User:JCoffey
From MariachiWiki
Joe Coffey
Week 1
Over the summer I love to spend my weekends at the beach, either surfing, playing frisbee, or just relaxing. During the fall I love to head out east and go apple picking. All year long though I love to play soccer, I have been playing since I was 5 years old and I will never stop. I play on a mens league over the summer, and help to train the varisty boys at my local high school during the year. As well, I play on a mens deck hockey team. I run in local 5K and 10K road races, I hope this September to finally run in the Cow Harbor 10K which I have had to withdraw from the past 2 years due to unforseen illnesses. A website that I love to visit when I get a free moment is, How Stuff Works. A site that has caught my eye on the MARIACHI home page is, Cosmic Rays. I hope that I can someday take the information and knowledge that I will learn from this website and class instruction and implement it into my physics classroom.
Week 2
Our goal this week was to determine an optimal voltage to run our detectors, in order to collect the largest number of cosmic rays with as little interference or "noise" as possible. In order to do this mini-experiment we calculated the fficiency of a cetnral detector surrounded on the top and bottom by two other detectors. We were analyzing the amount of doulbe concidences which were how many cosmic rays passed through the top and bottom detector, and triple coincidences which measured how many cosmic rays passed through all three detectors. In order to calculate the "noise", divided the total number of coutns registered by the middle detector and divided this number by duration of the experiment (60 seconds). We found the optimal voltage to around 5.7V - 5.9V. Between these voltages the "noise" is minimal and our effeciency rate has platued. The data for this experiment is below:
Week 3
One of the most important elements of the lecture today was our discussion regarding error. Specifically we talked about systematic errors which occur from measurements or miscalculations in an experiment (e.g. determining the area of a scnitillator). As well, we discussed random errors which can be avioded by completing an experiment numerous times and averaging them together. With respect to the count rate, the error can be found by taking the square root of the total number of counts. If N = number of counts, and dN, is the error we would obtain: N = 16, dN = 4, = 4/16 = 1/4 = 25% N= 1000, dN = 10, = 10/1000 = 1/100 = 1% We discussed that as the total number of counts increases as does the error, but as you see from above the percentage of error drastically decreases.
In groups (Harry, Tania, and myself) we decided to analyze the count rate versus area of the scintillator. We began my measuring the area of the top, middle, and bottom scintiallors: 91.5 cm x 30.5 cm, 91.3 cm x 30.5 cm, and 91.3 x 30.5 cm respectively. Our group took a total of 4 measurements, our first was with the middle scintialltor directly between the other other two (no part of the middle scintialltor was pertruding out from between the top and bottom scintillator). Then we moved the middle scintiallor 12.9 cm to the right and kept the top and bottom ones in position, we continued with this procedure two more times, moving the middle scintialltor to the right approximately 15 cm each time. We ran each interval for a total of 300 seconds, and were interested in the triple coincidence rate. A graph of our data is below:
The graph clearly shows that there is a direct relationship between the area of the middle sintillator versus count rate. One of our major goals (well what I think a major goal of our experiments is) is to determine if the counts (our data) we are collecting are actually cosmic rays versus noise. We have discussed that a triple coincidence most likely correlates to a cosmic ray (or a particle thereof). Thus stacking at least 2 or even 3 detectors directly on top of one another would yield the most efficient way to distinguish between cosmic rays and noise. Harry, informed me of a calculation which would help us determine the count rate per cm^2 per s. This calculation is performed and shown on Harry's wiki site as well. The slope of our line 0.0059 represents the count rate per cm^2 per second. Since the efficiency of our middle detector is 93% (which I determined in our second class) we can find the actual count rate by 0.0059/0.93 = 0.0063 count/cm^2/s. Since we discussed a value of count/cm^2/s we can simply multiple 0.0063*60 s/minute = 0.38 counts/cm^2/minute. In our first class we discussed that the optimal rate is 1 cosmic ray (pion, muon, electron) per cm^2 per minute, so our value is significanlty lower.
