GSmithPHY315
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Lab Blog for PHY315 (Spring 2008)
Week 3
This was my first class because I registered late. For the third class, our group (Lena, Patrick and myself) tried to determine the accidental counting rate between two detectors. According to our
Two detectors were placed side by side, about a foot apart. To ensure that all coincidences were strictly accidental (and of no physical significance), one of the detector’s signal was delayed by 300 nanoseconds. This was accomplished by sending the signal through a length of wire (~300 feet long, since the speed of light is ~1 foot per nanosecond). Thus, any cosmic ray showers that happened to hit both detectors at the same time would not be recorded as a simultaneous event. Six runs were done in class. Dima ran an additional three runs, one was performed overnight for over sixteen hours.
An unexplained anomaly is present in our data: our seventh run has unusually low det1 and det2 frequencies (about 40 times lower than the other runs). It should be noted that the seventh run was the one done overnight, while the others were done in class or in the in morning by Dima. I cannot explain this discrepancy yet. The coincidence rate for this run was seemingly unaffected by the change in the det1 and det2 rates.
Questions
- Why were det1 and det2 rates so much lower for Run 7? Was it because the run was done at night, or because the run was done over a longer period of time? Does this reflect a systematic error or a physical reality?
- Why was the coin 1,2 rate unaffected by the changing det1, det2 rates?
- How can we predict the accidental coincidence rate?
Week 4
Dima suggested the use of this formula to predict the expected accidental coincidence rate for two detectors:
Such that:
- Rc is the count frequency of accidental coincidences between detectors (1,2)
- W is the window (the duration of each pulse)
- R1 is the count frequency of detector #1
- R2 is the count frequency of detector #2
Dima's formula can be extended to a more general formula for N detectors:
Our group (Lena and I) applied the formula to
Next, we changed the scope setup to view the pulses coming directly from the detectors. We observed that a pulse from one of the channels was usually (more than half of the time) followed very closely by a second (and sometimes a third) pulse. These repeating pulses never appeared on the other detector. A few time-lapse screenshots were taken of this effect (shown on the right). The time-lapse mode allowed us to see the general trend of the signal with respect to the start of coincidence pulse. As you can see, the noise on the left side of (before) the pulse is nearly constant. The signal should be fairly symmetrical about the center of the coincidence pulse, but there is significantly more activity to the right of (after) the pulse's peak. Multiple peaks can be easily seen in this screenshot.
What is the source of these single-detector multiple peaks? It would be very unlikely that a flurry of charged particles were repeatedly hitting one detector while the other detector was only being exposed to single-particle events. It was concluded that we had witnessed after-pulsing, which was most likely the result of a breached vacuum seal in the photomultiplier tube. A small amount of gas present in the photomultiplier tube could be ionized by the multitude of electrons passing through it. The ionized particle is responsible for starting a chain reaction within the photomultiplier tube that results in multiple pulses. It seems like the amplitude of the after-pulses decreases exponentially with time and they occur with regular frequency.
Dima had taken additional measurements since last week's meeting. He ran the same experiment, but with det2 delayed 600ns. The det1 count frequency was unchanged; the delayed det2 count frequency was ~16 Hz, significantly lower than the ~70 Hz associated with a 300ns delay. Recall that the signal is delayed by passing it through several hundred feet of wire. The wire has a nonzero resistance, which attenuates (reduces the amplitude of) the pulses. Also, different frequencies travel at different velocities through the wire medium (dispersion, which will make each pulse appear wider). Both of these effects should increase linearly with the length of wire, which explains why a longer wire has a lower det2 frequency. We may be able to reduce the effects of dispersion by converting the signal to a single frequency such as a sine wave, instead of a square wave prior to delaying it. (A square wave should be dispersed more because it is the sum of many individual frequencies: see 4 term, 10 term and 100 term approximations of a square wave. This can be explained by Fourier Series.)
One possible experiment would be to see precisely how the length of cable affects the det2 count frequency. We could experiment with various setups to minimize the dispersion and attenuation. Ultimately, we want to find the rate of accidental coincidences so that we can improve the accuracy of our measurements. The frequency of legitimate coincidences should be closer to the measured frequency, less the frequency of accidental coincidences.
