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Lin – Wilks 1

Introduction

In today’s world, there is still much that is unknown about the universe and its

workings. Everyday scientists are exploring new paths and trying new things in search of

answers to questions we have only begun to ask. One fairly recent discovery in the world

of physics is the muon, an elementary lepton that is 100 times heavier than an electron.

Muons are the decayed product of unstable mesons called pions which are made when a

cosmic ray, high energy protons originating from supernovas, collides with earth

elements in the atmosphere. While scientists have a basic understanding of the muon,

there is still much they do not know.

In order to learn more about muons, this experiment was conducted as an

exploration into their behaviors, in this case the direction where muons go when they are

formed. The purpose of this experiment was to determine at which angle muon detectors

would be able to view the highest muon flux. The relevance of this research is that not

only does it determine some behavioral elements of muons, but it also has many practical

applications. Initially, findings from this data can be used to determine at which angle the

highest muon flux occurs, which can be used by scientists to collect more muons for

testing. In addition, the direction in which muons travel could reveal information about

cosmic rays and the supernovae they originate from, such as how they occur or how they

disperse their energy. This research also allows for potential future applications such as

for muon catalysts. Muon catalysts are a source of unlimited energy by forming

deuterium molecules with muons and then breaking it apart. It is also very clean, the by-

products from a muon catalysts is high energy and helium. The flaw with muon catalysts

is generating enough muons to make enough energy to become a viable energy source.

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This experiment was designed to allow for optimal data to determine the effects

of the angle at which the muon detector was placed on the muon flux. In order to collect

the data, muon sensors were attached to rotatable mounts and covered with foil to allow

muons to pass through without light disturbance. The sensors then relayed the data to a

computer which decoded and analyzed the information from each muon that struck the

panel. This was done for many muons at angles of zero, forty-five, and ninety degrees, as

well as with differing numbers of sensors to determine where the highest muon flux

occurs. This process allows for the collection of data pertaining to the path of muons to

determine just how angle affected the muon flux.

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Review of Literature

Nano-particle physics are becoming the new front of the scientific community. As

recently as last year a new elementary particle, the Higgs Boson, was discovered. As

technology advances, scientists are continuously uncovering new information and

discovering new atomic structures. One fairly recent discovery is the muon, an

elementary particle discovered in 1936 by Carl D. Anderson (Nave). As with all newer

discoveries, there is often a lot that scientists have yet to learn about them. The muon is

no different, and in order to learn more about it, an adequate sample of data must be

collected. One of the main topics of exploration for muons is how the angle of a muon’s

path affects muon flux or the rate of muon hits in an area at a given time, the

concentration of muons within an area at a given time. The purpose of this experiment is

to answer the question: What effect does angle have on muon flux? To understand the

importance of this subject requires understanding what muons are, where they come

from, and how they are made.

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Figure 1. Production of Muons from Cosmic Rays

Figure 1 shows the production of muons from cosmic rays. The diagram shows

Primary cosmic rays can interact with nucleons in Earth's upper atmosphere. Showers

occur when these primaries are extremely energetic, and produce large numbers of

secondary particles (mostly pions and kaons). The secondary’s promptly decay into the

particles that strike Earth's surface. During a shower, thousands of these particles can

strike an area as large as several square kilometers nearly simultaneously. The direction

of the muons, as a result of the collision is completely random (Sonier).

The current understanding is that muons come to Earth when a cosmic ray - a ray

of high energy particles from somewhere in the universe made of protons, electrons, and

atomic nuclei - enters the Earth’s atmosphere (refer to Figure 1 above). These cosmic

rays are hypothesized by some to be the by-products of supernovae, but the rays contain

much more energy than is released by an exploding star, so we are unsure of where all the

energy actually comes from (Mattson). After the rays enter the Earth’s atmosphere, the

protons of the cosmic rays then collide with the nuclei of Earth elements and form pions,

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which further decay into muons (Mantsch). The muons split off into multiple directions,

all with different corresponding angles. Each muon travels a different distance to reach

the earth’s surface depending on the angle of its path. However, because muons decay

rapidly some may not be able to make it to the surface. Therefore angle may have a great

effect on whether or not a muon can make it all the way to earth.

Figure 2. Elementary Particle

Figure 2 shows a table on the elementary particles. The elementary particles

consist of leptons, quarks and force carriers. The quarks are what make up the protons

and neutrons. The leptons have negative half spin. The force carriers are responsible for

the interaction between particles (Elementary Particle).

Muons are an elementary subatomic particle; this means it is not comprised of

other particles. Muons are leptons which mean that have a negative half spin and they

also have a counterpart of an anti-muon which has a positive half spin. Muons have

similar properties to electrons, but muons have 200 times the mass of an electron. Due to

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muons being leptons they do not undergo much interaction. This means that they are able

to pass through any matter while still traveling near the speed of light. During this time

however, the muon is rapidly decaying and is traveling at the speed of light for its

lifetime of 2.2 microseconds, but this is not fast enough to be able to reach the surface of

the earth before it decays. The muons are able to reach to the surface of the earth though

due to time dilation. Time dilation is the theory developed by Einstein and it states that

objects traveling near the speed of light will observe a slower time than an object that is

not moving (Richmond).