Week 4
This week Harry and myself worked on a rather interesting experiment. First, we discussed some of the possible difficulties that we may encounter in many of our experiments with respect to detecting cosmic rays at the most optimal rate possible. For example, the simple fact that we are in the basement of a four story building makes me curious as to how many "cosmic rays" do not make it to our detector because of the shielding effect that the building has. Professor Marx then informed Harry and I about cosmic ray flux and directed us to a website that will allow you to calculate exactly that. The formula is:
Flux = [Count Rate*d^2]/[Area 1*Area 2]
The cosmic ray flux as stated from the website,Cosmic Ray Flux, is "The standard way to compare rates between different detectors is to calculate what is called the "flux", which in this case is the rate of cosmic ray muons divided by the subtended solid angle and also divided by the area of the detector. This flux measurement is independent of the details of the detector."
Rearranging the above flux formula yields:
Count Rate = [Flux*Area 1*Area 2]/d^2This formula can be tested using the wall set up in the lab. Two detectors are already conveniently attached perpendicular to the wall approximately 2 meters up, and 1 detector is attached to a pulley system allowing it to be move up down on the length of the wall. We measured 10 different seperation distances (d^2) and were concerned with a two fold coincidence rate between the top detector and the bottom detector (the middle detector was not hooked up). We did so using a 100 second time interval. The following is the data that was taken:
The following graph shows the Count Rate verus 1/d^2 which relates to our rearranged Flux formula:
This graph is not linear as I would have expected it to be but this what our group had to use to calcualte the flux. Harry added a regression line to this graph and determined its slope to be 14407. The slope = Flux*Area 1*Area 2. From this Flux = 14407/[91 cm * 30.5 cm]^2 = .11 particle/cm^2/min. The value given in the first weeks of class was 1 particle/cm^2/min, our value is obviously much lower. This of course is a part of our systematic error and many other factors, such as shielding by the building, efficiency of the detectors, and barometric pressure.
Week 5
From last weeks graph of count rate vs. 1/Distance^2 Harry came up with a very intersting idea. He said since the first few points of the original graph appeared to be linear, why don't we construct a count rate vs. 1/Distance^2 graph using only those points. The graph is shown below. When analyzing the graph I determined the slope value to produce a flux of 0.29 counts/min/cm^2/sterad (from the SLAC website). This is compared the to the theoretical flux value of 0.48 counts/min/cm^2/sterad, so our value was substantially lowwer. This could be contributed to building shielding, and possible errors based upon noise interferance.
Now Professor Marx led us into another interesting aspect of this experiment. He informed of us the real paths the muons could travel through the 2 scintillators. Meaning that the muons could pass through a large range of angles in a 2-fold coincidence count. So the maximum distance a muon would travel could be described as from corner of the top detector to the opposite corner of the bottom detector. The minimum distance that a muon could travel would be vertical to the 2 detectors versus the path described above (corner to opposite corner). This is something that we needed to take into account when computing the experimental flux.
Another aspect that we could further refine is analyzing the efficiency of the detectors. To do this Dr. Vavilov told us that we could divide our calculated flux by the product of the efficiences which would give us a more accurate flux. To measure the efficieny we could not use the mehtod in Week 2, so Professor Marx suggested that we measure them together as one single unit (giving us an approximate value of efficiency). We did discover that these 2 detectors most likely had the poorest efficiencies in the lab because this wall setup is used primarly to calculate speed of the muons. Once we started taking the measurments the count rate was very odd, it would reach nearly 65,000 single counts, roll over and begin counting again to 65,000 counts. We later discovered that the bottom detector had a problem (I do not exaclty know what), but the detector had to be replaced. Below from the data and graph you can the efficiency of the top detector only:
During the experiment last week we choose to use a voltage of 5.8 V and from the graph above it shows an efficiency of 56%. This is an extremely poor efficiency especially compared to the efficiency we saw on our detectors in Week 2. Due to the fact that we could not determine the efficiency for the bottom detector we thought it would be safe to assume they had a similar efficiency. This of course now made us think: "How accurate is our data?" We did not really know the efficiency of the bottom detector, and the efficiency of the top was horrific, making it impossible to judge if we were collecting real particles (muons) or noise.
The next step for me was to utilize these efficiences in order recalcuate an appropriate flux rate. And I use the word appropriate with some hesitiation. When there is this much error associated with an experiment I think it would be necessary to go back and use detectors that have high efficiencies (94% - 98%), and recalcualte the flux. However, with time constraints and the data we have taken the following calculation could be used to find an extremely approximate value of the flux. In other words, in an attempt to take into account our extreme error we could multiply the efficiencies of the top and bottom detector together and divide that value by .30 particles/min/cm^2/sterad. Doing so yields: .30/(.56*.56) = 0.95 particles/min/cm^2/sterad which is much higher that the 0.48 particles/min/cm^2/sterad value presented on the SLAC website. Again though this value to me really does not have much meaning due to the numerous errors in our experiment. However, I think that stumbling upon these errors is valuable in its own respect. In an real world experiment (as we are conducting) there is going to be much room for error and mistakes, it just depends how persistant and willing you are to go and correct and analyze these errors that makes the difference and improvement in your experiment possible.
