User:Benner
From MariachiWiki
Personal Information
Hello everyone this is my new Wiki site.
Anyone out there (teachers/peers) should feel welcome to call me Randy at any time, though I don't find Randall offensive.
My family lives in Pennsylvania (Harrisburg area) but I was born in up-state NY.
I am a Biochem major (Senior) with interests in physics, chemistry, and bio. My ultimate goal is Med school or graduate school.
I enjoy sports, particularly basketball. I played in highschool but have recently accepted the fact that I am minimally athletically inclined. Today I try to spend most of my time in my studies. After all everyone knows after college the athletes get passed by the Nerds. Nerds get all the chicks...
Cosmic Rays
Main Page
Cloud Chamber external link
If you were unable to view the demonstration in class the above link might be helpful.
Now lets chat about the Cosmic Ray detector that we encountered in the lab. I will briefly outline my current understanding of how the scintillator works.
The action begins when a cosmic ray strikes the organic plastic scintillator. The scintillating panel is made up of highly polished, highly reflective plastic.
A small number of photons are emitted as charged particles pass through the plastic and bombard the luminescent molecules. The photons excite electrons in these compounds which cause the electrons to move to a higher energy level. The electrons then "fall" from the higher energy level valence (back to ground state) releasing energy as a photon. These original photons are at a higher frequency than we can see (Ultra-Violet) so the plastic is doped with compounds that convert UV light into the visible range (blue/violet). The plastic is wrapped in black paper. This paper attempts to minimize false detections due to photons bouncing around the lab.
The photons emitted from the plastic are channeled to the end of the plastic where they run into the photomultiplier tube. If I correctly understood Dr. Vavilov a thin film called a "cookie" is placed between the end of the plastic and the photomultiplier tube and provides much better transfer of photons to the photomultiplier tube.
The photomultiplier tube uses the photoelectric effect to transmit a light signal (photon) into a very small electrical current. The photo-electric effect refers to the phenomena of electron emission from metals due to photon bombardment (Thankyou Einstein). The photomultiplier tube has its name because the original electrical signal is amplified by the apparatus. A photon will emit a single electron (upon striking the metal) which will proceed to the first dynode where a higher voltage is applied. This single electron causes the emission of several electrons at the first dynode and the process proceeds along the photomultiplier tube amplifying the electrical signal at each successive dynode. The photoelectric effect is encouraged by using a cathode and anode. This charge gradient is used to accelerate the electrons. Each successive dynode has a higher voltage (less negative). The voltage supply can affect the efficiency of the detector as discussed in class. Higher Voltages will improve the likelihood that an actual event will be detected but increases the likelihood a "false event" will be recorded.
The electrical signal at the end of the photomultiplier tube is an analog signal. The amplitude of the signal roughly correlates to the energy of the absorbed particle. A threshold voltage is chosen to minimize false detections and isolate actual incidences. This analog signal is converted to a digital (logical/square) signal that is simpler and better understood by the detection software.
Several detectors can be used in concordance to find out more information about occurences. If stacked, several detectors can be used to detect the same particle passing through several detectors. These detectors very commonly will have a coincidence within nanoseconds temporally. This suggests 2 things.
1. The detection from each successive stacked detector comes from the same cosmic wave (charged particle).
2. The charged particle in question is moving at a very high velocity (in the order of the speed of light).
This stacked configuration can also be used to find the efficiency of the detector. 3 detectors are stacked on top of one another. The efficiency of the central detector can be found by #of occurences that SHOULD have been detected/#of occurences actually detected. In other words #of coincidences between panel 1 and 2 without 3/#of coincidences between all three panels.
Experimental Data
Justyn's Wiki- This is my partner's wiki
Efficiency Determination Experiment (Data taken 9/11/07)
This experiment was used to calculate the efficiency of a detector (Detector #91107). In order to determine the efficiency of a given detector, 3 detectors must be used. The detector whose efficiency is in question should be stacked between 2 other detectors (middle). The convention will be to name the detectors numerically beginning with detector 1 on the top, 2 on the bottom, and 3 in the middle. This arrangement isn't consecutive... Don't get confused! With three detectors 2 things can be deduced:
1. How many particles were detected by the scintillator in question?
2. How many particles passed through the scintillator in question without being detected?
-The total number of particles detected= # of coincidences between all 3 panels. If all three panels have a coincidence it was very likely caused by the same particle.
