Table of contentsSummaryIntroductionMethodExpected resultsSeasonal temperature and differences in summer and winterCorrelation in muon detection in summer and winterReducing uncertainty in muon detectionConclusionSummaryThe aim of the experiment is to determine the relationship between the number of muon detections for a given period in summer and winter and how temperature and pressure affect the muon shower. The project provides evidence that winter has a higher average number of muon detections of 47 ± 2.95 per hour than summer. The result also shows that summer has an average temperature 13.37° higher than winter, while the average pressure remains relatively the same (1014 hPa). A single station was chosen to reduce the effect of altitude since muon production differs with height {3} I developed a linear model that assigns the number of events per hour using temperature and pressure exterior at an altitude of 56.18 m above sea level. I found a strong negative correlation (r = -0.80) between the number of muons detected per hour and the outside temperature, while a weak negative correlation (r = -0.13) between the number of muons detected and the outside temperature. The number of events can be calculated using (-3.906 ± 0133) T + (-12.068 ± 0.095) P + (4616.6 ± 151.665) assuming that pressure and temperature are only one factor. I found that the most likely number of muon detections is around 2,273 to 2,301 per hour. The project answers the question regarding the correlation between the number of muons detected in summer and winter and (pressure and temperature), but additional studies are needed to determine the average energy of muons in summer and winter. Say no to plagiarism. Get a tailor-made essay on “Why Violent Video Games Should Not Be Banned”? Get the original essay The hypothesis was that there was no statistically significant relationship between (summer and winter) and the number of events. There is also no statistically significant relationship between (pressure and temperature) and the number of events. The number of muon detections is random and occurs at a constant rate regardless of temperature and pressure. {1}IntroductionCosmic radiation comes from our sun and other stars, but high-energy cosmic radiation (10^15eV) is created during the explosion of super novae and the shedding of black holes. The lower spectrum of cosmic radiation (Φ = aE −b [1] Where Φ is the muon flux density, E is the muon energy and a & b is constant. The HiSPARC project started in the Netherlands in 2002 where all detectors are connected to the main server of the Nikhef scientific institute via the Internet and forming a larger network. The aim of the HiSPARC project was to provide interested young students with the opportunity to participate in scientific research on ultra-cosmic rays. high energy. the roofs of the university and high school buildings. These ultra-high cosmic rays have a shower area of ​​1 km, which is the average distance between two high schools. The number of muon detections in each nearby detector can. be used to approximate the location of the cosmic radiation source. {11} The result calculated throughout the project is based only on the 501 Nikhef station The Nikhef station is located in the Netherlands, in Amsterdam. latitude of 52.36° and a latitude of 4.95098°. The detector is placed at 56.18 m above sea level and the threshold frequency. is configured between 81ADC and 150ADC. {4}MethodThe data is downloaded from the HiSPARC 501 Nikhef station. Downloaded data is saved every timethat a muon is detected with a time reference, external temperature, external pressure and other data. It is possible for the student to perform data analysis using Excel, but Excel is not designed for large data sets, as is Python. The data is encoded using Python where it saves the file to Excel with the time, the number of events during that given hour, the average temperature during that given hour, and the average pressure during that this time given in each column. The Python code and flowchart are provided in the appendix. The data is analyzed using Excel functionalities. Expected results Where Io, To, Po and Ho are the average intensity, temperature, pressure and production rate and the others represent a constant. The first term represents the atmospheric mass above the detector and the following terms show the dependence of pressure, temperature and surviving muon at a given altitude. Using only 501 Nikhef stations reduces the dependence on altitude and counting since it is always constant and can be ignored when calculating the dependence of pressure, temperatures and number of events. {5}The atmosphere is not isothermal, so there is a variation in temperature and pressure depending on the altitude and the environment.