Week 6
This week each group presented their projects for the first round of experimentation.
Group 1: Horizontal Separation and Four-Fold Coincidence Rates presented by Tom and Karyn dealth with four detectors, two stacked on top of one another. Their set up was concerned with looking for two seperate particles from the same "cosmic ray" shower. They described and it was obvious from their graphs that as the distance between the detectors (2 sets of detectors with 2 stacked on top of one another) increased the number of four-fold coincidences decreased. However, as Tom, Karyn, and Professor Marx explained that the four-fold coincidences platued rather than approaching the x-axes (or reaching 0).
Group 2: Anglular Dependence and Cosmic Ray Flux presented by Desiree, Mildred, and Gillian dealt with two detectors that wre placed in the octagonal plywood structure. The octagonal structure was rotated and it was noticed that the further the 2 detectors became from being perpedicular to the floor the smaller the count rate became between them. This group also presented the formula to calculate flux, which was shown through the SLAC website (which my group also used in our presentation).
Group 3: Systematic Errors presented by Greg, Lena, and Patrick dealth with many of the problems that are associated with the detectors we use in experimentation. One interesting fact I took from their presenation was the idea that the photomultiplier tube may not be perfectly sealed leaving a little glass in the tube, and thus is not a good enough vacuum. I am curious if this defect in manufacturing is caused when sanding down the sides of the photomultiplier tube or during its construction at a lab/factory. They actually (I am not sure if they produced it themselves) presented a formula to calculate the accidental counts measured by a detector. As well they explained that by adding one extra detector to some combination of detectors would reduce accidental counts by nearly 10,000 times.
Group 4: This was our group, again please refer to Harry's Wiki Week 5 for our presentation.
Group 5: Cosmic Ray Count Rate Variations with Height Above Ground by James, Vincent, and Brad dealt with cosmic Chris and the collecting of count rates on the 5 levels of the physics building. I really liked this presentation because it confirmed what my group found to be a systematic error in our experiment. This group found as the heigt in the building increased the number of count rates also increased. I am curious to see if there is any way to calculate this error into our data since we are located in the basement through many layer of concrete (similar to how we calculate in the efficiency errors of our detectors).
Week 7
I was a little late to this session, so Harry informed me after we broke into our groups that Professor Marx discussed the idea that our detectors can be used to calculate the energy of the "cosmic rays" deposited in the scintillator. Our group for our second project has decided to determine the amount of energy deposited into the scintillator, we began our experiment by twisting and changing the position of the detector setup. An important tool that we will be using in this experiment is the digital oscilloscope. In the digital oscilloscope the pulse amplitude of the analog signal measures the energy deposited in the scintillator. We collected energy data with our 2 detector setup in 4 different positions. The first postion was standard, the two detectors laid flat on top of one another, the second set up we stood one scintillator up on its side (over the length of the scintillator, or the width is perpendicular to the bottom scintillator), the third setup we stood the scintillator on its width (the length of the scintillator was vertical and parallel to the bottom scintillator), and the fourth setup we stood the scintillaor on its width (the length of the scintillator was vertical and perpendicular to the bottom detector). To collect our data we set the oscilloscope to collect 16 pulses and determine the average (energy). An image of the oscilloscope sreen is shown below along with our data:
From the data it is evident that as the "thickness" of the scintialltor increased, the energy deposited also increased (the pulse amplitude is the highest). Simply put the more distance that each muon travels through in the scintialltor the greater the energy that is deposited. In our fourth setup the probability that muon would travel through the scintillator at long distance between the point it entered and then exited was greatest.
Week 8
This week our group decided to take single counts of the energy deposited by the particles, as in comparison to last week experiment in which we averaged 16 counts. Analayzing single events would allow us to take into account the extremes (the minimums and the maximums) of the energy deposited by the particles, which is not able to be seen when taking 16 count averages. As well, we interested in determining the frequency of the various energies deposited (we created frequency histograms in excel which are shown below).
