-- JorgeRodriguez - 2013-10-29

Lab Assignment: Cosmic Ray Lab

In this lab, the primary goal is to measure the cosmic ray flux as a function of the zenith angle and determine its shape by fitting your data with a function that represents theoretical expectations. There is also a computing component in which you will use the Monte Carlo methods developed earlier to generate a sample of data simulating the data taken by the cosmic ray telescope under the circumstances you will follow to conduct the experiment. The lab is separated again into 3 parts, at first simulating the data on a computer before you embark on the actual experiment.

Part A: Generate a sample of simulated Cosmic Ray data

Here you are referred to the Particle Data Group's section on cosmic rays (Links to an external site.), which describes that the cosmic ray flux at the earth's surface is approximately determined to be distributed as ~ cos2(q). Here the angle is the azimuthal angle, where 0 is in the verticle direction and the functional form complies with the expectation that rays incident vertically are more probably than horizontally. There are a variety of effects contributing to this form, which you are encouraged to report on from your research, see PDG above. Here we will not attempt to simulate this distribution from first principles, although that could be done instead, you will take the shape as a given and create that on the computer, later confirming in real data.

In principle one could attempt to generate deviates drawn from a cos2 distribution as we did previously using conservation of probabilities and then solving for the angle in the argument but unfortunately integrating the cos2 function leads to a transcendental polynomial function which is somewhat difficult to deal with. Instead, we will employ a short cut given that we will be analyzing the data in terms of bins of azimuthal angles. We can thus use a Monte Carlo Poisson smearing on a bin by bin basis to create a simulated sample of data we can easily create on a computer. Here is how:

1. First decide on a number of bins from or -pi/2 to + pi/2 corresponding to the range of position one can orient the CRT in. The center of these bins will be your azimuth angle q.
2. Now create a "perfect" number of counts for each of the azimuth angle bins defined above using a formula such a here N represents the total number of cosmic ray events in a given interval of time so is unitless. The parameters A and B scale the function and capture the length of time over which the experiment is conducted, collection efficiencies, and allow for small but expected backgrounds. Remember you are collecting events if and only if both scintillators fire within a nanosecond or so so the likelihood of significant backgrounds are small.
3. Now you will smear the "perfect" data count rate above by a Poisson. Remember histogram bins are Poisson so the mean is the count N while the uncertainty is the N. These smeared counts will be the sample of simulated data you will use to compare to real data collected with the CRT.

Setup and calibration

Before you begin your flux measurements you should become familiar with the experimental apparatus know here as the Cosmic Ray Telescope (CRT). To do this we'll first perform a calibration of the phototubes by determining at what high voltage gives a reliable number of counts, with minimal fluctuations vs. voltage.

Here how to do this

First: Connect the HV supply to the PMTs and use the oscilloscope to find the output signal from the PMT. You will likely need to adjust the time scale or sweep (horizontal axis) and the voltage scale (vertical axis) on the scope. We expect output signals from the PMT to be 10-20 ns long and the output voltage to be a few millivolts for the Cosmic Ray telescope setup. You will also need to set up the scope on a self trigger mode or trigger on the PMT output. Note that the output will only trigger the scope if it exceeds a set discriminator (disc) threshold (this level is controlled by the "level" knob located on the trigger portion of the scope). Adjust the level knob to some fraction of the PMT's average output voltage. Since our PMT output voltage is negative you'll want to set the threshold below 0 V to display any events.

Once you have your scope displaying multiple PMT pulses and have ascertained a reasonable value for your discriminator threshold you can take the PMT output and redirect it to the discriminator NIM module. As with the disc threshold on the scope, the disc threshold on the NIM Module is used to filter out noise pulses. You can adjust the disc threshold on the NIM module by turning the tiny set screw hidden inside the whole labeled "THR". The threshold voltage can be read with a multimeter with leads connected to the ground and the disc reading pad.

Before you proceed with the experiments, PART B and C below lets first determine the proper input voltage to tune the PMTs for optimal performance, at the chosen disc threshold settings that you selected earlier. We do this to ensure that the PMT pulses and thus count rates are stable across a sizable range of input voltages. We will "calibrate: or AKA "plateau the PMT" by simply monitoring the count rate as a function of the input voltage. Make a plot of the input voltage on the PMT verse count rate using the counter NIM module and the radioactive source placed a few centimeters away from the scintillator. The proper input voltage will be somewhere on the "plateau" of that input voltage vs. counts you just made for the PMT.

Begin by setting up the cosmic telescope by connecting the PMT output to the NIM discriminator then connect the disc output to the counter. Set the counter time window to collect a few 100 events. Make sure that you are counting real signals by ensuring that the disc is set sufficiently high, check with the scope. Take count reading at various PMT input voltage and plot the results. Please DO NOT go beyond 2000 VOLTS. What you should see is that the count rates vary a lot when the voltage is set too high or too low. You should use a random source of events, such as the Sr 90 source in the toolbox to ensure you have real triggers instead of noise. DO this for BOTH PMTs and include both plots in your lab report in the procedure section.

Part B: Observation of Poisson and Gaussian distributions from Sr 90.

You will only need to use one of the scintillator/PMTs for this part of the experiment. Decide on how to best setup your cosmic telescope viz. discr setting and HV input from the calibration setup above.

