“Cosmic rays” 2009).
The cosmic rays of interest in this paper are classified as galactic cosmic rays (GCR).
GCR are usually atomic nuclei or elementary particles and originate from within the
Milky Way Galaxy (“Imagine the universe”, 2009). While cosmic rays may originate
from within this galaxy, the Milky Way’s magnetic fields are able to bend the paths of
the cosmic rays, confining the particles to within our galaxy and subsequently disorient
the particle’s paths, causing cosmic rays to appear isotropic (“Galactic cosmic rays”,
2009 ; Hams, 2009). These cosmic rays travel at extraordinarily high velocities, often
very close to that of the speed of light, and due to these high velocities, atomic nuclei
cosmic rays have all their electrons stripped away, leaving particles fully ionized
(“Galactic cosmic rays”, 2009). The question of cosmic rays is usually one of their origin:
What is the source composition, where are the sources and how are cosmic rays
accelerated to such high energies?
While there are many convincing models on the origins of cosmic rays, none have
been conclusively proved. When considering the source material, or the source of cosmic
rays, the reigning models mostly differ on the extent that one astronomical process
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 3
contributes to the cosmic ray material over others. Wolf Rayet stars are one possible
source as this massive star class blasts out large “amounts of stellar material into
space” (Cain, 2009). Other likely sources are interstellar gas and dust, particles from the
“stellar coronae” or from supernovae (Ramaty, Kozolvsky, & Lingenfelter, 1998).
The second question of cosmic rays, is how did they get to such high energies, or
what was their accelerator. It has been noted that particles appear to accelerate from the
shock front of a supernova blast wave (Blandford & Minkel, 2008 ; “Cosmic rays” 2009 ;
Particle Physics & Astronomy Research Council, 2004). Other theories suggest that
supernova might not provide the full acceleration and rather the magnetic fields
associated with the expanding clouds of gases may accelerate the particles over
thousands of years (“Imagine the universe”, 2009). Another possibility is when neutron
starts are born and collapse, as in both events large jets of gamma rays are produced
which in turn could accelerate particles (Dar & Plaga, 1999). Luckily, as cosmic rays play
an important role in nucleosynthesis (process of creating new atomic nuclei), by
analyzing the isotopic composition of cosmic rays, one can make reasonable and
sometimes definitive conclusions of their origins (“Galactic cosmic rays”, 2009 ;
Ramaty, Kozolvsky, & Lingenfelter, 1998).
Purpose - The long-duration balloon flights in 2001 and 2003 of Trans-Iron
Galactic Element Recorder (TIGER) experiment, gathered data to help address the
origins of cosmic rays. The results of the TIGER experiment suggested that Galactic
Cosmic Rays originate from “core-collapse supernovae… mixed with interstellar
material” for the vast majority of the cosmic rays, while about 20% of GCRs originate
from the “ejecta from Wolf-Rayet stars”, however for more conclusive results, more
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 4
statistics are needed , particularly for rarer elements
(de Nolfo, et al., 2009a). This is the
scientific motivation for the
experiment Super-TIGER. Specifically
the Super-TIGER experiment is designed to test
some of the emerging models of cosmic-ray origins by
particularly uncovering the “atomic processes
by which nuclei” become accelerated (de
Nolfo, et al., 2009a). Measurements of the elements with a Z(charge)>30 are especially
helpful for probing the associations for the enrichments expected from nucleosynthesis,
but cosmic rays with the higher charge (Z) are also much rarer (“Super-TIGER”, 2007).
Thus Super-TIGER, pictured in Figure 1, is a larger instrument than its predecessor and
will be flying and collecting data for a longer duration of time (de Nolfo, et al., 2009b).
This is expected to yield up to eight times more data compared to TIGER and thus
should provide a sufficient statistics on the rarer elements to make a solid conclusion
(de Nolfo, et al., 2009b).