Our setup this week was simply two detectors stacked on top of one another, the scintialltors were parallel to one antoher and aligned as accurately as possible. The setup consisted of the top detector being connected to the oscilloscope (channel 1) and then connected to (input 1) on the FPGA. The bottom detector was connected only to the (input 2) on the FGPA We are of course interested in the coincidences of the two detectors and thus had to connect from output #3 on the FGPA which was connected to channel 2 on the oscilloscope. From this output we could read the amplitude of the spike directly from the oscilloscope screen. We measured the spike of the oscilloscope in mV (milli volts) which determines the energy dopisted by a paritcle. It was difficult to determine the exact energy, I am still curious if there is anyway that the oscilloscope could determine this value for us (rather than having to read the height of the spike and eyeballing its value).
To begin the experiment we took data for 100 single counts. We then constructed a histogram on excel showing the number of counts at specific energy levels. I learned that the bin size given in mV (mili volts) is the x-axis of the histogram and helps to group the energy levels obtained. For example, if the biz size is 5mV then starting from 0-5,6-10,11-15,... each energy level would be placed in the approriate range. The first histogram below is based on a bin size of 5, and is was determined from 100 events. Professor Marx told our group that our histogram should have on peak and have some type of bell curve shape to it. In the first histogram it was clear that our peeks were from 40-45 and 60-65 with a drop between 46-59. The reason for this could have been that our bin size was to small and we needed to group energies of a larger range together as one peak. We then proceeded to take an additional 200 counts. Again we created a histogram now with a total of 300 counts, and a bin size of 5. Again there were two peaks at 35-40 and 55-60 with a drop off in between at 41-54. Next Professor Marx suggested that we change the bin size. First, we changed the bin size to 10 which created two peaks from 30-40 and 50-60, with a drop in the middle again, but nearly as significant. Finally, we changed the bin size to 15 and our data looked just as we would have hoped when analyzing the histogram, with a single peak from 45-60 and you can see that the counts decreases as energy increases, just as expected. You must be careful when changing the bin size because I can not help, but think that we are altering or massaging our data a bit too much to give us our desired results.
100 Count Bin Size 5
300 Count Bin Size 5
300 Count Bin Size 10
Week 9
Our attention was now directed toward determining the maximum or total value of energy deposited in the scintillators. To do so we discovered that we could relate the energy deposited to the energy lossed as the muon passes through the scintillators. Professor Marx at this point actually told us that this is related to radiation treatment, this is because knowing where all of the energy of a particle is deposited in the human body is helpful to shrink (kill the cells) of a tumor. Also, Professor Marx informed us that the energy deposited is roughly the inverse square of the particles speed. This gave us the basis for this nights work. This is because the particle would move through the scintillators depositing roughly the same amount of energy in each until it stopped and then would deposite one large amount of energy in that scintillator. You can see this on the graph above, as their is a huge drop in momentum (p = mv) there is also a loss in energy deposited. We created a stack of 5 detectors, we were hoping that this would be enough time or distance for the muon to travel through and eventually stop and deposit its energy. The detectors were stacked as follows:
Anothe important aspect of this energy deposition is the following ideas; if the muon was to stop in detector 5 we would get a reading in detectors 1,4,3,and 2 that should be almost equivalent, and detector 5 would have the largest energy deposit. If the particle did not reach detector 5 and detector 2 was were it stopped the maximum amount of energy would be deposited in detector 2, and detectors 1,4, and 3 should have equivalent energies associated with them.
