Re: Cosmic ray power question

Hello Neil,

Cosmic rays in outer space are abundant and diverse. There's a whole periodic table worth of nuclei (mostly H, He, C, and Fe), electrons and positrons, neutrons, and high-energy photons (x rays, gamma rays) ... ejected by solar winds, distant supernovae, and all sorts of ill-understood processes.

At the Earth's surface things are completely different. The atmosphere is dense enough to stop basically everything that comes in (except neutrinos!) and only some of the secondaries, the by-products of the collisions that stopped the original particles, manage to percolate down. These secondary particles are typically lightweight (certainly nothing heavier than a proton) and most of them are pretty rare ... a few protons and a few tens of electrons, say, per square meter per second.

The one secondary that doesn't have to percolate is the muon. Muons produced very high in the atmosphere are able to penetrate all the way to the surface (and a ways underground as well!) without losing all of their energy. This is because they're very heavy (lots of inertia) and they don't interact strongly with nuclei (which is what stops cosmic-ray protons and neutrons so quickly). So muons are the most important component of cosmic rays at the surface.

When building and testing new particle detectors, we do see cosmic ray muons on a regular basis. They're a quick and dirty way to make sure a detector is working properly: if it gets triggered too often, or too infrequently, with respect to the cosmic ray flux, then you want to know why. The number to remember is ~70 muons per square meter per second, or one per square centimeter per minute.

As for the energy flux? First of all, it'll be fantastically small amounts of energy, when you think about it on the scales we're used to. The mean muon energy is ~4 giga-electron-volts (GeV), so that gives you an energy flux of 280 GeV/second. But one electron volt is ~10^-19 joules. That's fantastically small. This does't imply that we can't detect them; in fact, it's not too hard to detect them at all, as you know if you've seen a simple cloud-chamber setup. Fortunately, even a tiny amount of energy - a few electron volts - is enough to ionize an atoms, and free ions and electrons are what we detect. But you're not going to see your detector heating up.

You also mentioned one-foot-thick concrete walls and roof. Now, that will attentuate the muons somewhat ... if you want an order-of-magnitude answer we can ignore it. It'll be a factor of 2, not 10. This is calculable, though; check out Chapter 23 of "The Passage of Particles through Matter" in the Review of Particle Physics (click here)... Figure 23.4 can give you the mean range of particle if you know the material (remember, concrete is mostly silicon and oxygen), its density, and the momentum of the particle. If you make all of the units work out, you can figure out the mean range of a 4 GeV muon in concrete.

Also in the Review is an excellent overview of cosmic rays, including spectra in space, at the surface, and underground.

Feel free to email me (bmonreal (@) mit.edu) if you need help with more detailed calculations.

-Ben Monreal