-The total number of particles that passed through the detector without being detected= number of occurences between detectors 1+2 without detector 3(center detector). If the top and bottom detector get a "hit" while the middle does not this would indicate the middle detector failed to pick up the particle. We know that the middle detector should have been hit because we assume that these particles are moving linearly (which is a fairly safe assumption at such short distance in my humble opinion).
With these 2 numbers the efficiency can be calculated.
Once again, the efficiency of the central detector can be found by #of occurences that SHOULD have been detected/#of occurences actually detected. In other words #of coincidences between panel 1 and 2 without 3/#of coincidences between all three panels.
The independent variable in this experiment affecting the efficiency of the detector is the voltage supplied to the detector. The higher the voltage the more likely a particle passing through the detector will be detected. At the same time as voltage increases the number of false detections will increase. Calibrating the detector involves both maximizing detector efficiency while minimizing noise (false detections).
We carried out the experiment at 6 voltages and plotted efficiency vs. voltage and # of counts for detector 3 vs. voltage (noise). The voltage I chose in order to minimize noise and maximize detector efficiency is approximately 5.45V.
9/11/07
Efficiency Data for detector #91107 (original Data)
9/16/07
Efficiency Data for detector #91107 (Version 2 /w graphs)
Experiment 1- Flux (Data taken 9/18/07)
The purpose of this experiment was to see how Cosmic Ray flux and detector surface area are related.
In order to do this we chose a simple 3 stacked detector configuration. To stick to our convention outlined above the detectors are named numerically beginning with detector 1 on the top, 2 on the bottom, and 3 in the middle. The independent variable (lambda) involved moving the middle detector out from between the other detectors. The distance displaced is defined as lambda and is measured in cm. Lambda is illustrated in the excel file.
The data of interest to our experiment is the coincidences between 1+2 (Top and bottom), and the coincidences between 1+2+3 (all detectors). The coincidences between 1+2 should stay constant assuming flux is constant considering these detectors are never moved. The data of particular interest is the coincidences between all 3 detectors. As lambda increases, the area that a particle might pass through detector 1+2 without passing through the middle detector increases as well. With that knowledge it can be expected that as lambda increases, the threefold coincidences should decrease. This trend was observed in our experiment. The trend is described in the excel file not only by count but also by fraction. The fraction in this case is threefold coincidences/1+2 coincidences. As lambda increases, the fraction decreases as expected. This dependence of coincidences and lambda illustrates the concept of flux. Flux is described as the number of particles passing through a unit area/unit time. Cosmic ray flux at ground level vs. energy of particles is depicted ===>.
Since flux is in units of particles/s/cm**2 detector area is taken into consideration in calculating flux from total counts. Since the area we are measuring (detector area) is known, the flux should be able to be calculated. Varying detector area (by changing lambda) should change the count rate in a predictable way. The relationship should be that flux is constant (or somewhat constant) independent of detector area. The relationship between detector area and count rate should in theory PROVE that flux is constant, and not dependent on the surface area of the detector.
The experiment was successful in showing a linear relationship between detector area and count rate. The experiment could be taken one step further in the analysis, by calculating flux using the number of misses. The number of misses (difference between 3-fold and 2-fold hits) tells you the total number of particles traveling through the exposed detector (exposed by lambda cm). With lambda, and the width of the detector (~20cm) known the area of the panel is easily calculated. With the number of misses and the area of the detector known, calculating the flux is easy. Comparing the flux at each lambda will tell you whether or not flux is constant, and how constant it is.
10/9/07 Preliminary experiment 1 data analysis V2.2. This is my personal analysis WITH error bars for rate
Experiment 2- Flux & Detector separation (Data taken 9/25/07)
9/26/07 Experiment 2 excel sheet Version 1
In experiment 1 we used the adjustable height detector setup. This setup allowed us to change the height (radius between the 2 detectors). With height defined as r, the dependent variable of interest in the experiment is the coincidences between the 2 separated detectors. The purpose of this experiment is to investigate the relationship between solid angle and flux. Defining solid angle would be better left to a mathematician than a biologist. My simple understanding of the concept is that solid angle is related to the surface area of a sphere in the same way an ordinary angle is related to the circumference of a circle. The units are unimportant, the concept of a large and small solid angle are the important part.