The Detector - One of the two Super-TIGER detector modules, with all of its
primary components is pictured in Figure 2 on the next page. It’s active volume is about
7 feet by 14 feet along its side and about 3 feet high (Hams, 2009). A hodoscope is used
to measure the trajectory of the particle which allows the data to be adjusted for
particular angles and any “instrument non-uniformities” (de Nolfo, et al., 2009a). To
identify the charge of the particle, Super-TIGER uses three scintillators, which are each
employed to provide an independent charge (Z) measurement of the particle (de Nolfo,
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 5
SuperSuper--TIGER InstrumentationTIGER Instrumentation
Two TIGERTwo TIGER--like modules, each twice the Size of TIGERlike modules, each twice the Size of TIGER
** More than 4!
greater collecting power from cross-over
events & more efficient use of detector elements.Figure 1- View of Super-TIGER instrumentImage from de Nolfo, et al., 2009b
et al., 2009a). Then two
Cherenkov counters are
used to do “velocity
corrections to the charge
measurements” of the
particles, which helps
distinguish between the
lower and higher energy
particles (de Nolfo, et al., 2009a).
The Cherenkov Counter - Due
to their high energy, cosmic-ray particles travel at relativistic speeds, or speeds near
that of light. While physics does not allow for any particle to travel faster than the speed
of light in vacuum, it is possible for a particle to travel faster than light within an
optically dense medium (local speed of light), or a medium in which light slows down
according to the equation:
cmed = c/n
where n is the refractive index of the medium that has a value greater than one (Jelley,
1958). When a charged particle does travel at a velocity higher than cmed, Cherenkov
radiation is emitted (Jelley, 1958). This situation is similar to that of a sonic boom, when
the source of the sound waves exceeds the speed of those waves, “a wave front or a shock
wave” is produced (Gladney). In the case of Cherenkov radiation, as the charged particle
travels, it electromagnetically interacts with the medium to create a dipole field in the
material as shown in Figure 3. This dipole field will have brief electromagnetic pulses of
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 6
SuperSuper--TIGER Detector ElementsTIGER Detector Elements
–– Three planes of plastic scintillator Three planes of plastic scintillator !!
measure chargemeasure charge
–– Two Cherenkov counters Two Cherenkov counters !!
velocity & chargevelocity & charge
–– Scintillating fiber hodoscope Scintillating fiber hodoscope !!
trajectory determinationtrajectory determination
Figure 2- Exploded view of one of the two identical detector modules of the Super-TIGER instrument; “S1”,
“S2”, “S3” refers to each Scintillation counterImage from de Nolfo, et al., 2009b
radiation over a band of frequencies but because
the particle is relativistic, this radiation is in
phase resulting in the different frequencies to
have constructive interference. This in turn
creates an electromagnetic field which is light
(Jelley, 1958). Similarly to other shock waves,
Cherenkov radiation is at an angle dependent on
the medium and the speed of the particle. The
angle of Cherenkov radiation is given by:
cosθc = 1/βn where β= vp/c
where n is the index of refraction, vp is the velocity of the particle and β is the velocity of
the particle as its proportion to the vacuum speed of light. This equation is critically
important as it states that the Cherenkov radiation is emitted at a fixed angle (the
Cherenkov angle) depending on the particle’s velocity and the refraction index of the
medium. Thus Cherenkov light is emitted in a relative cone shape, as determined by its
Cherenkov angle. If one could measure this Cherenkov angle, a very precise
measurement of β could be made (Jelley, 1958). Unfortunately, to make such a
measurement, a highly segmented photo sensitive detection area is needed, adding great
expense, size and weight to the counter. Super-TIGER is designed to give a precise
measurement of the charge of the particle, and to do this, it is important to show the
relationship between the amount of Cherenkov light created and the particle’s charge
and velocity. To show this, one must develop an equation for the amount of energy lost
per unit path length to Cherenkov radiation. After making six assumptions about the
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 7
68
velocity of light in the medium, the radiation is in phase, resulting in constructive
interference creating a field, and hence radiation, at a distant point. Cherenkov, Frank
and Tamm were awarded the Nobel Prize in Physics in 1958 for their discovery and
interpretation of this effect.