Using a random source, that 90 Sr is as good a random source as any. Take 100 measurements with the count time interval set to collect on average 1 event per time interval. Histogram the results. Your histogram will have on the horizontal axis the number of counts per interval and on the vertical axis the number of times you record a particular number of counts. How is the data distributed? Then repeat the exercise twice setting the equipment up to now collect 10 events and repeat with 100 events per time interval. You can adjust any of the experimental conditions you control to achieve these measurements. You can change the distance between the source and the scintillator or adjust the discriminator level. Whatever you do make sure you retain the randomness of the events by ensuring you are not picking up PMT or other sources of noise. There is no need to fit the distributions in this part of the lab but please do feel free to comment on what you observe and compare it with the corresponding exercise in the Monte Carlo Lab where you essentially did the same thing on a computer, although with a significantly larger set of data.

Part C: Cosmic Ray Flux

Using both PMTs, both of which you should have already plateaued and are running in the optimal configuration for your experiment, perform the flux vs. angle measurement. Here you'll need to use the coincide NIM module inline between the discriminator outputs and the counter. The coincidence counter will trigger and output a NIM pulse when it detects two NIM pulses. This particular coincidence counter uses the size of the input pulse to select the size of the window used to determine whether a coincidence condition has been met. You can check the manual for the device if you are interested in details, something you'll have to find online. As you take data plot the distribution. In the SLAC paper, linked below you'll see an estimate of the count rate. Make sure your count rate is consistent with your expectation. You can take data for as long as you like but given the constraints, on class time I recommend taking data in 20-minute blocks per azimuthal angle. Also, plot the data as you take it. You do not want to take 10 measurements, each 20 minutes long, and then find that something is wrong with your data. In your report, your primary result is the histogram of counts vs. angle and the fit of your data to the expected distribution. In this lab finding that your data is consistent with the expected experimentally determined function is sufficient. We do not need to try to find or establish why it is distributed as a cos2. For that, we would need a lot more time and much more elaborate equipment. There is a nice write up on this part that you can access as a reference. See document from SLAC linked below.

Comments on the CRT apparatus:

Our Cosmic Ray Telescope consists of a piece of plastic (organic) scintillator made out of material that when exposed to charged particles reacts by emitting light. The light travels through the transparent plastic material, reflecting from surfaces until eventually some of the photons emerge at the front face of the PMT. The PMT is an electronic device based on the photoelectric effect that first converts a small number of photons, into an amplified electrical signal sufficiently large to be easily recorded by standard laboratory equipment. You should provide in your write-up a short description, longer than this, of how this works. You should also include a paragraph or two about cosmic rays, what are they where do they come from and what does our detector actually "sees".

The list of necessary equipment is:

• Scintillation counters each with its own PMT (Cosmic Ray Telescope: Note for this experiment you will need to use both counters)
• High Voltage Supply (to power the PMT)
• NIM module Discriminator (to decide whether the signal is a true PMT pulse and not noise)
• NIM module Linear Fan In Fan-Out (this allows you to duplicate RF signals from the PMT and NIM modules
• NIM module Counter/timer (to count the number of NIM output signals)
• NIM module Quad Coincide (produces a NIM output when two signal arrive within an interval of time determined by module's internal logic)
• Oscilloscope (Links to an external site.) (to examine the output of the PMT and help set discriminator levels etc.)
• 90Sr radioactive source

Turning in your lab report

Because of the nature of this lab please provide an expanded introduction that includes the following elements. A few paragraphs, on the physics of cosmic rays, what are they where do they come from, etc. You can include some history if you wish but focus a little on the particle physics aspect, including the fact that what we see at sea level are mostly muons. What are these, briefly. In your introduction, you should also describe the operation of the various parts of the CRT. For example:

1. The Scintillator: Look up references on how organic or plastic scintillators work. The scintillator you are using is a Bicron BC 400 series plastic scintillator
2. The Photomultiplier: Describe how a PMT works. You should provide as much detail as you need to demonstrate that you understand how this device functions and why it is used.
3. The High Voltage supply, Just noting that one is used is sufficient.
4. The data acquisition equipment: The various NIM modules you used in your experiment. You should be familiar with the operation of each and report on their use and function in your write up.

Upload your lab report (article) to the Turnitin via the gray box under the "This tool needs to be loaded in a new browser window" line below. It will be graded along the rubric described in this page Grading Rubric. Read through the rubric carefully to maximize your score. If you have any questions please ask. Remember lab reports are usually due on Friday evening after you complete the experiment in class. If you have questions please ask.

Turning in your coding project

Please upload your code to the assignment Monte Carlo Project under the Python Coding Project group. Along with a grade for your report you will be graded separately on the coding sample you provide via upload. Here are important steps you should take to earn a good grade.

1. Make sure each "Part" is in its own file. You can label your program as you wish as long as I can identify it when I run it.
2. Make sure your program(s) run in the spyder IDE.
3. Make sure your program is well commented as I will need to figure out what you did in order to evaluate the programming.

This tool needs to be loaded in a new browser window

GradingRubric

• slac-tn-95-001.pdf: SLAC Cosmic Ray Telescope paper