Figure 3. Time Dilation Diagram

Figure 3 shows a diagram on the reason of time dilation (Richmond). The diagram

represents two objects moving at the speed of light and one sends a signal to the other

object and when the other object receives the signal it sends it back; the signal always

travel at the speed of light. The objects are H distance away from each other and they are

moving at an L distance. If the two objects are standing still the distance the signal travels

is twice of H. However, if the two objects are moving a t the speed of light the signal has

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to travel the distance of twice of L. This means that it traveled more distance but the

objects are H distance apart. Distance L is longer than H, so this means that in order to

compensate for the increase of distance of L over H the time it takes for the signal to

travel increases, thus time is different for an object at a stand-still than an object traveling

at the speed of light (Whiston).

The time dilation allows the muon to reach the surface of the earth; however,

when the muons are created they travel in different directions. This means that they

would travel different distances. Experimentation with angle orientation for muon flux

would find out if muons would reach the surface of the earth or if they would decay

before they reach it. The effect of different angles of muon could be found by using

scintillators and photomultipliers (refer to Figure 4 below).

Figure 4. Scintillators

Figure 4 shows an assortment of scintillators. Scintillators are a material that

gives off light when a charged particle passes through it. Typically scintillators are made

of plastic that has been doped with molecules that gain energy from the passing electric

field of charged particles. The energy is stored in electron orbitals and then promptly

release in the form of photons. Even though muons are leptons, scintillators respond to

muons made from cosmic rays and the flux of muons could be calculated using a

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photomultiplier to count the amount of muons that make contact with the scintillator

(Scintillator).

Recently a research project was done on the muon flux versus the angle and

direction by Juandell Mathews and Adrian Ionascu. The purpose of their experiment is to

determine if angles affect the muon flux. Their procedures were to run muon flux studies

at various angles facing in the west east direction. The angles that were tested were thirty

degrees and sixty degrees. The data showed that at thirty degrees the muon flux rate on

average was 100 events per meter squared per minute. At sixty degrees, the muon flux

was 3000 events per meter squared per minute. The orientation of east to west had similar

data. The research concluded that there is a higher muon flux for the higher degree, most

likely due to the fact that the muon travels a shorter distance at this angle and makes it to

the Earth before the end of its lifetime (Mathews and Ionascu). The research only tested

two different angles, thus further angles could be explored to find out more on the effect

of angles on muon flux. Further research could be done to find the maximum muon flux

for an angle in order to maximize efficiency of muon collection for future research.

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Problem Statement

Problem:

To determine the effect that angle orientation has on muon flux.

Hypothesis:

An angle of ninety degrees from the horizontal axis will produce the highest

muon flux.

Data Measured:

There were two independent variables used for this experiment. The first was the

angle at which the panels were orientated in respect to the horizontal axis. The angles

used for the panels were zero, forty-five, and ninety degrees. The other independent

variable was the coincidence level, the number of panels a muon is required to hit to

register as a data point, measured as either one-fold or two-fold. The dependent variable

for the experiment was muon flux, the rate of muons in an area at a given time, measured

in events per meter squared per minute (events/m2/min). After data collection, an

ANOVA statistical test along with descriptive analysis was performed for the zero, forty-

five, and ninety degree angles to determine if there was a difference in muon flux

between them. Afterwards, a two-sample t-test was conducted to determine which angle

included the highest muon flux.

There were six muon flux studies (trial sets) randomly ordered for this

experiment, three for one-fold coincidence at each angle and three for two-fold

coincidence at each angle. The averages of the data and the standard deviations were

found for each muon flux study to perform the corresponding ANOVA test and two-

sample t-tests.

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Experimental Design

Materials:

(4) Photomultiplier Tubes(4) ScintillatorsCelestron GPS Computer with HyperTerminal

Cosmic Ray e-LabDAQ BoardRotatable Mount

Procedures:

1. Construct four muon detectors by connecting four scintillators and

photomultipliers and connect the muon detectors to the DAQ Board (see

Appendix A for construction of muon detectors).

2. Connect the Celestron GPS to the DAQ Board.

3. Connect the DAQ Board to the Computer with HyperTerminal (see Figure 1 for

setup for steps 1 -3 and see Appendix B on HyperTerminal use).

4. Place the four muon detectors on the rotatable mount at 90 degrees (see appendix

C for rotatable mount construction).

5. Run a performance study to calibrate muon sensors until acceptable (see appendix

D for instructions for a performance study).

6. Assign the angle trials of 0 degrees, 45 degrees and 90 degrees integers of 1, 2,

and 3 respectively. Use a random integer generator to randomize the trials of 0

degrees, 45 degrees and 90 degrees using the three assigned integers.

7. Set wooden mount accordingly to the angle of the trial (angle orientation would

be at south/north direction and angle will be displaced from the south).

8. Set up the HyperTerminal to run a one fold coincidence and start data collection

on the HyperTerminal for eight hours (see appendix E on one fold coincidence).

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9. Stop data collection on the HyperTerminal and upload data onto the Cosmic Ray

e-Lab using the GPS coordinates of the muon sensors (see appendix F on muon

flux study for Cosmic Ray e-Lab).

10. Save graphs and data generated by Cosmic Ray e-Lab.

11. Repeat steps 8-10 but with a two-fold coincidence for sixteen hours (see appendix

G on two-fold coincidence).