Complete discussions of the electromagnetic theory behind the production of
Cherenkov radiation can be found in books by Jelley (1958) or Jackson (1999). From the
+ -
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Charged Particle
Cherenkov radiator
medium (n > 1.0)
Figure 4.3 Dipole field set up by the passage of a charged particle through the
medium. The passage of a relativistic particle through a Cherenkov radiator
medium will create a constructive set of electromagnetic waves resulting in
Cherenkov radiation. (Based on a figure in Jelly, 1958)
Figure 3- Image from Jelley, 1958
condition [(i) The medium is considered a continuum with the dielectric constant being
the only parameter of the medium, (ii) Ignoring dispersion, or the dependence of the
refractive index for the wavelength of the electromagnetic wave in the optical medium,
(iii) Radiation reaction is ignored, (iv) Medium is assumed to be a perfect dielectric, (v)
the particle is moving at a constant velocity and (iv) the medium is unbounded with an
infinite track length] the energy radiated per unit length from Cherenkov radiation is
given by (Jelley, 1958):
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Where W is the energy radiated by the particle, ℓ being the length the particle traveled in
the medium, ω being the frequency of the resulting radiation, e being the charge of an
electron and Z being the charge count of the particle (Jelley, 1958). As no limits of
integration for the frequency for this function, it might seem that the energy output
would be infinite as it would encompass all frequencies of light. However in reality, any
real medium is dispersive, thus restricting radiation following
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where n(ω) is the index of refraction as a function of the frequency bands and ϵ is the
relative dielectric constant for the medium (Jelley, 1958)
While it is nice to have a function for energy output, for the Super-TIGER
experiment it is more useful for a function of the number of Cherenkov photons created
over a band of wavelengths. This wavelength band and thus the light yield, is
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 8
determined by the experimental setup and will be the focus of this thesis. Given the
variables and constants
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with α being the fine structure constant and ℏ is the planck constant over 2π and λ
being the wavelength. Utilizing the function of energy output in relation to number of
photons, a differential function can be made
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where N is the number of photons. Substituting this in for our function for Cherenkov
radiation and then integrating over two frequencies gives us:
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Some simplification returns:
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Further integration and some substitution yields our final equation (Jelley, 1958):
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Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 9
Thus, given the amount of electric charge, Z, of the incident particle, the effective
wavelength range of the light detected, the index of refraction, a fine structure constant
and the velocity of the particle, it is possible to determine the “number of photons
emitted per unit of path length for a particle passing through a radiator” (Link, 2003).
Important to recognize with Cherenkov radiation is the radiator. This optically
dense medium is the key element in establishing a controlled experiment utilizing
Cherenkov radiation. Two different radiators are used in the Super-TIGER experiment,
namely aerogel and acrylic. Acrylic is a type of plastic, while Aerogel is noted for being
like solid air and has a refractive index in the range of 1.010-1.030 (Wogsland, 2006).
In order to collect all of the Cherenkov light produced in a detector, it is necessary
to have reflectors, or a very highly reflective surface to prevent the photons from being
absorbed so they may be collected by Photo-multiplier tubes. The two of interest within
this paper are Gore-Tex and Tyvek. As Cherenkov radiation usually produces photons at
different wavelengths, the most important aspect of a good reflector is to have a very
high reflectivity in the particular wavelengths of interest. While Tyvek is a very good
reflector in the visible range of the spectrum, its reflectivity begins to fall off in the ultra-
violet spectrum. Gore-Tex on the other hand, as a very high reflectivity for most of the
ultra-violet spectrum, though Gore-Tex has been shown to produce some Cherenkov
radiation of its own, meaning the possibility that the number of Cherenkov photons
detected could be skewed. Nevertheless this high reflectivity in the ultra-violet spectrum
should not be misrepresented. Most of the Cherenkov light produced is usually in the
shorter wavelengths, meaning a high reflectivity in that range is crucial.
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 10
Detector and Cherenkov Counter Design- Super-TIGER employs two
Cherenkov counters, labeled C0 and C1 (“Super-TIGER”, 2007). Both C0 and C1 have
radiators placed inside rectangular boxes with the inside surface being lined with the
highly reflective material Gore-Tex (“Super-TIGER”, 2007). The C0 counter utilizes an
aerogel radiator with a refractive index of n= 1.04 (“Super-TIGER”, 2007). The C1
counter utilizes an acrylic radiator with a refractive index of about n=1.5 (“Super-
TIGER”, 2007). The acrylic radiator is 1.1 cm thick and rather than a single large sheet,
“the acrylic radiator will consist of a 1 x 2 matrix of 1.15 m x 2.3 m modules” (“Super-
TIGER”, 2007). For the aerogel radiator, four aerogel blocks with approximately 3 cm
thickness will be used, each with a size of approximately 55 cm x 55 cm (“Super-TIGER”,
2007).