The larger the r (separation of detectors), the smaller the effective solid angle of the detector array. The following is an illustration of solid angles:
10/8/07 Experiment 2 excel sheet Version 2
This analysis simplified the data and error analysis by converging the data from each height. Coincidences are no longer analyzed but rather rate (rate takes time interval into consideration).
We found that the coincidences went as a factor of 1/r^2
Experiment 3- Detector array orientation and Flux- Which way are the rays coming from? (Data Taken 10/2/07-10/9/07)
The purpose of this experiment was to change the orientation of separated detectors by rotating them in respect to the ground in order to infer the direction that the cosmic rays are traveling. In this experiment we used the octagonal detector orientation as depicted below. The independent variable of the experiment is angle theta. The angle theta is depicted below, with the opposite leg being the height of the shim, the adjacent is the original bottom position, and the hypotenuse representing the new bottom position. Since you know the opposite (shim height) and the adjacent (width of base) you can use Tan(theta)=opposite(shim height)/adjacent(base height) to find the angle theta to a high degree of accuracy. Since the setup is an octagon some other angles are possible and easy to measure (in intervals of 45 degrees). This angle theta is the independent variable used in our experiment.
The angle theta is in reference to the original position (4 on left and 2 on right) as depicted in the diagram. Data is taken using the coincidences between detector 4+2 (in the diagram). Data refers to the detectors by detector 1+2 (due to limitations of the daq). Detector 1 corresponds to detector 4 in the diagram, and detector 2 refers to detector 2 in the diagram. All angles theta are in reference to this initial position, and the shim is on the side of detector 2 and the fulcrum is on the side of detector 4 (as seen in the diagram above).
10/2/07 Octagon Experiment Excel Spreadsheet Version 1.0
10/2/07 Octagon Experiment Excel Spreadsheet Compiled Version 1.1
10/11/07Octagon Experiment Excel Spreadsheet Version 2.0
As you may see, the data seems to resemble a sine wave. This is interesting, and suggests the cosmic waves are moving in a vertical direction (up or down) at the highest frequency. With that being said, the data also does not zero at the horizontal. That means that the particles move in all directions. The frequency of each direction is what is important.
It is important to note the x error bars on the graph. These error bars represent the uncertainty in the incidence angle. The octagonal setup will record incidents at the angle noted + or - 20 degrees.
The most probable physical explanation for the observed rate distribution is in terms of earth's atmospheric shielding. The earth's atmosphere is a blanket around the sphere with a uniform thickness. The incidence angle of a cosmic ray hitting the earth's surface dictates the distance the ray must travel through the earth's atmosphere. 2 difference incidence angles are depicted above. The red is the path the cosmic ray must take through the atmosphere. Notice the most horizontal incident angle has a significantly larger distance to travel. This additional shielding gas drastically decreases the cosmic ray rate at ground level.
Experiment 4- Rate vs. Detector orientation about the vertical axis (Data taken 10/16/07)
The purpose of this experiment was to observe the relationship between incident rate and detector orientation. Instead of rotating the octagon on its sides like in the previous experiment, this rotation is around the vertical axis. The angle is simply referred to as angle in this experiment and is in relation to angle 0=North wall. It should be noted north refers to an architectural North and doesn't necessarily mean geographic North (but its close). We decided to collect data with an angle theta of 45 degrees (refer to the prior experiment for a diagram and explanation of theta). We did this for 2 reasons.
1. Count rates with a horizontal (0 degree theta) orientation will yield much lower count rates, making data analysis more difficult.
2. We would like to minimize shielding effects as much as possible. The higher in the sky we look, the less shielding material from the physics building will be in the solid angle of the detector.
The difficulty of this experiment lies in drawing conclusions from the data. Since the experiment is being performed in the basement of the physics building significant shielding can occur (as illustrated by the other group's data using Cosmic Chris- Thanks guys!). Different amounts of shielding material will block each direction due to our location in the building.