12. Repeat steps 7-11 with the next randomized angle.

Diagrams:

Figure 5. Setup of Muon Flux Data Collection

Figure 5 is a setup of a muon flux data collection. The scintillators and

photomultiplier tubes are made into muon detectors which connect to the DAQ Board,

and the GPS is directly connected to the DAQ Board. The DAQ board sends the hits from

the muon detectors and the coordinates from the GPS to the computer with

HyperTerminal to be stored until analyzed by the Cosmic Ray e-Lab.

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Figure 6. Rotatable Mount Setup

Figure 6 displays the three different angle orientations for the trials. The mounts

are oriented at north/south direction, and the angle displacement is the degrees away from

south for the experiment.

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Data and Observations

Table 1Muon Flux One-Fold Coincidence

Degrees Vertical from South Horizontal

Mean (Events Per Meter Squared Per 60 Seconds)

Standard Deviation

0 5797 28045 7079 21090 8270 200

Table 1 shows the mean of the muon flux measured in events per meter squared

per 60 seconds for a one-fold coincidence setting. The raw data could not be shown as

there were millions of data points that are in hex-decimal form in the HyperTerminal.

The values shown in table one was uploaded and analyzed by the Cosmic Ray e-Lab

website.

Table 2Muon Flux Two-Fold Coincidence

Degrees Vertical from South Horizontal


Standard Deviation

0 118 745 473 7390 1040 172

Table 2 shows the mean of the muon flux measured in events per meter squared

per 60 seconds for a two-fold coincidence setting. The raw data could not be shown as

there were millions of data points that are in he-decimal form in the HyperTerminal. The

values shown in table two was uploaded and analyzed by the Cosmic Ray e-Lab website.

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Table 3Observations for One-Fold Coincidence Degrees Vertical from

South HorizontalObservations

0The DAQ meter was hitting at a high rate, on average of 5797 events per meter squared per 60 seconds

45The DAQ meter was hitting at a very high rate, on average of 7079 events per meter squared per 60 seconds

90The DAQ meter was hitting at an extremely high rate, on average of 8270 events per meter squared per 60 seconds.

Table 3 shows the observations for the trials done in Table 1. Each trail was run

for eight hours and during the eight hours the set-up was not disturbed.

Table 4Observations for Two-Fold CoincidenceDegrees Vertical from

South HorizontalObservations

0The DAQ meter was hitting at an extremely low rate, on average of 7 events per meter squared per 60 seconds

45The DAQ meter was hitting at a very low rate, on average of 73 events per meter squared per 60 seconds

90The DAQ meter was hitting at a low rate, on average of 172 events per meter squared per 60 seconds.

Table 5 shows the observations for the trials done in Table 2. Each trail was run

for eight hours and during the eight hours the set-up was not disturbed.

Data Analysis and Interpretation

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The purpose of this experiment was to identify the effect that angle has on muon

flux. This was done by comparing the recorded muon flux between three angles (0°, 45°,

and 90°) for each flux study (one-fold and two-fold). Muon flux data was collected by

mounting muon detectors at different angles with the angle mount for approximately

eight hours and recording the muon hits on the computer. The statistical tests performed

on the muon flux between angles followed the CRR statistical test method involving a

control within the test variable of angle randomization of hit collection to reduce bias,

and replication to view consistency and any apparent data trends. This method of

statistical testing was used as it allowed for any difference in muon flux to be seen

between different angles with each other and the control. In this experiment, the control

used was an angle of 45°, as it is halfway between 0° and 90°. The trials in this

experiment were randomized by collecting the average data within equal periods of time.

The trials were replicated by performing over 50,000 trials per angle in each flux study in

order to reduce variability and bias within the data. This statistical test method allowed

for unbiased data and lead to a normality of the data which can be seen in the figures

below.

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Figure 7. One-Fold Muon Flux Study Graphical Data

Figure 7 shows the graphical data for the one-fold muon flux study data at each of

the three angles. The graph shows a relative normality for the data collected at each

angle, as the majority of data points for each angle were clumped together in a mostly

linear pattern. The graph also shows that there is no overlap for the muon flux values for

the different angles, so it stands to reason that there is a definite difference between the

muon flux at each angle, with 90° having the highest relative muon flux.

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Figure 8. Linear Regression for Muon Flux for One-Fold Coincidence Angles

Figure 8 shows that there is a strong positive correlation between angle and muon

flux as the “r” value is approximately one. It appears that as the angle increases towards

the vertical (90°), so does the muon flux, meaning that an angle will have a larger muon

flux than any angle that is smaller.

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Figure 9. Two-Fold Muon Flux

Study Graphical Data

Figure 9 shows the graphical data for the two-fold muon flux study data at each of

the three angles. The graph shows a relative normality for the data collected at each

angle, as the majority of data points for each angle were clumped together in a mostly

linear pattern (data for 45° is relatively normal within bounds). The graph also shows that

there is no overlap for the muon flux values for the different angles, so it can be noted

that there is a definite difference between the muon flux at each angle, with 90° having

the highest relative muon flux.

