Time of Flight of Cosmic Ray Muons

Time of Flight of Cosmic Ray Muons

Sean Lynch and Jingqiao Wang

Abstract

The experiment's aim is to measure the time of flight (velocity) of cosmic ray muons using scintillator panels connected to photomultiplier tubes. This was done by measuring the time in between pulses from the scintillator panels at different heights. Due to the energy losses that muons experience when traveling through a medium, a spread of time measured will appear. By taking the mean time measured at each height, and applying a linear fit to the data, the speed can be calculated from the slope of the line. The measured speed is 0.89c ± 0.01c, which falls within the momentum spectrum of cosmic ray muons.

Introduction

Cosmic ray muons are subatomic particles that are byproducts of collisions between cosmic rays and the Earth’s atmosphere. These atmospheric collisions create a constant shower of muons and other particles, peons, kaons, high energy photons, on the surface of the Earth. The muons velocity on Earth can be found by measuring the time required for the muons to travel a known distance. The velocity of these muons is (0.993 ± 0.002)c [1] and our experiment sets out to confirm that. This will be achieved using scintillator panels connected to photomultiplier tubes. Timing for the experiment will be measured using a time to amplitude converter connected to a multichannel analyzer, which will be fed into a computer for analysis.

Figure 1. Diagram of cosmic ray interactions and their byproducts. Cosmic ray muons are secondary products, represented by μ- in the diagram.

Theory

The experiment is essentially measuring the time it takes for the muon to travel a known distance. Since the times measured will be very short, on the order of nanoseconds, the timing circuit used was a time-to-amplitude converted, which takes the measured time and converts it to a voltage. That voltage data is sent to a multichannel analyzer, which logs the measured voltages on a histogram for analysis. The histogram will then be analyzed using the program MAESTRO on a computer.

The muon is a charged particle, and thus will experience an electrostatic force when passing through an electrostatic field, such as near charged atoms in materials. This electrostatic force causes the muon to loose energy, and thus speed, depending on the initial speed of the muon and the material properties that the muon is passing through. This, along with the range of initial speeds that muons can have, leads to a spread of velocities that will be measured.

This experimental application can be developed into muon tomography applications, which uses cosmic ray muons to image internal structures non-invasively. Muon tomography has wide applications in archeology and geology, which is used to detect open pockets in structures or underground [2]. Muon tomography can also be used to detect fissile material such as uranium and plutonium, as well as the lack of fissile material, such as in nuclear reactors that have undergone meltdowns to determine cleanup plans [3].

Experimental Setup

Our setup used five scintillators connected to five photomultiplier tubes (PMTs) powered by high voltage DC for muon detection. The data acquisition hardware included two quad discriminators (one LeCroy Model 821 and one LRS 621 BLP), one dual coincidence units (CAEN Model N455 Quad Coincidence Logic Unit), a time-to-amplitude converter (ORTEC Model 556 TAC), a Tennelec TC 412A delay box, and a multi-channel analyzer (ORTEC “EASY-MCA” 2k Multichannel Analyzer). This was all housed in and powered by an EG&G ORTEC Model M250/N NIMBIN.

For the experiment, the scintillators and PMTs were assembled together into a single unit referred to as panels. The five panels were arranged on a ladder with two pairs of panels at the top, Panels A and B, and the bottom, Panels D and E, with the middle Panel C position being adjusted to determine the measured distance Y. All the panels outputs are fed to a discriminator unit each output pule being 20ns. The top and bottom pairs of panels signals are then inputted to a coincidence unit, where the four panels are connected together in an AND gate. That gate output is then sent to the "start" trigger on the TAC. The signal for Panel C is sent to the delay box, where it is delayed by 60ns, which is then sent to the "stop" trigger on the TAC. The output for the TAC is sent to the MCA which is then fed into the computer, where the data is read using MAESTRO. A wiring diagram of the experimental assembly is shown below

Figure 3. A picture of the experimental setup and a wiring diagram of the final experimental setup.

The heights for Panel C were determined by the ladder rung spacing, in addition to two positions where Panel C was placed as close as possible to the top and bottom pairs of panels. This gives a total of 7 positions for heights. At each height, the experiment was run to collect data over a period of 48 hours.

Data Analysis

Since Maestro plots the data on a histogram, a conversion from histogram bin to delay time needed to be calculated. This was done by using a square wave pulse generator, with the pulse signal being split using a BNC tee, with one with one output going through a discriminator and into the START input on the TAC and the other output going through another discriminator, through the delay box, and into the STOP input on the TAC. The delay was adjusted on the delay box. Plotting out the data and applying a linear fit to the data, the conversion factor from Bins to time in ns is 5.0462 ± 0.0126 bins for every change of 1ns.