Another possibility is that different angles might give different count rates due to alignment of particles. These particles, if charged should bend under a magnetic field. We might expect these particles to bend according to the right hand rule (if +) or the left hand rule (if -). This might bend incoming particles in a particular direction.
Deducing which effect we are observing is the challenge of this experiment.
Excel Data analysis for experiment 4
^^Please note the graph's Y axis does not begin at 0. We did this to spread out the points for effect but remember the points are closer together than they appear.
The x error bars are a product of the detector configuration as described in experiment 3. The error bars are larger because the effective detector length is longer with this orientation. The incidence angles are as described + or - 45 degrees.
Experiment 5- Rate vs. Detector orientation about the vertical axis Day 2 (Data taken 10/22/07)
In this experiment we tried to improve the data from our previous experiment by doing 3 things.
1. We took MORE data at directions with "interesting" coincidence behavior.
2. We took data between points where the nature of the function seemed particularly questionable.
3. We used cosmic Chris to verify whatever trends we seem to be observing
Excel Data Sheet for Experiment 5
Please note graph's Y axis doesn't begin at 0.
The data seems to confirm that there is significant shielding going on West of the detector. The data from cosmic Chris is somewhat unclear. His data shows low counts in the direction of West as predicted by the Octagon data. The enigmatic part of this data occurs when cosmic Chris was pointed South. He observed a significantly lower flux than would be expected following the octagonal data.
This might be explained by several experimental factors-
1. The data taken in the octagonal experiment was taken with a 45 degree angle Theta (described above). The data from cosmic Chris was taken with him standing upright. That means that he is measuring a different solid angle than the octagon.
2. The vertical orientation of cosmic Chris also means he is observing cosmic rays entering not only traveling through his face but also through his back from the opposite direction. That means that data taken pointing north for example, is measuring particles traveling both North to South, and South to North.
To further explore this notion I compiled the data at 0+180 degrees and 90+145 degrees. The result is plotted below with accurate error bars.
It appears as if cosmic chris might be observing something more than a statistical variance. We might use Chi square error analysis to find a more definitive, quantitative answer.
3. Cosmic Chris has 2 panels closer together than those used in the octagonal experiment. That means that he measures data with a larger solid angle than with the octagon. He observed higher rates for this reason.
Experiment 6- Shielding Experiment using Cosmic Chris. (Data taken 10/30/07)
The purpose of this experiment was to observe how shielding can affect cosmic ray flux.
This experiment utilized Cosmic Chris to investigate how location in the physics building can effect cosmic ray flux. The independent variables were two-fold, one being direction (in degrees clockwise from N) and the other location in the basement (see figure).
Experiment 6 Excel Data
As you can see from the figure above, 4 series of data were taken, each at a different location. The locations were chosen in order to more closely observe shielding objects in the basement.
The object of particular interest is the wall to the West. This wall was constructed as a shielding device for the accelerator next door. Our previous experiment (with the octagon) appeared to detect this shielding device.
We placed Cosmic Chris in various locations around that wall in order to construct data of rays coming from the direction of the wall, and every other direction. 2 of the series' (series 2+4) have only 2 points and are intended to spread out the points (in rate) as much as possible by butting Cosmic Chris up against the wall in question.
Data sets 1+3 are constructed with identical points on the X axis (directions) in order to accurately use chi-square analysis and draw conclusions about rate. The Chi-square data was crunched on the excel sheet and the resulting values are .972 and 1.952 for series 1 and 3 respectively. This data seems to suggest that you are more likely to reject the null hypothesis at location 3 close to the wall. The null hypothesis states that any variation in rate away from the mean is due to statistical error. Thus if you reject the null hypothesis you are saying that the variation is due to something more than standard statistical error. If a somewhat arbitrary value of 1 is used as a cutoff to accept or reject the null hypothesis then the null hypothesis has been proven in series 1 and rejected for series 3 according to our data.
The largest thing to take away from all of this chatter is that series 1 showed less statistical spread than series 3 meaning that we are probably doing one of 2 things with our data from series 3 that we are not doing in series 1.
1. Observing an actual phenomena. E.g. Shielding effects blocking particles approaching from the direction of the North wall.