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Figure 10. Linear Regression for Muon Flux for Two-Fold Coincidence Angles

Figure 10 shows that there is a strong positive correlation between angle and

muon flux as the “r” value is approximately one. It appears that as the angle increases

towards the vertical (90°), so does the muon flux, meaning that an angle will have a

larger muon flux than any angle that is smaller.

After data collection, ANOVA statistical tests were performed to compare the

data between the angles used for each flux study. The ANOVA statistical test was

selected as the compared data comes from three separate populations and involves

comparing the means of their data which an ANOVA test aims to do. In order to conduct

the ANOVA statistical test, though, the assumptions had to be met for the test. The

assumptions for this test are that the data must be normally distributed, have multiple

independent populations, have a SRS from each independent population, and have the

largest standard deviation of the populations being no more than twice the size of the

smallest standard deviation. All assumptions were met with the data from this experiment

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with the data having a relative normal distribution as seen in Figures 1 and 2, all angle

populations were independent from each other, the trials were randomized, and the

largest standard deviation was less than twice the size of the largest. The values used for

the assumptions and ANOVA tests can be seen in the following tables (Tables 1 and 2).

Table 5Standard Data Values for All Angles in One-Fold Flux Study

Table 5 shows the standard values found for the different angles in the one-fold

flux study, including the mean, standard deviation, and the number of data points.

Table 6Standard Data Values for All Angles in Two-Fold Flux StudyDegrees Vertical from South

(Two fold Coincidence)Mean (Events Per Meter

Squared Per 60 Seconds)Standard Deviation Number of Trials

0 118 7 3245 473 73 2590 1040 172 46

Table 6 shows the standard values found for the different angles in the two-fold

flux study, including the mean, standard deviation, and the number of data points.

Following the check of the assumptions for the ANOVA statistical test for each

flux study test set, the tests were performed. The hypothesis for the tests can be seen in

Figure 11.

Ho: µ0° = µ45° = µ90°

Ha: µ0°, µ45°, and µ90° are not all equal

Figure 11. ANOVA Statistical Test Null and alternative Hypotheses

Figure 11 shows the null and alternative hypothesis for the ANOVA statistical

test. The null hypothesis for the test is that the mean muon flux at each angle is equal.

The alternative hypothesis is that the mean muon flux at each angle is not equal.

Degrees Vertical from South(One fold Coincidence)


Standard Deviation Number of Trials

0 5797 280 4045 7079 210 7590 8270 200 38

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Figure 12. P-value of ANOVA Test for One-Fold Flux Study

Figure 12 shows a p-value of 6.71x10-92 for the one-fold flux study ANOVA test

of the data.

Figure 13. P-value of ANOVA Test for Two-Fold Flux Study

Figure 5 shows a p-value of 1.78x10-55 for the two-fold flux study ANOVA test of

the data.

The ANOVA statistical test for the one-fold flux study produced a p-value of

6.71x10-92, which is below the accepted alpha level of 0.05, meaning the null hypothesis

is to be rejected. This shows that the mean muon flux at each angle in the one-fold flux

study is not equal, meaning that there exists and angle or angles that have a greater muon

flux than others. Also, this p-value shows that data this extreme would only occur as it

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did approximately 6.71x10-92 percent of the time by chance alone (see Appendix G for

sample calculations).

The ANOVA statistical test for the two-fold flux study produced a p-value of

1.78x10-55, which is below the accepted alpha level of 0.05, meaning the null hypothesis

is to be rejected. This shows that the mean muon flux at each angle in the two-fold flux

study is not equal, meaning that there exists an angle or angles that have avgreater muon

flux than others. Also, this p-value shows that data this extreme would only occur as it

did approximately 1.78x10-55 percent of the time by chance alone (see Appendix G for

sample calculations).

Due to the fact that the ANOVA test showed that the three angle populations were

not equal, the difference in the muon flux between angles was to be checked to determine

if which angles had the most significant muon flux if any.

To determine the significance of the muon flux between the angles tested, two

two-sample t tests had to be performed per flux study. Two two-sample t tests were

chosen to compare the data for the angles because it compares sample means to one

another to help determine the significance of any differences between populations.

The first two-sample t-test was performed to compare the muon flux at angles of

0° and 45° for both the one-fold and two-fold flux study, and the second between the

angles 45° and 90° for both flux studies. Assumptions first had to be checked and met so

that the statistical tests could be performed. The assumptions for a two-sample t-test are

that there are two simple random samples from two independent populations, normally

distributed data, and that the population means and standard deviation are not known.

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The data for this experiment met each and every assumption as the two angle data sets

being randomized, each being independent from each other, and having data with a fairly

normal distribution (See Figures 7 and 9). After having met the various assumptions, the

two-sample t-test was performed. The hypothesis for a two-sample t-test is shown in

Figure 14.

Ho: µAngle1 = µAngle2

Ha: µAngle1 > µAngle2

Figure 14. Hypotheses for Two-Sample t-Test

Figure 14 shows the null and alternative hypotheses for a two-sample t-test

between two angles. The null hypothesis states that the two angles have an equal mean

muon flux, while the alternative hypothesis states that the first angle (larger angle) has a

greater mean muon flux than the second angle (smaller angle).

Figure 15. Two-Sample t-Test for 0° vs. 45° in One-Fold Flux Study and Density Curve

Figure 15 shows the p-value of 4.43x10-35 for the two-sample t test from the 0° vs.