{6} The outside temperature is measured using a temperature sensor placed outside the detector and measured with an accuracy of ± 0.5°. The external pressure is calculated using a barometric formula with an accuracy of ± 1hPa.P=Po×e^(-(gMh)/(R.To)) [3] Where P is the pressure at a certain altitude Po is the pressure at the reference point, g is the gravitational field intensity, M is the molar mass of air, R is the gas constant of air and To is the outside temperature {7} The number of muons is inversely proportional to atmospheric temperature. Increasing temperature causes the atmosphere to expand and increases the likelihood that primary radiation will interact at a higher altitude. This causes the muon to travel a longer distance, increasing the chance of decay before reaching the detector. {6} On the other hand, the expansion of the atmosphere causes the number of particles in a given unit volume to decrease (pressure decreases), thereby reducing the likelihood that cosmic radiation will interact with atmospheric molecules. Decreasing the pressure increases the number of muons. Seasonal temperature and differences between summer and winter. According to the average temperature and pressure calculated in winter and summer, this shows that summer had a temperature 13.37° higher than winter while the pressure was relatively the same (1014 hPa). which is explained by equation 3. This suggests that winter should have a greater average number of events detected for a given period. Data is collected for summer (June, July and August) and winter (December, January and February) over a three-year period. From December 2016 to August 2018. The line graph (N_frequency) represents the expected value of frequency for a given bin and it is calculated using the Excel function “Normal Random Number Generator” with observed mean and standard deviation. From the data, winter has a mean of 2342.846 ± 2.981 and a standard deviation of 190.623 and summer has a mean of 2300.031 ± 1.852 and a standard deviation of 118.353. As expected, it shows that winter has the greatest number of muon events for a given period, but the result excludes muon shower energy, so there is a lack of evidence to determine whether summer or l Winter has a higher average muon energy. The number of muons detected per given time period is Gaussian. Thatcan be interpreted by calculating the mean, median and mode. The closer the values ​​are, the better the Gaussian fit. The uncertainty in the three-year Gaussian average shows a correlation of 2298.05 ± 0.1 in muon detection in summer and winter. Data is collected for summer (June, July and August) and winter (December, January and February) over three years, from December 2016 to August 2018. For the data provided, the p-value is less than 0, 05, so there is 95% confidence that the slope is not zero, so the data can reject the null hypothesis and shows that there is a relationship between counts and temperature. The p-values ​​for intercepts and pressure are zero, so there is no effect. The standard error for counts, pressure, and temperature are 1.769, 0.119, and 0.085, respectively. I found a strong negative correlation (r = -0.80) between the number of muons detected per hour and the outside temperature, while a weak negative correlation (r = -0.13) between the number of muons detected and the outside temperature. As the linear residual plot for (numbers and temperature) and (numbers and pressure) forms, the data shows a linear fit. Assuming that there is a perfectly linear fit between (temperature + pressure) and that the number of events and other factors are ignored, the number of events can be calculated using equation 4. D 'after the data, the number of events has an average of 2321.48 ± 1.77 and a standard norm. difference of 160.16. counts=(-3.906±0133)T +(-12.068±0.095)P +(4616.6±151.665) [4]The light intensity reached by the earth's atmosphere is relatively the same but the radiation emitted by the sun differs . Several factors affect muon detection, such as detector position relative to the sun (angle), atmospheric pressure {5}, distance between sun and detector, atmospheric temperature, magnetic activity on the sun's surface and solar energy. flares. {10}The HISPARC scintillator contains a small amount of organic scintillator that uses muon energy to generate visible light. The visible light created by the scintillating plate is collected by the photomultiplier where the light energy is converted into an electron through the photoelectric effect process. This electron is accelerated by an electric field and amplified by dynodes. {10} ,{1} This allows current to be detected and the intensity of the current over time can be used to measure the number of muons detected and the energy of the pulse. The current fluctuation depends on the energy and trajectory of the electron as well as the material of the diode. {1} The work function of the metal differed depending on its material, so the rate at which the electron is ejected (current) depends on the material of the photocathode and diode. Where h is Planck's constant, m is the mass of the electron, v is the speed of the electron, Φ is the work function of the material, f is the frequency of incident light, I is the current, Δe /Δt is the number of electrons per given period of time. {8} The shower front is not flat because it has some thickness, so it is unknown whether the detected cosmic ray particle front is close or late, so it has a percentage uncertainty in the measurement time. Reducing the uncertainty in muon detection We can reduce the uncertainty in muon detection by setting the threshold at such a level, it does not miss real events and does not take into account lower spectrum energy radiation , well below the muon energy. Station 501 Nikhef was set between 81ADC and 150ADC. There is random error in detecting other charged particles and radiation created from the Earth's surface that are not.. 68-83.