My questions from last week were answered: the program allocates a limited amount of memory to the det1, det2 counts (16 bits), thus limiting the total number of counts it can store. Since the several million counts were detected overnight, the counter rolled back several times. The count frequency was probably very similar to the other runs; it does not make sense to ask why the coin 1,2 rate was unaffected by the changing det1, det2 rates.
Week 5
In an effort to reduce the effects of after pulsing on our measurements, Dima supplied us with a pair of higher quality detectors. These detectors, running on high voltage, were less susceptible to after-pulsing. We viewed the output of one detector on the oscilloscope to confirm this. It was observed that the magnitude of "background noise" present before and after each pulse was much lower on the high quality detectors. (Referring to last week's screenshots, this background noise can be seen to the left of each pulse. The background noise from the regular detectors is about four times larger than the noise from the high quality detectors.)
It was observed that these detectors produced after pulses less frequently than the regular detectors. The time-lapse feature on the oscilloscope was used to view general trends of the output data. After about a minute of time-lapse data collection, the oscilloscope showed about as many after pulse peaks as the regular detectors did after about five seconds of data collection. However, we cannot know how many pulses occurred in this time frame: the oscilloscope only records the temporal location (relative to the peak pulse) and height of the pulses. The oscilloscope would display the same information if only one or 100 pulses were to occur at exactly the same time (relative to the initial pulse).
The accidental coincidence rate was measured (with one detector delayed 300 ns) with the detectors in a side-by-side configuration and again in a stacked configuration. The coincidence rate was much lower than that of the regular detectors in similar configurations. (Dima explained to me that the after pulses prevented us from accurately measuring the accidental coincidence rate of the other detectors. Since the after pulses increase the coincidence rate, the measurements from previous weeks put an upper limit on the accidental coincidence rate.)
Three regular detectors were arranged in this configuration. The distance d between the stack and the solitary detector was varied. Our results can be seen here. (A similar experiment was done by Karyn and Tom. They used four detectors and took more measurements. Their results can be seen here.) Although additional measurements are required to reduce the uncertainties, the count rate appears to decrease to a nonzero plateau as the separation distance increases.
Week 6
During this session, each group presented their results from the first round of experiments. The topics were the angular dependence of flux (by Gillian, Mildred & Desiree), cosmic ray showers (Karyn & Tom), systematic errors (Lena, Pat & myself), flux as a function of the separation between detectors (Joseph, Tania & Harry) and flux as a function of height (Brad, Vincent & James).
The data collected by Karyn and Tom was of particular interest to me, as mentioned in last week’s post. They reported a plateau, similar to the one that had motivated our investigation of systematic errors. During our presentation, I mentioned that it was improbable that their plateau was solely due to accidental coincidences (i.e., due to the random noise of the detectors). Applying Dima’s formula to the data provided by Karyn & Tom, I calculated the expected four-fold accidental rates for each run of their experiment. The rates were on the order of 10 − 16 Hz, corresponding to about 10 − 13 counts every 3 minutes. Put another way, the four detectors would have to be recording at about 36,000 Hz before 1 accidental coincidence count would be recorded per 3 minute period on a regular basis. Thus, the assertion that the existence of their plateau was not solely due to accidental coincidences was justified. However, the predominant source of the plateau is still unknown to me. As mentioned last week, more data is needed on the subject.
Correction to our presentation
The after pulsing effects prevent us from accurately measuring the accidental coincidence rate - they do not change the rate (accidental coincidence rates are independent of after pulsing). The after pulses 'pollute' our accidental coincidence rate data (by providing false positives); the measured coincidence rate reported in our presentation is an upper limit for the rate. A system with fewer after pulses would allow us to put a better upper limit on the number of accidental coincidences. Our conclusion that the more expensive detectors had lower accidental coincidence rates simply because they had fewer after pulses was incorrect.
Week 7 (March 11, 2008)
During this session, we reviewed our progress to date and discussed ideas for future experiments. The following ideas were suggested:
- The velocity of the particles
- The number of particles
- The direction of the particles
- Energy
- Rate vs. separation distance
- Energy lost vs. direction of particles
New groups were formed and they chose experiments. Lena and I decided to explore the relation between the angle of cosmic ray showers (relative to the ground) and the time difference between two detector's measurements. If a cosmic ray shower comes from directly overhead the two detectors should detect particles at the same time. (Please see the first figure.) A comic ray shower coming from an angle would result in different detection times (in the second figure, #2 would detect an event before #1).