As the primary purpose of Super-TIGER is to identify particles based on their
velocity and charge. The Cherenkov modules have the task to “make velocity corrections
to the charge identification, to separate low energy from high energy nuclei…. and to
measure the energy spectra of the nuclei over the range” of 0.3 GeV per nucleon to about
10 GeV per nucleon (“Super-TIGER”, 2007). Having two radiators, each with its own
index of refraction allows for these goals. Because both C0 and C1 have their own index
of refraction, each has its own energy threshold, meaning each counter has a distinct
amount of energy required per particle for Cherenkov radiation to occur and the an
upper limit of a particle’s energy for when the radiation produced saturates, or “the light
produced becomes nearly independent of energy” of the cosmic ray particle (“Super-
TIGER”, 2007).
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 11
The outcome of such design follows. As a cosmic-ray particle travels through the
C0 detector, Cherenkov radiation is produced in relation to the particle’s energy given
that the particle has an energy of at-least 2.5 GeV per nucleon. The resulting Cherenkov
photons will be reflected on the reflective lining inside the light integration volume of
the Cherenkov counter and continue to be reflected until they are either absorbed by the
radiator, reflector (lost) or be detected in a photomultiplier tube. As this occurs, the
cosmic-ray particle continues its travel through the detector stack and as it passes
through the C1 counter, there is a similar occurrence. Within the C1 counter, Cherenkov
radiation is once again produced in relation to the particle’s energy, but this time it must
have a minimum energy of .3 GeV per nucleon. With the except of a different radiator in
C1, the process of Cherenkov photon collection is similar to that in the above mentioned
C0 counter. The number of photons detected by the photomultiplier tubes in each
counter it is possible to draw conclusions on the given particle’s charge and velocity.
Assuming the particle does not interact during its travel through the detector and
that the particle does not lose significant amount of energy during its travel, one can
show from the number of photons created function, that the two signals will have a clear
relationship:
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Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 12
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Where S0 is the signal of the C0 counter and S1 is the signal of C1 counter. Then using
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Once the β has been removed, the combined equation can be used to solve for Z2, or the
charge of the incoming particle:
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Further simplification yields a function for the charge count (Z) of the cosmic-ray
particle as a function of the signals from both counters and the constants associated
with each counter:
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 13
! !! !""!#$%"
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Additionally, this proves that a linear
relationship between both the C0 and C1
signals can be drawn which is shown in
Figure 4. This figure of the C0 and C1
signals plotted against each other clearly
identifies the charges of each particle, as
each roughly horizontal line are the events
associated with a specifically charged
particle. Thus Super-TIGER will be able to
properly identify the particles detected,
which should give us hints of their origins.
III. Cherenkov Counter Design
Improvement
Need for Improved Performance- The Super-TIGER experiment, like many
scientific experiments searching for rare events, would benefit from greater data quality.
One aspect of data quality is improved statistics or a greater number of detected events.
When detecting cosmic-ray particles, by utilizing a larger sensitive detection area in
conjunction with a longer observation time yields more detected events and less
statistical uncertainty. The other aspect of data quality is the uncertainty of the
measurement, or the precision with which the cosmic-ray particle is detected. As the
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 14
Figure 4- Cross-plot of the Aerogel Cherenkov versus the Acrylic Cherenkov signal from a small
sample of the TIGER experiment. Image from page 102 of Link, 2003
102
C0 Threshold Cut
High C0
Cutoff
Figure 5.5: Crossplot of Aerogel Cherenkov versus Acrylic Cherenkov signal. Note that this is only a small sample of the overall TIGER dataset (~133,000 events). Lines representing the High C0 cutoff used as a cut for Above C0 data and the C0 threshold cut used as a cut between Above C0
and Below C0 data are shown..
purpose goal of Super-TIGER was a long
flight time and greater detection area over
TIGER, the focus of this paper will be on
on lowering the systematic uncertainty of
the counter by increasing the light
collection of the Cherenkov counter. These
greater statistics and greater certainty will
remove more possible error and allow for
more definitive conclusions.