Once we started running the program we were looking for 5-fold coincidences. However, we noticed that detector 5 was extremely noisy and so we had to stop the run and make a quick switch. Overall, we ended up collecting a total of 587 data points. From here again with the help of Harry I was able to construct 3 graphs based upon two characteristics channel 4 as a nonzero, and channel 4 as a zero (zero referring to the idea that there is no pulse or energy deposited). As well, the graphs were broken down further (I do need to give Harry credit for help with breaking the graphs down further); so the channel 4 events that were zero were broken down into channel 1 greater than or equal to channel 2 and channel 2 greater than channel 1. Were channel 1 corresponds to detector 1, channel 2 corresponds to detector 2, channel 3 corresponds to detector 3, and channel 4 corresponds to detector 5 (refer to the detector setup above). The following three graphs were created:
Now to analyze the graphs: In the first graph of Pulse 1 verus Pulse 2 (Channel 4 not equal to zero) which is when a muon would travel thru all five detectors (should be a linear graph of the 2 pulse heights); the data points were scattered. From the graph you can see that their was a slope of .74 and correlation coefficient of 0.0082. Both which are far off the mark. The next graph depicts a muon traveling through the first four detectors, but missing the 5th detector. This again should have a slope of approximately 1 because the energy deposited in each detector should be about equal. The slope in this case is 1.1 not to far off, but again the correlation coefficient is 0.0862 terrible far off as the data points are very scattered. The final graph depicts a muon that would travel through the first 3 detectors and finally stop in the fourth detctor from the top (detector 2). This graph hopefully would have a slope of less than 1, which it did 0.46, but again the points are scattered and the correlation coefficient is only 0.1867. The data overall is extremely scattered and at this point I think it would be beneficial to completely redo this experiment with correctly calibrated detectors. This is because throughout the experiment detector 3 was giving extremely high readings as compared to any of the other 3 detectors. So the hypothesis about the energy deposition scattering can not be proven by this experiment "exactly". However, I would never discard this hypothesis as I do in fact believe it is true (especially because we know it happens in the real world: radiation treatment). For a more in depth analysis please refer to our groups presentation below.
Week 10
This week each group presented their projects to the class.
Group 1 Measuring the Speed of Cosmic Rays: The wall setup was utilized for this experiment. The group collected data based on time, distance, and 2-fold coincidences. They constructed a graph of distance vs. time and their slope or velocity was recorded as 3.08 x 10^8 m/s.
Group 2 Cosmic Ray Showers (Continuation from 1st project): The main idea of the experiment was to determine if the 4-fold coincidence rate would either steadly decrease or become asymptotic to the x-axis. This time around the group collected more data giving them larger count rates. When graphing coincidence versus distance it was clear that the 4-fold coincidence rate was leveling off, and became asymptotic with the x-axis (it did not continue to steadily decline).
Group 3 Cosmic Ray Showers and Angular Dependence of Delayed Detections: The main idea of this experiment was to determine the effets of a vertical or angular shower. The group analyzed detector setups at 45, 90, and 135 degrees.
Group 4 Cosmic Ray Energy Depostion: Please click on the following link to see Harry, Tania, and Joe's Presentation:Cosmic Ray Energy Deposition in Detector Scintillator
Group 5 Cosmic Chris: Outside, between the physics and math building 5 locations were marked off and count rates were measured. As well, counts were taken at various heights above the ground. It was clear that the lower cosmic Chris was to the ground the lower the count rate. This could be attributed to the shielding effect that each group experiences during their experiments. Also, the count rate was lower closest to the math building as compared to the physics building due to the simple fact that the math builidng is two stories higher (shielding effect again).
Group 6 Cosmic Rays and Smithtown High School The presentation dealt with the data collected at Smithtown High School by Gillian Winters classes. An interesting part of her presentation dealt with barometric pressure versus 2 fold coincidences. There was a strong correlation between the increase in pressure and the decrease in cosmic ray rate.
Week 11
This week we began our 3rd and final experiments. The basis for our next study was a continuation of what we worked on in our 2nd experiment, energy deposition. For the 3rd experiment we wanted to analyze the energy deposited by a muon based upon the location at which the muon passes through the scintillator. Dr. Vavilov explained that it is possible to notice a factor of 3 increase between a muon hitting near the pmt as opposed to the end of the scintiallor (as far away from the pmt as possible). Our ultimate goal for the experiment was to analyze energy based upon a 3 detector setup with large and low angles (with respect to the muon hitting the scintillator).
The first step in the experiment was to find the efficiency of our middle, or operating detector. A procedure that we conducted on the 2nd day of class, the following curce determined our efficiency:
Efficiency Curve Detector 703938 (Please click on image for higher resolution)
From the above graph it is clear that the optimal running voltage for detector 703938 (the detector from which we collected our energy data) is 6.1 V with an efficiency of 98%.
The setup of the detectors was actually a bit tricky. One other problem we ran into was the fact that the bottom detector in the setup was producing a lot of noise at 5.5 V, and so Dr. Vavilov instructed us to lower the voltage to obtain a reasonable value for the noise.