45° angles One-Fold Flux Study. The t-value of 25.3973 shows that the data for the

angles of 0°and 45° data were about 25.3973 standard deviations away from each other.

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The density curve shows that the p-value or probability of the null hypothesis being true

is approximately zero as no visible part of the graph is shaded.

Figure 16.

Two-Sample t-Test for 45° vs. 90° in One-Fold Flux Study and Density Curve

Figure 16 shows the p-value of 2.07x10-44 for the two-sample t test from the 45°

vs. 90° angles One-Fold Flux Study. The t-value of 29.6262 shows that the data for the




Figure 17.

Two-Sample t-Test for 0° vs. 45° in Two-Fold Flux Study and Density Curve

Figure 17 shows the p-value of 7.44x10-19 for the two-sample t test from the 0° vs.

45° angles Two-Fold Flux Study. The t-value of 24.3451 shows that the data for the

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Figure 18. Two-Sample t-Test for 45° vs. 90° in Two-Fold Flux Study and Density Curve

Figure 18 shows the p-value of 2.84x10-29 for the two-sample t test from the 45°

vs. 90° angles Two-Fold Flux Study. The t-value of 19.3764 shows that the data for the




The two-sample t-test for the angles of 0° and 45° for the one-fold flux study

produced a p-value of, which was less than the alpha level of 0.05. Due to this the null

hypothesis was rejected. This means that the mean muon flux of the two angles were

significantly different from one another. The P-value also shows that there is a 4.43x10-35

percent chance that the data received would be this extreme by chance alone were the

null hypothesis true (See Appendix H for the two-sample t-test sample calculation).

After the two-sample t-test between the first two angles was performed, a two-

sample t-test was conducted between the second set of angles for the one-fold muon flux

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study, 45° and 90°. The assumptions were checked and met for this test, and using the

hypotheses from Figure 10 and the information from Table 1 the test was conducted.

The two-sample t-test for the angles of 45° and 90° for the one-fold flux study

produced a p-value of 2.07x10-44, which was less than the alpha level of 0.05. Due to this

the null hypothesis was rejected. This means that the mean muon flux of the two angles

were significantly different from one another. The P-value also shows that there is a

2.07x10-44 percent chance that the data received would be this extreme by chance alone

were the null hypothesis true (See Appendix H for the two-sample t-test sample

calculation).

The two-sample t-test for the angles of 0° and 45° for the two-fold flux study






calculation).

After the two-sample t-test between the first two angles was performed, a two-

sample t-test was conducted between the second set of angles for the two-fold muon flux

study, 45° and 90°. The assumptions were checked and met for this test, and using the

hypotheses from Figure 10 and the information from Table 2 the test was conducted.

The two-sample t-test for the angles of 45° and 90° for the two-fold flux study


Lin – Wilks 27





calculation).

Overall, the descriptive analysis graphs (Figures 7 and 9) showed a distinct

difference between the muon flux of the angles, with ninety degrees having the highest

flux. The ANOVA tests at both coincidences were conducted to confirm a difference

between the angles, and showed that not all angles were equal meaning either one or

more angles produced a greater muon flux than others. The two-sample t-tests conducted

after were done to differentiate which angle had the greatest muon flux in comparison to

the others, and showed that at both coincidences for the zero and forty-five degree angles

that there were p-values close to zero. This meant that the null hypothesis that both angles

were the same was false, but that the alternative that the first angle (the larger angle) had

a higher muon flux than the second angle (the smaller angle) was true. The same true for

the forty-five and ninety degree angles at both coincidences as the p-values of the tests

were approximately zero so the alternative hypothesis that the first angle (larger angle)

had a significantly greater muon flux than the second angle (smaller angle) was true.

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Conclusion

The goal of this experiment was to determine which angle orientation of the muon

detectors would result in the highest muon flux. After having conducted this experiment,

the hypothesis that an angle of ninety degrees would provide the largest muon flux was

accepted. In order to test the hypothesis, six muon flux studies were conducted: three

were ran under a one-fold coincidence setting at zero, forty-five, and ninety degrees, the

other three were ran under a two-fold coincidence setting at zero, forty-five, and ninety

degrees. Each study was ran for at least eight hours and then analyzed on the Cosmic Ray

e-Lab. The result for the one-fold coincidence show that the angle of zero degrees had the

lowest muon flux mean of 5797 events per meter squared per sixty seconds, the next

highest was forty-five degrees with 7079 events per meter squared per sixty seconds. The

overall highest muon flux was at ninety degrees with 8270 events per meter squared per

sixty seconds. The data was then graphed for a descriptive analysis and it showed there

was a positive linear relationship between angle and muon flux, and at an angle of ninety

degrees muon flux was the highest. The results were similar under the two-fold

coincidence. The lowest muon flux was at zero degrees at 118 events per meter squared

per sixty seconds, and the next highest was at forty-five degrees with 473 events per

meter squared per sixty seconds. The overall highest was again at ninety degrees with

1040 events per meter squared per sixty seconds. The data for the two-fold coincidence

also showed a positive linear relationship between angel and muon flux. Through

descriptive analysis it can be concluded that muon detectors oriented at ninety degrees

would produce the highest muon flux. However, an ANOVA test and two sample t-test

Lin – Wilks 29

were conducted in order to reinforce the conclusion. The ANOVA test for the one fold

coincidence resulted in a p-value of 6.71 x 10 – 92, which meant that there was

approximately a zero percent chance of getting similar results were the null hypothesis

true. The results were similar with the two-fold coincidence, but the p-value was 1.78 x

10 -55. After the ANOVA test was done, four two sample t-tests were conducted to

determine if zero and forty-five degrees, forty-five and ninety degrees are statistically

significant with each other. All four p-values calculated were below the significance of

0.05 which means that for both coincidences, the forty-five degrees muon flux were

statistically significantly higher than zero degrees, and the ninety degrees muon flux were

statistically significantly higher than forty-five degrees.