Whether or not possible
improvements are found, new ideas or
possibilities for greater performance may always make it into future experiments to
gather further data on related or completely different areas of study. When optimizing
the Cherenkov Counter in Super-TIGER, one of the most important tools at the team’s
disposal is the Geant4 simulation program. Its roots dating back to 1993; Geant4 is a
“detector simulation program” spearheaded by CERN and created in an C++ based
programming environment (“Chapter 2 history of Geant4”, 2009). With this program it
is possible to simulate the performance of the Cherenkov counter as it is designed now.
This most current design as programed into Geant4 is pictured in Figure 5. In addition,
potential changes to the counter can be implemented in the simulation code and their
effects on the performance of the counter can be studied without actually building a new
detector for this test. The original code for the simulation of the Aerogel Cherenkov
counter was developed by Dr. Hams, and in almost all cases, the code will remain in its
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 15
Figure 5- a visualization of the Aerogel Cherenkov Counter based on the Dr. Ham’s Geant4 simulation code of the original design. Image created from the Stanford's HepRep Application.
original form, with only slight temporary modifications in order to simulate, and then
analyze the results of altered performance. The primary method for judging
performance in simulating the Cherenkov counter will be the overall light collection, or
the number of Cherenkov photons detected per event. An visualization of a this type of
simulation is shown in Figure 6, where the the green lines are some of the Cherenkov
photons produced by the cosmic ray muon (red line) and where each detected photon is
shown as a small white dot.
Ideally, the Cherenkov counter would detect every Cherenkov photon created by
the cosmic-ray particle while allowing for a sufficiently large number of photons to be
created by the Cherenkov effect for each cosmic-ray particle. In reality of course, this is
impossible, but the purpose of improving
the performance relies on designing the
Cherenkov counter as close to this ideal as
possible. An ideal Cherenkov counter would
also minimize the chances for unwanted
particle interactions. In this case unwanted
particle interactions are the nuclear
reactions between the cosmic-ray particle
and the mediums in which it travels, and
thus the instrument design must maximize
the active detector material and reduce the
amount of inactive mechanical support in
the path of the particle. Nuclear reactions can drastically change the composition of the
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 16
Figure 6- A visualization of an incoming negatively charged muon (red), and all of the trajectories of the resulting Cherenkov photons (bright green). Note not all photons created are shown. Each white dot represents a photon being detected by a PMT. Image created from the Stanford's HepRep Application based on the Geant4 simulation code provided by Dr. Hams.
particle, resulting in a particle losing significant amounts of mass and energy, or
splitting the particle (Sasaki 2010). Since one of the primary focuses of the experiment is
to identify these particles, any data associated with a particle that underwent a nuclear
reaction within the detector must be thrown away, as not to corrupt the data (Sasaki
2010). As a general rule of thumb, the more material the particle travels through, the
greater probability that a nuclear interaction will occur (Sasaki 2010).
Possible Reflector Improvements- Some of the possible improvements to
the Cherenkov counter are deceptively simple. Simply changing the reflector to a
material with a higher reflectivity in the Cherenkov photon wavelengths should result in
greater collection, as a result of photons having a greater probability to bounce around and be
detected by a Photosensitive device, rather than
being absorbed by the boundaries. In the
original TIGER experiment a material called
Tyvek was used, but for Super-TIGER it looks
likely that the new reflector will be Gore-Tex.
Gore-Tex has the advantage of maintaining a
very high reflectivity across a wider range of
wavelengths, whereas Tyvek drops off at
about 425 nm as shown in Figure 7. This
change alone should increase the performance
of Super-TIGER over TIGER as any small
change in reflectivity can have a great effect on light
collection. However other reflective materials do
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 17
Figure 7- A plot of the reflectivity of GoreTex and different types of Tyvek over
different photon wavelengths. Image from Hams, 2005
exists and could be viable alternatives. One such alternative is PolarKote, a diffuse
reflectance material produced by Light Beam Industries which claims to have “highest
diffuse reflectance of any known material or coating over the UV-VIS-NIR region of the
spectrum” (“About PolarKote”)(UV- ultra violet spectrum, VIS, refers to visible
spectrum, and NIR refers to infrared spectrum). Another alternative is the GORE™
Diffuse Reflectors by W. L. Gore & Associates, which also claims “World’s most diffuse
reflective material” (“Gore DRP: diffuse reflector”, 2009). Even though the Gore DRP
does provide some data
on its reflectivity at given
wavelengths as shown in
Figure 8, more
information and data is
needed before it can
become a viable
alternative. The main
obstacles involved are the
materials themselves, whether
they can be properly incorporated in the instrument, whether they will cause unwanted
interactions with the particles, and whether they effectively cover the full interval of
photon wavelengths. Additionally, the Gore DRP is slightly thicker than the current
Gore-tex and thus may produce more of its own unwanted Cherenkov radiation.
