taking rough numbers from here and here, it seems that with natural cosmic radiation sources, we could sustain $10^6$ muon-catalyzed fusion reactions per square-meter per minute. This would be $14 \times 10^6$ MeV of neutron energy (for D-T reactions, assuming 14 MeV per event) per square-meter per minute. In Watts-hour this would be $4 \times 10^{-12}$ KWh
I think this is the right estimate, but wanted to check if someone spots a problem with my estimate
cheers
Moun catalyzed fusion requires very specific kinematics, but cosmic muons come in all energies from stopped to tens of GeV at any particular spot.
Care to work out the cross-section for having the right kinematics? If you're having trouble I know a graduate student who is familiar with several of the common cosmic muon Monte Carlo generators.
Muon catalyzed fusion needs the muons to be low enough energy to replace an electron and stay in a stable orbit. Since the reason the catalysis happens is because the atom is much smaller and two protons can get close together enhancing the probability of overlap and fusion, one needs a large number of low energy muons so that the probability of two muonic hydrogens to be in contact would be high. Fusion has been observed in molecules that have an orbital electron replaced by a muon, binding the atoms of the molecule into closer distances, so that the nuclear force can have a probability of fusing the two nuclei, of H2 for example, and releasing the muon for a next round.
The 10.000 muons per minute per square meter are mainly above GeV energies whereas for atomic sizes one needs keV at best, so your calculations cannot be correct. In addition the muon decays in 10^-6 seconds, so it cannot accumulate in a volume to keep on catalyzing.
OK, so the effin muons are too fast to be useful in the ground frame. How inconvenient?
So, obviously, that means we have to accelerate the h, d, t etc. fuel particles to the same frame as the muons. (Or, alternatively, electrostatically decelerate the muons to the ground frame).
For example, drill a 3 km-deep bore hole straight down (or, lease an abandoned oil well), and use a particle accelerator to fire your fuel species straight down at a speed comparable to the downward-plunging muons'. Some of them will end up running along right next to those ol muons, and they'll make friends as they jog along side by side, and maybe even hook up. (Vibrate your fuel beam through a teeny, tiny, microscopic angle just to give a little transverse nudge to that process)
Alternatively, build a big negatively charged grid, rather like a solar panel, to slow down the incoming muons, and have your fuel chamber right underneath your "muon panel".
Do you get net power out of any of this? Probably not. But hey, you wanted ideas for building a prototype fusion reactor using cosmic-ray muons, so there it is. (Note to self, patent these concepts)