2. Observing statistical spread due to some type of systematic error.
Our previous experiments have attempted to display the accuracy and utility of our detection devices so I would venture to say that what is going on is that Cosmic Chris can only observe shielding objects that block a significant portion of his large detection field (solid angle). That is why he has to be so close to the object to observe it.
The Octagon is much better at measuring directionality because it's field of view (solid angle) is much smaller. Thus Cosmic Chris needs smaller panels to do experiments with directionality :-D
The reason we took data at position 2+4 was to directly show how proximity to the wall effects count rate. Overall rate was observed to be higher in position 2 than in position 4. This observation can be explained by proximity to the shielding object. Position 4 is closer to the thick wall and experienced less cosmic ray flux. More of the detector's field of view contains the shielding object due to it's proximity.
The spread of the data in series 2+4 is interesting to me because it seems counter-intuitive. Chi-Square analysis wasn't necessary to analyze spread because there are only 2 points in each data set. These points are spread further apart in series 2 than in series 4. I would expect that the difference between rate would be larger the closer you are to the shielding device as observed in series 1+3. I cannot offer an explanation for this observation beyond that very little data was taken, and the building is a complicated structure (not a simple box with a single heavy shielding device).
Experiment 7- Multiple detector array to measure multiple particles (Data taken 11/13/07 and 12/4/07)
The purpose of this experiment is to use a multiple detector array to observe multiple particles from the same cosmic event.
The primary objective is to prove that a multiple detector array is capable of distinguishing between random coincidences between all 4 panels and actual events involving multiple particles striking at or around the same time.
A secondary objective for this experiment involves quantifying the size of the particle field showering the earth from each primary cosmic event (or particle).
The experiment was conducted using a 4 detector setup as illustrated below. 2 stacks of 2 detectors were placed parallel to one another on the ground. The variable manipulated was the distance between the 2 stacks of counters. The relationship between separation of counters and 4-fold coincidences is plotted below.
Excel Data for experiment 7
After consulting the data and the graph two things are evident:
1. Most importantly, and perhaps least obviously you notice that there are more 4-fold coincidences than would be expected by accident. My understanding of the definition of an accidental hit in this case is as follows: The number of 4-fold coincidences expected within a given time interval assuming a constant random rate at each individual counter.
Quantification of the number of random counts expected in a given time period with our apparatus would be invaluable in deciding whether our data collected is viable. If the expected number of 4-fold counts due to random counting is close to the number observed our data should not be considered viable.
When in doubt always turn to the experts! In our case the expert on the matter is Pierre Auger whose formula we briefly borrowed for this experiment.
Link to Auger Paper on particle showers
In the case of our experiment we will present these variables as conservative estimations (rounding).
n=5000
x=4
r=100e-9S or 100 nanoseconds
N=1.7361e-10 or 1/5760000000
As you can see the likelihood of such a random coincidence between 4 detectors is quite low. Low enough to safely consider our 1440 4-fold coincidences per hour impossible to have been caused by random counting.
2. The size of some of the observed showers was quite large with 17 4-fold coincidences observed in 20 mins at a separation of 828cm. 288 4-fold coincidences were observed at the minimum separation (60cm). The resulting ratio of small showers to large is around 20:1.
With this information the maximum size of cosmic ray showers cannot be definitively concluded but the general size of a typical shower can be estimated.
An extension to the experiment was proposed by Prof. Marx, and implemented on 12/4/07. The extension simply involved observing 2-fold coincidences with a 2 detector setup rather than 4-fold with the 4- detector setup. The data was taken at the maximum separation (828cm). We were interested in comparing the coincidence rate in both setups.
Coincidences per 20 min:
2-fold/2-detector- 118
4-fold/4-detector- 17
The resulting ratio is around 7:1 for 2-fold over 4-fold.
Summary of Experiments
What have we investigated?
2.1.1 Efficiency Determination Experiment (Data taken 9/11/07)-
This experiment was used to calculate the efficiency of a detector (Detector #91107).
2.1.2 Experiment 1- Flux (Data taken 9/18/07)-
The purpose of this experiment was to see how Cosmic Ray flux and detector surface area are related.
2.1.3 Experiment 2- Flux & Detector separation (Data taken 9/25/07)-
The purpose of this experiment is to investigate the relationship between solid angle and flux in a 2 detector separated setup.
