Cosmic Ray Statistics using LabVIEW
written by
David B. Pengra
Counting statistics of cosmic rays is explored using a LabVIEW based computer program on a computer connected to a National Instruments data acquisition unit. The program collects the interval times between successive coincident pulses from a stack of plastic scintillator detectors. Analysis of the data set allows students to see the distribution of N-pulse intervals for various values of N; this is the Erlang distribution. With N = 1, the Erlang
distribution is exponential with a characteristic time equal to mean count interval t. When N is increased, the distribution becomes peaked at Nt with a fractional width proportional to 1/?N. This is an instance of the central limit theorem. Students may also examine the data set according to the distribution of numbers of pulses recorded for a series of fixed-length intervals, which for random pulses follows the Poisson distribution. Again, as the length of the interval increases, the distribution conforms to the central limit theorem: it becomes normal with a well-defined mean and width, both related to mean and width of the underlying distribution. The software also allows students to simulate pulse-intervals that follow a uniform distribution (e.g., any real number between 0 and 1 has equal probability) or a Gaussian one. In these cases, one can see that the counts per fixed interval length do not follow the Poisson distribution, although all types become normal at longer intervals or greater numbers of pulses per interval length. This serves to drive home the point that cosmic ray counts are truly a Poisson process and also to illustrate the significant power of the central limit theorem-- that regardless of the underlying probability distribution function, when N becomes large the distribution becomes normal with a well-defined mean and width. Presented at the 2013 AAPT Summer Meeting in Portland, Oregon. W36: Advanced Labs Workshop
ComPADRE is beta testing Citation Styles!
Record Link
<a href="https://www.compadre.org/portal/items/detail.cfm?ID=12915">Pengra, David B.. Cosmic Ray Statistics using LabVIEW. July 9, 2013.</a>
AIP Format
D. Pengra, (2008), WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12915&DocID=3474).
AJP/PRST-PER
D. Pengra, Cosmic Ray Statistics using LabVIEW (2008), <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12915&DocID=3474>.
APA Format
Pengra, D. (2013, July 9). Cosmic Ray Statistics using LabVIEW. Retrieved April 19, 2024, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12915&DocID=3474
Chicago Format
Pengra, David B.. Cosmic Ray Statistics using LabVIEW. July 9, 2013. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12915&DocID=3474 (accessed 19 April 2024).
MLA Format
Pengra, David B.. Cosmic Ray Statistics using LabVIEW. 2008. 9 July 2013. 19 Apr. 2024 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12915&DocID=3474>.
BibTeX Export Format
@misc{
Author = "David B. Pengra",
Title = {Cosmic Ray Statistics using LabVIEW},
Volume = {2024},
Number = {19 April 2024},
Month = {July 9, 2013},
Year = {2008}
}
Refer Export Format
%A David B. Pengra %T Cosmic Ray Statistics using LabVIEW %D July 9, 2013 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12915&DocID=3474 %O application/pdf
EndNote Export Format
%0 Electronic Source %A Pengra, David B. %D July 9, 2013 %T Cosmic Ray Statistics using LabVIEW %V 2024 %N 19 April 2024 %8 July 9, 2013 %9 application/pdf %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12915&DocID=3474 Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.
Citation Source Information
The AIP Style presented is based on information from the AIP Style Manual. The APA Style presented is based on information from APA Style.org: Electronic References. The Chicago Style presented is based on information from Examples of Chicago-Style Documentation. The MLA Style presented is based on information from the MLA FAQ. This resource is stored in a shared folder. You must login to access shared folders. |
SupplementsContributeSimilar Materials |