James A. Petrait




      Primary cosmic rays striking the upper atmosphere of the earth produce a cascade of secondary particles. Many of the secondary particles are muons. A muon is about 206 times heavier than an electron and it has a lifetime of about 2 microseconds. In traveling the distance from the higher parts of the atmosphere, muons arrive at the surface of the earth and below after their lifetimes have expired. But because the muons are traveling near the speed of light, a time dilation effect allows them to complete their journey.

     Magnetic fields affect the arrival directions of the primary cosmic rays which in turn affect the arrival directions of muons which are also spread out from the creation of the particle cascade. The constant arrival of muons on the surface of the earth results in a muon flux which varies with the coordinates of the arrival location. This is a result of the magnetic fields and the muon flux variation and has been calculated by J. F. Ziegler (see resources) for various locations on the earth using New York as a base reference value of one. The Ziegler article was written as study of how cosmic radiation affects the failure rate of computer chips at different locations.

     Geiger counters detect the muon flux which is around 5% to 10% of the total background radiation which is picked up. This is not an accurate way to find the muon flux rate and its variations. A better way is to place two geiger counters together and connect them with a coincidence counter (c-box). Only those muon particles that go through both geiger counters at the same time interval are counted with the help of the c-box.

     During the past year, I have consulted many websites and several books on the subject and I have found much theory and calculations but little on the actual study of the muon count variations on the surface of the earth. There seems to be many sophisticated experiments on measuring the various components of cosmic radiation but little on actually measuring and monitoring the muons reaching the surface of the earth at various locations and times. Despite the magnetic fields which change their directions, I think that it is worthwhile to study the variations in the peaks of the muon flux on the surface of the earth with the location and local and sidereal time.

     The sources of cosmic radiation which could affect the muon flux variation are the sun, our galaxy, and the rest of the universe. Variations in the radiation from the sun could affect the muon flux variation after large solar flares which tend to suppress the cosmic radiation reaching the earth while they are active. I think that a better candidate would be the cosmic radiation reaching the earth from the center of our galaxy. The galactic center has a strong radio source (Sagittarius A at around RA 17 deg. 45 min and DEC -28 deg. 48 min.).

     I am interested in finding changes in the muon flux which can be related to solar activity, activity from the center of our galaxy, and unusual events that may occur anywhere in the universe. This project is concerned with gathering background data on the feasibility of measuring muon flux variations related to the above events. This project is also intended to be educational and perhaps will facilitate a number of investigators sharing their data online to be able to develop an accurate model for explaining the variations of the muon flux on the surface of the earth.

     Accuracy and expense are 2 important aspects of this project. The setup that I am using makes use of the following items (shown in the top photo without the computer): 1) A PC computer with a free serial port input, 2) Two RM-60 geiger counters and software from Aware Electronics (see Resources), 3) Coincidence box (c-box) from Aware Electronics, 4) Several elastic bands, 5) Compass, 6) Level, 7) Protractor, and 8) Pile of index cards or other device for changing the angle of the array. The Photo section will show how these items are used. The computer hookup directions are available from Aware Electronics. Optional items could include a GPS device to indicate the exact location and a barometer. It is possible that the muon count rate could be affected by the density of the air which is related to barometric readings but it is possibly a very small variation.

     The RM-60 geiger counters have geiger tubes which have a higher pickup rate from the sides. The geiger counter is housed in a plastic box (see Photos). The 2 geiger counters are placed on top of each other with the sides of the geiger tubes parallel to each other. They are secured with 3 elastic bands. The geiger counters and c-box and computer port connector all make use of standard phone plugs and jacks. The 2 geiger counters are connected to the c-box with phone line cords and the c-box is connected to the computer serial port with another phone line cord (refer to Aware Electronics directions for the proper connection sequence as the c-box may not work properly if their connection sequence is not followed). The software from Aware Electronics includes a program (aw-srad.exe) which finds the counts from the geiger counter and shows the counts as an updating bar graph. This can be saved as a file and viewed as a bar graph or line graph using another program (aw-graph.exe). I recorded the data for this project and viewed it with the aw-graph.exe program which enables screen capturing of the graph displayed on the screen. You can see an extensive collection of data graphs by clicking on the screen below. There are 19 small graphs each which can be viewed in a large, detailed format. (Give the Data Graphs page time to load.)