2.1.4 Experiment 3- Detector array orientation and Flux- Which way are the rays coming from? (Data Taken 10/2/07-10/9/07)-
The purpose of this experiment was to change the orientation of separated detectors by rotating them in respect to the ground in order to infer the direction that the cosmic rays are traveling.
2.1.5 Experiment 4- Rate vs. Detector orientation about the vertical axis (Data taken 10/16/07)-
The purpose of this experiment was to observe the relationship between incident rate and detector orientation. Instead of rotating the octagon on its sides like in the previous experiment, this rotation is around the vertical axis.
2.1.6 Experiment 5- Rate vs. Detector orientation about the vertical axis Day 2 (Data taken 10/22/07)-
In this experiment we tried to improve the data from our previous experiment. Cosmic Chris was used to attempt to confirm trends.
2.1.7 Experiment 6- Shielding Experiment using Cosmic Chris. (Data taken 10/30/07)-
The purpose of this experiment was to observe how shielding can affect cosmic ray flux.
2.1.8 Experiment 7- Multiple detector array to measure multiple particles (Data taken 11/13/07 and 12/4/07)-
The purpose of this experiment is to use a multiple detector array to observe multiple particles from the same cosmic event.
Future Study
Immediate Future
For the final day of data collection we will use an electronic delay device in order to delay the signal from one or 2 of the panels in our array in order to stagger their signal. This will effectively cause our array to count only coincidences caused by random counting not by actual event coincidences related to the same primary particle.
Other Potential Avenues
Some potential exists in expanding the possibilities of this class.
The first way improvement is possible is with the equipment used in the class.
Smaller Panels
As you may recall from the discussed experiments; a smaller detector might be advantageous in some cases.
Such experiments include directionality experiments where smaller panels allow you to observe smaller solid angles. Measurement of smaller solid angles allows for greater directional data resolution.
Cosmic Chris
Cosmic Chris leaves something to be desired in the rhealm of directional measurement for the reasons mentioned above. His panels are relatively large and very close together, resulting in a detection field with a very large solid angle. This large solid angle allows for very little directional data resolution. For that reason, some changes need to be made to Cosmic Chris to improve his directional resolution.
Considering Cosmic Chris needs to be transportable it is not feasable to improve his resolution by spreading his panels apart.
The effective solid angle can be made smaller by using much smaller panels.
The next way Cosmic Chris might be improved would be by setting up his transportable dolly in such a way that it has an adjustable angle. Right now Cosmic Chris is limited to standing up, laying down, and "sitting down" (as invented by Randy). If his carrying equipment could include some kind of propping apparatus for various angles, Chris would make a very good measurement of Directionality vs. Rate.
Octagon
The next possible equipment improvement involves the Octagon setup. The setup could be made even more convenient by making the octagon an equilateral 16 sided (hexadecagon) polygon. That way we could observe more data points on the graph of Theta vs. Rate. We accomplished median points between established angles using shims, but a 16-sided setup would be more convenient.
The other way the octagon setup could be improved would be with smaller scintillating panels, or by making the octagon larger (separating the panels). This would improve the directional resolution of the data taken from this setup.
DAQ
It would be great if the data aquisition software we were using allowed us to put in the coincidences that we would like to count. The current setup shows coincidences between fixed combinations of channels. An ideal system would allow you to enter which channel coincidences were of interest.
More potential exists for the class in prospective experiments.
1. A quantitative description of flux needs to be established. The data above is sufficient for the calculation if you know the area of the panels.
2. The directionality of particles in relation to the vertical axis has been observed in the basement of the physics building but not elsewhere. In this environment shielding effects predominate. It would be interesting to take this measurement in a place where no shielding from objects other than the atmosphere exist. I would be interested to know if magnetic fields can influence the movement of particles.
3. Experiment 7 (multiple particle experiment) was performed using a maximum detector separation in the order of 800-900cm. Several showers of this size or larger were observed suggesting that the experiment could be extended by separating the detectors even further. Unfortunately the basement of the Physics building is only so large, limiting the size of the showers that we can observe. An extension to this experiment would involve placing the detectors somewhere where infinate separation is possible in order to measure the maximum shower size.