There is a sound scientific explanation for the results produced from the

experiment. As previously stated, it was found that an angle of ninety degrees produced

the highest muon flux out of the three angles tested (0°, 45°, and 90°). Muons are

produced from cosmic rays, which when they collide with the nuclei of atmospheric

elements produce particles such as the muon. These muons then pass through the

atmosphere and come down to the Earth’s surface. However, muons have a short lifespan

of 2.2 microseconds, which added to the large span of distance muons must travel means

that muons will dissipate before reaching the planet’s surface. Time dilation though as

explained previously within the Review of Literature, allows for some muons to survive

long enough making it to the surface. Still, many muons will not make it, and those that

can travel the distance will lose energy as they pass through solid matter. In turn, the

shorter the distance traveled the higher the chance that muons will survive long enough to

make contact. In this experiment, the angle of 90° came vertically down and provided the

Lin – Wilks 30

shortest, most direct path for muons to travel. Therefore it makes sense that as the muons

traveled vertically down at 90° they traveled a shorter distance than they would at other

angles, which allowed for them to make the most of their short lifetime without using up

all of their energy.

The results of the experiment happen to agree with current work being done in

this field of particle physics. Around the world experiments such as this have been

conducted to determine whether or not this hypothesis that the vertical angle (90°) would

provide the highest muon flux regardless of location. Juandell Mathews and Adrian

Ionascu for example, tested muon flux at angles of 30° and 60° and found that the 60°

angle (the most vertical angle) produced the highest muon flux (Mathews). These

experiments all found the same result, which was that the shortest distance occurring at

the most vertical angle (typically 90°) provided the highest muon flux which supports the

data received in this experiment.

Although the experiment produced statistically valid data and a conclusive

outcome that is backed up by science, there were still flaws in the experiment. These

flaws mostly occurred within the set-up of the muon detectors. When testing for muon

flux, the coordinates of the muon panels had to be found; this was needed for the two-

fold coincidence because the DAQ board will only record a hit if a muon goes through

two or more detectors next to each other. If the measurements are not correct, the DAQ

could record a hit if two muons go through different panels at the same time. In order to

find the coordinates of the muon panels, meter sticks were used to find the distance away

from a GPS and from there the law of cosine and sine were used to find the coordinate of

the muon panels, which resulted in a change in the data of the two fold coincidence. In

Lin – Wilks 31

addition, the plateauing, calibration for the photomultiplier, for the performance study

was not perfect because a muon going through each of the different panels did not

generate the same exact amount photons due to different amounts of reactive materials in

the scintillators; however, Dr. Harr had approved the performance study that was

conducted because there was only slight change between the panels. The differences

between the panels would have caused a higher muon flux recording than others. In

addition, each of the muon flux studies was ran for at least eight hours but some ran for

longer, maximum of thirteen hours, which might change the data because there might be

differences in muon flux and the time of day, but there is not a significant research

proving this claim.

The experiment only scratched the surface of possible research on muons. Further

muon flux study could have been done by testing more angles to determine if certain

ranges or specific angles produced higher muon fluxes than others. Also, testing the

angles under three and four fold coincidence could be done to determine the effect of

energy loss on muons and muon flux. Using the knowledge of the angle that will produce

the highest muon flux, further research in muons could be made more efficient collection

of muons for experimentation by setting their detectors at ninety degrees. This could be

applicable for a muon catalyzed fusion which could lead to an unlimited energy resource.

However, the problem is producing enough pions to make muons. If a muon catalyzed

fusion factory uses a large enough panels oriented at 90 degrees, it could potentially

collect enough muons for the muon catalyzed fusion.

Lin – Wilks 32

Appendix A: Construction of Muon Detectors

Materials:

(4) Scintillator panels(4) PhotomultipliersAluminum foilBlack duct tape

Celestron GPSDAQ boardLens adhesive

Procedures:

1. Connect a photomultiplier tube to a scintillator panel at the base with lens

adhesive.

2. Wrap the scintillator panel with aluminum foil with reflective side facing towards

the pane.

3. Wrap the foil with black duct tape to prevent light from entering.

4. Take the photomultiplier tube and connect it to one of the ports on the DAQ board

with a cable.

5. Repeat steps 1-4 to make a total of four muon detectors.

6. Connect the Celestron GPS receiver to the DAQ board to allow for the detection

of muons as they contact the scintillator panel.

7. Connect the DAQ board to a power supply to allow for functional operation.

Lin – Wilks 33

Figure 19. Setup of Muon DetectorsFigure 19 shows the diagram for the setup of the muon detectors used in the

experiment. The lines that go from the photomultipliers to the DAQ board represent the

cables used. The foil, which is under the duct tape, and the power supply are not pictured.