We then began our energy measurements, by marking off the middle detector into 3 equal segments of rouhgly 30 cm. To take our energy measurements we twisted the middle detector so it formed a right angle with the top and bottom detectors. The ultimate goal was to determine how the relative distance from the PMT would effect the energy of a muon passing through the detectors. Using LabView as usual, we were looking for 3-fold coincidences and produced output would trigger the oscilloscope. The oscilloscope is how we would actually determine and collect the enrgy values, you can do so by looking at the amplitude of each peak which is given in mV. When we first began the experiment we ran into an immdediate problem. The bottom detector was reading 0 Volts, and so with the help of Dr. Vavilov we had to make a switch and use another detector. With these minor delays we ended up collecting 190 energy values for the first setup (described above) and 160 counts for the second setup where we moved the middle detector so the scintialltor was as far away from the PMT as possible.
Two frequency charts were then produced to help analyze the data. The first histogram, and data chart shows data when the scintillator was closest to the PMT. The peak value seems to be between 0.055 V and 0.07 V. The second histrogram and data chart represent the scintillator when it is furthest from the PMT. The peak values are between 0.045 V and 0.055 V. Overall, the data seemed to prove Dr. Vavilov's hypothesis, the muon that travels through the scintillaor closest to the PMT will tend to be recorded at a higher energy value than those further away from the PMT (most of the time).
Please click on image to enhance it.
Week 12
This week was a continuation of last week, except we wanted to take a large sampling of data (nearly 500 counts for each setup). A reminder, we were interested in the energy deposited based upon the location at which the muon passes through the scintillator relative to the PMT. We were specifically always looking only for 3-fold coincidences between the top, middle, and bottom detectors. We were intesrested in 3 different setups: (1). 1/3 of scintillator closest to PMT, (2). 1/3 of scintillaor in the middle of the top and bottom scintillators (middle range), (3). 1/3 of scintillator furthest from PMT. We did one other setup which would lead to large angles (muons passing through scintillators at large angles). Due to time constraints we were only able to record 100 counts for this final setup. Please take note of the diagrams below:
Setup 1: 1/3 of scintillator closest to PMT
Setup 2: Middle Range
Setup 3: 1/3 of scintillator furthest from PMT
Setup 4: Large Angles to the Vertical
Data for 1/3 of scintillator closest to PMT
For setup 1 the peek was at 0.060 V. Only because of Harry was I able to produce the statistical data as he has on his wiki, allowing me to determine that this peak value was more than 0.010 less than the mean value. As hypothesized the were many high value energy counts as expected. Looking at the standard deviation from the statistical analysis showed that the range of the voltage was 0.04657 to 0.09457. And using excel, I was able to determine that this consisted of 379 data points out of the 518 or 73% (normal distribution curve is 68%). So this value is very close and gives a fairly good reading.
Data for Middle Range
For setup 2 (middle range) the peek was at 0.055 V, which is extremely close to the mean: 0.055046. Again using the standard deviation the range of the voltages were 0.037809 to 0.072283. This included 374 of the data points (74 %).
Data for 1/3 of Scintillator furthest from PMT
For setup 3 (1/3 of scintillator furthest from PMT) the peek at 0.040 V, which is smaller than the mean at 0.04775 V. Utilizing the standard deviation again the range of the voltages was 0.027474 to 0.06804. There were 374 data points in this range which accounted for 85% of the total points. This is clearly much higher than the expected 68%, showing that this setup did not create a bell shaped curve (gaussian).
Data for Large Angles
For the final setup (large angles) the peak voltage was 0.070 V, which was smaller than the mean 0.074893. I believe this peek was so high because muons would be traveling through the scintillators for the greatest distance as compared to the other setups based upon geometry. The range based upon the standard deviation was 0.049577 V to 0.0100209 V. There were 71 out of teh 102 data points, yielding 70% of the total number of points (close to the expected 68%). The reason which Dr. Vavilov informed me of for the extreme outliers to the right is that the histogram in excel has a limitation on the x-axis. Meaning any value greater than 0.165 gets grouped together creating a large freuqence of values on the tail end.
From the 4 setups it seems to now be clear that a muon which passes through a scintillator closer to the PMT will be recorded with a higher energy value as compared to a muon that passes at the furthest end of the scintillator (away from the PMT). As well, with the help of Harry we conlcuded that the distribution for the 4 setups were Gaussion in nature.