Three detectors were set up as shown in the third figure. The angle θ of Detectors 2 and 3 relative to the ground was measured (45 degrees). Detectors 1 and 2 were at the same height; their horizontal separation (from center to center) d was measured. A T-connector was used to connect Detector 1’s signal to the scope, and then to the coincidence box. The same was done for detector 2. Detector 3 was attached directly to the coincidence box. The coincidence box was programmed to output a pulse when triple coincidences occurred; this output was connected to the EXT trigger scope input. The scope was set to trigger on the EXT signal. Using the ‘SINGLE SEQ’ setting on the scope, the scope would wait for a triple coincidence and keep the image on-screen until the ‘RUN/STOP’ button was pressed.
As expected, there was a horizontal displacement between CH1 and CH2 (i.e., they occurred at different times.) This displacement was measured using the vertical cursor feature of the scope: the beginning of the two pulses were identified, the cursors were placed at these two points and the scope displayed the corresponding time difference δt between the two cursor positions. For each event, the absolute value of δt was recorded, in addition to the relative positions of CH1 and CH2 (i.e., which one was recorded first).
Since our oscilloscope only had two inputs, we could directly observe triple coincidences. To confirm that we were only measuring data from triple coincidences, detector 1 was placed between detector 2 and 3. It was observed that the frequency of events increased.
Week 8 (March 18, 2008)
A four channel oscilloscope was used this week to verify that we were actually triggering on triple coincidences. The oscilloscope was connected via USB cable to the computer, which recorded data from each channel. Since only three detectors (channels) were used, the data from CH4 was discarded.
Five runs were done this session. The setup from the previous week was used. For each run, d and θ were measured. Angles of 45, 90 and 135 degrees were used, the separation was varied from 50.75 to 172 inches. The first four experiments were run until about 20 pulses had been recorded. The last experiment was allowed to run overnight; the system recorded over 1300 pulses.
After the data had been collected, it was analyzed with software by Dima and forwarded to the members of our group. The time difference between detectors 1 and 2 (t1 - t2) from the final run was plotted in a histogram (see figure). Since the angle was 90 degrees, it was expected t1 = t2. It was difficult to draw any general trends from the data for the other runs, as not enough data was collected.
Week 9
We continued our experiment, collecting large sets of data to minimize uncertainties. While the detectors were running, we discussed 
Week 10
It was suggested that large values of (t1-t2) be discarded from our statistical analysis of previous data; doing so would yield lower standard deviations and uncertainties. (Due to computer problems, I have not yet done this analysis.) It should be noted that the uncertainty bars displayed on this plot in
Also, it was suggested that we move detector 1 close to detectors 2 & 3 for our next experiment. If our hypothesis was correct, the value of (t1-t2) should approach a constant 1.57 nanoseconds as the separation is decreased. This constant, used as a correction factor, was implemented in our "(t1-t2) vs. angle" plot.
Week 11
The setup shown to the right was used for 45 and 135 degree angles. As before, only coin(1,2,3) events were recorded. The experiment ran for several days in each configuration. The oscilloscope was connected to the computer via USB cable; this data was analyzed by Dima and sent to us. A 4-fold coincidence should indicate a vertical shower; a 3-fold coincidence should indicate an angled shower.
For the 45 degree setup, 1,529 data points were recorded: 22 were invalid data points, 1,507 were 3-fold coincidences, and 968 of these were 4-fold coincidences (64% of the valid data). For the 135 degree setup, 3,159 data points were recorded: 42 were invalid data points, and 3,117 were 3-fold coincidences, and 1,509 were 4-fold coincidences (48% of the valid data). The average time difference (t1-t2) was calculated for each configuration:
45 degrees, 3-fold coin: +2.97 (+/-) 0.18 ns
45 degrees, 4-fold coin: +2.63 (+/-) 0.21 ns
135 degrees, 3-fold coin: -0.97 (+/-) 0.12 ns
135 degrees, 4-fold coin: +0.92 (+/-) 0.17 ns
While I have not had sufficient time to fully analyze the data, it is curious that the two 135 degree data sets do not agree with each other. Also, the large percentage (48 and 64) of 4-fold coincidences suggests that our initial experiment (that was the subject of our last presentation) was flawed: we were not selecting the desired angles for our measurements.