Lin – Wilks 34

Appendix B: HyperTerminal Setup/Execution

Materials:

ComputerHyperTerminal program

Procedures:

1. Load the HyperTerminal program onto a computer.

2. Enter the following codes into the HyperTerminal screen:a. CD - counter disable (to stop data from collecting from previous tests)b. RB - reset board c. DG - display GPS (this is for data upload on e-lab)

3. To start capture text enter the following codes into the HyperTerminal program:a. CD - counter disable b. DG - display gpsc. DC - setup registersd. DS - display scalarse. DT - display TMC registers 0-3 f. BA - display barometerg. TH - thermometer datah. TI - display timei. V1 - setup registersj. V2 - setup registers k. ST 3 5 - status line plus counts, channels and coincidence l. ST 2 5 - status line plus counts, channels and coincidencem. TL - terminal locationn. SA 1 - save any configurations changes o. CE - counters enable (hex-decimal numbers should show up rapidly, this

means that it is collecting data information from a muon hit).

4. After starting capture text, enter these codes into the HyperTerminal:a. CD - counter disable b. DG - display gpsc. DC - setup registersd. DS - display scalarse. DT - display TMC registers 0-3 f. BA - display barometerg. TH - thermometer datah. TI - display timei. V1 - setup registersj. V2 - setup registers

Lin – Wilks 35

5. Enter 1.25 for the bin width for the 6000 DAQ model.

6. Upload to the Cosmic Ray e-lab data base for analysis.

Lin – Wilks 36

Appendix C: Instructions on Performance Studies

Purpose:

The purpose of a performance study is for calibration of the muon detector setup.

The sensitivity of the DAQ board is determined by the amount of muon hits and the

voltage given to each of the panels. In order to have proper calibration the muon hits and

the voltage must be plateaued.

Materials:

(4) Muon detectorsHyperTerminal programStopwatchVoltmeter

Procedures:

1. Stack all the muon detectors on top of each other.

2. Set the HyperTerminal to one-fold coincidence by entering “WC 00 0F”.

3. Set ‘w’ and ‘d’ to card defaults of d = 6 and w = 10 .

4. Run the procedures for Appendix B.

5. Upload the data from the HyperTerminal into the cosmic ray e-lab and analyze it .

6. Enter the following into the HyperTerminal.

a. CD

b. WC 00 0F set one fold coincidence

7. Type ‘ST 3 1’ to display status line each minute.

8. Follow Step 1 in Quarknet direction manual in excel spreadsheet for experiment.

a. Disconnect all counters except top one C0 (counter zero). Note counters

are 0, 1, 2, and 3.

Lin – Wilks 37

b. Adjust PMT voltage for C0 until counter on DAQ read between 2300 and

3000 per minute. Use stopwatch and reset counter button on DAQ. read

this directly from the counter on DAQ

c. Connect C1. It should have both C0 and C1 connected

d. Type WC 00 1F set two fold counter coincidence

e. Adjust PMT voltage for C1 until you are just seeing a count on DAQ.

Around 5 per minute

f. Record both PMT voltages in spreadsheet.

g. To start a run, increase PMT voltage of C1 by small increments (0.01 V),

press “Enter” a couple of times to leave space in the data to let you know

when you change the voltage. The ST command line will display but do

not use the first one after the spaces. Wait one minute until ST line

appears again.

h. Repeat increasing PMT voltage for C.

i. Record all three data from status line in proper column in spreadsheet. (S0,

S1, S2, S4 and S4).

j. Continue until steps (8g – 8i) you see last data line (coincidence) start to

level out (plateau).


a. Disconnect C1 and connect C2 and repeat sweeping voltage (steps 8g -8j)

for C2.


a. Disconnect C2 and connect C3 and repeat sweeping voltage for C3.

Lin – Wilks 38


a. Increase the voltage on C3 to about the voltage used for C0

b. Decrease voltage on C0 until you are just starting to get a count of 5 per

minute.

c. Repeat steps 8g – 8j sweeping voltage for C0.

d. Select tab on bottom of spreadsheet called “Charts” - find the voltage that

corresponds with. The separation of the test channel and the coincidence

channel.

e. Record each voltage for each channel. This should be close to the final

plateau voltage

f. Type WC 00 3F for a four-fold coincidence.

g. Set each PMT to its corresponding plateau voltage.

h. Collect data for at least 30 minutes and upload to e-lab.

The plateauing is done in order to calibrate each of the muon sensors. After the

data is uploaded the graph should have 4 lines that are stacked on top of each other. if not

run the whole plateau study over again. The performance study graph should look like the

Figure 1 below

Lin – Wilks 39

Figure 20. Proper Performance Study Graph

Figure 20 shows a proper performance study graph from a muon detector setup

after correct plateau. The four graphs should stack on top of each other because the muon

detectors are stacked on top of each other when the performance study was done.

Lin – Wilks 40

Appendix D: Coincidence on Muon Scintillators

Coincidence is how many panels a muon must pass through to count as a data

point. Codes can be entered into the HyperTerminal in order to change the coincidence.