For each height data, the histogram data was "smoothed" where the counts across 5 bins were summed together into 1 bin. This was done to better aid the fitting algorithm applying the gaussian fit, since it is difficult to discern the central peak from the raw data. A gaussian fit is then applied to the smoothed data using fit() command in MATLAB with the 'gauss1' fit type used. The "mean" parameter of the gaussian fits were used in the final calculation of the measured speed.

Figures of the raw data, the smoothed data, and the data with a Gaussian fit applied are shown below.

Figure 3. Figures of each step in the data analysis are shown. The first plot is the raw histogram data, the second plot is the smoothed histogram data, and the third plot is the smoothed data with a gaussian fit applied to it.

Since the data is now using the smoothed histogram bins, the bin-to-time conversion factor is divided by 5. This gives a new conversion factor of 1.0092 ± 0.0025 Bins/ns. For the distance measured for each height, the distance between the bottom edges of Panels C and E was used.

Results

Figure 4. Linear fit fir Distance Traveled vs Time Taken. The reduced Chi-squared is calculated is calculated to be 2.28, which indicates that the linear fit is acceptable. The blue points with error bar are our peak values in each height, and the orange line is the linear fit of it.

The error bar for each data point is from the mean calculating of the gaussian fit by Curve fitting tool. It gives a function that Bin=-0.0375*Distance+34.3366. To convert it into the speed of muon, the following equation is needed:

Inverting the slope gives a value of 26.64 ±0.58 cm/Bins. Multiplying this value by the smoothed conversion value of 1.0092 ± 0.0025 Bins/ns gives the final measured speed of cosmic ray muons as 26.89 ± 0.59 cm/ns, or 0.89c ± 0.01. According to the literature, the average speed of cosmic ray muons is (0.993 ± 0.002)c [1], which is not quite agree with our result. This may cause by systematic delay within the the equipment used in the experiment. The accuracy of the delay box was not known and was not tested and can affect our bin-to-conversion factor and thus can affect the calculated speed. So, it is necessary to test all equipment to see if they work properly. Although we cannot say that how we test the equipment is very accurate, it is still helpful to reduce the uncertainties. Also, the lab room is underground, where the muons will lose energy when they pass through every floor. In this case, those muons with lower initial energy will stop before they hit the panel. Thus, it is predictable that the average speed of muon is not quite agree with our result.

However, since this is only the average speed of muons, which means not all muons were in this speed. It is normal to see muons with higher and lower speed occur. We can use Lorenz factor formula to confirm our result.

When the Lorenz factor is equal or larger than 2, a muon should have 0.866c or above at its initial. This indicates that our result is still reasonable.

To double check the result, we also calculated the momentum of the muon to be 0.214GeV.

Figure 5. This figure includes measurements of muons at different momentums at two locations in North America. Our result is on the left of both axis, on the lower edge of the momentum spectrum. [4]

The diagram confirms that muons with momentum between 0.2-0.3GeV were being measured and confirmed existence in the past, where our calculated value of muon momentum is 0.214GeV. This indicates that our measurement of muon is in the spectrum, and it is reasonable get a value of 0.89c for the speed of muons.

Conclusion

By using five scintillator panels, we measured the time of flight of cosmic ray muon and calculated its speed to be 0.89c ± 0.01. However, our result of speed did not show a good agreement with article. To confirm our result is reasonable, we found an article which shows muons with similar monument as what we have were measured and confirmed existence in the past. In this case, our measurement of speed of muon is acceptable and reasonable. For some further improvements that may increase the accuracy of the measurement, it will be helpful to move the equipment to upper floors or to the roof. Since muons will lose energy when they go through the building, it would be harder for us to capture muons especially in lower speed within the same amount of time compare to outside. Many muons just stop before they hit the panels. It will be better to move the equipment upward since there are less obstacles that muons need to pass through. In this case, a histogram with wider range of muons can be detected, which can increase the accuracy of the result.

References

[1] G. Remmen and E. McCreary, "Measurement of the Speed and Energy Distribution of Cosmic Ray Muons," Journal of Undergraduate Research in Physics, 2012.

[2] CERN. Muon Tomography. https://cms.cern/content/muon-tomography.

[3] Tokyo Electric Power Company. Reactor imaging technology for fuel debris detection by cosmic ray muon. March 2015, https://www.tepco.co.jp/en/nu/fukushima-np/handouts/2015/images/handouts_150319_01-e.pdf. PowerPoint Presentation

[4] Kremer et al. (1999) Measurements of Ground-Level Muons at Two Geomagnetic Locations. Physical review letters, Vol.83 (21), p.4241-4244.