     I placed the 2 geiger counter array at a straight up (90 deg.) angle for some parts of this project. That is the position for the maximum muon count rate. The muons do not have enough energy to come from the direction of the earth so that only the ones from the overhead sky are counted. To prove this one would have to place many lead blocks below the geiger counter array. When turned sideways (0 deg. angle) which can be indicated as N/S, E/W etc. the muon count drops to around 10 % or less of its straight up angle. I used angles of 40 deg. and 20 deg. South for some of the counts. The average count rate for 20 deg. S was 20 % of the straight up angle rate and for 40 deg. S was around 35% of the straight up angle rate. The 20 deg. S angle was the optimum direction for pointing towards the center of our galaxy.

     The accuracy of the data in this project is related to the size of the geiger tubes and their capture rate. More or larger geiger tubes would increase the accuracy but would also increase the cost. Another way to increase the accuracy is to average the data counts over one or two hour periods instead of just one minute periods. This can be done automatically by the aw-graph.exe program. This results in reliability factors in the high ninety percents for many of the peaks on the muon graphs that were made as a part of this project. The values given in the project graphs are in counts per minute. These values need to be multiplied by 60 for the hour graphs and 120 for the 2 hour graphs before calculating the probability statistics.

     To calculate the probability of the curve of interest on a graph being significant, the following math can be used: 1) Determine the average counts per time period and take the square root of it - this is the standard deviation. 2) Find the difference between the curve of interest in counts per time period and the average counts per time period. 3) Divide the difference by the standard deviation. 4) Use the results of the division to look up the areas in a standard curve table which will give the probability that the curve of interest was not caused by random variations.

     As an example of the above, I will use the curve in muon graph # 02. The curve of interest has a value of 1.68 counts per minute and it took place at 5:45 AM EDT on 7/04/01. The average muon flux for this graph is 1.22. The graph is done in intervals of one hour each so the counts per minute need to be multiplied by 60 first to get the counts per hour. The curve of interest becomes 1.68 X 60 = 100.8. The average muon flux becomes 1.22 X 60 = 73.2. The square root of the average muon flux is 8.56 and the difference between the curve of interest and the average is 27.6. The next step is to divide the 27.6 by the standard deviation of 8.56 and that equals 3.22 which has a probability of 0.9994 in the standard curve table. The table is available from an online link at Aware Electronics but quick estimates in the 90 % range can be made from the following. 1.29 = 0.9015, 1.65 = 0.9505, 2 = 0.9744

     Using the above example, the curve which peaked at 5:45 AM EDT on 7/04/01 was not due to chance but was caused by a source definitely increasing the muon count rate. In order to connect muon count increase with a definite celestial event, it needs to be related to the sidereal time of the event and it needs to be in a repeating pattern. If the repeating pattern is not apparent, then corrections for other factors (for example, the magnetic field) need to be taken into account. It could also be a one-time event which could be correlated to the observations of others at the same time.

      This project is meant to be a starter project giving the basic instructions for assembling the components and some idea on the values to be received under different conditions. The large data graphs together with all of the explanations given in this report, should enable you to draw some ideas involving the times of the significant events on the graphs. My analysis of the data is given on the DATA TABLE, ANALYSIS, SUGGESTIONS FOR MORE RESEARCH page. I hope that we can collaborate in this project to further investigate this unknown area of knowledge. Perhaps a network could be set up to share the data. Feel free to contact me for any questions that you may have regarding the project. Also check out the RESOURCES page of this report, the PHOTO page, and DATA GRAPH page.









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