The DAQ board can also determine whether signals in separate channels are coincident in

time. For example, if the trigger criterion is set to 2-fold, then as soon as any channel

goes above threshold, a time window is opened. (Window time width is adjustable.) If

any other channel goes above threshold during this time window, all event data are

latched and outputted for the overlap time interval when both are active. Notice that pulse

data are reported for a time interval that is not of fixed length but just covers the overlap

period when two or more channels are active. Leading and trailing edge times reported

for any active channels (not just for the two channels that launched the trigger), with

empty data entries for channels that remained inactive during the trigger window. For a

single event trigger, the DAQ board may need to output several lines of data. The first

line has an “event flag” for identification. Any following lines without this flag are

simply additional data for the same event.

WC 00 0F = one fold coincidence WC 00 1F = two fold coincidenceWC 00 2F = three fold coincidenceWC 00 3F = four fold coincidence

Setting a high fold coincidence would mean the muon path would be closer to 90

degrees to the panel; however, setting a high fold coincidence would require at least 24

hours of trial collection in order to collect enough measurable data.

Lin – Wilks 41

Appendix E: Muon Flux Study Analysis on Cosmic Ray E lab

Procedures:

1. Send data to or collect data with the Cosmic Ray E lab.

2. Go to http://www.i2u2.org/elab/cosmic/analysis-flux/.

3. Use the drop-down box and the advanced search box to select the location of the

testing, then click search.

4. Choose ‘Start Date’ in the drop-down list for the date and select the initial testing

date and select the ending test date in the second date box.

5. Select ‘Yes’ for the ‘stacked’ box and click the search data button.

6. Click the arrow next to the name of the location and click the arrow next to the

date that appears for the data.

7. Click the date to view the data and the thought bubble to view any comments

added along with the data.

8. Chose the detector used and click the dates for the data to be analyzed, then select

‘Run flux study’.

9. In the analysis settings, change the bin width to 7200 and click the ‘Analyze’

button under the area titled ‘Execution Controls’.

10. Click the ‘Data’ tab and select the ‘Analyses’ drop-down tab.

11. Click the flux study conducted and hit the link to view the plot.

12. To change parameters hit the button that says ‘change parameters’ and enter the

parameters that best fit the data.

Lin – Wilks 42

Figure 21. Correct Flux Study Graph

Figure 21 shows the graph of normal muon flux study. The graph should represent

a sinusoidal graph but it should not have high variability. The flux values vary with the

setting of the coincidence. A high coincidence would result in a low flux.

Lin – Wilks 43

Appendix F: Professional Contact

Name: Marco Lin and Kristian Wilks

Research Topic: The Effect of Angle Orientation of Muon Detectors on Muon Flux

Professional Contact Information

Name: Dr. Robert Harr

Title: Professor P.H.D

Organization: Wayne State University Department of Physics and Astronomy

Phone (area code and extension): 1-313-577-2677

Email: [email protected]

Mailing Address: 666 W. Hancock St. Detroit MI, 48201

Dialogue Information

1. Contact Goal: To see if we could improve our experiment/presentation and also to seek a scientific explanation of why we received the data we did

Answer: Find the regression equation of muon flux in relation to degrees to see if the relationship is either linear, quadratic etc. The most probable cause of the data that you did is because the muon has a very short life time and in order for the muon to hit the detector at zero degrees it would have to travel a further distance than compared to ninety degrees. For improving the experiment, a higher coincidence level could have been used so the muon path has to go through more detectors and in part the direction of the muon would be closer to the degree angle set. In addition, more angles could have been tested. (This dialogue is not word for word, Dr. Harr gave us his criticism after we presented the research to him).

Lin – Wilks 44

Appendix G: ANOVA Statistical Test Sample Calculation

F= MSGMSE

=mean square groupmean square error

=2.01032 x 10−9

1.9507 x 10−7 =105.5

x=n1 x1+n2 x2+n3 x3

N=

(20)(71098.1)+(20)(71314.07)+(20)(46680.33)60

=¿63030.8

MSG=n1 ( x1−x )2+n2 ( x2−x )2+n3(x3−x )2

I−1 =20 (71098.1−63030.8 )2+20 (71314.07−63030.8 )2+20(46680.33−63030.8)2

3−1 =¿

2.01032x109

MSE=(n1−1 ) s1

2+(n2−1 ) s22+(n3−1)s3

2

N−I=

(20−1 ) 4851.82+(20−1 ) 4602.572+(20−1)3850.212

60−2=1.9507 x10

-7

Figure 22. ANOVA Statistical Test Sample Calculation

Figure 22 above shows the equation for an ANOVA test to calculate the F

statistic. In the equation, n represents the number of subjects in each sample, x represents

the means of the various samples and overall population, s represents the standard

deviation, N represents the total number of subjects, and I represents the number of

populations.

Lin – Wilks 45

Appendix H: Two-Sample t-Test Sample Calculation

t=x1− x2

√ s12

n1+√ s2

2

n2

= 71098.1−71314.1

√ 4851.82

20 +√ 4602.572

20

=−0.14

Figure 23. Two-Sample t-Test Sample Calculation

Figure 23 above shows the equation for two-sample t-test to calculate the t test

statistic. In the equation, t is the test statistic being calculated, x represents the sample

mean, s represents the sample standard deviation, and n represents the number of

subjects.

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