S16_CherenkovRadiation

Measuring Cosmic Ray Muon Momentum Distribution from Cherenkov Radiation

Bilal Ahmad and Michael Whitney

Abstract:

We use a carbon dioxide ­based Cherenkov radiation detector to measure the integral flux of vertical cosmic ray muons in the momentum range of 1.4 GeV/c to 3.6 GeV/c. Sources for a possible over-detection of muons at these threshold momenta are investigated. The momentum distribution is fitted to a power law with a parameter value of α = − (1.02 ± 0.04)c/GeV .

Introduction:

The measurement of muon momentum flux is beneficial because muons are constituents and byproducts in the search for many new particles [1][2], which makes it integral to develop an accurate system that can detect these muons.

The main goal of this experiment is to measure the shape of the cosmic ray muon momentum distribution for threshold momenta between 1.4GeV/c and 3.6Gev/c by using a gaseous carbon dioxide-based Cherenkov detector. The number of muons detected at a threshold momentum should correspond to a power law [3]:

. (1)

Theory:

Cherenkov radiation is produced when a charged particle travels faster than the speed of light in the medium through which it passes. The emitted radiation is emitted at an angle, ɸ, and can be determined by the equation

(2)

where n is the index of refraction and β=v/c. This geometry is shown in Figure 1.

Figure 1: The red arrow represents the trajectory of the muon while the blue arrows represent the trajectory of the Cherenkov photons. t represents time, and β represents the ratio of the particle's speed to the speed of light in a vacuum. Image retrieved from Wikimedia Commons [4].

For Cherenkov radiation to be produced, a threshold velocity, β > 1/n, is needed; otherwise, Cherenkov radiation will not be emitted. When a particle is traveling at this velocity, it will be emitted at an angle of ɸ=0 degrees. This threshold velocity corresponds to a threshold momentum of the particle:

(3)

This equation is a function of the index of refraction only, which can be approximated by the Lorentz-Lorenz formula [5]:

(4)

where R is the universal gas constant, T is the absolute temperature, A is the molar refractivity of the medium and P is the pressure. Substituting eq. 4 into eq. 3 yields the result:

(5)

Experimental Setup:

The layout of the experiment is shown in Figure 3. The main component of the experiment is a stainless steel tube with a radius of 4.58cm and a length of 140cm that is placed in a vertical position and contains pressurized carbon dioxide gas of which can be adjusted with a pressure regulator. On the bottom of the main component is a T-junction structure; the one side of which has a pressure release valve, while the other side has a series of mirrors that reflect the Cherenkov radiation towards a short wavelength sensitive photomultiplier tube (PMT). Above and below the main component are crossed pairs of scintillators with corresponding PMTs. The scintillators give off pulses of light that can be detected by the attached PMT when an ionizing particle passes through them.

Figure 2: When the scintillators at the top and bottom of the apparatus detect events within a 100 ns frame of each other, a coincidence unit will trigger the oscilloscope to record the signal that was produced from the short wavelength-sensitive PMT. This data is then analyzed by a computer program that filters out non-muon events. Original image.

Data Collection Process:

When an event triggers all four scintillators in a time scale of 100 ns, a coincidence unit will send a signal to the computer to record the output of the Cherenkov PMT. If the peak of this pulse is more negative than a preset value of -0.005V, which is a value that is greater in magnitude than that of the noise threshold, then the waveform starting 15 ns before the peak through 85 ns after the peak will be recorded. The integral of the pulse and the relative time interval between it and the trigger are evaluated and should both undergo Gaussian distributions. Any pulse which is found to not be within the expected values of the Gaussian distribution can then be determined to be a non-muonic event.

Results:

A Python script is used to determine to relative time interval between a pulse and the coincidence trigger for each pulse. The script also determines the area under each pulse ( in mV*ns). Figure 3 shows the time intervals following a Gaussian distribution. Pulses with time intervals or pulse integrals outside three standard deviations of their means are considered non-muonic events.

Figure 3: The time interval frequency is graphed for each pulse. As seen in the figure, the frequencies follow a Gaussian distribution between approximately 45 and 70 ns. Original figure.

Using the Python script to filter our non-muonic events, a muon rate is determined at different threshold momentums. Figure 4 shows the muon flux at different threshold momentums.

Figure 4: The plots the vertical muon flux against the threshold momentum. For the muons flux units, the cm^2 component corresponds to the cross sectional area of the steel tube in the apparatus and the sr (steradian) component is the solid angle of the steel tube. The dotted curve is the expected result from Rastin’s experiment [2]: y=e^[(-.33±.03)x-4.600±05] and the solid curve is the observed result: y=e^[(-1.02±.04)x-1.47±.04]. For each equation, the coefficient of the first term in the exponent corresponds to the alpha value from Eq. 1.

Table 1 summarizes the results:

Table 1: Final Results

As evident from Table 1, the observed results of the experiment did not match the expected results. One possible source of error is the small data sample. At each pressure, data was taken for approximately three hours. Ideally more data would have been taken but the LabView program was plagued by a timeout error. As a result, data taking involved sitting in the lab room at hours on end continually restarting the program whenever it timed out. This limited the amount of data taken which makes the results more prone to anomalies. Another possible error is the lack of normalizing the muon counts. This experiment was conducted under the assumption that the total amount of muons produced by the muon source (cosmic rays), would stay at a consistent rate throughout the experiment.

References

1. "Mu2e: Muon to Electron Conversion Experiment." Fermilab. U.S. Department of Energy, Feb. 2015. Web. 06 Apr. 2016.

2. Taylor, Lucas. "Muon Detectors." Compact Muon Solenoid Experiment at CERN's LHC. European Organization for Nuclear Research, 23 Nov. 2011. Web. 06 Apr. 2016.

3. Rastin, B.C. "An Accurate Measurement of the Sea­level Muon Spectrum within the Range 4 to 3000 GeV/c." Journal of Physics G: Nuclear Physics 10 (1984): 1609­-1628

4. Cherenkov. Digital image. Wikimedia Commons. N.p., 16 Mar. 2006. Web. 24 Feb. 2016.

5. Daintith, John. "Lorentz­Lorenz Equation." A Dictionary of Chemistry. 6th ed. New York: Market House, 2008. Oxford Reference. Oxford University, 2008. Web. 6 Apr. 2016.