Week 12
I was unable to upload the Excel file for last week's data (probably because it was too large for the wiki); I uploaded a plot instead (please see figure to the right). This is a plot of the average time difference between detector 1 and detector 2 (t1-t2) in nanoseconds vs. the angle in degrees. The "4-fold" coincidences should have occurred at the same time (corresponding to a time difference of ~1.3 ns). The "3, not 4" fold coincidences should have the maximum time difference (about 6 ns). The "3-fold" coincidences are a mix of "3, not 4" and "4-fold" coincidences -- their average values should be between these two. As you can see, the 135-degree measurements fit this general trend; the 45-degree measurements do not. The experiment was repeated during the Week 12 session, since it was concluded that the 45-degree experiment was somehow compromised.
Due to the nature of our recent experiments (3- or 4-fold shower coincidences), each run required several hours to complete. By running the experiment over the course of several days, we were able to collect several thousand data points. This had the effect of greatly reducing our uncertainties, especially when analyzing smaller subsets of our original data (for example, strictly 3-fold coincidences were relatively few in number).
Additional data analysis was done on the Week 11 data during the Week 12 session. It was speculated that valid data was being omitted from the analysis: only events with pulse heights of 10 mV or high were considered. (Actually, the pulse heights are negative -- originally only pulses with heights less than -10 mV were considered.) The Week 12 data was emailed to us by Dima, who monitored the experiment during the week.
The results of Week 12 are shown on the right. Two cutoff voltages (pulse heights) were used: 0 mV and 5 mV. (Here, "0 mV cutoff" means the smallest pulse considered had an absolute value of 10 mV; "5 mV cutoff" means the smallest pulse considered had an absolute value of 5 mV. This confusing notation arises from the way the scope's pulses were originally analyzed: any pulse that was smaller than 10 mV was given a negative height. Although the sign of the pulse height was negative, the absolute value of the pulse height was correctly extracted from the data analysis program.) Note the different vertical scales on the two plots. By including the "5 mV cutoff" data, we reduced the number of "3, not 4" fold coincidences (and therefore increased the uncertainty of the averages). Note that the 3-fold "5 mV cutoff" time difference is closer to the expected value; this is because the "0 mV cutoff" data included some 4-fold coincidences (which were most likely coming from directly overhead, not at the desired angle.)
Notes on Data Analysis
It is important to be able to efficiently analyze large sets of data. I found Excel's logical conditional formulas to be the most useful when trying to separate our data into subsets (for example, "3-fold", "4-fold", "3, not 4-fold" coincidences or pulse height restrictions). Unfortunately, it took me some time to figure out the optimal way to do this. For future reference, the following Excel formula was used to calculate the time difference (t1-t2) for four-fold coincidences with pulses with an absolute height H or greater:
The above function will compute the time difference (t1-t2) in nanoseconds if the event was a four fold coincidence (with appropriate pulse heights); it will return a blank cell otherwise.
Notes:
- h1, h2, h3 and h4 are the cells corresponding to the heights of the four detector pulses;
- H is the cutoff height in Volts;
- t1 and t2 are the times corresponding to the first two detectors;
- the 1000000000 factor converts the time difference from seconds to nanoseconds;
- The AND(logical1, logical2, ... ) will return a value of TRUE if "logical1, logical 2, ..." are all TRUE; otherwise it will return a FALSE value;
- The IF(logical_test, value_if_true, value_if_false) will return "value_if_true" (in this case, the time difference) if the "logical_test" is TRUE; it will return "value_if_false" (a blank cell in this case) if the "logical_test" is FALSE;
- To look at "3, not 4-fold" coincidences, change "ABS(h4)>H" to "NOT(ABS(h4)>H)".
Week 13
The final experiment performed in this class is shown to the right. Two runs were done: triggering on two-fold coincidences(run 1) and triggering on three-fold coincidences (run 2). The most probable events for both runs are illustrated to the right. Run 1 collected approximately 446 data points; run 2 collected 68 data points. Only the pulse height from detector 1 was considered when analyzing the data. The results are shown to the right. The average pulse height on the top detector was 37.87 (+\-) 1.8 mV for 2-fold coincidences; for 3-fold coincidences, the average was 72 (+\-) 8.8 mV. More data is needed for a better distribution.
Week 14
Final presentations were made this week. I have uploaded the slides from my presentation and my notes.