Suppose either one of these reflectors is able to clear these hurdles, incorporating these
reflectors into the simulation to see if any improvements also presents challenges, as the
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 18
Figure 8- A graph of the reflectivity of two types of GORE DRP Reflector in comparison to other reflectors over
different photon wavelengths. Image from “Gore DRP: diffuse reflector”, 2009
user must predefine the reflectivity for each wavelength, which without the proper data
could dissolve into guesswork (Sasaki, 2010).
Another possible way to improve the reflectors, is to increase their thickness.
Theoretically, an increase of the thickness should increase the reflectivity, however
testing the results in the lab is slightly more difficult (Sasaki, 2010). Again the main
challenge here is insufficient data on how the reflectivity increases with increase in
thickness with any of these materials. Thus, without an in depth experiment examining
each reflector, there are no experimentally determined values for the change in
reflectivity to use in the simulation, and thus one cannot be sure of any meaningful
improvement in light collection. Additionally the limitations of the size, weight and
expense of the entire instrument also limit the amount and type of the reflector used.
But whatever the limitations may be, the importance of the reflector should not
be forgotten. The importance of even a minimal increase in reflectivity is highlighted
with the light-box formula. In this approach, we have a given number of photons
entering the detector and a certain proportion hit a photomultiplier detector and the
other proportion hits the reflector. These two proportions are given by the proportion of
the area of the PMT compared to the total interior area of the counter and the
proportion of the area of the reflector compared to the total interior area. Then those
photons that hit the reflector are either absorbed or reflected based on the probability of
reflection. Those photons reflected then restart the process. This process to find the total
number of photons detected can be described mathematically as:
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!! #!!" #"!$" !!! !" & #"!$" &!! !" ' #"!$" '%%%%!"$ #"!$" $( )
" #"!$"
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%
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!
#"" #"!$" !
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 19
Where R is the reflectivity of the interior of the counter, and ε is the probability that the
photon will be detected by a PMT from the total surface area of the PMT divided by the
total surface area of the interior of the counter. This can be simplified to
!!! !"#" !!$"!!! !"#"!$"!"#"!$"!!! !"#"!$"!"#"!$"!"#"!$"!%%%%
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" #"!$"
!#$ $ *
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This can be further simplified into an infinite series:
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!! #!!" #"!$" !!! !" & #"!$" &!! !" ' #"!$" '%%%%!"$ #"!$" $( )
" #"!$" !* !#
!#$ $ +
%
"$ #"!$" $!!$ !!
!
#"" #"!$" ! given
!!! !"#" !!$"!!! !"#"!$"!"#"!$"!!! !"#"!$"!"#"!$"!"#"!$"!%%%%
!! #!!" #"!$" !!! !" & #"!$" &!! !" ' #"!$" '%%%%!"$ #"!$" $( )
" #"!$" !* !#
!#$ $ +
%
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!
#"" #"!$" !
This is geometric infinite series which given the assumption that the product of the
reflectivity, R and the probability that the photon hits the reflector and not the PMT, (1-
ε) is less than one ends up being convergent to a definite value as shown. This is fair
assumption to make as the reflectivity of any material is never a perfect 100%, and the ε
of the Cherenkov Counter is about 1 to 2%. What this formula shows is that any minute
increase in the reflectivity of the interior of the counter, will result in a significant
increase in the number of photons detected.
Possible Photomultiplier Detector Improvements- Another possible area
for improvement would be the type, position and number of Photomultiplier
tubes(PMT). As PMTs vary greatly in size and efficiency, finding the most efficient type
of PMT is the most obvious improvement and has largely been completed as well.
Greater efficiency easily translates into a greater number of photons being detected and
with greater precision, the number and position of PMTs has possible benefits as well.
As the end goal of the detector is to get the maximum number of photons detected by
the PMTs, a greater number of PMTs covering a greater interior surface area of the
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 20
detector, should greatly increase the probability of a photons being detected before they
are absorbed by some other process.
