Muon Telescopes...Attack! Part II

Cosmic rays flying through space with a tremendous amount of energy enter the earth's atmosphere and collide with the sparse matter in the upper atmosphere. A shower of particles emerge from the collision, and even more particles are made from subsequent high energy collisions. These particles travel through the atmosphere in a fraction of a second retaining a large amount of their original velocity. Below the ground surface, daughter products from these collisions called muons penetrate deep into the earth. And there they can interfere with sensitive measurement devices intended to detect neutrinos. Here, I want to look at the way that particle physicists observe this muon flux in order to subtract that effect out from their neutrino detection efforts.

In researching this topic, I had a few specific questions that I wanted to answer while thinking about muon "telescopes".
-What is the velocity of muon particles, and how would the effect the size/configuration of the telescope?
-What is the approximate flux of muon particles that might be detected?
-Are there any other considerations that might influence a telescope design?

As an amateur scientist without access to expensive "Peer Reviewed Journals" I am forced to use random undergraduate term papers and wikipedia to determine my facts. In this case, I found a great looking MIT undergrad physics paper. "The Speed and Lifetime of Cosmic Ray Muons" by Lulu Liu, an MIT Undergrad, dated November 17, 2007 is worth the read if you have any interest in this stuff. (http://web.mit.edu/lululiu/Public/pixx/not-pixx/muons.pdf Warning, PDF)

The velocity of muon particles is relativistic, at about 99% the speed of light. The relativistic speed of the particles change the apparent decay rate and so the flux is actually higher at the ground surface than one would expect. Does the increased mass of the particle change how the system works?

The flux they reported was 20 muon counts per second at sea level. This flux would likely be decreased by placing a detector in a deep lab with significant geological shielding above. My next question is what factor of decrease that shielding will provide? Also, is this true flux, or is it only the flux that was counted? What percentage of the muons pass through the scintilators without an interaction?

The relativistic effects on expected flux is significant. Because the muon is travelling at a speed greater than 99% the speed of light, relativistic effects have an impact on the apparent decay rate. If we just had some muons lying around they would have a certain decay rate. But because the very high velocity of cosmic ray daughter particle muons relative to our frame, the muon experiences less time in a trip through the atmosphere than we do measuring time from the ground. The muons would decay less frequently as measured from our frame and we would measure a larger flux at sea level.

Another scenario where relativistic decay could impact muon measurements is during the measurement itself. You would expect a certain number of muons to decay between the two scintillators, which will reduce the number of interactions that would be counted as a muon. But, because of those relativistic effects, there will be a higher count of muons that will be detected.

So, how quickly do we need to measure pulses in order to determine if a pulse is a muon? Using the number for muon velocity provided by Liu, ~30 cm/nanoseconds, we can estimate that scintilators separated by 10 m will require a time resolution of 33 ns. The frequency of a measurement that can time resolve a 33 ns event is about 33 Gigahertz. Agilent, the most expensive oscilloscope make I know lists a maximum frequency measurement of 1 GHz, "The World's fastest uncompromised update rate: up to 100,000 waveforms/sec" making this measurement impossible. There must be some kind of trick that they use to make the measurement or they have really good oscilloscopes at these labs.

This is a super-interesting, fiddly measurement that only the most dedicated and downtrodden interns and graduate students can be successful at. I look forward to seeing this work advance at DUSEL over the next few years.

PS I love how all of the papers I found had the same complaints about bad PMTs as Mark. Apparently they are very flaky, personality ridden devices.