Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER

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



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



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,



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



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



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



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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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.



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).



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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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:



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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



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



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



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



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



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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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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This can be further simplified into an infinite series:

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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



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.



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



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.



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Documents

Exploring Areas for Improved Performance of Cherenkov Counters in Super-TIGER