Additionally, changing the position of the PMTs to cover more of the interior
surface area would have a similar effect. Unfortunately, this possible improvement has
its own set of hitches. In addition to the limited weight capacity of the entire instrument,
the actual thickness of the detector limits the number of PMTs able to fit along its side.
While the position of PMTs could be altered to allow PMTs to be placed in the middle of
the detector, or above and below it, it puts the experiment into risky territory. The
particular problem in placing the PMTs above, below and within the detector, is that it
places the PMTs in the direct path of the cosmic-rays the experiment is designed to
detect. Thus, this would dramatically increase the number of unwanted reactions and
reduce the number of Cherenkov photons detected.
Possible Radiator Improvements- the most promising improvements lie
with the radiator, or the medium responsible for the Cherenkov process in the detector.
While it is certainly possible to find better radiators than aerogel and acrylic, collecting
the experimental data to properly incorporate them into a valid simulation is both
difficult and costly, effectively making this approach a dead end for Super-TIGER
(Sasaki, 2010). One of the most favorable areas of improvement, would be the thickness
of the radiators (Sasaki, 2010). The major benefit of a thicker radiator would be the
cosmic ray particle induces the Cherenkov effect for a path-length through the radiator,
resulting in substantial increases in the number of Cherenkov photons created. With
such an increase in the number of photons created, there should be a sizable increase in
the number of photons detected.
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 21
While the idea is promising, it is not without its detractors as well. In addition to
more Cherenkov radiation with an increase of thickness, there also comes an increased
probability of unwanted nuclear interactions and photons being absorbed by the
radiator itself (Sasaki, 2010). Because each material had an experimentally determined
absorption length, or the probability that a photon is absorbed per unit path length
through the material as the material’s thickness increases, the photons travel through a
greater amount of the material, increasing the chances for absorption. This is magnified
greatly as it might take a particle multiple bounces off the sides of the detector before it
hits a PMT, and with each bounce, the photon must travel through the radiator once
more. This is a promising area to test in the Geant4 simulation program, as comparing
the number of photons created by the increased thickness of the radiator, versus the
increased percentage of photons absorbed by the radiator. However even if an optimal
thickness is determined from those two constraints, the number of nuclear reactions
that might occur in this increased thickness must be carefully considered. Simulating
the number of nuclear reactions a particle has through the Cherenkov counter would be
wise to judge whether the increase in light collection might be enough to offset any lost
events to unwanted nuclear interactions. As usual, the problems of size and weight of
the overall detector must also be taken in close consideration when modifying the
aerogel components.
Possible Long-Term Detector Improvements- While there are very clear
and persistent limitations for improved performance of Super-TIGER, one should not
rule out possible improvements for future experiments. One idea is other reflector and
radiator materials, which with a future experiment, there may be both the time and
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 22
budget to run experiments to properly test their properties. A more unique idea would
be a more cylindrical detector shape, rather than a rectangular one. With this shape, the
conventional PMT set up around the perimeter of the detector would be unfeasible, but
light collection could still be achieved using carefully placed light shifting tubes or bars
around the perimeter (Sasaki, 2010). These would utilize the idea of total internal
reflection to transport the photons through the tubes into PMTs where they would be
detected. Testing this approach to detector design would certainly be an interesting
endeavor in a future simulation. Again, all of these possible improvements though are
still limited by the difficulties in identifying appropriate numerical values for the
simulations as well as weight and size constraints. One of the most pressing problems
for any possible improvement will be its effect on unwanted particle interactions which
can often be difficult to simulate in their own right.
IV. Conclusion
Using the given knowledge of the purpose of the Super-TIGER experiment, the
physics of Cherenkov Radiation, and the general design of Cherenkov Counters, this
paper discussed possible areas for increased performance within the Cherenkov
Counters of the Super-TIGER experiment. The areas of most interest for the current
experiment, proved to be the possible types of reflectors and the thickness of the
radiator materials, while other materials and a different overall shape of the detector
could prove to be promising in future experiments. However, the difficulties in
obtaining the appropriate values for these changes and accounting for changes in the
frequency of particle interactions within a simulation, make verifying and subsequently
justifying these changes a difficult task.
Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER
April 1st , 2010 Eaton 23
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