Week 13 This is our final work session. With the help of Harry, I was able to create a plot of average energy versus distance from the PMT. I used the data that we collected from Week 12. On graph as I have learend this semester the linear regression, best fit line, and error bars are included (I need to give credit to Harry for the error bars, but I have a good understanding of them now). So the graph is shown below.
Average Energy versus distanct from PMT
From the line graph it is clear again that as the further away from the PMT a muon travels through the scintillator the smaller the energy value will be. In other words as distance from the PMT decreases energy will increase. The correlation coefficient in this case is .946 which is pretty good showing a fairly high correlation in our data points. This plot constructed from the previous weeks data was constructed taking into account over 1500 data points, which seems to be reasonable for this type of experiment, and helps to more accurately depict our results.
We then decided to collect more data for the large angles, as we only had a little over 100 total data points from Week 12. Also, Professor Marx, suggested we compare the results for the small angle trials as compared to the large angle trials. For the experiment we used the following 3 setups.
Middle 1/3 of scintillator (small angles)
Large Angles (1)
Large Angles (2)
For the first setup the small angles, the angle at which a muon would strike the scintillator at a range of 60 degrees from the vertical. Data for Middle Range was already recorded and analyzed in Week 12 and is reproduced below. For the 2 setups with large angles we again collected over 500 data points for each: the first setup is with the top detector near the PMT and the (2) is with the bottom detector near the PMT. Again, we were looking only for 3-fold coincidences.
This data was already taken and analyzed in Week 12. It is for setup 1, and represents 1/3 of the scintillator in the middle range.
Data for setup 2: the top detector is closest to the PMT:
Data for setup 3: the bottom detector is clsoes to the PMT:
When comparing the 3 setups as a whole the following results are clear. In setup 2 (top detector closest to PMT) there was a peek voltage of 0.075 V. As well, setup 3 (bottom detector closest to PMT) showed a peak of roughly 0.075 V. From the statistical analysis package that our group discovered in excel we could determine the mean for setup 2 and setup 3: they were 0.073 V and 0.070 V respectively. From this we can draw the conclusion that there is no significant difference between the energies of the particles traveling through the scintillators in setup 2 or setup 3. I believe that this is because to obtain a 3-fold coincidence the distance that the particle (muon) would have to travel through the scintillator was virtually the same. As well, it did not particularly matter if the top or bottom detector was closest to the PMT, just the simple idea that one of the detectors was actually closest and one furthest would produce similar energy values. As we learned in Week 12 the mean and peak for the middle range or setup 1 was 0.055 V, which is considerable lower than the mean and peak for setup 2 or 3. This again is due mostly impart to geometry, the larger the angle a muon travels through a scintillator the longer the particle is in the scintillator and thus the more energy that particle will deposit. If you closesly analyze the histogram you will notice that there are outliers for setup 2 and setup 3. I later learned from Dr. Vavilov that this is because any value greater than 0.165 volts would be grouped together. So if the limit on the x-axis was larger we would most likely see a count rate of 1 or 2 spread out amongst the 15 outliers in the one histogram.
Week 14
This final week was devoted to individual presentations. Professor Marx gave us alot of freedom to discuss basically whatever we wanted. I was thinking of what I should do and why I had taken this course. First off I took the course to help me become a New York State certified physics teacher, and my second reason was to determine how I could incorporate cosmic rays into my classroom. Since I knew Harry would do an amazing job with our groups work and experiment for the last 3 sessions, I decided to create a lab that my furutre physics and research students could do in the MARIACHI lab. The beginnig of the lab is an introduction to cosmic rays describing what they are where they come from, their energy levels, effect on humans, why we study them, and how we can detect them. The next portion asks the students to determine the efficiency of a detector, and finally to determine how orientation of a detector effects its efficiency. For a more detailed look at the lab please follow the following link: *****Apparently my file has been corrupted and I can not access the document. I did however hand out printed copies in class and once I found out how to open the file I will post it on my wiki.
This semester I learned what cosmic rays, how to incorporate them into my classroom, and just how interesting studying physics and science can be. A few things that I learned this semester is acutally how to conduct a realistic science experiment. Up until this point in my college career I was always given guided procedures in labratory experiments, but never had to create and produce a plan to follow by myself. Also, I discovered how useful excel could be in producing histrogram, data analysis, and many other features. I hope to someday bring my students to the MARIACHI lab, and hopefully spark their interest about research science. A special thanks to Harry and Tania for an awesome group.
